tag:blogger.com,1999:blog-34216080668862712962018-03-05T21:01:41.453+05:00financial managementsolution manual of fundamentals of financial management by brigham 4th consie edition.saleem shahzadhttp://www.blogger.com/profile/09805156883366876837noreply@blogger.comBlogger21125tag:blogger.com,1999:blog-3421608066886271296.post-78694966669783710442010-12-14T15:22:00.006+05:002011-02-08T14:01:45.295+05:00Chapter 20Chapter 20<br />Hybrid Financing: Preferred Stock, Leasing,<br />Warrants, and Convertibles<br />SOLUTIONS TO END-OF-CHAPTER PROBLEMS<br /><br />20-1 If the company purchased the equipment its balance sheet would look like:<br /><br />Current assets $300 Debt $500<br />Fixed assets 600 Equity 400<br />Total assets $900 Total claims $900<br /><br />Therefore, the company’s debt ratio = $500/$900 = 55.6%.<br /><br />If the company leases the asset and does not capitalize the lease, its debt ratio = $400/$800 = 50%.<br /><br />The company’s financial risk (assuming the implied interest rate on the lease is equivalent to the loan) is no different whether the equipment is leased or purchased.<br /><br /><br />20-2 First issue: 20-year straight bonds with an 8 percent annual coupon.<br />Second issue: 20-year bonds with 6 percent annual coupon with warrants. Both bonds issued at par $1,000. Value of warrants = ?<br /><br />First issue: N = 20; PV = -1000, PMT = 80, FV = 1000 and solve for I = kd = 8%. (Since it sold for par, we should know that kd = 8%.)<br /><br />Second issue: $1,000 = Bond + Warrants.<br />This bond should be evaluated at 8 percent (since we know the first issue sold at par) to determine its present value. Then, the value of the warrants can be determined as the difference between $1,000 and the bond’s present value.<br /><br />N = 20; I = kd = 8; PMT = 60, FV = 1000, and solve for PV = $803.64.<br /><br />Value of warrants = $1,000 - $803.64 = $196.36.<br /><br /><br />20-3 Convertible Bond’s Par value = $1,000; Conversion price, Pc = $40; CR = ?<br /><br />CR =<br /><br /><br /><br />20-4 a. Year<br />0 1 2 3 4<br />I. Cost of Owning:<br />Net purchase price ($1,500,000)<br />Depr. tax savingsa $198,000 $270,000 $ 90,000 $ 42,000<br />Net cash flow ($1,500,000) $198,000 $270,000 $ 90,000 $ 42,000<br /><br />PV cost of owning<br />at 9% ($ 991,845)<br /><br />II. Cost of Leasing:<br />Lease payment (AT) (240,000) (240,000) (240,000) (240,000)<br />Purch. option priceb (250,000)<br />Net cash flow $ 0 ($240,000) ($240,000) ($240,000) ($490,000)<br /><br />PV cost of leasing<br />at 9% ($ 954,639)<br /><br />III. Cost Comparison<br />Net advantage to leasing (NAL) = PV cost of owning - PV cost of leasing<br />= $991,845 - $954,639<br />= $37,206.<br /><br />a Cost of new machinery: $1,500,000.<br />b Cost of purchasing the machinery after the lease expires.<br /><br />MACRS Deprec. Tax Savings<br />Year Allowance Factor Depreciation T(Depreciation)<br />1 0.33 $495,000 $198,000<br />2 0.45 675,000 270,000<br />3 0.15 225,000 90,000<br />4 0.07 105,000 42,000<br /><br />Note that the maintenance expense is excluded from the analysis since Morris-Meyer will have to bear the cost whether it buys or leases the machinery. Since the cost of leasing the machinery is less than the cost of owning it, Morris-Meyer should lease the equipment.<br /><br />b. We assume that Morris-Meyer will buy the equipment at the end of<br />4 years if the lease plan is used; hence the $250,000 is an added cost under leasing. We discounted it at 9 percent, but it is risky, so should we use a higher rate? If we do, leasing looks even better. However, it really makes more sense in this instance to use a lower rate so as to penalize the lease decision, because the residual value uncertainty increases the uncertainty of operations under the lease alternative. In general, for risk-averse decision makers, it makes intuitive sense to discount riskier future inflows at a higher rate, but risky future outflows at a lower rate. (Note that if Morris-Meyer did not plan to continue using the equipment, then the $250,000 salvage value (less taxes) should be a positive (inflow) value in the cost of owning analysis. In this case, it would be appropriate to use a higher discount rate.)<br />The cash flows for borrowing and leasing, except for the residual value cash flow, are relatively certain because they’re fixed by contract, and thus, are not very risky.<br /><br />20-5 a. Exercise value = Current price - Striking price.<br /><br />Ps = $18: Exercise Value = -$3 which is considered $0.<br /><br />Ps = $21: Exercise Value = $0.<br /><br />Ps = $25: Exercise Value = $4.<br /><br />Ps = $70: Exercise Value = $49.<br /><br />b. No precise answers are possible, but some “reasonable” war¬rant prices are as follows:<br /><br />Ps = $18: Warrant = $1.50; Premium = $4.50.<br /><br />Ps = $21: Warrant = $3.00; Premium = $3.00.<br /><br />Ps = $25: Warrant = $5.50; Premium = $1.50.<br /><br />Ps = $70: Warrant = $50.00; Premium = $1.00.<br /><br />c. 1. The longer the life, the higher the warrant value.<br /><br />2. The less variable the stock price, the lower the warrant value.<br /><br />3. The higher the expected EPS growth rate, the higher the warrant price.<br /><br />4. Going from a 0 to 100 percent payout would have two possible effects. First, it might affect the stock price causing a change in the exercise value of the warrant; however, it is not at all clear that the stock price would change, let alone what the change would be. Second, and more important here, the increase in the payout ratio would drastically lower the expected growth rate. This would reduce the chance of the stock’s price going up in the future. This would lower the expected value of the warrant, hence the premium and the price of the warrant.<br /><br />d. Vpackage = $1,000<br />=<br />= VB + 50($1.50) = VB = $1,000 - $75 = $925.<br /><br />Using a financial calculator, input the following: N = 20, I = 10,<br />PV = -925, FV = 1000, PMT = ? PMT = $91.19 ≈ $90. Consequently, the coupon interest rate = $90/$1,000 = 9%.<br /><br /><br />20-6 a. Balance sheets before lease is capitalized:<br /><br />McDaniel-Edwards Balance Sheet (thousands of dollars):<br /><br />Debt $400<br />Equity 200<br />Total liabilities<br />Total assets $600 and equity $600<br /><br />Debt/assets ratio = $400/$600 = 67%.<br /><br />Jordan-Hocking Balance Sheet (thousands of dollars):<br /><br />Debt $200<br />Equity 200<br />Total liabilities<br />Total assets $400 and equity $400<br /><br />Debt/assets ratio = $200/$400 = 50%.<br /><br />b. Balance sheet after lease is capitalized:<br /><br />Jordan-Hocking Balance Sheet (thousands of dollars):<br /><br />Assets $400 Debt $200<br />Value of leased asset 200 PV of lease payments 200<br />Equity 200<br />Total liabilities<br />Total assets $600 and equity $600<br /><br />Debt/assets ratio = $400/$600 = 67%.<br /><br />c. Perhaps. Net income, as reported, might well be less under leasing because the lease payment might be larger than the interest expense plus reported depreciation. Additionally, total assets are significantly less under leasing without capitalization. The net result is difficult to predict, but we can state positively that both ROA and ROE are affected by the choice of financing.<br /><br /><br />20-7 a. 0 1 2 3 4<br /><br />Net purchase price (250,000)<br />Depr’n tax savingsa 20,000 32,000 19,000 12,000<br />Maintenance (AT) (12,000) (12,000) (12,000) (12,000)<br />Salvage value 42,500<br />Net cash flow (250,000) 8,000 20,000 7,000 42,500<br /><br />PV cost of owning at 6% = -$185,112.<br />Notes:<br />1. There is no tax associated with the loom’s salvage value since salvage value equals book value.<br /><br />2. The appropriate discount rate is the after-tax cost of debt =<br />kd(1 - T) = 10%(1 - 0.4) = 6%.<br /><br />a Depreciation tax savings are calculated as follows:<br /><br />Depreciation Schedule<br />MACRS<br />Allowance *Depreciation End of Year Depreciation<br />Year Factor Expense Book Value Tax Savings<br />1 0.20 $50,000 $200,000 $20,000<br />2 0.32 80,000 120,000 32,000<br />3 0.19 47,500 72,500 19,000<br />4 0.12 30,000 42,500 12,000<br /><br />*Note that the loom’s depreciable basis is $250,000.<br />The cost of leasing can be placed on a time line as follows:<br /><br />0 1 2 3 4<br /><br />Lease payment (AT) -42,000 -42,000 -42,000 -42,000 -42,000<br /><br />PV at 6% = -$187,534.<br /><br />Thus, the present value of the cost of owning is $187,534 - $185,112 = $2,422 less than the present value of the cost of leasing. Tanner-Woods Textile should purchase the loom.<br /><br />b. Here we merely discount all cash flows in the cost of owning analysis at 6 percent except the salvage value cash flow, which we discount at<br />9 percent, the after-tax discount rate (15%(1 - 0.4)):<br /><br />0 1 2 3 4<br /><br />($250,000) PVs of all other cash flows<br />7,547 @ 6%<br />17,800<br />5,877<br />0<br />30,108 @ 9% $42,500<br />NPV = (188,668)<br /><br />When differential risk is considered, the cost of owning is now higher than the $187,534 cost of leasing; thus, the firm should lease the loom.<br /><br />c. This merely shifts the salvage value cash flow from the cost of owning analysis to the cost of leasing analysis. If Tanner-Woods Textile needed the loom after four years, it would have it if the loom were purchased, but would have to buy it if the loom were leased. The decision would remain the same. If differential salvage value risk is not considered, the loom should be purchased. In fact, the advantage to purchasing would be exactly the same.<br /><br /><br />20-8 a. Investment bankers sometimes use the rule of thumb that, to serve as a sweetener, the premium over the present price should be in the range between 20 and 30 percent. Since the stock has an indicated growth in earnings of 10 percent a year, a good argument could be made for setting the premium near the midpoint of the range, that is, 25 percent. A 25 percent premium results in a conversion price of $21(1.25) = $26.25. There has been heavy use of 20 to 30 percent premiums in recent years.<br /><br />b. Yes, to be able to force conversion if the market price rises above the call price. If, in fact, EPS rises to $2.42 in 2005, and the P/E ratio remains at 14, the stock price will go to $33.88, making forced conversion possible. However, potential investors will insist on call protection for at least 5 and possibly for 10 years.<br /><br /><br /><br />20-9 a. Howe Computer Company Balance Sheet:<br /><br />Alternative 1:<br /><br />Total current<br />liabilities $ 50,000<br />Long-term debt --<br />Common stock,<br />par $1 75,000<br />Paid-in capital 225,000<br />Retained earnings 25,000<br />Total liabilities<br />Total assets $375,000 and equity $375,000<br /><br />Alternative 2:<br /><br />Total current<br />liabilities $ 50,000<br />Long-term debt --<br />Common stock,<br />par $1 70,000<br />Paid-in capital 230,000<br />Retained earnings 25,000<br />Total liabilities<br />Total assets $375,000 and equity $375,000<br /><br />Alternative 3:<br /><br />Total current<br />liabilities $ 50,000<br />Long-term debt (10%) 250,000<br />Common stock,<br />par $1 70,000<br />Paid-in capital 230,000<br />Retained earnings 25,000<br />Total liabilities<br />Total assets $625,000 and equity $625,000<br /><br />b. Original Plan 1 Plan 2 Plan 3<br />Number of Keith<br />Howe’s shares 40,000 40,000 40,000 40,000<br />Total shares 50,000 75,000 70,000 70,000<br />Percent ownership 80% 53% 57% 57%<br /><br />c. Original Plan 1 Plan 2 Plan 3<br />Total assets $275,000 $375,000 $375,000 $625,000<br /><br />EBIT $ 55,000 $ 75,000 $ 75,000 $125,000<br />Interest 15,000 0 0 25,000<br />EBT $ 40,000 $ 75,000 $ 75,000 $100,000<br />Taxes (40%) 16,000 30,000 30,000 40,000<br />Net income $ 24,000 $ 45,000 $ 45,000 $ 60,000<br /><br />Number of shares 50,000 75,000 70,000 70,000<br /><br />Earnings per share $0.48 $0.60 $0.64 $0.86<br /><br />d. Total debt $200,000 $ 50,000 $ 50,000 $300,000<br /><br />Debt/assets ratio 73% 13% 13% 48%<br />e. Alternative 1 results in the lowest percentage ownership, but Keith Howe would still maintain control. Indicated earnings per share increases, and the debt ratio is reduced considerably (by 60 percent). Alternative 2 also results in maintenance of control (57 percent) for Keith Howe. Earnings per share increases, while a reduction in the debt ratio like that in Alternative 1 occurs. Under Alternative 3 there is also maintenance of control (57 percent) for Keith Howe. This plan results in the highest earnings per share (86 cents), which is an increase of 79 percent on the original earnings per share. The debt ratio is reduced to 48 percent.<br />Conclusions: If the assumptions of the problem are borne out in fact, Alternative 1 is inferior to 2, since earnings per share increases more in the latter. The debt-to-assets ratio (after conver-sion) is the same in both cases. Thus, the analysis must center on the choice between 2 and 3. The differences between these two alter-natives, which are illustrated in parts c and d, are that the increase in earnings per share is substantially greater under Alternative 3, but so is the debt ratio. With its low debt ratio (13 percent), the firm is in a good position for future growth under 2. However, the 48 percent ratio under 3 is not unbearable and is a great improvement over the original situation. The combina¬tion of increased earnings per share and reduced debt ratios indicates favorable stock price movements in both cases, particularly under Alternative 3. There is the remote chance that Howe could lose its commercial bank financing under 3, since it was the bank that initiated the permanent financing suggestion. The additional funds, especially under 3, may enable Howe to become more current on its trade credit. Also, the bonds will doubtless be subordi¬nated debentures. Both Alternative 2 and Alternative 3 are favorable alternatives, with 3 being slightly more attrac¬tive, if Howe is willing to assume the risk of higher leverage. The actual attractiveness of Alternative 3 de¬pends, of course, on the assumption that funds can be invested to yield 20 percent. It is this fact that makes the additional leverage favorable and raises the earnings per share. (Note that Alternatives 2 and 3 also assume that convertibles will be converted and warrants will be exercised; this involves uncertainty plus a time lag!)<br /><br /><br />20-10 Facts and analysis in the problem:<br /><br />kd = 12%; D0 = $2.46; g = 8%; P0 = $38.<br /><br />ks = D1/P0 + g = $2.66/$38.00 + 8% = 15%.<br /><br />Convertible:<br /><br />Par = $1,000, 20-year; Coupon = 10%; CR = 20 shares.<br />Call = Five-year deferment; Call price = $1,075 in Year 6, declines by $5 per year.<br /><br />Will be called when Ct = 1.2(Par) = $1,200.<br /><br /><br />Find n (number of years) to anticipated call/conversion:<br /><br />(P0)(CR)(1 + g)n = $1,200<br />($38)(20)(1 + 0.08)n = $1,200<br />($760)(1.08)n = $1,200.<br /><br />Using a financial calculator, input the following:<br />I = 8, PV = -760, PMT = 0, FV = 1200, N = ? N = 5.93 6.<br /><br />Straight-debt value of the convertible at t = 0: (Assumes annual payment of coupon)<br /><br />Using a financial calculator, input the following: N = 20, I = 12, PMT = 100, FV = 1000, PV = ? PV = $850.61 $851.<br /><br />PV at t = 5 (n = 15): $864. PV at t = 10 (n = 10): $887.<br />PV at t = 15 (n = 5): $928. PV at t = 20 (n = 0): $1,000.<br /><br />Conversion value:<br /><br />Ct = P0(1.08)n(20). C0 = $38(20) = $760. C5 = $38(1.08)5(20) = $1,117.<br />C6 = $38(1.08)6(20) = $1,206. C10 = $38(1.08)10(20) = $1,641.<br /><br />a. See the graph to the right.<br /><br />b. P2 = $38(1.08)2 = $44.32 = Price of stock just before change in growth expectation. P3 = $2.87/0.15 = $19.13 = Price of stock after changed growth expectations. Percentage de-cline in stock price = 57%.<br /><br />Assuming zero future growth, the value of the stock will not increase, and the value of the convertible will depend only upon its value as a straight bond. Since the firm’s inter¬est payments are relatively low compared to what they would have been had straight debt been issued originally, the firm is unlikely to call the bond issue. Therefore, it would be valued according to its coupon, the current market rate on debt of that risk, and years remaining to maturity (18):<br /><br />VBond = = $855.<br /><br />Prior to the change in expected growth from 8 to 0 percent, the market value would have been above the straight bond value: According to the graph, the bond would sell for about $1,025. Thus, there would be a percentage decline of 17 percent in the value of the convertible, about one-third the 57 percent loss on the stock.<br /><br /><br /><br />20-11 a. The value of the 9% coupon bonds, evaluated at 12%, can be found as follows:<br /><br />N = 20; I = 12; PMT = 90; and FV = 1000. Solve for PV = $775.92.<br /><br />If investors are willing to pay $1,000 for these bonds with warrants attached, then the value of the warrants must be $1,000 - $775.92 = $224.08. Since there are 20 warrants issued with each bond, the value per warrant must be $11.20.<br /><br />b. The firm’s current market value of equity is $25 x 10 million shares = $250 million. Combined with a $100 million bond issue ($1,000 x 100,000 bonds), the firm’s current total value is $350 million. The firm’s operations and investments are expected to grow at a constant rate of 10%. Hence, the expected total value of the firm in 10 years is:<br /><br />Total firm value (t = 10) = $350,000,000 (1.10)10<br />Total firm value (t = 10) = $907,809,861.<br /><br />c. With 10 years left to maturity, each of the 100,000 bonds will be worth;<br /><br />N = 10; I = 12; PMT = 90; and FV = 1000. Solve for PV = $830.49.<br /><br />Thus, the total value of debt would be 830.49 x 100,000 = $83,049,331. Hence, the value of equity would be $907,809,861 - $83,049,331 = $824,760,530. If no warrants were issued, there would still be 10 million shares outstanding, which would each have a value of $82.48.<br /><br />With warrants being issued and exercised, there would be 20 warrants exercised for each of the 100,000 bonds, resulting in 2 million new shares. Therefore, there will be 12 million shares outstanding if the warrants are exercised, and an additional $60 million of equity (2 million warrants x $30 exercise price). The value of each share of stock would be ($824,760,530 + $60,000,000)/12,000,000 = $73.73.<br /><br />d. The investors would be expected to receive $90 per year and $1,000 in Year 20 (the face value). In addition, if warrants are exercised then the investors will receive a profit of $73.73 - $30.00 = $43.73 per share, or a total cash flow of $874.60 ($43.73 x 20) in Year 10. Therefore, in Year 10 investors will receive $90 + $874.60 = $964.60. Hence, the component cost of these bonds can be found by determining the IRR of a cash flow stream consisting of each coupon payment, the face value, and the profit from exercising the warrants.<br /><br />Input CF0 = -1000, CF1-9 = 90, CF10 = 964.60, CF11-19 = 90, and CF20 = 1090. Solve for IRR = 12.699%.<br /><br />The component cost is 12.699%, and the premium associated with the warrants is 12.699% - 12% = 0.699%, or roughly 70 basis points.saleem shahzadnoreply@blogger.com1tag:blogger.com,1999:blog-3421608066886271296.post-2604478089163893322010-12-14T15:22:00.005+05:002011-02-08T14:01:29.043+05:00Chapter 19Chapter 19<br />Multinational Financial Management<br />SOLUTIONS TO END-OF-CHAPTER PROBLEMS<br /><br /><br />19-1 $1 = 4.0828 Israeli shekel; $1 = 111.23 Japanese yen; Cross exchange rate, yen/shekel = ?<br /><br />Cross Rate: .<br /><br />Note that an indirect quotation is given for Israeli shekel; however, the cross rate formula requires a direct quotation. The indirect quotation is the reciprocal of the direct quotation. Since $1 = 4.0828 shekel, then 1 shekel = $0.244930.<br /><br />Yen/Shekel = $0.244930 per shekel 111.23 yen per dollar<br />= 27.2436 yen per shekel.<br /><br /><br />19-2 kNom, 6-month T-bills = 7%; kNom of similar default-free 6-month Japanese bonds = 5.5%; Spot exchange rate: 1 yen = $0.009; 6-month forward exchange rate = ?<br /><br />.<br /><br />kf = 5.5%/2 = 2.75%.<br /><br />kh = 7%/2 = 3.5%.<br /><br />Spot exchange rate = $0.009.<br /><br />=<br />1.0275 Forward exchange rate = $0.00932<br />Forward exchange rate = $0.00907.<br /><br />The 6-month forward exchange rate is 1 yen = $0.00907.<br /><br /><br />19-3 U.S. T.V. = $500; EMU T.V. = 725 euros; Spot rate between euro and dollar = ?<br /><br />Ph = Pf(Spot rate)<br />$500 = 725 euros(Spot rate)<br />500/725 = Spot rate<br />$0.68966 = Spot rate.<br /><br />1 euro = $0.68966 or $1 = 1.45 euros.<br /><br />19-4 Dollars should sell for 1/1.50, or 0.6667 pound per dollar.<br /><br /><br />19-5 The price of krones is $0.14 today. A 10 percent appreciation will make it worth $0.154 tomorrow. A dollar will buy 1/0.154 = 6.49351 krones tomorrow.<br /><br /><br />19-6 Cross rate = kronas/dollar dollars/pound = kronas/pound<br />= 10 1.5 = 15 kronas per pound.<br /><br /><br />19-7 The answer to this question would depend upon the rates existing at the time the assignment is made. Using the rates quoted in the Foreign Exchange table of the February 7, 2003, issue of The Wall Street Journal:<br /><br />U.S. $ Equivalent Currency per U.S. $<br />British pound 1.6385 0.6103<br />Swedish krona 0.1179 8.4818<br /><br />Cross rate = kronas/dollar dollars/pound = kronas/pound<br />= 8.4818 1.6385 = 13.8974 kronas per pound.<br /><br /><br />19-8 D1 = 3 pounds; Exchange rate = $1.60/pound; Pound depreciates 5% against $1. Dividend grows at 10% and k = 15%. 10 million shares outstanding.<br /><br />g = - 1 = 4.7619%.<br /><br />P0 =<br />P0 =<br />=<br />= $46.88372093.<br /><br />Total equity = $46.88372093 10 million shares<br />= $468,837,209.<br /><br /><br />19-9 The U.S. dollar liability of the corporation falls from $0.75(5,000,000) = $3,750,000 to $0.70(5,000,000) = $3,500,000, corresponding to a gain of 250,000 U.S. dollars for the corporation. However, the real economic situation might be somewhat different. For example, the loan is presumably a long-term loan. The exchange rate will surely change again before the loan is paid. What really matters, in an economic sense, is the expected present value of future interest and principal payments denominated in U.S. dollars. There are also possible gains and losses on inventory and other assets of the firm. A discussion of these issues quickly takes us outside the scope of this introductory textbook.<br />19-10 a. If a U.S. based company undertakes the project, the rate of return for the project is a simple calculation, as is the net present value.<br /><br />Rate of return = $1,200/$1,000 – 1 = 20%.<br /><br />NPV = -$1,000 + $1,200/1.14 = $52.63.<br /><br />b. According to interest rate parity, the following condition holds:<br /><br />ft/e0 = (1 + kSWISS)/(1 + kUS)<br />ft/1.62 = (1 + 0.045)/(1 + 0.0725)<br />ft/1.62 = 0.97436<br />ft = 1.5785 SF per U.S. $.<br /><br />c. First, we must adjust the cash flows to reflect Solitaire's home currency.<br /><br />Year CF ($) CF (SFrancs)<br />0 -1,000 -1,620.00<br />1 1,200 1,894.15<br /><br />Using the Swiss Franc-denominated cash flows, the appropriate rate of return and NPV can be found.<br /><br />Rate of return = 1,894.15SF/1,620SF - 1 = 16.92%.<br /><br />NPV = -1,620 + 1,894.15/1.14 = 41.54 Swiss Francs.<br /><br /><br />19-11 From Table 19-1:<br /><br />U.S. Dollars<br />Required to<br />Buy One Unit of Purchase Price<br />Currency Foreign Currency 1,000 = in Dollars<br />British pound 1.5398 1,000 = $1,539.80<br />Canadian dollar 0.6308 1,000 = 630.80<br />EMU euro 0.9666 1,000 = 966.60<br />Japanese yen 0.008273 1,000 = 8.27<br />Mexican peso 0.1027 1,000 = 102.70<br />Swedish krona 0.1033 1,000 = 103.30<br /><br /><br /><br />19-12 a. Again the answer to this problem depends on the date it is assigned.<br />If the exchange rates taken from the February 7, 2003 issue of The Wall Street Journal are used; then the following information is obtained:<br /><br />U.S. Dollars<br />Required to<br />Buy One Unit of Purchase Price<br />Currency Foreign Currency 1,000 = in Dollars<br />British pound 1.6385 1,000 = $1,638.50<br />Canadian dollar 0.6591 1,000 = 659.10<br />EMU euro 1.0835 1,000 = 1,083.50<br />Japanese yen 0.008343 1,000 = 8.34<br />Mexican peso 0.0917 1,000 = 91.70<br />Swedish krona 0.1179 1,000 = 117.90<br /><br />b. Pound = ($1,638.50 - $1,539.80)/$1,539.80 = +0.0641 = +6.41%.<br /><br />Canadian dollar = ($659.10 - $630.80)/$630.80 = +0.0449 = +4.49%.<br /><br />Euro = ($1,083.50 - $966.60)/$966.60 = +0.1209 = +12.09%.<br /><br />Yen = ($8.34 - $8.27)/$8.27 = +0.0085 = +0.85%.<br /><br />Peso = ($91.70 - $102.70)/$102.70 = -0.1071 = -10.71%.<br /><br />Krona = ($117.90 - $103.30)/$103.30 = +0.1413 = +14.13%.<br /><br /><br />19-13 a. The automobile’s value has increased because the dollar has declined in value relative to the yen.<br /><br />b. 245/121 = 2.0248, so $9,000 2.0248 = $18,223.14 $18,223.<br /><br />Note that this represents a 3.8 percent compound annual increase over 19 years.<br /><br /><br />19-14 a. C$4,000,000/C$1.4430 = $2,772,002.77 $2,772,003, or<br />C$4,000,000 $0.6930 = $2,772,000.<br />(Difference is due to rounding.)<br /><br />b. C$4,000,000/C$1.4401 = $2,777,585, or<br />C$4,000,000 0.6944 = $2,777,600.<br /><br />c. If the exchange rate is C$1.20 to $1 when payment is due in 3 months, the C$4,000,000 will cost:<br /><br />C$4,000,000/C$1.20 = $3,333,333,<br /><br />which is $561,330 more than the spot price today and $555,748 more than purchasing a forward contract for 90 days.<br />19-15 a. kNom of 90-day U.S. risk-free securities = 5%; kNom of 90-day British risk-free securities = 5.3%; spot rate: 1 pound = $1.65; forward rate selling at premium or discount = ?<br /><br />.<br /><br />kh = 5%/4 = 1.25%; kf = 5.3%/4 = 1.325%; spot rate = $1.65.<br /><br />=<br />= 0.9993<br />Forward exchange rate = $1.6488.<br /><br />The forward rate is selling at a discount, since a pound buys fewer dollars in the forward market than it does in the spot. In other words, in the spot market $1 would buy 0.6061 British pounds, but at the forward rate $1 would buy 0.6065 British pounds; therefore, the forward currency is said to be selling at a discount.<br /><br />b. The 90-day forward rate is $1.6488.<br /><br /><br />19-16 Spot rate: 1 yen = $0.0086; Forward rate: 1 yen = $0.0086; kNom of 90-day Japanese risk-free securities = 4.6%; kNom of 90-day U.S. risk-free securities = ?<br /><br />kf = 4.6%/4 = 1.15%; kh = ?<br /><br />=<br />=<br />1 =<br />1 + kh = 1.0115<br />kh = 0.0115.<br /><br />kNom = 1.15% 4 = 4.6%.<br /><br /><br />19-17 $1 = 7.8 pesos; CD = $15.00; Price of CD in Mexico = ?<br /><br />1 Peso = 1/7.8 = $0.1282.<br /><br />Ph = Pf(Spot rate)<br />$15 = Pf($0.1282)<br />= 117 pesos.<br /><br />Check: Spot rate = $15/117 pesos = $0.1282 for 1 peso.saleem shahzadnoreply@blogger.com0tag:blogger.com,1999:blog-3421608066886271296.post-21509157166693296062010-12-14T15:23:00.005+05:002011-02-08T14:01:06.388+05:00Chapter 21<div dir="ltr" style="text-align: left;" trbidi="on">Chapter 21<br />Mergers and Acquisitions<br />SOLUTIONS TO END-OF-CHAPTER PROBLEMS<br /><br />21-1 D1 = $2.00; g = 5%; b = 0.9; kRF = 5%; RPM = 6%; P0 = ?<br /><br />ks = kRF + RPM(b)<br />= 5% + 6%(0.9)<br />= 10.4%.<br /><br />P0 =<br />=<br />= $37.04.<br /><br /><br />21-2 D1 = $2.00; g = 7%; b = 1.1; kRF = 5%; RPM = 6%; P0 = ?<br /><br />ks = kRF + RPM(b)<br />= 5% + 6%(1.1)<br />= 11.6%.<br /><br />P0 =<br />=<br />= $43.48.<br /><br /><br />21-3 On the basis of the answers in Problems 21-1 and 21-2, the bid for each share should range between $37.04 and $43.48.<br /><br /><br />21-4 a. The appropriate discount rate reflects the riskiness of the cash flows to equity investors. Thus, it is Vaccaro’s cost of equity, adjusted for leverage effects. Since Apilado’s b = 1, its RPM = kM - kRF = 14% - 8% = 6%, then:<br /><br />ks = kRF + (kM - kRF)b = 8% + (14% - 8%)1.47 = 16.82% 16.8%.<br /><br /><br />b. The value of Vaccaro is $14.65 million:<br /><br />0 1 2 3 4 5<br /><br />1.30 1.50 1.75 2.00 2.12<br />1.11 19.63<br />1.10<br />1.10<br />11.62 21.63<br />V = $14.93 million<br /><br />CF5 = CF4(1.06) = $2.00(1.06) = $2.12.<br /><br />Value at t4 of CF5 and all subsequent cash flows is:<br /><br />V4 = = $19.63.<br /><br />Alternatively, input 0, 1.30, 1.50, 1.75, and 21.63(2.00 + 19.63) into the cash flow register, I = 16.8, NPV = ? NPV = $14.93.<br /><br />c. PMax = V/N = $14.93/1.2 = $12.44.<br /><br />Since Apilado is paying exactly what Vaccaro is worth, the acquisition has a zero net present value and Apilado’s share price should remain at its current price.<br /><br /><br />21-5 0 1 2 3 10<br />• • • <br />-400,000 64,000 64,000 64,000 64,000<br /><br />CF0 = -$400,000; CF1 - CF10 = $64,000; and k = 10%.<br /><br />Input -400,000 and 64,000 (10) into the cash flow register, I = 10, and solve for NPV = -$6,747.71. Since the NPV of the investment is negative, Stanley should not make the purchase.<br /><br /><br /><br />21-6 a. Since the net cash flows are equity returns, the appropriate discount rate is that cost of equity which reflects the riskiness of the cash flow stream. This cost is GCC’s cost of equity:<br /><br />ks = kRF + (RPM)b = 8% + (4%)1.50 = 14%.<br /><br />b. The terminal value is $1,143.4:<br /><br />TV =<br /><br /><br />Annual cash flows are calculated as follows:<br /><br />2003 2004 2005 2006<br />Sales $450.0 $518.0 $555.0 $600.0<br />COGS (292.5) (336.7) (360.7) (390.0)<br />Gross profit $157.5 $181.3 $194.3 $210.0<br />Selling/Admin (45.0) (53.0) (60.0) (68.0)<br />EBIT $112.5 $128.3 $134.3 $142.0<br />Interest (18.0) (21.0) (24.0) (27.0)<br />EBT $ 94.5 $107.3 $110.3 $115.0<br />Taxes (35%) (33.1) (37.6) (38.6) (40.3)<br />Net income $ 61.4 $ 69.7 $ 71.7 $ 74.8<br /><br />The value of GCC to TransWorld’s shareholders is the present value of the cash flows that accrue to the shareholders:<br /><br />V = = $877.2.<br /><br />Alternatively, input 0, 61.4, 69.7, 71.7, and 1218.2 (74.8 + 1143.4) into the cash flow register, I = 14, and solve for NPV = $877.2.</div>saleem shahzadnoreply@blogger.com0tag:blogger.com,1999:blog-3421608066886271296.post-60522219398788397412010-12-14T13:09:00.002+05:002011-01-18T16:25:54.882+05:00Chapter 1Chapter 1<br /> An Overview of Financial Management<br /> <br /><br /><br /><br />After reading this chapter, students should be able to:<br /><br />• Explain the career opportunities available within the three interrelated areas of finance.<br /><br />• Identify some of the forces that will affect financial management in the new millennium.<br /><br />• Describe the advantages and disadvantages of alternative forms of business organization.<br /><br />• Briefly explain the responsibilities of the financial staff within an organization.<br /><br />• State the primary goal in a publicly traded firm, and explain how social responsibility and business ethics fit in with that goal.<br /><br />• Define an agency relationship, give some examples of potential agency problems, and identify possible solutions.<br /><br />• Identify major factors that determine the price of a company’s stock, including those that managers have control over and those that they do not.<br /><br />• Discuss whether financial managers should concentrate strictly on cash flow and ignore the impact of their decisions on EPS.<br />ANSWERS TO END-OF-CHAPTER QUESTIONS<br /><br /><br /><br />1-1 The three principal forms of business organization are sole proprietorship, partnership, and corporation. The advantages of the first two include the ease and low cost of formation. The advantages of the corporation include limited liability, indefinite life, ease of ownership transfer, and access to capital markets.<br />The disadvantages of a sole proprietorship are (1) difficulty in obtaining large sums of capital; (2) unlimited personal liability for business debts; and (3) limited life. The disadvantages of a partnership are (1) unlimited liability, (2) limited life, (3) difficulty of transferring ownership, and (4) difficulty of raising large amounts of capital. The disadvantages of a corporation are (1) double taxation of earnings and (2) setting up a corporation and filing required state and federal reports, which are complex and time-consuming.<br /><br />1-2 No. The normal rate of return on investment would vary among industries, principally due to varying risk. The normal rate of return would be expected to change over time due to (1) underlying changes in the industry and (2) business cycles.<br /><br />1-3 An increase in the inflation rate would most likely in¬crease the relative importance of the financial manager. Virtually all of the manager’s functions, from obtaining funds for the firm to internal cost accounting, become more demanding in periods of high inflation. Usually, uncer¬tainty is also increased by inflation, and hence, the effects of a poor decision are magnified.<br /><br />1-4 Stockholder wealth maximization is a long-run goal. Companies, and consequently the stockholders, prosper by man¬agement making decisions that will produce long-term earnings increases. Actions that are continually shortsighted often “catch up” with a firm and, as a result, it may find itself unable to compete effectively against its competi¬tors. There has been much criticism in recent years that U.S. firms are too short-run profit-oriented. A prime example is the U.S. auto industry, which has been accused of continuing to build large “gas guzzler” auto¬mobiles because they had higher profit margins rather than retooling for smaller, more fuel-efficient models.<br /><br />1-5 Even though firms follow generally accepted accounting prin¬ciples (GAAP), there is still sufficient margin for firms to use different procedures. Leasing and inventory accounting (LIFO versus FIFO) are two of the many areas where procedural differences could complicate relative performance measures.<br /><br /><br />1-6 The management of an oligopolistic firm would be more likely to engage voluntarily in “socially conscious” practices. Competitive firms would be less able to engage in such prac¬tices unless they were cost-justified, because they would have to raise prices to cover the added costs--quickly finding themselves uncompetitive.<br /><br />1-7 Profit maximization abstracts from (1) the timing of profits and (2) the riskiness of different operating plans. How¬ever, both of these factors are reflected in stock price maximiza¬tion. Thus, profit maximization would not necessar¬ily lead to stock price maximization.<br /><br />1-8 The president of a large, publicly owned corporation should maximize shareholders’ wealth or he risks losing his job. Many have argued that when only a small percentage of the stock is owned by management shareholder wealth maximization can take a back seat to any number of conflicting managerial goals. Such factors as a compensation system based on management performance (bonuses tied to profits, stock op¬tion plans) as well as the possibility of being removed from office (voted out of office, an unfriendly tender offer by another firm) serve to keep management’s focus on stockhold¬ers’ interests.<br /><br />1-9 a. Corporate philanthropy is always a sticky issue, but it can be justified in terms of helping to create a more attractive community that will make it easier to hire a productive work force. This corporate philanthropy could be received by stockholders negatively, especially those stockholders not living in its headquarters city. Stockholders are interested in actions that maximize share price, and if competing firms are not making similar contributions, the “cost” of this philanthropy has to be borne by someone--the stockholders. Thus, stock price could decrease.<br /><br />b. Companies must make investments in the current period in order to generate future cash flows. Stockholders should be aware of this, and assuming a correct analysis has been performed, they should react positively to the decision. The Mexican plant is in this category. Capital budgeting is covered in depth in Part 4 of the text. Assuming that the correct capital budgeting analysis has been made, the stock price should increase in the future.<br /><br />c. Provided that the rate of return on assets exceeds the interest rate on debt, greater use of debt will raise the expected rate of return on stockholders’ equity. Also, the interest on debt is tax deductible and this provides a further advan¬tage. However, (1) greater use of debt will have a negative impact on the stockholders if the company’s return on assets falls below the cost of debt, and (2) increased use of debt increases the chances of going bankrupt. The effects of debt usage, called “financial leverage,” are spelled out in detail in the chapter titled, “Capital Structure and Leverage.”<br /><br />d. Today (2003), nuclear generation of electricity is regarded as being quite risky. If the company has a heavy investment in nuclear generators, its risk will be high, and its stock price will be adversely affected unless its costs are much lower, hence its profits are much higher.<br /><br /><br />e. The company will be retaining more earnings, so its growth rate should rise, which should increase its stock price. The decline in dividends, however, will pull the stock price down. It is unclear whether the net effect on its stock will be an increase or a decrease in its price, but the change will depend on whether stockholders prefer dividends or increased growth. This topic will be discussed in greater detail in the chapter titled, “Distributions to Shareholders: Dividends and Share Repurchases.”<br /><br />1-10 The executive wants to demonstrate strong performance in a short period of time, which can be demonstrated either through improved earnings and/or a higher stock price. The current board of directors is well served if the manager works to increase the stock price; however, the board is not well served if the manager takes short-run actions that bump up short-run earnings at the expense of long-run profitability and the company’s stock price. Consequently, the board may want to rely more on stock options and less on performance shares that are tied to accounting performance.<br /><br />1-11 As the stock market becomes more volatile, the link between the stock price and the management ability of senior executives is weakened. Therefore, in this environment companies may choose to de-emphasize the awarding of stock and stock options and rely more on bonuses and performance shares that are tied to other performance measures besides the company’s stock price. Moreover, in this environment it may be harder to attract or retain top talent if the compensation is tied too much to the company’s stock price.<br /><br />1-12 a. No, TIAA-CREF is not an ordinary shareholder. Because it is one of the largest institutional shareholders in the United States and it controls nearly $280 billion in pension funds, its voice carries a lot of weight. This “shareholder” in effect consists of many individual shareholders whose pensions are invested with this group.<br /><br />b. The owners of TIAA-CREF are the individual teachers whose pensions are invested with this group.<br /><br />c. For TIAA-CREF to be effective in wielding its weight, it must act as a coordinated unit. In order to do this, the fund’s managers should solicit from the individual shareholders their “votes” on the fund’s practices, and from those “votes” act on the majority’s wishes. In so doing, the individual teachers whose pensions are invested in the fund have in effect determined the fund’s voting practices.<br /><br />1-13 a. If the capital markets perceive the project as risky and therefore increasing the firm’s risk, the value of the firm’s outstanding bonds will decline--hurting the firm’s existing bondholders. Subsequently, if management’s analysis of the project proves to be correct, the value of the firm’s bonds should increase.<br /><br />b. Dividends are paid from earnings after bondholders and the government have been paid. A dividend increase decreases the firm’s addition to retained earnings and subsequently lowers its growth rate; however, shareholders receive more dividends so the net effect on stock price is indeterminate. If the firm’s stock price increases as current management believes it will, this may cause some bondholders to sell their bonds and buy the firm’s stock to earn a higher return. So, the proposed dividend increase may cause a decline in the value of the firm’s existing bonds.<br /><br />c. Yes, assuming that management has performed the correct analysis it should undertake projects/actions that will increase the firm’s stock price. Stockholder wealth maximization is the goal of management.<br /><br />d. Bondholders can take the following actions to protect themselves against managerial decisions that reduce bond values:<br /><br />1. Place restrictive covenants in debt agreements.<br />2. Charge a higher-than-normal interest rate to compensate for the risk of possible exploitation.<br />3. Refuse to deal with management entirely.<br /><br />Firms that deal unfairly with creditors either lose access to the debt markets or are saddled with high interest rates and restrictive covenants, all of which are detrimental to shareholders.<br /><br />1-14 a. Increasing corporate tax rates and reducing individual tax rates will cause the firm to remain as an unincorporated partnership. In addition to higher corporate tax rates, corporations are exposed to double taxation.<br /><br />b. By increasing environmental and labor regulations to include firms with 50+ employees, this firm will choose to remain an unincorporated partnership due to the additional costs it would have to bear if it operated as a corporation.<br /><br />1-15 Earnings per share in the current year will decline due to the cost of the investment made in the current year and no significant performance impact in the short run. However, the company’s stock price should increase due to the significant cost savings expected in the future.saleem shahzadnoreply@blogger.com1tag:blogger.com,1999:blog-3421608066886271296.post-59783501851571147812010-12-14T15:11:00.003+05:002011-01-18T16:24:14.436+05:00Chapter 6<div align="left">Chapter 6<br /><strong><span style="font-size:130%;">Time Value of Money<br /></span></strong>SOLUTIONS TO END-OF-CHAPTER PROBLEMS<br /><br /><br /><br />6-1 0 1 2 3 4 5<br /><br />PV = 10,000 FV5 = ?<br /><br />FV5 = $10,000(1.10)5<br />= $10,000(1.61051) = $16,105.10.<br /><br />Alternatively, with a financial calculator enter the following: N = 5,<br />I = 10, PV = -10000, and PMT = 0. Solve for FV = $16,105.10.<br /><br /><br />6-2 0 5 10 15 20<br /><br />PV = ? FV20 = 5,000<br /><br />With a financial calculator enter the following: N = 20, I = 7, PMT = 0, and FV = 5000. Solve for PV = $1,292.10.<br /><br /><br />6-3 0 n = ?<br /><br />PV = 1 FVn = 2<br /><br />2 = 1(1.065)n.<br /><br />With a financial calculator enter the following: I = 6.5, PV = -1, PMT = 0, and FV = 2. Solve for N = 11.01 ≈ 11 years.<br /><br /><br />6-4 Using your financial calculator, enter the following data: I = 12; PV =<br />-42180.53; PMT = -5000; FV = 250000; N = ? Solve for N = 11. It will take 11 years for John to accumulate $250,000.<br /><br /><br />6-5 0 18<br /><br />PV = 250,000 FV18 = 1,000,000<br /><br />With a financial calculator enter the following: N = 18, PV = -250000, PMT = 0, and FV = 1000000. Solve for I = 8.01% ≈ 8%.<br /><br /><br />6-6 0 1 2 3 4 5<br /><br />300 300 300 300 300<br />FVA5 = ?<br /><br />With a financial calculator enter the following: N = 5, I = 7, PV = 0, and PMT = 300. Solve for FV = $1,725.22.<br />6-7 0 1 2 3 4 5<br /><br />300 300 300 300 300<br /><br />With a financial calculator, switch to “BEG” and enter the following: N = 5, I = 7, PV = 0, and PMT = 300. Solve for FV = $1,845.99. Don’t forget to switch back to “END” mode.<br /><br /><br />6-8 0 1 2 3 4 5 6<br /><br />100 100 100 200 300 500<br />PV = ? FV = ?<br /><br />Using a financial calculator, enter the following:<br /><br />CF0 = 0<br />CF1 = 100, Nj = 3<br />CF4 = 200 (Note calculator will show CF2 on screen.)<br />CF5 = 300 (Note calculator will show CF3 on screen.)<br />CF6 = 500 (Note calculator will show CF4 on screen.)<br />and I = 8. Solve for NPV = $923.98.<br /><br />To solve for the FV of the cash flow stream with a calculator that doesn’t have the NFV key, do the following: Enter N = 6, I = 8, PV = -923.98, and PMT = 0. Solve for FV = $1,466.24. You can check this as follows:<br /><br />0 1 2 3 4 5 6<br /><br />100 100 100 200 300 500<br />324.00<br />233.28<br />125.97<br />136.05<br />146.93<br />$1,466.23<br /><br /><br />6-9 Using a financial calculator, enter the following: N = 60, I = 1, PV =<br />-20000, and FV = 0. Solve for PMT = $444.89.<br /><br />EAR = - 1.0<br />= (1.01)12 - 1.0<br />= 12.68%.<br /><br />Alternatively, using a financial calculator, enter the following: NOM% = 12 and P/YR = 12. Solve for EFF% = 12.6825%. Remember to change back to P/YR = 1 on your calculator.<br /><br /><br /><br />6-10 a. 1997 1998 1999 2000 2001 2002<br /><br />-6 12 (in millions)<br /><br />With a calculator, enter N = 5, PV = -6, PMT = 0, FV = 12, and then solve for I = 14.87%.<br /><br />b. The calculation described in the quotation fails to take account of the compounding effect. It can be demonstrated to be incorrect as follows:<br /><br />$6,000,000(1.20)5 = $6,000,000(2.4883) = $14,929,800,<br /><br />which is greater than $12 million. Thus, the annual growth rate is less than 20 percent; in fact, it is about 15 percent, as shown in Part a.<br /><br /><br />6-11 0 1 2 3 4 5 6 7 8 9 10<br /><br />-4 8 (in millions)<br /><br />With a calculator, enter N = 10, PV = -4, PMT = 0, FV = 8, and then solve for I = 7.18%.<br /><br /><br />6-12 0 1 2 3 4 30<br />• • •<br />85,000 -8,273.59 -8,273.59 -8,273.59 -8,273.59 -8,273.59<br /><br />With a calculator, enter N = 30, PV = 85000, PMT = -8273.59, FV = 0, and then solve for I = 9%.<br /><br /><br />6-13 a. 0 1 2 3 4<br /><br />PV = ? -10,000 -10,000 -10,000 -10,000<br /><br />With a calculator, enter N = 4, I = 7, PMT = -10000, and FV = 0. Then press PV to get PV = $33,872.11.<br /><br />b. 1. At this point, we have a 3-year, 7 percent annuity whose value is $26,243.16. You can also think of the problem as follows:<br /><br />$33,872(1.07) - $10,000 = $26,243.04.<br /><br />2. Zero after the last withdrawal.<br /><br /><br />6-14 0 1 2 3 4 5 6<br /><br />1,250 1,250 1,250 1,250 1,250 ?<br />FV = 10,000<br /><br />With a financial calculator, get a “ballpark” estimate of the years by entering I = 12, PV = 0, PMT = -1250, and FV = 10000, and then pressing the N key to find N = 5.94 years. This answer assumes that a payment of $1,250 will be made 94/100th of the way through Year 5.<br /><br />Now find the FV of $1,250 for 5 years at 12 percent; it is $7,941.06. Compound this value for 1 year at 12 percent to obtain the value in the account after 6 years and before the last payment is made; it is $7,941.06(1.12) = $8,893.99. Thus, you will have to make a payment of $10,000 - $8,893.99 = $1,106.01 at Year 6, so the answer is: it will take 6 years, and $1,106.01 is the amount of the last payment.<br /><br /><br />6-15 Contract 1: PV =<br />= $2,727,272.73 + $2,479,338.84 + $2,253,944.40 + $2,049,040.37<br />= $9,509,596.34.<br /><br />Using your financial calculator, enter the following data: CF0 = 0; CF1-4 = 3000000; I = 10; NPV = ? Solve for NPV = $9,509,596.34.<br /><br />Contract 2: PV =<br />= $1,818,181.82 + $2,479,338.84 + $3,005,259.20 + $3,415,067.28<br />= $10,717,847.14.<br /><br />Alternatively, using your financial calculator, enter the following data: CF0 = 0; CF1 = 2000000; CF2 = 3000000; CF3 = 4000000; CF4 = 5000000; I = 10; NPV = ? Solve for NPV = $10,717,847.14.<br /><br />Contract 3: PV =<br />= $6,363,636.36 + $826,446.28 + $751,314.80 + $683,013.46<br />= $8,624,410.90.<br /><br />Alternatively, using your financial calculator, enter the following data: CF0 = 0; CF1 = 7000000; CF2 = 1000000; CF3 = 1000000; CF4 = 1000000; I = 10; NPV = ? Solve for NPV = $8,624,410.90.<br /><br />Contract 2 gives the quarterback the highest present value; therefore, he should accept Contract 2.<br /><br /><br />6-16 PV = $100/0.07 = $1,428.57. PV = $100/0.14 = $714.29.<br /><br />When the interest rate is doubled, the PV of the perpetuity is halved.<br /><br /><br />6-17 0 4 8 12 16<br /><br />PV = ? 0 0 0 50 0 0 0 50 0 0 0 50 0 0 0 1,050<br /><br />iPER = 8%/4 = 2%.<br /><br />The cash flows are shown on the time line above. With a financial calcu-lator enter the following cash flows into your cash flow register: CF0 = 0, CF1-3 = 0, CF4 = 50, CF5-7 = 0, CF8 = 50, CF9-11 = 0, CF12 = 50, = 0,<br />CF16 = 1050; enter I = 2, and then press the NPV key to find PV = $893.16.<br /><br /><br />6-18 This can be done with a calculator by specifying an interest rate of<br />5 percent per period for 20 periods with 1 payment per period.<br /><br />N = 10 2 = 20.<br />I = 10%/2 = 5.<br />PV = -10000.<br />FV = 0.<br /><br />Solve for PMT = $802.43.<br /><br />Set up an amortization table:<br /><br />Beginning Payment of Ending<br />Period Balance Payment Interest Principal Balance<br />1 $10,000.00 $802.43 $500.00 $302.43 $9,697.57<br />2 9,697.57 802.43 484.88<br />$984.88<br /><br />You can also work the problem with a calculator having an amortization function. Find the interest in each 6-month period, sum them, and you have the answer. Even simpler, with some calculators such as the HP-17B, just input 2 for periods and press INT to get the interest during the first year, $984.88. The HP-10B does the same thing.<br /><br /><br />6-19 $1,000,000 loan @ 15 percent, annual PMT, 5-year amortization. What is the fraction of PMT that is principal in the second year? First, find PMT by using your financial calculator: N = 5, I/YR = 15, PV = -1000000, and<br />FV = 0. Solve for PMT = $298,315.55.<br /><br />Then set up an amortization table:<br /><br />Beginning Ending<br />Year Balance Payment Interest Principal Balance<br />1 $1,000,000.00 $298,315.55 $150,000.00 $148,315.55 $851,684.45<br />2 851,684.45 298,315.55 127,752.67 170,562.88 681,121.57<br /><br />Fraction that is principal = $170,562.88/$298,315.55 = 0.5718 = 57.18% ≈ 57.2%.<br /><br /><br />6-20 a. Begin with a time line:<br /><br />0 1 2 3 4 5 6 7 8 9 10 16 17 18 19 20 6-mos.<br />0 1 2 3 4 5 8 9 10 Years<br />• • •<br />100 100 100 100 100 FVA<br /><br />Since the first payment is made today, we have a 5-period annuity due. The applicable interest rate is 12%/2 = 6%. First, we find the FVA of the annuity due in period 5 by entering the following data in the financial calculator: N = 5, I = 12/2 = 6, PV = 0, and PMT = -100. Setting the calculator on “BEG,” we find FVA (Annuity due) = $597.53. Now, we must compound out for 15 semiannual periods at 6 percent.<br /><br />$597.53 20 – 5 = 15 periods @ 6% $1,432.02.<br /><br />b. 0 1 2 3 4 5 40 quarters<br />• • •<br />PMT PMT PMT PMT PMT FV = 1,432.02<br /><br />The time line depicting the problem is shown above. Because the payments only occur for 5 periods throughout the 40 quarters, this problem cannot be immediately solved as an annuity problem. The problem can be solved in two steps:<br /><br />1. Discount the $1,432.02 back to the end of Quarter 5 to obtain the PV of that future amount at Quarter 5.<br /><br />Input the following into your calculator: N = 35, I = 3, PMT = 0, FV = 1432.02, and solve for PV at Quarter 5. PV = $508.92.<br /><br />2. Then solve for PMT using the value solved in Step 1 as the FV of the five-period annuity due.<br /><br />The PV found in step 1 is now the FV for the calculations in this step. Change your calculator to the BEGIN mode. Input the following into your calculator: N = 5, I = 3, PV = 0, FV = 508.92, and solve for PMT = $93.07.<br /><br /><br />6-21 Here we want to have the same effective annual rate on the credit extended as on the bank loan that will be used to finance the credit extension.<br />First, we must find the EAR = EFF% on the bank loan. Enter NOM% = 15, P/YR = 12, and press EFF% to get EAR = 16.08%.<br />Now recognize that giving 3 months of credit is equivalent to quarterly compounding--interest is earned at the end of the quarter, so it is available to earn interest during the next quarter. Therefore, enter P/YR = 4, EFF% = EAR = 16.08%, and press NOM% to find the nominal rate of 15.19 percent. (Don’t forget to change your calculator back to P/YR = 1.)<br />Therefore, if you charge a 15.19 percent nominal rate and give credit for 3 months, you will cover the cost of the bank loan.<br /><br />Alternative solution: We need to find the effective annual rate (EAR) the bank is charging first. Then, we can use this EAR to calculate the nominal rate that you should quote your customers.<br /><br />Bank EAR: EAR = (1 + iNom/m)m - 1 = (1 + 0.15/12)12 - 1 = 16.08%.<br /><br /><br />Nominal rate you should quote customers:<br /><br />16.08% = (1 + iNom/4)4 - 1<br />1.1608 = (1 + iNom/4)4<br />1.0380 = 1 + iNom/4<br />iNom = 0.0380(4) = 15.19%.<br /><br /><br />6-22 Information given:<br /><br />1. Will save for 10 years, then receive payments for 25 years.<br /><br />2. Wants payments of $40,000 per year in today’s dollars for first payment only. Real income will decline. Inflation will be 5 percent. Therefore, to find the inflated fixed payments, we have this time line:<br /><br />0 5 10<br /><br />40,000 FV = ?<br /><br />Enter N = 10, I = 5, PV = -40000, PMT = 0, and press FV to get FV = $65,155.79.<br /><br />3. He now has $100,000 in an account that pays 8 percent, annual compounding. We need to find the FV of the $100,000 after 10 years. Enter N = 10, I = 8, PV = -100000, PMT = 0, and press FV to get FV = $215,892.50.<br /><br />4. He wants to withdraw, or have payments of, $65,155.79 per year for 25 years, with the first payment made at the beginning of the first retirement year. So, we have a 25-year annuity due with PMT = 65,155.79, at an interest rate of 8 percent. (The interest rate is 8 percent annually, so no adjustment is required.) Set the calculator to “BEG” mode, then enter N = 25, I = 8, PMT = 65155.79, FV = 0, and press PV to get PV = $751,165.35. This amount must be on hand to make the 25 payments.<br /><br />5. Since the original $100,000, which grows to $215,892.50, will be available, we must save enough to accumulate $751,165.35 - $215,892.50 = $535,272.85.<br /><br />6. The $535,272.85 is the FV of a 10-year ordinary annuity. The payments will be deposited in the bank and earn 8 percent interest. Therefore, set the calculator to “END” mode and enter N = 10, I = 8, PV = 0, FV = 535272.85, and press PMT to find PMT = $36,949.61.<br /><br /><br />6-23 a. Begin with a time line:<br /><br />0 1 19 20<br />• • •<br />1.75 1.75 1.75 (in millions)<br />PV = ?<br /><br />It is important to recognize that this is an annuity due since payments start immediately. Using a financial calculator input the following after switching to BEGIN mode:<br /><br />N = 20, I = 8, PMT = 1750000, FV = 0, and solve for PV = $18,556,299.<br /><br />b. 0 1 19 20<br />• • •<br />1.75 1.75 1.75 (in millions)<br />FV = ?<br /><br />It is important to recognize that this is an annuity due since payments start immediately. Using a financial calculator input the following after switching to BEGIN mode:<br /><br />N = 20, I = 8, PV = 0, PMT = 1750000, and solve for FV = $86,490,113.<br /><br />c. 0 1 19 20<br />• • •<br />1.75 1.75 1.75 (in millions)<br />PV = ?<br /><br />Using a financial calculator input the following:<br /><br />N = 20, I = 8, PMT = 1750000, FV = 0, and solve for PV = $17,181,758.<br /><br />0 1 19 20<br />• • •<br />1.75 1.75 1.75 (in millions)<br />FV = ?<br /><br />Using a financial calculator input the following:<br /><br />N = 20, I = 8, PV = 0, PMT = 1750000, and solve for FV = $80,083,438.<br /><br /><br />6-24 a. Begin with a time line:<br /><br />40 41 64 65<br />• • •<br />5,000 5,000 5,000<br /><br />Using a financial calculator input the following:<br /><br />N = 25, I = 12, PV = 0, PMT = 5000, and solve for FV = $666,669.35.<br /><br />b. 40 41 69 70<br />• • •<br />5,000 5,000 5,000<br />FV = ?<br /><br />Using a financial calculator input the following:<br /><br />N = 30, I = 12, PV = 0, PMT = 5000, and solve for FV = $1,206,663.42.<br /><br />6-25 Begin with a time line:<br /><br />0 1 2 3 4 5<br />12/31/01 12/31/02 12/31/03 12/31/04 12/31/05 12/31/06 01/01/07<br /><br />34,000 36,000 37,080 38,192.40 39,338.17 40,518.32 41,733.87<br />100,000<br />20,000<br />PV = ?<br /><br />Step 1: Calculate the PV of the lost back pay:<br />$34,000(1.07) + $36,000 = $72,380.<br /><br />Step 2: Calculate the PV of future salary (2003 - 2007):<br />CF0 = 0<br />CF1 = 36,000(1.03) = 37080.00<br />CF2 = 36,000(1.03)2 = 38192.40<br />CF3 = 36,000(1.03)3 = 39338.17<br />CF4 = 36,000(1.03)4 = 40518.32<br />CF5 = 36,000(1.03)5 = 41733.87<br />I = 7<br />Solve for NPV = $160,791.50.<br /><br />Step 3: Because the costs for pain and suffering and court costs are already on a present value basis, just add to the PV of costs found in Steps 1 and 2.<br /><br />PV = $72,380 + $160,791.50 + $100,000 + $20,000 = $353,171.50.<br /><br /><br />6-26 Begin with a time line:<br /><br />0 1 2 3<br /><br />5,000 5,500 6,050<br />FV = ?<br /><br />Use a financial calculator to calculate the present value of the cash flows and then determine the future value of this present value amount:<br /><br />Step 1: CF0 = 0<br />CF1 = 5000<br />CF2 = 5500<br />CF3 = 6050<br />I = 7<br />Solve for NPV = $14,415.41.<br /><br />Step 2: Input the following data:<br />N = 3, I = 7, PV = -14415.41, PMT = 0, and solve for FV = $17,659.50.<br /><br /><br /><br />6-27 Begin with a time line:<br /><br />0 1 5 6 15<br />• • • • • •<br />-340.4689 50 50 PMT PMT<br /><br />This security is essentially two annuities and the present value of the security is the sum of the present values for each of the two annuities. Using a financial calculator solve as follows:<br /><br />Step 1: Determine the present value of the first annuity:<br />Input N = 5, I = 9, PMT = 50, FV = 0, and solve for PV = $194.4826.<br /><br />Step 2: Calculate the present value of the second annuity:<br />$340.4689 - $194.4826 = $145.9863.<br /><br />Step 3: Calculate the value of the second annuity as of Year 5:<br /><br />Input N = 5, I = 9, PV = -145.9863, PMT = 0, and solve for FV = $224.6180.<br /><br />Step 4: Calculate the payment amount of the second annuity:<br />Input N = 10, I = 9, PV = -224.6180, FV = 0, and solve for PMT = $35.00.<br /><br /><br />6-28 0 1 2 3 4 5 6 7 8 Qtrs<br /><br />20 20 20 20<br />FV = ?<br /><br />To solve this problem two steps are needed. First, determine the present value of the cash flow stream. Second, calculate the future value of this present value. Using a financial calculator input the following:<br /><br />CF0 = 0; CF1 = 0; CF2 = 20; CF3 = 0; CF4 = 20; CF5 = 0; CF6 = 20; CF7 = 0; CF8 = 20; I = 7/4 = 1.75; and then solve for NPV = $73.4082.<br /><br />Calculate the future value of this NPV amount:<br />Input N = 8, I = 1.75, PV = -73.4082, PMT = 0, and solve for FV = $84.34.<br /><br /><br />6-29 a. Using the information given in the problem, you can solve for the length of time required to reach $1 million.<br /><br />I = 8; PV = 30000; PMT = 5000; FV = -1000000; and then solve for N = 31.7196.<br /><br />Therefore, it will take Erika 31.72 years to reach her investment goal.<br /><br />b. Again, you can solve for the length of time required to reach $1 million.<br /><br />I = 9; PV = 30000; PMT = 5000; FV = -1000000; and then solve for N = 29.1567.<br />It will take Katherine 29.16 years to reach her investment goal. The difference in time is 31.72 - 29.16 = 2.56 years.<br /><br />c. Using the 31.7196 year target, you can solve for the required payment.<br /><br />N = 31.7196; I = 9; PV = 30000; FV = -1000000; then solve for PMT = 3,368.00.<br /><br />If Katherine wishes to reach the investment goal at the same time as Erika, she can contribute as little as $3,368 every year.<br /><br /><br />6-30 a. If Crissie expects a 7% annual return upon her investments:<br /><br />1 payment 10 payments 30 payments<br />N = 10 N = 30<br />I = 7 I = 7<br />PMT = 9500000 PMT = 5500000<br />FV = 0 FV = 0<br /><br />PV = 61,000,000 PV = 66,724,025 PV = 68,249,727<br /><br />Crissie should accept the 30-year payment option as it carries the highest present value ($68,249,727).<br /><br />b. If Crissie expects an 8% annual return upon her investments:<br /><br />1 payment 10 payments 30 payments<br />N = 10 N = 30<br />I = 8 I = 8<br />PMT = 9500000 PMT = 5500000<br />FV = 0 FV = 0<br /><br />PV = 61,000,000 PV = 63,745,773 PV = 61,917,808<br /><br />Crissie should accept the 10-year payment option as it carries the highest present value ($63,745,773).<br /><br />c. If Crissie expects a 9% annual return upon her investments:<br /><br />1 payment 10 payments 30 payments<br />N = 10 N = 30<br />I = 9 I = 9<br />PMT = 9500000 PMT = 5500000<br />FV = 0 FV = 0<br /><br />PV = 61,000,000 PV = 60,967,748 PV = 56,505,097<br /><br />Crissie should accept the lump-sum payment option as it carries the highest present value ($61,000,000).<br /><br /><br />6-31 Using the information given in the problem, you can solve for the maximum car price attainable.<br /><br />Financed for 48 months Financed for 60 months<br />N = 48 N = 60<br />I = 1 (12%/12 = 1%) I = 1<br />PMT = 350 PMT = 350<br />FV = 0 FV = 0<br /><br />PV = 13,290.89 PV = 15,734.26<br /><br />You must add the value of the down payment to the present value of the car payments. If financed for 48 months, Jarrett can afford a car valued up to $17,290.89 ($13,290.89 + $4,000). If financing for 60 months, Jarrett can afford a car valued up to 19,734.26 ($15,734.26 + $4,000).<br /><br /><br />6-32 a. Using the information given in the problem, you can solve for the length of time required to eliminate the debt.<br /><br />I = 2 (24%/12); PV = 305.44; PMT = -10; FV = 0; and then solve for N = 47.6638.<br /><br />Because Simon makes payments on his credit card at the end of the month, it will require 48 months before he pays off the debt.<br /><br />b. First, you should solve for the present value of the total payments made through the first 47 months.<br /><br />N = 47; I = 2; PMT = -10; FV = 0; and then solve for PV = 302.8658.<br /><br />This represents a difference in present values of payments of $2.5742 ($305.44 - $302.8658). Next, you must find the value of this difference at the end of the 48th month.<br /><br />N = 48; I = 2; PV = -2.5742; PMT = 0; and then solve for FV = 6.6596.<br /><br />Therefore, the 48th and final payment will be for $6.66.<br /><br />c. If Simon makes monthly payments of $30, we can solve for the length of time required before the account is paid off.<br /><br />I = 2; PV = 305.44; PMT = -30; FV = 0; and then solve for N = 11.4978.<br /><br />With $30 monthly payments, Simon will only need 12 months to pay off the account.<br /><br />d. First, we must find out what the final payment will be if $30 payments are made for the first 11 months.<br /><br />N = 11; I = 2; PMT = -30; FV = 0; and then solve for PV = 293.6054.<br /><br />This represents a difference in present values of payments of $11.8346 ($305.44 - $293.6054). Next, you must find the value of this difference at the end of the 12th month.<br /><br />N = 12; I = 2; PV = -11.8346; PMT = 0; and then solve for FV = 15.0091.<br /><br />Therefore, the 12th and final payment will be for $15.01.<br /><br />The difference in total payments can be found to be:<br /><br />[(47 $10) + $6.66] - [(11 $30) + $15.01] = $131.65.<br /><br /><br />6-33 Using the information given in the problem, you can solve for the return on the investment.<br /><br />N = 5; PV = -1300; PMT = 400; FV = 0; and then solve for I = 16.32%.<br /><br /><br />6-34 a. 0 1<br />$500(1.06) = $530.00.<br />-500 FV = ?<br /><br />b. 0 1 2<br />$500(1.06)2 = $561.80.<br />-500 FV = ?<br /><br />c. 0 1<br />$500(1/1.06) = $471.70.<br />PV = ? 500<br />d. 0 1 2<br />$500(1/1.06)2 = $445.00.<br />PV = ? 500<br /><br /><br />6-35 a. 0 1 2 3 4 5 6 7 8 9 10<br />$500(1.06)10 = $895.42.<br />-500 FV = ?<br /><br />b. 0 1 2 3 4 5 6 7 8 9 10<br />$500(1.12)10 = $1,552.92.<br />-500 FV = ?<br /><br />c. 0 1 2 3 4 5 6 7 8 9 10<br />$500/(1.06)10 = $279.20.<br />PV = ? 500<br /><br />d. 0 1 2 3 4 5 6 7 8 9 10<br /><br />PV = ? 1,552.90<br /><br />$1,552.90/(1.12)10 = $499.99.<br />$1,552.90/(1.06)10 = $867.13.<br />The present value is the value today of a sum of money to be received in the future. For example, the value today of $1,552.90 to be received 10 years in the future is about $500 at an interest rate of 12 percent, but it is approximately $867 if the interest rate is<br />6 percent. Therefore, if you had $500 today and invested it at 12 percent, you would end up with $1,552.90 in 10 years. The present value depends on the interest rate because the interest rate determines the amount of interest you forgo by not having the money today.<br /><br /><br />6-36 a. ?<br /><br />-200 400<br /><br />With a financial calculator, enter I = 7, PV = -200, PMT = 0, and FV = 400. Then press the N key to find N = 10.24. Override I with the other values to find N = 7.27, 4.19, and 1.00.<br /><br />b. ?<br />Enter: I = 10, PV = -200, PMT = 0, and FV = 400.<br />-200 400 N = 7.27.<br /><br />c. ?<br />Enter: I = 18, PV = -200, PMT = 0, and FV = 400.<br />-200 400 N = 4.19.<br /><br />d. ?<br />Enter: I = 100, PV = -200, PMT = 0, and FV = 400.<br />-200 400 N = 1.00.<br /><br /><br />6-37 a. 0 1 2 3 4 5 6 7 8 9 10<br /><br />400 400 400 400 400 400 400 400 400 400<br />FV = ?<br /><br />With a financial calculator, enter N = 10, I = 10, PV = 0, and PMT =<br />-400. Then press the FV key to find FV = $6,374.97.<br /><br />b. 0 1 2 3 4 5<br /><br />200 200 200 200 200<br />FV = ?<br /><br />With a financial calculator, enter N = 5, I = 5, PV = 0, and PMT =<br />-200. Then press the FV key to find FV = $1,105.13.<br /><br />c. 0 1 2 3 4 5<br /><br />400 400 400 400 400<br />FV = ?<br /><br />With a financial calculator, enter N = 5, I = 0, PV = 0, and PMT =<br />-400. Then press the FV key to find FV = $2,000.<br /><br />d. To solve Part d using a financial calculator, repeat the procedures discussed in Parts a, b, and c, but first switch the calculator to “BEG” mode. Make sure you switch the calculator back to “END” mode after working the problem.<br /><br />1. 0 1 2 3 4 5 6 7 8 9 10<br /><br />400 400 400 400 400 400 400 400 400 400 FV = ?<br /><br />With a financial calculator on BEG, enter: N = 10, I = 10, PV = 0, and PMT = -400. FV = $7,012.47.<br /><br />2. 0 1 2 3 4 5<br /><br />200 200 200 200 200 FV = ?<br /><br />With a financial calculator on BEG, enter: N = 5, I = 5, PV = 0, and PMT = -200. FV = $1,160.38.<br /><br />3. 0 1 2 3 4 5<br /><br />400 400 400 400 400 FV = ?<br /><br />With a financial calculator on BEG, enter: N = 5, I = 0, PV = 0, and PMT = -400. FV = $2,000.<br /><br /><br />6-38 The general formula is PVAn = PMT(PVIFAi,n).<br /><br />a. 0 1 2 3 4 5 6 7 8 9 10<br /><br />PV = ? 400 400 400 400 400 400 400 400 400 400<br /><br />With a financial calculator, simply enter the known values and then press the key for the unknown. Enter: N = 10, I = 10, PMT = -400, and FV = 0. PV = $2,457.83.<br /><br />b. 0 1 2 3 4 5<br /><br />PV = ? 200 200 200 200 200<br /><br />With a financial calculator, enter: N = 5, I = 5, PMT = -200, and FV = 0. PV = $865.90.<br /><br />c. 0 1 2 3 4 5<br /><br />PV = ? 400 400 400 400 400<br /><br />With a financial calculator, enter: N = 5, I = 0, PMT = -400, and FV = 0. PV = $2,000.00.<br /><br />d. 1. 0 1 2 3 4 5 6 7 8 9 10<br /><br />400 400 400 400 400 400 400 400 400 400<br />PV = ?<br /><br />With a financial calculator on BEG, enter: N = 10, I = 10, PMT = -400, and FV = 0. PV = $2,703.61.<br />2. 0 1 2 3 4 5<br /><br />200 200 200 200 200<br />PV = ?<br /><br />With a financial calculator on BEG, enter: N = 5, I = 5, PMT =<br />-200, and FV = 0. PV = $909.19.<br /><br />3. 0 1 2 3 4 5<br /><br />400 400 400 400 400<br />PV = ?<br /><br />With a financial calculator on BEG, enter: N = 5, I = 0, PMT =<br />-400, and FV = 0. PV = $2,000.00.<br /><br /><br />6-39 a. Cash Stream A Cash Stream B<br />0 1 2 3 4 5 0 1 2 3 4 5<br /><br />PV = ? 100 400 400 400 300 PV = ? 300 400 400 400 100<br /><br />With a financial calculator, simply enter the cash flows (be sure to enter CF0 = 0), enter I = 8, and press the NPV key to find NPV = PV = $1,251.25 for the first problem. Override I = 8 with I = 0 to find the next PV for Cash Stream A. Repeat for Cash Stream B to get NPV = PV = $1,300.32.<br /><br />b. PVA = $100 + $400 + $400 + $400 + $300 = $1,600.<br />PVB = $300 + $400 + $400 + $400 + $100 = $1,600.<br /><br /><br />6-40 These problems can all be solved using a financial calculator by entering the known values shown on the time lines and then pressing the I button.<br /><br />a. 0 1<br /><br />+700 -749<br /><br />With a financial calculator, enter: N = 1, PV = 700, PMT = 0, and FV = -749. I = 7%.<br /><br />b. 0 1<br /><br />-700 +749<br /><br />With a financial calculator, enter: N = 1, PV = -700, PMT = 0, and FV = 749. I = 7%.<br /><br />c. 0 10<br /><br />+85,000 -201,229<br /><br />With a financial calculator, enter: N = 10, PV = 85000, PMT = 0, and FV = -201229. I = 9%.<br /><br />d. 0 1 2 3 4 5<br /><br />+9,000 -2,684.80 -2,684.80 -2,684.80 -2,684.80 -2,684.80<br /><br />With a financial calculator, enter: N = 5, PV = 9000, PMT =<br />-2684.80, and FV = 0. I = 15%.<br /><br /><br />6-41 a. 0 1 2 3 4 5<br /><br />-500 FV = ?<br /><br />With a financial calculator, enter N = 5, I = 12, PV = -500, and PMT = 0, and then press FV to obtain FV = $881.17.<br /><br />b. 0 1 2 3 4 5 6 7 8 9 10<br /><br />-500 FV = ?<br /><br />Enter the time line values into a financial calculator to obtain FV = $895.42.<br /><br />Alternatively, FVn = PV = $500<br />= $500(1.06)10 = $895.42.<br /><br />c. 0 4 8 12 16 20<br /><br />-500 FV = ?<br /><br />Enter the time line values into a financial calculator to obtain FV = $903.06.<br /><br />Alternatively, FVn = $500 = $500(1.03)20 = $903.06.<br /><br />d. 0 12 24 36 48 60<br /><br />-500 ?<br /><br />Enter the time line values into a financial calculator to obtain FV = $908.35.<br /><br />Alternatively, FVn = $500 = $500(1.01)60 = $908.35.<br /><br /><br />6-42 a. 0 2 4 6 8 10<br /><br />PV = ? 500<br /><br />Enter the time line values into a financial calculator to obtain PV = $279.20.<br />Alternatively, PV = FVn = $500<br />= $500 = $279.20.<br /><br />b. 0 4 8 12 16 20<br /><br />PV = ? 500<br /><br /><br />Enter the time line values into a financial calculator to obtain PV = $276.84.<br /><br />Alternatively, PV = $500 = $500 = $276.84.<br /><br />c. 0 1 2 12<br />• • •<br />PV = ? 500<br /><br />Enter the time line values into a financial calculator to obtain PV = $443.72.<br /><br />Alternatively, PV = $500 = $500 = $443.72.<br /><br /><br />6-43 a. 0 1 2 3 9 10<br />• • •<br />-400 -400 -400 -400 -400<br />FV = ?<br /><br />Enter N = 5 2 = 10, I = 12/2 = 6, PV = 0, PMT = -400, and then press FV to get FV = $5,272.32.<br /><br />b. Now the number of periods is calculated as N = 5 4 = 20, I = 12/4 = 3, PV = 0, and PMT = -200. The calculator solution is $5,374.07. The solution assumes that the nominal interest rate is compounded at the annuity period.<br /><br />c. The annuity in Part b earns more because some of the money is on deposit for a longer period of time and thus earns more interest. Also, because compounding is more frequent, more interest is earned on interest.<br /><br /><br /><br />6-44 a. First City Bank: Effective rate = 7%.<br /><br />Second City Bank:<br /><br />Effective rate = - 1.0 = (1.015)4 – 1.0<br />= 1.0614 – 1.0 = 0.0614 = 6.14%.<br /><br />With a financial calculator, you can use the interest rate conversion feature to obtain the same answer. You would choose the First City Bank.<br /><br />b. If funds must be left on deposit until the end of the com¬pounding period (1 year for First City and 1 quarter for Second City), and you think there is a high probability that you will make a withdrawal during the year, the Second City account might be preferable. For example, if the withdrawal is made after 10 months, you would earn nothing on the First City account but (1.015)3 – 1.0 = 4.57% on the Second City account.<br />Ten or more years ago, most banks and S&Ls were set up as described above, but now virtually all are computerized and pay interest from the day of deposit to the day of withdrawal, provided at least $1 is in the account at the end of the period.<br /><br /><br />6-45 a. With a financial calculator, enter N = 5, I = 10, PV = -25000, and FV = 0, and then press the PMT key to get PMT = $6,594.94. Then go through the amortization procedure as described in your calculator manual to get the entries for the amortization table.<br /><br />Repayment Remaining<br />Year Payment Interest of Principal Balance<br />1 $ 6,594.94 $2,500.00 $ 4,094.94 $20,905.06<br />2 6,594.94 2,090.51 4,504.43 16,400.63<br />3 6,594.94 1,640.06 4,954.88 11,445.75<br />4 6,594.94 1,144.58 5,450.36 5,995.39<br />5 6,594.93* 599.54 5,995.39 0<br />$32,974.69 $7,974.69 $25,000.00<br /><br />*The last payment must be smaller to force the ending balance to zero.<br /><br />b. Here the loan size is doubled, so the payments also double in size to $13,189.87.<br /><br />c. The annual payment on a $50,000, 10-year loan at 10 percent interest would be $8,137.27. Because the payments are spread out over a longer time period, each payment is lower but more interest must be paid on the loan. The total interest paid on the 10-year loan is $31,372.70 versus interest of $15,949.37 on the 5-year loan.<br /><br /><br />6-46 a. Using your financial calculator, input the following data: N = 30 12 = 360; I = 8/12 = 0.6667; PV = -125000; FV = 0; PMT = ? Solve for PMT = $917.21.<br /><br />b. After finding the monthly mortgage payment, use the amortization feature of your calculator to find interest and principal repayments during the year and the remaining mortgage balance as follows:<br />1 INPUT 12 AMORT<br />= $ 9,962.23 (Interest)<br />= $ 1,044.29 (Principal)<br />= $123,955.71 (Balance)<br /><br />Total mortgage payments made during the first year equals 12 $917.21 = $11,006.52.<br /><br />Portion of first year mortgage payments that go towards interest equals $9,962.23/$11,006.52 = 90.51%.<br /><br />c. After finding the monthly mortgage payment, use the amortization feature of your calculator to find interest and principal payments during the first five years and the remaining mortgage balance as follows:<br />1 INPUT 60 AMORT<br />= $ 48,869.66 (Interest)<br />= $ 6,162.68 (Principal)<br />= $118,837.32 (Balance)<br /><br />The remaining mortgage balance after 5 years will be $118,837.32.<br /><br />d. Using your financial calculator, input the following data: N = 30 12 = 360; I = 8/12 = 0.6667; PMT = 1200; FV = 0; PV = ? Solve for PV = $163,540.19.<br /><br />If the Jacksons are willing to have a $1,200 monthly mortgage payment, the can borrow $163,540.19 today.<br /><br /><br />6-47 0 9 10<br />• • •<br />Z: -422.41 0 0 0 1,000.00<br />B: -1,000.00 80 80 80 1,080.00<br /><br />a. With a financial calculator, for Z, enter N = 10, PV = -422.41, PMT<br />= 0, FV = 1000, and press I to get I = 9.00%. For B, enter N = 10, PV = -1000, PMT = 80, FV = 1000, and press I to get I = 8%. (Alternatively, enter the values exactly as shown on the time line in the CF register, and use the IRR key to obtain the same answer.)<br /><br />b. With a calculator, for the “zero coupon bond,” enter N = 10, I = 6, PMT = 0, FV = 1000, and press PV to get the value of the security today, $558.39. The profit would be $558.39 - $422.41 = $135.98, and the percentage profit would be $135.98/$422.41 = 32.2%.<br />For the “coupon bond,” enter N = 10, I = 6, PMT = 80, FV = 1000, and then press PV to get PV = $1,147.20. The profit is $147.20, and the percentage profit is 14.72 percent.<br /><br />c. Here we compound cash flows to obtain a “terminal value” at Year 10, and then find the interest rate that equates the TV to the cost of the security.<br />There are no intermediate cash flows with Security Z, so its TV is $1,000, and, as we saw in Part a, 9 percent causes the PV of $1,000 to equal the cost, $422.41. For Security B, we must compound the cash flows over 10 years at 6 percent. Enter N = 10, I = 6, PV = 0, PMT = 80, and then press FV to get the FV of the 10-year annuity of $80 per year: FV = $1,054.46. Then add the $1,000 to be received at Year 10 to get TVB = $2,054.46. Then enter N = 10, PV = -1000, PMT = 0, FV = 2054.46, and press I to get I = 7.47%.<br />So, if the firm buys Security Z, its actual return will be 9 percent regardless of what happens to interest rates--this security is a zero coupon bond that has zero reinvestment rate risk. However, if the firm buys the 8 percent coupon bond, and rates then fall, its “true” return over the 10 years will be only 7.47 percent, which is an average of the old 8 percent and the new 6 percent.<br /><br /><br />d. The value of Security Z would fall from $422.41 to $321.97, so a loss of $100.44, or 23.8 percent, would be incurred. The value of Security B would fall to $773.99, so the loss here would be $226.01, or 22.6 percent of the $1,000 original investment. The percentage losses for the two bonds is close, but only because the zero’s original return was 9 percent versus 8 percent for the coupon bond.<br />The “actual” or “true” return on the zero would remain at 9 percent, but the “actual” return on the coupon bond would rise from 8 percent to 9.17 percent due to reinvestment of the $80 coupons at 12 percent.<br /><br /><br />6-48 a. First, determine the annual cost of college. The current cost is $12,500 per year, but that is escalating at a 5 percent inflation rate:<br /><br />College Current Years Inflation Cash<br />Year Cost from Now Adjustment Required<br />1 $12,500 5 (1.05)5 $15,954<br />2 12,500 6 (1.05)6 16,751<br />3 12,500 7 (1.05)7 17,589<br />4 12,500 8 (1.05)8 18,468<br /><br />Now put these costs on a time line:<br /><br />13 14 15 16 17 18 19 20 21<br /><br />-15,954 –16,751 –17,589 –18,468<br /><br />How much must be accumulated by age 18 to provide these payments at ages 18 through 21 if the funds are invested in an account paying<br />8 percent, compounded annually?<br /><br />With a financial calculator enter: CF0 = 15954, CF1 = 16751, CF2 = 17589, CF3 = 18468, and I = 8. Solve for NPV = $61,204.41.<br />Thus, the father must accumulate $61,204 by the time his daughter reaches age 18.<br /><br />b. She has $7,500 now (age 13) to help achieve that goal. Five years hence, that $7,500, when invested at 8 percent, will be worth $11,020:<br /><br />$7,500(1.08)5 = $11,020.<br /><br /><br />c. The father needs to accumulate only $61,204 - $11,020 = $50,184. The key to completing the problem at this point is to realize the series of deposits represent an ordinary annuity rather than an annuity due, despite the fact the first payment is made at the beginning of the first year. The reason it is not an annuity due is there is no interest paid on the last payment that occurs when the daughter is 18.<br /><br />Using a financial calculator, N = 6, I = 8, PV = 0, and FV = -50184. PMT = $6,840.85 ≈ $6,841.<br /></div>saleem shahzadnoreply@blogger.com0tag:blogger.com,1999:blog-3421608066886271296.post-6307974705073782262010-12-14T15:13:00.001+05:002011-01-18T16:15:12.721+05:00Chapter 7Chapter 7<br />Bonds and Their Valuation<br />SOLUTIONS TO END-OF-CHAPTER PROBLEMS<br /><br /><br /><br />7-1 With your financial calculator, enter the following:<br /><br />N = 10; I = YTM = 9%; PMT = 0.08 1,000 = 80; FV = 1000; PV = VB = ?<br />PV = $935.82.<br /><br /><br />7-2 With your financial calculator, enter the following to find YTM:<br /><br />N = 10 2 = 20; PV = -1100; PMT = 0.08/2 1,000 = 40; FV = 1000; I = YTM = ?<br />YTM = 3.31% 2 = 6.62%.<br /><br />With your financial calculator, enter the following to find YTC:<br /><br />N = 5 2 = 10; PV = -1100; PMT = 0.08/2 1,000 = 40; FV = 1050; I = YTC = ?<br />YTC = 3.24% 2 = 6.49%.<br /><br /><br />7-3 The problem asks you to find the price of a bond, given the following facts: N = 16; I = 8.5/2 = 4.25; PMT = 45; FV = 1000.<br /><br />With a financial calculator, solve for PV = $1,028.60.<br /><br /><br />7-4 VB = $985; M = $1,000; Int = 0.07 $1,000 = $70.<br /><br />a. Current yield = Annual interest/Current price of bond<br />= $70/$985.00<br />= 7.11%.<br /><br />b. N = 10; PV = -985; PMT = 70; FV = 1000; YTM = ?<br />Solve for I = YTM = 7.2157% 7.22%.<br /><br />c. N = 7; I = 7.2157; PMT = 70; FV = 1000; PV = ?<br />Solve for VB = PV = $988.46.<br /><br /><br />7-5 a. 1. 5%: Bond L: Input N = 15, I = 5, PMT = 100, FV = 1000, PV = ?, PV = $1,518.98.<br />Bond S: Change N = 1, PV = ? PV = $1,047.62.<br /><br />2. 8%: Bond L: From Bond S inputs, change N = 15 and I = 8, PV = ?, PV = $1,171.19.<br />Bond S: Change N = 1, PV = ? PV = $1,018.52.<br /><br />3. 12%: Bond L: From Bond S inputs, change N = 15 and I = 12, PV = ?, PV = $863.78.<br />Bond S: Change N = 1, PV = ? PV = $982.14.<br /><br />b. Think about a bond that matures in one month. Its present value is influenced primarily by the maturity value, which will be received in only one month. Even if interest rates double, the price of the bond will still be close to $1,000. A 1-year bond’s value would fluctuate more than the one-month bond’s value because of the difference in the timing of receipts. However, its value would still be fairly close to $1,000 even if interest rates doubled. A long-term bond paying semiannual coupons, on the other hand, will be dominated by distant receipts, receipts that are multiplied by 1/(1 + kd/2)t, and if kd increases, these multipliers will decrease significantly. Another way to view this problem is from an opportunity point of view. A 1-month bond can be reinvested at the new rate very quickly, and hence the opportunity to invest at this new rate is not lost; however, the long-term bond locks in subnormal returns for a long period of time.<br /><br /><br />7-6 a. VB =<br /><br />M = $1,000. I = 0.09($1,000) = $90.<br /><br />1. VB = $829: Input N = 4, PV = -829, PMT = 90, FV = 1000, I = ? I = 14.99%.<br /><br />2. VB = $1,104: Change PV = -1104, I = ? I = 6.00%.<br /><br />b. Yes. At a price of $829, the yield to maturity, 15 percent, is greater than your required rate of return of 12 percent. If your required rate of return were 12 percent, you should be willing to buy the bond at any price below $908.88.<br /><br /><br />7-7 The rate of return is approximately 15.03 percent, found with a calculator using the following inputs:<br /><br />N = 6; PV = -1000; PMT = 140; FV = 1090; I = ? Solve for I = 15.03%.<br /><br /><br />7-8 a. Using a financial calculator, input the following:<br /><br />N = 20, PV = -1100, PMT = 60, FV = 1000, and solve for I = 5.1849%.<br /><br />However, this is a periodic rate. The nominal annual rate = 5.1849%(2) = 10.3699% 10.37%.<br /><br />b. The current yield = $120/$1,100 = 10.91%.<br /><br />c. YTM = Current Yield + Capital Gains (Loss) Yield<br />10.37% = 10.91% + Capital Loss Yield<br />-0.54% = Capital Loss Yield.<br /><br />d. Using a financial calculator, input the following:<br /><br />N = 8, PV = -1100, PMT = 60, FV = 1060, and solve for I = 5.0748%.<br /><br />However, this is a periodic rate. The nominal annual rate = 5.0748%(2) = 10.1495% 10.15%.<br /><br /><br />7-9 The problem asks you to solve for the YTM, given the following facts:<br /><br />N = 5, PMT = 80, and FV = 1000. In order to solve for I we need PV.<br /><br />However, you are also given that the current yield is equal to 8.21%. Given this information, we can find PV.<br /><br />Current yield = Annual interest/Current price<br />0.0821 = $80/PV<br />PV = $80/0.0821 = $974.42.<br /><br />Now, solve for the YTM with a financial calculator:<br /><br />N = 5, PV = -974.42, PMT = 80, and FV = 1000. Solve for I = YTM = 8.65%.<br /><br /><br />7-10 The problem asks you to solve for the current yield, given the following facts: N = 14, I = 10.5883/2 = 5.29415, PV = -1020, and FV = 1000. In order to solve for the current yield we need to find PMT. With a financial calculator, we find PMT = $55.00. However, because the bond is a semiannual coupon bond this amount needs to be multiplied by 2 to obtain the annual interest payment: $55.00(2) = $110.00. Finally, find the current yield as follows:<br /><br />Current yield = Annual interest/Current price = $110/$1,020 = 10.78%.<br /><br /><br />7-11 The bond is selling at a large premium, which means that its coupon rate is much higher than the going rate of interest. Therefore, the bond is likely to be called--it is more likely to be called than to remain outstanding until it matures. Thus, it will probably provide a return equal to the YTC rather than the YTM. So, there is no point in calculating the YTM--just calculate the YTC. Enter these values:<br /><br />N = 10, PV = -1353.54, PMT = 70, FV = 1050, and then solve for I.<br /><br />The periodic rate is 3.2366 percent, so the nominal YTC is 2 3.2366% = 6.4733% 6.47%. This would be close to the going rate, and it is about what the firm would have to pay on new bonds.<br /><br /><br />7-12 a. To find the YTM:<br />N = 10, PV = -1175, PMT = 110, FV = 1000<br />I = YTM = 8.35%.<br /><br />b. To find the YTC, if called in Year 5:<br />N = 5, PV = -1175, PMT = 110, FV = 1090<br />I = YTC = 8.13%.<br />c. The bonds are selling at a premium which indicates that interest rates have fallen since the bonds were originally issued. Assuming that interest rates do not change from the present level, investors would expect to earn the yield to call. (Note that the YTC is less than the YTM.)<br /><br />d. Similarly from above, YTC can be found, if called in each subsequent year.<br /><br />If called in Year 6:<br />N = 6, PV = -1175, PMT = 110, FV = 1080<br />I = YTM = 8.27%.<br /><br />If called in Year 7:<br />N = 7, PV = -1175, PMT = 110, FV = 1070<br />I = YTM = 8.37%.<br /><br />If called in Year 8:<br />N = 8, PV = -1175, PMT = 110, FV = 1060<br />I = YTM = 8.46%.<br /><br />If called in Year 9:<br />N = 9, PV = -1175, PMT = 110, FV = 1050<br />I = YTM = 8.53%.<br /><br />According to these calculations, the latest investors might expect a call of the bonds is in Year 6. This is the last year that the expected YTC will be less than the expected YTM. At this time, the firm still finds an advantage to calling the bonds, rather than seeing them to maturity.<br /><br /><br />7-13 First, we must find the amount of money we can expect to sell this bond for in 5 years. This is found using the fact that in five years, there will be 15 years remaining until the bond matures and that the expected YTM for this bond at that time will be 8.5%.<br /><br />N = 15, I = 8.5, PMT = 90, FV = 1000<br />PV = -$1,041.52. VB = $1,041.52.<br /><br />This is the value of the bond in 5 years. Therefore, we can solve for the maximum price we would be willing to pay for this bond today, subject to our required rate of return of 10%.<br /><br />N = 5, I = 10, PMT = 90, FV = 1041.52<br />PV = -$987.87. VB = $987.87.<br /><br />We are willing to pay up to $987.87 for this bond today.<br /><br /><br />7-14 Before you can solve for the price, we must find the appropriate semiannual rate at which to evaluate this bond.<br /><br />EAR = (1 + NOM/2)2 - 1<br />0.0816 = (1 + NOM/2)2 - 1<br />NOM = 0.08.<br /><br />Semiannual interest rate = 0.08/2 = 0.04 = 4%.<br /><br />Solving for price:<br />N = 20, I = 4, PMT = 45, FV = 1000<br />PV = -$1,067.95. VB = $1,067.95.<br /><br /><br />7-15 a. The current yield is defined as the annual coupon payment divided by the current price.<br /><br />CY = $80/$901.40 = 8.875%.<br /><br />b. Solving for YTM:<br />N = 9, PV = -901.40, PMT = 80, FV = 1000<br />I = YTM = 9.6911%.<br /><br />c. Expected capital gains yield can be found as the difference between YTM and the current yield.<br /><br />CGY = YTM - CY = 9.691% - 8.875% = 0.816%.<br /><br />Alternatively, you can solve for the capital gains yield by first finding the expected price next year.<br />N = 8, I = 9.6911, PMT = 80, FV = 1000<br />PV = -$908.76. VB = $908.76.<br /><br />Hence, the capital gains yield is the percent price appreciation over the next year.<br /><br />CGY = (P1 - P0)/P0 = ($908.76 - $901.40)/$901.40 = 0.816%.<br /><br />7-16 Using the TIE ratio, we can solve for the firm's current operating income.<br /><br />TIE = EBIT/Int Exp<br />3.2 = EBIT/$10,500,000<br />EBIT = $33,600,000.<br /><br />Using the same methodology, you can solve for the maximum interest expense the firm can bear without violating its covenant.<br /><br />2.5 = $33,600,000/Int Exp<br />Max Int Exp = $13,440,000.<br /><br />Therefore, the firm can raise debt to the point that its interest expense increases by $2.94 million ($13.44 $10.50). The firm can raise $25 million at 8%, which would increase the cost of debt by $25 0.08 = $2 million. Additional debt will be issued at 10%, and the amount of debt to be raised can be found, since we know that only an additional $0.94 million in interest expense can be incurred.<br /><br />Additional Int Exp = Additional Debt Cost of debt<br />$0.94 million = Additional Debt 0.10<br />Additional Debt = $9.40 million.<br /><br />Hence, the firm may raise up to $34.4 million in additional debt without violating its bond covenants.<br />7-17 First, we must find the price Baili paid for this bond.<br /><br />N = 10, I = 9.79, PMT = 110, FV = 1000<br />PV = -$1,075.02. VB = $1,075.02.<br /><br />Then to find the one-period return, we must find the sum of the change in price and the coupon received divided by the starting price.<br /><br />One-period return =<br />One-period return = ($1,060.49 - $1,075.02 + $110)/$1,075.02<br />One-period return = 8.88%.<br /><br /><br />7-18 The answer depends on when one works the problem. We used The Wall Street Journal, February 3, 2003:<br /><br /><br />a. AT&T’s 8.625%, 2031 bonds had an 8.6 percent current yield. The bonds sold at a premium, 100.75% of par, so the coupon interest rate would have to be set lower than 8.625% for the bonds to sell at par. If we assume the bonds aren’t callable, we can do a rough calculation of their YTM. Using a financial calculator, we input the following values:<br /><br />N = 29 2 = 58, PV = 1.0075 -1,000 = -1007.50, PMT = 1,000 = 86.25/2 = 43.125, FV = 1000, and then solve for YTM = kd = 4.2773% 2 = 8.5546%.<br /><br />Thus, AT&T would have to set a rate of 8.55 percent on new long-term bonds.<br /><br />b. The return on AT&T’s bonds is the current yield of 8.6 per¬cent, less a small capital loss in 2031. The total return is about 8.55 percent.<br /><br /><br />7-19 a. Yield to maturity (YTM):<br /><br />With a financial calculator, input N = 28, PV = -1165.75, PMT = 95, FV = 1000, I = ? I = kd = YTM = 8.00%.<br /><br />Yield to call (YTC):<br /><br />With a calculator, input N = 3, PV = -1165.75, PMT = 95, FV = 1090,<br />I = ? I = kd = YTC = 6.11%.<br /><br />b. Knowledgeable investors would expect the return to be closer to 6.1 percent than to 8 percent. If interest rates remain substantially lower than 9.5 percent, the company can be expected to call the issue at the call date and to refund it with an issue having a coupon rate lower than 9.5 percent.<br /><br />c. If the bond had sold at a discount, this would imply that current interest rates are above the coupon rate. There¬fore, the company would not call the bonds, so the YTM would be more relevant than the YTC.<br /><br />7-20 Percentage<br />Price at 8% Price at 7% change<br />10-year, 10% annual coupon $1,134.20 $1,210.71 6.75%<br />10-year zero 463.19 508.35 9.75<br />5-year zero 680.58 712.99 4.76<br />30-year zero 99.38 131.37 32.19<br />$100 perpetuity 1,250.00 1,428.57 14.29<br /><br /><br />7-21 a. t Price of Bond C Price of Bond Z<br />0 $1,012.79 $ 693.04<br />1 1,010.02 759.57<br />2 1,006.98 832.49<br />3 1,003.65 912.41<br />4 1,000.00 1,000.00saleem shahzadnoreply@blogger.com0tag:blogger.com,1999:blog-3421608066886271296.post-33995088784500096542010-12-14T15:15:00.005+05:002011-01-18T16:09:52.201+05:00Chapter 8Chapter 8<br />Stocks and Their Valuation<br />SOLUTIONS TO END-OF-CHAPTER PROBLEMS<br /><br /><br /><br />8-1 D0 = $1.50; g1-3 = 5%; gn = 10%; D1 through D5 = ?<br /><br />D1 = D0(1 + g1) = $1.50(1.05) = $1.5750.<br />D2 = D0(1 + g1)(1 + g2) = $1.50(1.05)2 = $1.6538.<br />D3 = D0(1 + g1)(1 + g2)(1 + g3) = $1.50(1.05)3 = $1.7364.<br />D4 = D0(1 + g1)(1 + g2)(1 + g3)(1 + gn) = $1.50(1.05)3(1.10) = $1.9101.<br />D5 = D0(1 + g1)(1 + g2)(1 + g3)(1 + gn)2 = $1.50(1.05)3(1.10)2 = $2.1011.<br /><br /><br />8-2 D1 = $0.50; g = 7%; ks = 15%; = ?<br /><br /><br /><br /><br />8-3 P0 = $20; D0 = $1.00; g = 10%; = ?; ks = ?<br /><br />= P0(1 + g) = $20(1.10) = $22.<br /><br />ks = + g = + 0.10<br />= + 0.10 = 15.50%. ks = 15.50%.<br /><br /><br />8-4 Dp = $5.00; Vp = $60; kp = ?<br /><br />kp = = = 8.33%.<br /><br /><br />8-5 a. The terminal, or horizon, date is the date when the growth rate becomes constant. This occurs at the end of Year 2.<br /><br />b. 0 1 2 3<br /> <br />1.25 1.50 1.80 1.89<br /><br />37.80 =<br /><br />The horizon, or terminal, value is the value at the horizon date of all dividends expected thereafter. In this problem it is calculated as follows:<br /><br /><br />c. The firm’s intrinsic value is calculated as the sum of the present value of all dividends during the supernormal growth period plus the present value of the terminal value. Using your financial calculator, enter the following inputs: CF0 = 0, CF1 = 1.50, CF2 = 1.80 + 37.80 = 39.60, I = 10, and then solve for NPV = $34.09.<br /><br /><br />8-6 The firm’s free cash flow is expected to grow at a constant rate, hence we can apply a constant growth formula to determine the total value of the firm.<br /><br />Firm Value = FCF1/(WACC – g)<br />Firm Value = $150,000,000/(0.10 - 0.05)<br />Firm Value = $3,000,000,000.<br /><br />To find the value of an equity claim upon the company (share of stock), we must subtract out the market value of debt and preferred stock. This firm happens to be entirely equity funded, and this step is unnecessary. Hence, to find the value of a share of stock, we divide equity value (or in this case, firm value) by the number of shares outstanding.<br /><br />Equity Value per share = Equity Value/Shares outstanding<br />Equity Value per share = $3,000,000,000/50,000,000<br />Equity Value per share = $60.<br /><br />Each share of common stock is worth $60, according to the corporate valuation model.<br /><br /><br />8-7 a. 0 1 2 3 4<br /> <br />3,000,000 6,000,000 10,000,000 15,000,000<br /><br />Using a financial calculator, enter the following inputs: CF0 = 0;<br />CF1 = 3000000; CF2 = 6000000; CF3 = 10000000; CF4 = 15000000; I = 12; and then solve for NPV = $24,112,308.<br /><br />b. The firm’s terminal value is calculated as follows:<br /><br /><br /><br /><br />c. The firm’s total value is calculated as follows:<br /><br />0 1 2 3 4 5<br /> <br />3,000,000 6,000,000 10,000,000 15,000,000 16,050,000<br /><br />PV = ? 321,000,000 =<br /><br />Using your financial calculator, enter the following inputs: CF0 = 0; CF1 = 3000000; CF2 = 6000000; CF3 = 10000000; CF4 = 15000000 + 321000000 = 336000000; I = 12; and then solve for NPV = $228,113,612.<br /><br />d. To find Barrett’s stock price, you need to first find the value of its equity. The value of Barrett’s equity is equal to the value of the total firm less the market value of its debt and preferred stock.<br /><br />Total firm value $228,113,612<br />Market value, debt + preferred 60,000,000 (given in problem)<br />Market value of equity $168,113,612<br /><br />Barrett’s price per share is calculated as:<br /><br /><br /><br /><br />8-8 FCF = EBIT(1 – T) + Depreciation – - <br />= $500,000,000 + $100,000,000 - $200,000,000 - $0<br />= $400,000,000.<br /><br />Firm value =<br />=<br />=<br />= $10,000,000,000.<br /><br />This is the total firm value. Now find the market value of its equity.<br /><br />MVTotal = MVEquity + MVDebt<br />$10,000,000,000 = MVEquity + $3,000,000,000<br />MVEquity = $7,000,000,000.<br /><br />This is the market value of all the equity. Divide by the number of shares to find the price per share. $7,000,000,000/200,000,000 = $35.00.<br /><br />8-9 a. Terminal value = = = $713.33 million.<br /><br />b. 0 1 2 3 4<br /> <br />-20 30 40 42.80<br />($ 17.70)<br />23.49<br />522.10 753.33<br />$527.89<br /><br />Using a financial calculator, enter the following inputs: CF0 = 0;<br />CF1 = -20; CF2 = 30; CF3 = 753.33; I = 13; and then solve for NPV = $527.89 million.<br /><br />c. Total valuet=0 = $527.89 million.<br />Value of common equity = $527.89 - $100 = $427.89 million.<br />Price per share = = $42.79.<br /><br /><br />8-10 The problem asks you to determine the value of , given the following facts: D1 = $2, b = 0.9, kRF = 5.6%, RPM = 6%, and P0 = $25. Proceed as follows:<br /><br />Step 1: Calculate the required rate of return:<br /><br />ks = kRF + (kM - kRF)b = 5.6% + (6%)0.9 = 11%.<br /><br />Step 2: Use the constant growth rate formula to calculate g:<br /><br /><br /><br />Step 3: Calculate :<br /><br />= P0(1 + g)3 = $25(1.03)3 = $27.3182 $27.32.<br /><br />Alternatively, you could calculate D4 and then use the constant growth rate formula to solve for :<br /><br />D4 = D1(1 + g)3 = $2.00(1.03)3 = $2.1855.<br />= $2.1855/(0.11 – 0.03) = $27.3182 $27.32.<br /><br /><br />8-11 Vp = Dp/kp; therefore, kp = Dp/Vp.<br /><br />a. kp = $8/$60 = 13.3%.<br />b. kp = $8/$80 = 10.0%.<br /><br />c. kp = $8/$100 = 8.0%.<br /><br />d. kp = $8/$140 = 5.7%.<br /><br /><br />8-12<br /><br /><br />8-13 a. ki = kRF + (kM - kRF)bi.<br />kC = 9% + (13% - 9%)0.4 = 10.6%.<br />kD = 9% + (13% - 9%)(-0.5) = 7%.<br /><br />Note that kD is below the risk-free rate. But since this stock is like an insurance policy because it “pays off” when something bad happens (the market falls), the low return is not unreasonable.<br /><br />b. In this situation, the expected rate of return is as follows:<br /><br />= D1/P0 + g = $1.50/$25 + 4% = 10%.<br /><br />However, the required rate of return is 10.6 percent. Investors will seek to sell the stock, dropping its price to the following:<br /><br /><br /><br />At this point, , and the stock will be in equilibrium.<br /><br /><br />8-14 Calculate the dividend cash flows and place them on a time line. Also, calculate the stock price at the end of the supernormal growth period, and include it, along with the dividend to be paid at t = 5, as CF5. Then, enter the cash flows as shown on the time line into the cash flow register, enter the required rate of return as I = 15, and then find the value of the stock using the NPV calculation. Be sure to enter<br />CF0 = 0, or else your answer will be incorrect.<br /><br />D0 = 0; D1 = 0; D2 = 0; D3 = 1.00; D4 = 1.00(1.5) = 1.5; D5 = 1.00(1.5)2 = 2.25; D6 = 1.00(1.5)2(1.08) = $2.43. = ?<br /><br />0 1 2 3 4 5 6<br /> <br />1.00 1.50 2.25 2.43<br /><br />0.658 +34.71 =<br />0.858<br />18.378 36.96<br />$19.894 =<br /><br />= D6/( - g) = $2.43/(0.15 - 0.08) = $34.71. This is the stock price at the end of Year 5.<br /><br />CF0 = 0; CF1-2 = 0; CF3 = 1.0; CF4 = 1.5; CF5 = 36.96; I = 15%.<br /><br />With these cash flows in the CFLO register, press NPV to get the value of the stock today: NPV = $19.89.<br /><br /><br />8-15 a. The preferred stock pays $8 annually in dividends. Therefore, its nominal rate of return would be:<br /><br />Nominal rate of return = $8/$80 = 10%.<br /><br />Or alternatively, you could determine the security’s periodic return and multiply by 4.<br /><br />Periodic rate of return = $2/$80 = 2.5%.<br />Nominal rate of return = 2.5% 4 = 10%.<br /><br />b. EAR = (1 + NOM/4)4 - 1<br />EAR = (1 + 0.10/4)4 - 1<br />EAR = 0.103813 = 10.3813%.<br /><br /><br />8-16 The value of any asset is the present value of all future cash flows expected to be generated from the asset. Hence, if we can find the present value of the dividends during the period preceding long-run constant growth and subtract that total from the current stock price, the remaining value would be the present value of the cash flows to be received during the period of long-run constant growth.<br /><br />D1 = $2.00 (1.25)1 = $2.50 PV(D1) = $2.50/(1.12)1 = $2.2321<br />D2 = $2.00 (1.25)2 = $3.125 PV(D2) = $3.125/(1.12)2 = $2.4913<br />D3 = $2.00 (1.25)3 = $3.90625 PV(D3) = $3.90625/(1.12)3 = $2.7804<br /><br /> PV(D1 to D3) = $7.5038<br /><br />Therefore, the PV of the remaining dividends is: $58.8800 – $7.5038 = $51.3762. Compounding this value forward to Year 3, we find that the value of all dividends received during constant growth is $72.18. [$51.3762(1.12)3 = $72.18.] Applying the constant growth formula, we can solve for the constant growth rate:<br /><br />= D3(1 + g)/(ks – g)<br />$72.1807 = $3.90625(1 + g)/(0.12 – g)<br />$8.6616 - $72.18g = $3.90625 + $3.90625g<br />$4.7554 = $76.08625g<br />0.0625 = g<br />6.25% = g.<br /><br /><br /><br />8-17 First, solve for the current price.<br /><br />P0 = D1/(ks – g)<br />P0 = $0.50/(0.12 - 0.07)<br />P0 = $10.00.<br /><br />If the stock is in a constant growth state, the constant dividend growth rate is also the capital gains yield for the stock and the stock price growth rate. Hence, to find the price of the stock four years from today:<br /><br />= P0(1 + g)4<br />= $10.00(1.07)4<br />= $13.10796 ≈ $13.11.<br /><br /><br />8-18 a.<br /><br />b.<br /><br /><br />8-19 0 1 2 3 4<br /> <br />D0 = 2.00 D1 D2 D3 D4<br />g = 5%<br /><br />a. D1 = $2(1.05) = $2.10; D2 = $2(1.05)2 = $2.21; D3 = $2(1.05)3 = $2.32.<br /><br />b. Financial Calculator Solution: Input 0, 2.10, 2.21, and 2.32 into the cash flow register, input I = 12, PV = ? PV = $5.29.<br /><br />c. Financial Calculator Solution: Input 0, 0, 0, and 34.73 into the cash flow register, I = 12, PV = ? PV = $24.72.<br /><br />d. $24.72 + $5.29 = $30.01 = Maximum price you should pay for the stock.<br /><br />e.<br /><br />f. No. The value of the stock is not dependent upon the holding period. The value calculated in Parts a through d is the value for a 3-year holding period. It is equal to the value calculated in Part e except for a small rounding error. Any other holding period would produce the same value of ; that is, = $30.00.<br /><br /><br /><br />8-20 a. 1.<br /><br />2. = $2/0.15 = $13.33.<br /><br />3.<br /><br />4.<br /><br />b. 1. = $2.30/0 = Undefined.<br /><br />2. = $2.40/(-0.05) = -$48, which is nonsense.<br /><br />These results show that the formula does not make sense if the required rate of return is equal to or less than the expected growth rate.<br /><br />c. No.<br /><br /><br />8-21 The answer depends on when one works the problem. We used the February 3, 2003, issue of The Wall Street Journal:<br /><br />a. $16.81 to $36.72.<br /><br />b. Current dividend = $0.75. Dividend yield = $0.75/$19.48 3.9%. You might want to use ($0.75)(1 + g)/$19.48, with g estimated somehow.<br /><br />c. The $19.48 close was up $0.98 from the previous day’s close.<br /><br />d. The return on the stock consists of a dividend yield of about 3.9 percent plus some capital gains yield. We would expect the total rate of return on stock to be in the 10 to 12 percent range.<br /><br /><br />8-22 a. End of Year: 02 03 04 05 06 07 08<br /> <br />D0 = 1.75 D1 D2 D3 D4 D5 D6<br /><br />Dt = D0(1 + g)t<br />D2003 = $1.75(1.15)1 = $2.01.<br />D2004 = $1.75(1.15)2 = $1.75(1.3225) = $2.31.<br />D2005 = $1.75(1.15)3 = $1.75(1.5209) = $2.66.<br />D2006 = $1.75(1.15)4 = $1.75(1.7490) = $3.06.<br />D2007 = $1.75(1.15)5 = $1.75(2.0114) = $3.52.<br /><br /><br />b. Step 1:<br /><br />PV of dividends = .<br /><br />PV D2003 = $2.01/(1.12) = $1.79<br />PV D2004 = $2.31/(1.12)2 = $1.84<br />PV D2005 = $2.66/(1.12)3 = $1.89<br />PV D2006 = $3.06/(1.12)4 = $1.94<br />PV D2007 = $3.52/(1.12)5 = $2.00<br />PV of dividends = $9.46<br /><br />Step 2:<br /><br /><br /><br />This is the price of the stock 5 years from now. The PV of this price, discounted back 5 years, is as follows:<br /><br />PV of = $52.80/(1.12)5 = $29.96.<br /><br />Step 3:<br /><br />The price of the stock today is as follows:<br /><br />= PV dividends Years 2003-2007 + PV of<br />= $9.46 + $29.96 = $39.42.<br /><br />This problem could also be solved by substituting the proper values into the following equation:<br /><br />.<br /><br />Calculator solution: Input 0, 2.01, 2.31, 2.66, 3.06, 56.32 (3.52 + 52.80) into the cash flow register, input I = 12, PV = ? PV = $39.43.<br /><br />c. 2003<br />D1/P0 = $2.01/$39.43 = 5.10%<br />Capital gains yield = 6.90*<br />Expected total return = 12.00%<br /><br />2008<br />D6/P5 = $3.70/$52.80 = 7.00%<br />Capital gains yield = 5.00<br />Expected total return = 12.00%<br /><br />*We know that ks is 12 percent, and the dividend yield is 5.10 percent; therefore, the capital gains yield must be 6.90 percent.<br />The main points to note here are as follows:<br /><br />1. The total yield is always 12 percent (except for rounding errors).<br /><br />2. The capital gains yield starts relatively high, then declines as the supernormal growth period approaches its end. The dividend yield rises.<br /><br />3. After 12/31/07, the stock will grow at a 5 percent rate. The dividend yield will equal 7 percent, the capital gains yield will equal 5 percent, and the total return will be 12 percent.<br /><br /><br />d. People in high income tax brackets will be more inclined to purchase “growth” stocks to take the capital gains and thus delay the payment of taxes until a later date. The firm’s stock is “mature” at the end of 2007.<br /><br />e. Since the firm’s supernormal and normal growth rates are lower, the dividends and, hence, the present value of the stock price will be lower. The total return from the stock will still be 12 percent, but the dividend yield will be larger and the capital gains yield will be smaller than they were with the original growth rates. This result occurs because we assume the same last dividend but a much lower current stock price.<br /><br />f. As the required return increases, the price of the stock goes down, but both the capital gains and dividend yields increase initially. Of course, the long-term capital gains yield is still 4 percent, so the long-term dividend yield is 10 percent.<br /><br /><br />8-23 a. Part 1: Graphical representation of the problem:<br /><br />Supernormal Normal<br />growth growth<br />0 1 2 3 <br /> ••• <br />D0 D1 (D2 + ) D3 D<br />PVD1<br />PVD2<br /><br />P0<br /><br />D1 = D0(1 + gs) = $1.6(1.20) = $1.92.<br />D2 = D0(1 + gs)2 = $1.60(1.20)2 = $2.304.<br /><br /><br /><br /><br />= PV(D1) + PV(D2) + PV( )<br />=<br />= $1.92/1.10 + $2.304/(1.10)2 + $61.06/(1.10)2 = $54.11.<br /><br />Financial Calculator solution: Input 0, 1.92, 63.364(2.304 + 61.06) into the cash flow register, input I = 10, PV = ? PV = $54.11.<br /><br />Part 2: Expected dividend yield:<br /><br />D1/P0 = $1.92/$54.11 = 3.55%.<br /><br />Capital gains yield: First, find , which equals the sum of the present values of D2 and discounted for one year.<br /><br /><br /><br /><br />Financial Calculator solution: Input 0, 63.364(2.304 + 61.06) into the cash flow register, input I = 10, PV = ? PV = $57.60.<br /><br />Second, find the capital gains yield:<br /><br /><br /><br />Dividend yield = 3.55%<br />Capital gains yield = 6.45<br />10.00% = ks.<br /><br />b. Due to the longer period of supernormal growth, the value of the stock will be higher for each year. Although the total return will remain the same, ks = 10%, the distribution between dividend yield and capital gains yield will differ: The dividend yield will start off lower and the capital gains yield will start off higher for the 5-year supernormal growth condition, relative to the 2-year supernormal growth state. The dividend yield will increase and the capital gains yield will decline over the 5-year period until dividend yield = 4% and capital gains yield = 6%.<br /><br />c. Throughout the supernormal growth period, the total yield will be 10 percent, but the dividend yield is relatively low during the early years of the supernormal growth period and the capital gains yield is relatively high. As we near the end of the supernormal growth period, the capital gains yield declines and the dividend yield rises. After the supernormal growth period has ended, the capital gains yield will equal gn = 6%. The total yield must equal ks = 10%, so the dividend yield must equal 10% - 6% = 4%.<br /><br />d. Some investors need cash dividends (retired people), while others would prefer growth. Also, investors must pay taxes each year on the dividends received during the year, while taxes on capital gains can be delayed until the gain is actually realized.<br /><br /><br />8-24 a. ks = kRF + (kM - kRF)b = 11% + (14% - 11%)1.5 = 15.5%.<br />= D1/(ks - g) = $2.25/(0.155 - 0.05) = $21.43.<br /><br />b. ks = 9% + (12% - 9%)1.5 = 13.5%. = $2.25/(0.135 - 0.05) = $26.47.<br /><br />c. ks = 9% + (11% - 9%)1.5 = 12.0%. = $2.25/(0.12 - 0.05) = $32.14.<br /><br />d. New data given: kRF = 9%; kM = 11%; g = 6%, b = 1.3.<br />ks = kRF + (kM - kRF)b = 9% + (11% - 9%)1.3 = 11.6%.<br />= D1/(ks - g) = $2.27/(0.116 - 0.06) = $40.54.<br /><br /><br /><br />8-25 a. Old ks = kRF + (kM - kRF)b = 9% + (3%)1.2 = 12.6%.<br /><br />New ks = 9% + (3%)0.9 = 11.7%.<br /><br />Old price:<br /><br />New price:<br /><br />Since the new price is lower than the old price, the expan¬sion in consumer products should be rejected. The decrease in risk is not sufficient to offset the decline in profita¬bility and the reduced growth rate.<br /><br />b. POld = $38.21. PNew = .<br /><br />Solving for ks we have the following:<br /><br />$38.21 =<br />$2.10 = $38.21(ks) - $1.9105<br />$4.0105 = $38.21(ks)<br />ks = 0.10496.<br /><br />Solving for b:<br /><br />10.496% = 9% + 3%(b)<br />1.496% = 3%(b)<br />b = 0.49865.<br /><br />Check: ks = 9% + (3%)0.49865 = 10.496%.<br /><br />= = $38.21.<br /><br />Therefore, only if management’s analysis concludes that risk can be lowered to b = 0.49865, or approximately 0.5, should the new policy be put into effect.saleem shahzadnoreply@blogger.com1tag:blogger.com,1999:blog-3421608066886271296.post-456528420294382912010-12-14T15:15:00.004+05:002011-01-18T16:08:23.251+05:00Chapter 9Chapter 9<br />The Cost of Capital<br />SOLUTIONS TO END-OF-CHAPTER PROBLEMS<br /><br />9-1 40% Debt; 60% Equity; kd = 9%; T = 40%; WACC = 9.96%; ks = ?<br /><br />WACC = (wd)(kd)(1 - T) + (wc)(ks)<br />0.0996 = (0.4)(0.09)(1 - 0.4) + (0.6)ks<br />0.0996 = 0.0216 + 0.6ks<br />0.078 = 0.6ks<br />ks = 13%.<br /><br /><br />9-2 Pp = $47.50; Dp = $3.80; kp = ?<br /><br />kp =<br />kp = = 8%.<br /><br /><br />9-3 P0 = $30; D1 = $3.00; g = 5%; F = 10%; ks = ?; ke = ?<br /><br />ks = + g = + 0.05 = 15%.<br /><br />ke = + g = + 0.05<br />= + 0.05 = 16.11%.<br /><br /><br />9-4 Projects A, B, C, D, and E would be accepted since each project’s return is greater than the firm’s WACC.<br /><br /><br />9-5 kd(1 - T) = 0.12(0.65) = 7.80%.<br /><br /><br />9-6 kp = = = 11.94%.<br /><br /><br /><br />9-7 a. ks = + g<br />ks =<br />ks = 14.83%.<br /><br />b. F = ($36.00 - $32.40)/$36.00 = $3.60/$36.00 = 10%.<br /><br />c. ke = D1/[P0(1 - F)] + g = $3.18/$32.40 + 6% = 9.81% + 6% = 15.81%.<br /><br /><br />9-8 Capital Sources Amount Capital Structure Weight<br />Long-term debt $1,152 40.0%<br />Equity 1,728 60.0<br />$2,880 100.0%<br /><br />WACC = wdkd(1 - T) + wcks = 0.4(0.13)(0.6) + 0.6(0.16)<br />= 0.0312 + 0.0960 = 12.72%.<br /><br /><br />9-9 ks = D1/P0 + g = $2(1.07)/$24.75 + 7%<br />= 8.65% + 7% = 15.65%.<br /><br />WACC = wd(kd)(1 - T) + wc(ks); wc = 1 - wd.<br /><br />13.95% = wd(11%)(1 - 0.35) + (1 - wd)(15.65%)<br />0.1395 = 0.0715wd + 0.1565 - 0.1565wd<br />-0.017 = -0.085wd<br />wd = 0.20 = 20%.<br /><br /><br />9-10 a. kd = 10%, kd(1 - T) = 10%(0.6) = 6%.<br />D/A = 45%; D0 = $2; g = 4%; P0 = $20; T = 40%.<br /><br />Project A: Rate of return = 13%.<br />Project B: Rate of return = 10%.<br /><br />ks = $2(1.04)/$20 + 4% = 14.40%.<br /><br />b. WACC = 0.45(6%) + 0.55(14.40%) = 10.62%.<br /><br />c. Since the firm’s WACC is 10.62% and each of the projects is equally risky and as risky as the firm’s other assets, MEC should accept Project A. Its rate of return is greater than the firm’s WACC. Project B should not be accepted, since its rate of return is less than MEC’s WACC.<br /><br /><br />9-11 Debt = 40%, Equity = 60%.<br /><br />P0 = $22.50, D0 = $2.00, D1 = $2.00(1.07) = $2.14, g = 7%.<br />ks = + g = + 7% = 16.51%.<br /><br />WACC = (0.4)(0.12)(1 - 0.4) + (0.6)(0.1651)<br />= 0.0288 + 0.0991 = 12.79%.<br /><br /><br />9-12 If the firm's dividend yield is 5% and its stock price is $46.75, the next expected annual dividend can be computed.<br /><br />Dividend yield = D1/P0<br />5% = D1/$46.75<br />D1 = $2.3375.<br /><br />Next, the firm's cost of new common stock can be determined from the DCF approach for the cost of equity.<br /><br />ke = D1/[P0(1 - F)] + g<br />ke = $2.3375/[$46.75(1 - 0.05)] + 0.12<br />ke = 17.26%.<br /><br /><br />9-13 a. Examining the DCF approach to the cost of retained earnings, the expected growth rate can be determined from the cost of common equity, price, and expected dividend. However, first, this problem requires that the formula for WACC be used to determine the cost of common equity.<br /><br />WACC = wd(kd)(1 - T) + wc(ks)<br />13.0% = 0.4(10%)(1 - 0.4) + 0.6(ks)<br />10.6% = 0.6ks<br />ks = 0.17667 or 17.67%.<br /><br />From the cost of common equity, the expected growth rate can now be determined.<br /><br />ks = D1/P0 + g<br />0.17667 = $3/$35 + g<br />g = 0.090952 or 9.10%.<br /><br />b. From the formula for the long-run growth rate:<br /><br />g = (1 - Div. payout ratio) ROE = (1 - Div. payout ratio) (NI/Equity)<br />0.090952 = (1 - Div. payout ratio) ($1,100 million/$6,000 million)<br />0.090952 = (1 – Div. payout ratio) 0.1833333<br />0.496104 = (1 – Div. payout ratio)<br />Div. payout ratio = 0.503896 or 50.39%.<br /><br /><br />9-14 If the investment requires $5.9 million, that means that it requires $3.54 million (60%) of equity capital and $2.36 million (40%) of debt capital. In this scenario, the firm would exhaust its $2 million of retained earnings and be forced to raise new stock at a cost of 15%. Needing $2.36 million in debt capital, the firm could get by raising debt at only 10%. Therefore, its weighted average cost of capital is: WACC = 0.4(10%)(1 - 0.4) + 0.6(15%) = 11.4%.<br /><br /><br />9-15 a. If all project decisions are independent, the firm should accept all projects whose returns exceed their risk-adjusted costs of capital. The appropriate costs of capital are summarized below:<br /><br />Required Rate of Cost of<br />Project Investment Return Capital<br />A $4 million 14.0% 12%<br />B $5 million 11.5 12<br />C $3 million 9.5 8<br />D $2 million 9.0 10<br />E $6 million 12.5 12<br />F $5 million 12.5 10<br />G $6 million 7.0 8<br />H $3 million 11.5 8<br /><br />Therefore, Ziege should accept projects A, C, E, F, and H.<br /><br />b. With only $13 million to invest in its capital budget, Ziege must choose the best combination of Projects A, C, E, F, and H. Collectively, the projects would account for an investment of $21 million, so naturally not all these projects may be accepted. Looking at the excess return created by the projects (rate of return minus the cost of capital), we see that the excess returns for Projects A, C, E, F, and H are 2%, 1.5%, 0.5%, 2.5%, and 3.5%. The firm should accept the projects which provide the greatest excess returns. By that rationale, the first project to be eliminated from consideration is Project E. This brings the total investment required down to $15 million, therefore one more project must be eliminated. The next lowest excess return is Project C. Therefore, Ziege's optimal capital budget consists of Projects A, F, and H, and it amounts to $12 million.<br /><br />c. Since Projects A, F, and H are already accepted projects, we must adjust the costs of capital for the other two value producing projects (C and E).<br /><br />Required Rate of Cost of<br />Project Investment Return Capital<br />C $3 million 9.5% 8% + 1% = 9%<br />E $6 million 12.5 12% + 1% = 13%<br /><br />If new capital must be issued, Project E ceases to be an acceptable project. On the other hand, Project C's expected rate of return still exceeds the risk-adjusted cost of capital even after raising additional capital. Hence, Ziege's new capital budget should consist of Projects A, C, F, and H and requires $15 million of capital.<br />9-16 a. ks = + g = + 7% = 9.3% + 7% = 16.3%.<br /><br />b. ks = kRF + (kM - kRF)b<br />= 9% + (13% - 9%)1.6 = 9% + (4%)1.6 = 9% + 6.4% = 15.4%.<br /><br />c. ks = Bond rate + Risk premium = 12% + 4% = 16%.<br /><br />d. The bond-yield-plus-risk-premium approach and the CAPM method both resulted in lower cost of common stock estimates than the DCF method. Since financial analysts tend to give the most weight to the DCF method, the firm’s cost of common equity should be estimated to be about 16.3 percent.<br /><br /><br />9-17 a. With a financial calculator, input N = 5, PV = -4.42, PMT = 0, FV = 6.50, and then solve for I = 8.02% 8%.<br /><br />b. D1 = D0(1 + g) = $2.60(1.08) = $2.81.<br /><br />c. ks = D1/P0 + g = $2.81/$36.00 + 8% = 15.81%.<br /><br /><br />9-18 a. ks = + g<br />0.09 = + g<br />0.09 = 0.06 + g<br />g = 3%.<br /><br />b. Current EPS $5.400<br />Less: Dividends per share 3.600<br />Retained earnings per share $1.800<br />Rate of return 0.090<br />Increase in EPS $0.162<br />Plus: Current EPS 5.400<br />Next year’s EPS $5.562<br /><br />Alternatively, EPS1 = EPS0(1 + g) = $5.40(1.03) = $5.562.<br /><br /><br />9-19 a. After-tax cost of new debt: kd(1 - T) = 0.09(1 - 0.4) = 5.4%.<br /><br />Cost of common equity:<br /><br />Calculate g as follows:<br /><br />With a financial calculator, input N = 9, PV = -3.90, PMT = 0, FV = 7.80, and then solve for I = 8.01% 8%.<br /><br />ks = + g = + 0.08 = + 0.08 = 0.146 = 14.6%.<br />b. WACC calculation:<br />After-tax Weighted<br />Component Weight Cost = Cost<br />Debt[0.09(1 - T)] 0.40 5.4% 2.16%<br />Common equity (RE) 0.60 14.6% 8.76%<br />WACC = 10.92%<br /><br /><br />9-20 a. kd(1 - T) = 0.10(1 - 0.3) = 7%.<br /><br />kp = $5/$49 = 10.2%.<br /><br />ks = $3.50/$36 + 6% = 15.72%.<br /><br />b. WACC:<br />After-tax Weighted<br />Component Weight Cost = Cost<br />Debt[0.10(1 - T)] 0.15 7.00% 1.05%<br />Preferred stock 0.10 10.20% 1.02%<br />Common stock 0.75 15.72% 11.79%<br />WACC = 13.86%<br /><br />c. Projects 1 and 2 will be accepted since their rates of return exceed the WACC.saleem shahzadnoreply@blogger.com2tag:blogger.com,1999:blog-3421608066886271296.post-67970661905599587222010-12-14T15:16:00.005+05:002011-01-18T16:07:04.328+05:00Chapter 10Chapter 10<br />The Basics of Capital Budgeting<br />SOLUTIONS TO END-OF-CHAPTER PROBLEMS<br /><br />10-1 $52,125/$12,000 = 4.3438, so the payback is about 4 years.<br /><br /><br />10-2 Financial Calculator Solution: Input CF0 = -52125, CF1-8 = 12000, I = 12, and then solve for NPV = $7,486.68.<br /><br /><br />10-3 Financial Calculator Solution: Input CF0 = -52125, CF1-8 = 12000, and then solve for IRR = 16%.<br /><br /><br />10-4 Project K’s discounted payback period is calculated as follows:<br /><br />Annual Discounted @12%<br />Period Cash Flows Cash Flows Cumulative<br />0 ($52,125) ($52,125.00) ($52,125.00)<br />1 12,000 10,714.29 (41,410.71)<br />2 12,000 9,566.33 (31,844.38)<br />3 12,000 8,541.36 (23,303.02)<br />4 12,000 7,626.22 (15,676.80)<br />5 12,000 6,809.12 (8,867.68)<br />6 12,000 6,079.57 (2,788.11)<br />7 12,000 5,428.19 2,640.08<br />8 12,000 4,846.60 7,486.68<br /><br />The discounted payback period is 6 + years, or 6.51 years.<br /><br />Alternatively, since the annual cash flows are the same, one can divide $12,000 by 1.12 (the discount rate = 12%) to arrive at CF1 and then continue to divide by 1.12 seven more times to obtain the discounted cash flows (Column 3 values). The remainder of the analysis would be the same.<br /><br /><br />10-5 MIRR: PV Costs = $52,125.<br /><br />FV Inflows:<br />PV FV<br />0 1 2 3 4 5 6 7 8<br /> <br />12,000 12,000 12,000 12,000 12,000 12,000 12,000 12,000<br />13,440<br />15,053<br />16,859<br />18,882<br />21,148<br />23,686<br />26,528<br />52,125 MIRR = 13.89% 147,596<br />Financial Calculator Solution: Obtain the FVA by inputting N = 8, I = 12, PV = 0, PMT = 12000, and then solve for FV = $147,596. The MIRR can be obtained by inputting N = 8, PV = -52125, PMT = 0, FV = 147596, and then solving for I = 13.89%.<br /><br /><br />10-6 Project A:<br /><br />Using a financial calculator, enter the following:<br /><br />CF0 = -15000000<br />CF1 = 5000000<br />CF2 = 10000000<br />CF3 = 20000000<br /><br />I = 10; NPV = $12,836,213.<br /><br />Change I = 10 to I = 5; NPV = $16,108,952.<br />Change I = 5 to I = 15; NPV = $10,059,587.<br /><br />Project B:<br /><br />Using a financial calculator, enter the following:<br /><br />CF0 = -15000000<br />CF1 = 20000000<br />CF2 = 10000000<br />CF3 = 6000000<br /><br />I = 10; NPV = $15,954,170.<br /><br />Change I = 10 to I = 5; NPV = $18,300,939.<br />Change I = 5 to I = 15; NPV = $13,897,838.<br /><br /><br />10-7 Truck:<br /><br />Financial Calculator Solution: Input CF0 = -17100, CF1-5 = 5100, I = 14, and then solve for NPV = $408.71 ≈ $409 and IRR = 1499% ≈ 15%.<br /><br />MIRR: PV Costs = $17,100.<br /><br />FV Inflows:<br />PV FV<br />0 1 2 3 4 5<br /> <br />5,100 5,100 5,100 5,100 5,100<br />5,814<br />6,628<br />7,556<br />8,614<br />17,100 MIRR = 14.54% (Accept) 33,712<br />Financial Calculator Solution: Obtain the FVA by inputting N = 5, I = 14, PV = 0, PMT = 5100, and then solve for FV = $33,712. The MIRR can be obtained by inputting N = 5, PV = -17100, PMT = 0, FV = 33712, and then solving for I = MIRR = 14.54%.<br /><br />Pulley:<br /><br />Financial Calculator Solution: Input CF0 = -22430, CF1-5 = 7500, I = 14, and then solve for NPV = $3,318.11 ≈ $3,318 and IRR = 20%.<br /><br />MIRR: PV Costs = $22,430.<br /><br />FV Inflows:<br />PV FV<br />0 1 2 3 4 5<br /> <br />7,500 7,500 7,500 7,500 7,500<br />8,550<br />9,747<br />11,112<br />12,667<br />22,430 MIRR = 17.19% (Accept) 49,576<br /><br />Financial Calculator Solution: Obtain the FVA by inputting N = 5, I = 14, PV = 0, PMT = 7500, and then solve for FV = $49,576. The MIRR can be obtained by inputting N = 5, PV = -22430, PMT = 0, FV = 49576, and then solving for I = 17.19%.<br /><br /><br />10-8 Using a financial calculator:<br /><br />NPVS = $448.86; NPVL = $607.20.<br />IRRS = 15.24%; IRRL = 14.67%.<br /><br />MIRR:<br /><br />PV costsS = $15,000.<br />FV inflowsS = $29,745.47.<br />MIRRS = 14.67%.<br /><br />PV costsL = $37,500.<br />FV inflowsL = $73,372.16.<br />MIRRL = 14.37%.<br /><br />Thus, NPVL > NPVS, IRRS > IRRL, and MIRRS > MIRRL. The scale difference between Projects S and L results in IRR and MIRR selecting S over L. However, NPV favors Project L, and hence Project L should be chosen.<br /><br /><br />10-9 a. The IRRs of the two alternatives are undefined. To calculate an IRR, the cash flow stream must include both cash inflows and outflows.<br /><br />b. The PV of costs for the conveyor system is -$556,717, while the PV of costs for the forklift system is -$493,407. Thus, the forklift system is expected to be -$493,407 - (-$556,717) = $63,310 less costly than the conveyor system, and hence the forklifts should be used.<br /><br /><br />10-10 Project X: 0 1 2 3 4<br /> <br />-1,000 100 300 400 700.00<br />448.00<br />376.32<br />140.49<br />1,000 13.59% = MIRRX 1,664.81<br /><br />$1,000 = $1,664.81/(1 + MIRRX)4.<br /><br />Project Y: 0 1 2 3 4<br /> <br />-1,000 1,000 100 50 50.00<br />56.00<br />125.44<br />1,404.93<br />1,000 13.10% = MIRRY 1,636.37<br /><br />$1,000 = $1,636.37/(1 + MIRRY)4.<br /><br />Thus, since MIRRX > MIRRY, Project X should be chosen.<br /><br />Alternate step: You could calculate NPVs, see that Project X has the higher NPV, and just calculate MIRRX.<br /><br />NPVX = $58.02 and NPVY = $39.94.<br /><br /><br />10-11 Input the appropriate cash flows into the cash flow register, and then calculate NPV at 10 percent and the IRR of each of the projects:<br /><br />Project S: NPVS = $39.14; IRRS = 13.49%.<br /><br />Project L: NPVL = $53.55; IRRL = 11.74%.<br /><br />Since Project L has the higher NPV, it is the better project.<br />IRRL = 11.74%.<br /><br /><br />10-12 Step 1: Determine the PMT:<br /><br />0 1 10<br /> • • • <br />-1,000 PMT PMT<br /><br />With a financial calculator, input N = 10, I = 12, PV = -1000, and FV = 0 to obtain PMT = $176.98.<br /><br />Step 2: Calculate the project’s MIRR:<br /><br />0 1 2 9 10<br /> • • • <br />-1,000 176.98 176.98 176.98 176.98<br />194.68<br />.<br />.<br />.<br />379.37<br />417.31<br />1,000 10.93% = MIRR TV = 2,820.61<br /><br />FV of inflows: With a financial calculator, input N = 10, I = 10, PV = 0, and PMT = -176.98 to obtain FV = $2,820.61. Then input<br />N = 10, PV = -1000, PMT = 0, and FV = 2820.61 to obtain<br />I = MIRR = 10.93%.<br /><br /><br />10-13 a. Purchase price $ 900,000<br />Installation 165,000<br />Initial outlay $1,065,000<br /><br />CF0 = -1065000; CF1-5 = 350000; I = 14; NPV = ?<br />NPV = $136,578; IRR = 19.22%.<br /><br />b. Ignoring environmental concerns, the project should be undertaken because its NPV is positive and its IRR is greater than the firm’s cost of capital.<br /><br />c. Environmental effects could be added by estimating penalties or any other cash outflows that might be imposed on the firm to help return the land to its previous state (if possible). These outflows could be so large as to cause the project to have a negative NPV, in which case the project should not be undertaken.<br /><br /><br />10-14 a. Year Sales Royalties Marketing Net<br />0 ($20,000) ($20,000)<br />1 75,000 ($5,000) ($10,000) 60,000<br />2 52,500 (3,500) (10,000) 39,000<br />3 22,500 (1,500) 21,000<br /><br />Payback period = $20,000/$60,000 = 0.33 year.<br /><br />NPV = $60,000/(1.11)1 + $39,000/(1.11)2 + $21,000/(1.11)3 - $20,000<br />= $81,062.35.<br /><br />Using a financial calculator, input CF0 = -20000; CF1 = 60000, CF2 = 39000, CF3 = 21000, and then solve for IRR = 261.90%.<br /><br />b. Finance theory dictates that this investment should be accepted. However, ask your students “Does this service encourage cheating?” If yes, does a businessperson have a social responsibility not to make this service available?<br /><br /><br />10-15 Facts: 5 years remaining on lease; rent = $2,000/month; 60 payments left, payment at end of month.<br /><br />New lease terms: $0/month for 9 months; $2,600/month for 51 months.<br /><br />Cost of capital = 12% annual (1% per month).<br /><br />a. 0 1 2 59 60<br /> • • • <br />-2,000 -2,000 -2,000 -2,000<br /><br />PV cost of old lease: N = 60; I = 1; PMT = -2000; FV = 0; PV = ? PV = -$89,910.08.<br /><br />0 1 9 10 59 60<br /> • • • • • • <br />0 0 -2,600 -2,600 -2,600<br /><br />PV cost of new lease: CF0 = 0, CF1-9 = 0; CF10-60 = -2600; I = 1. NPV = -$94,611.45.<br /><br />Sharon should not accept the new lease because the present value of its cost is $94,611.45 - $89,910.08 = $4,701.37 greater than the old lease.<br /><br />b. 0 1 2 9 10 59 60<br /> • • • • • • <br />-2,000 -2,000 -2,000 PMT PMT PMT<br /><br />FV of first 9 months’ rent under old lease:<br /><br />N = 9; I = 1; PV = 0; PMT = -2000; FV = ? FV = $18,737.05.<br /><br />The FV of the first 9 months’ rent is equivalent to the PV of the 51-period annuity whose payments represent the incremental rent during months 10-60. To find this value:<br /><br />N = 51; I = 1; PV = -18737.05; FV = 0; PMT = ? PMT = $470.80.<br /><br />Thus, the new lease payment that will make her indifferent is $2,000 + $470.80 = $2,470.80.<br /><br />Check:<br /><br />0 1 9 10 59 60<br /> • • • • • • <br />0 0 -2,470.80 -2,470.80 -2,470.80<br /><br />PV cost of new lease: CF0 = 0; = 0; = -2470.80; I = 1.<br />NPV = -$89,909.99.<br /><br />Except for rounding; the PV cost of this lease equals the PV cost of the old lease.<br />c. Period Old Lease New Lease Lease<br />0 0 0 0<br />1-9 -2,000 0 -2,000<br />10-60 -2,000 -2,600 600<br /><br />CF0 = 0; CF1-9 = -2000; CF10-60 = 600; IRR = ? IRR = 1.9113%. This is the periodic rate. To obtain the nominal cost of capital, multiply by 12: 12(0.019113) = 22.94%.<br /><br />Check: Old lease terms:<br /><br />N = 60; I = 1.9113; PMT = -2000; FV = 0; PV = ? PV = -$71,039.17.<br /><br />New lease terms:<br /><br />CF0 = 0; CF1-9 = 0; CF10-60 = -2600; I = 1.9113; NPV = ? NPV = -$71,038.98.<br /><br />Except for rounding differences; the costs are the same.<br /><br /><br />10-16 a. The payback periods for Projects A and B are calculated as follows:<br /><br />Project A Project B<br />Period Cash flows Cumulative (A) Cash flows Cumulative (B)<br />0 ($400) ($400) ($600) ($600)<br />1 55 (345) 300 (300)<br />2 55 (290) 300 0<br />3 55 (235) 50 50<br />4 225 (10) 50 100<br />5 225 215 50 150<br /><br />Project A's payback is 4 + $10/$225 = 4.04 years, while Project B's payback is 2 years. According to the payback rule, Project B would be preferred to Project A.<br /><br />b. The discounted payback periods for Projects A and B are calculated as follows:<br />Disc. @ 10% Disc. @ 10%<br />Project A Project B<br />Period Cash flows Cumulative (A) Cash flows Cumulative (B)<br />0 ($400.00) ($400.00) ($600.00) ($600.00)<br />1 50.00 (350.00) 272.73 (327.27)<br />2 45.45 (304.55) 247.93 (79.34)<br />3 41.32 (263.22) 37.57 (41.77)<br />4 153.68 (109.55) 34.15 (7.62)<br />5 139.71 30.16 31.05 23.42<br /><br />Project A's payback is 4 + $109.55/$139.71 = 4.78 years, meanwhile Project B's payback is 4 + $7.62/$31.05 = 4.245 years. According to the discounted payback rule, Project B would be preferred to Project A.<br /><br /><br />c. Finding net present values, use a financial calculator and enter the following data:<br /><br />Project A Project B<br />CF0 = -400 CF0 = -600<br />CF1 = 55 CF1 = 300<br />CF2 = 55 CF2 = 300<br />CF3 = 55 CF3 = 50<br />CF4 = 225 CF4 = 50<br />CF5 = 225 CF5 = 50<br /><br />I = 10 I = 10<br />NPV = $30.16 NPV = $23.42<br /><br />By the NPV criterion, Project A is preferred to Project B.<br /><br />d. Finding the IRR, use a financial calculator and enter the following:<br /><br />Project A Project B<br />CF0 = -400 CF0 = -600<br />CF1 = 55 CF1 = 300<br />CF2 = 55 CF2 = 300<br />CF3 = 55 CF3 = 50<br />CF4 = 225 CF4 = 50<br />CF5 = 225 CF5 = 50<br /><br />IRR = 12.21% IRR = 12.28%<br /><br />According to the IRR criterion, Project B is preferred to Project A.<br /><br />e. Project A:<br />0 10% 1 2 3 4 5<br /> <br />-400 55 55 55 225 225<br />247.50<br />66.55<br />73.21<br />80.53<br />692.78<br />$400 = $692.78/(1 + MIRRA )5<br />MIRRA = 11.61%.<br /><br />Project B:<br />0 10% 1 2 3 4 5<br /> <br />-600 300 300 50 50 50<br />55.00<br />60.50<br />399.30<br />439.23<br />1,004.03<br /><br />$600 = $1,004.03/(1 + MIRRA )5<br />MIRRA = 10.85%.<br /><br />According to the MIRR criterion, Project A is the superior project.<br />10-17 Since the IRR is the cost of capital at which the NPV of a project equals zero, the projects inflows can be evaluated at the IRR and the present value of these inflows must equal the initial investment.<br /><br />Using a financial calculator enter the following:<br /><br />CF0 = 0<br />CF1 = 7500<br />Nj = 10<br />CF1 = 10000<br />Nj = 10<br /><br />I = 10.98; NPV = $65,002.11.<br /><br />Therefore, the initial investment for this project is $65,002.11. Using a calculator, the project's NPV can now be solved.<br /><br />CF0 = -65002.11<br />CF1 = 7500<br />Nj = 10<br />CF1 = 10000<br />Nj = 10<br /><br />I = 9; NPV = $10,239.20.<br /><br /><br />10-18 The MIRR can be solved with a financial calculator by finding the terminal future value of the cash inflows and the initial present value of cash outflows, and solving for the discount rate that equates these two values. In this instance, the MIRR is given, but a cash outflow is missing and must be solved for. Therefore, if the terminal future value of the cash inflows is found, it can be entered into a financial calculator, along with the number of years the project lasts and the MIRR, to solve for the initial present value of the cash outflows. One of these cash outflows occurs in Year 0 and the remaining value must be the present value of the missing cash outflow in Year 2.<br /><br />Cash inflows Compounding Rate FV in Year 5 @ 10%<br />CF1 = 202 (1.10)4 295.75<br />CF3 = 196 (1.10)2 237.16<br />CF4 = 350 1.10 385.00<br />CF5 = 451 1.00 451.00<br />1368.91<br /><br />Using the financial calculator to solve for the present value of cash outflows:<br /><br />N = 5<br />I = 14.14<br />PV = ?<br />PMT = 0<br />FV = 1368.91<br /><br />The total present value of cash outflows is $706.62, and since the outflow for Year 0 is $500, the present value of the Year 2 cash outflow is $206.62. Therefore, the missing cash outflow for Year 2 is $206.62 ×(1.1)2 = $250.01.<br />10-19 a. At k = 12%, Project A has the greater NPV, specifically $200.41 as compared to Project B’s NPV of $145.93. Thus, Project A would be selected. At k = 18%, Project B has an NPV of $63.68 which is higher than Project A’s NPV of $2.66. Thus, choose Project B if k = 18%.<br /><br />b.<br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br />k NPVA NPVB<br />0.0% $890 $399<br />10.0 283 179<br />12.0 200 146<br />18.1 0 62<br />20.0 (49) 41<br />24.0 (138) 0<br />30.0 (238) (51)<br /><br />c. IRRA = 18.1%; IRRB = 24.0%.<br /><br />d. To find the crossover rate, construct a Project which is the difference in the two projects’ cash flows:<br /><br />Project =<br />Year CFA - CFB<br />0 $ 105<br />1 (521)<br />2 (327)<br />3 (234)<br />4 466<br />5 466<br />6 716<br />7 (180)<br /><br />IRR = Crossover rate = 14.53%.<br /><br />Projects A and B are mutually exclusive, thus, only one of the projects can be chosen. As long as the cost of capital is greater than the crossover rate, both the NPV and IRR methods will lead to the same project selection. However, if the cost of capital is less than the crossover rate the two methods lead to different project selections--a conflict exists. When a conflict exists the NPV method must be used.<br />Because of the sign changes and the size of the cash flows, Project has multiple IRRs. Thus, a calculator’s IRR function will not work. One could use the trial and error method of entering different discount rates until NPV = $0. However, an HP can be “tricked” into giving the roots. After you have keyed Project Delta’s cash flows into the cash flow registers of an HP-10B, you will see an “Error-Soln” message. Now enter 10 STO IRR/YR and the 14.53 percent IRR is found. Then enter 100 STO IRR/YR to obtain IRR = 456.22%. Similarly, Excel can also be used.<br /><br />e. Here is the MIRR for Project A when k = 12%:<br /><br />PV costs = $300 + $387/(1.12)1 + $193/(1.12)2<br />+ $100/(1.12)3 + $180/(1.12)7 = $952.00.<br /><br />TV inflows = $600(1.12)3 + $600(1.12)2 + $850(1.12)1 = $2,547.60.<br /><br />Now, MIRR is that discount rate which forces the TV of $2,547.60 in<br />7 years to equal $952.00.<br /><br />Using a financial calculator enter the following inputs: N = 7, PV =<br />-952, PMT = 0, and FV = 2547.60. Then solve for I = MIRRA = 15.10%.<br /><br />Similarly, MIRRB = 17.03%.<br /><br />At k = 18%,<br />MIRRA = 18.05%.<br />MIRRB = 20.49%.<br /><br /><br />10-20 a.<br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br />The crossover rate is approximately 16 percent. If the cost of capital is less than the crossover rate, then Plan B should be accepted; if the cost of capital is greater than the crossover rate, then Plan A is preferred. At the crossover rate, the two projects’ NPVs are equal. Thus, other criteria such as the IRR must be used to evaluate the projects. The exact crossover rate is calculated as 16.07 percent, the IRR of Project , the difference between the cash flow streams of the two projects.<br /><br />b. Yes. Assuming (1) equal risk among projects, and (2) that the cost of capital is a constant and does not vary with the amount of capital raised, the firm would take on all available projects with returns greater than its 12 percent cost of capital. If the firm had invested in all available projects with returns greater than 12 percent, then its best alternative would be to repay capital. Thus, the cost of capital is the correct reinvestment rate for eval¬uating a project’s cash flows.<br /><br /><br />10-21 a. Using a financial calculator, we get:<br /><br />NPVA = $14,486,808. NPVB = $11,156,893.<br />IRRA = 15.03%. IRRB = 22.26%.<br /><br />b.<br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br />The crossover rate is somewhere between 11 percent and 12 percent. The exact crossover rate is calculated as 11.7 percent, the IRR of Project , which represents the differences between the cash flow streams of the two projects.<br /><br />c. The NPV method implicitly assumes that the opportunity exists to reinvest the cash flows generated by a project at the cost of capital, while use of the IRR method implies the opportun¬ity to reinvest at the IRR. The firm will invest in all independent projects with an NPV > $0. As cash flows come in from these projects, the firm will either pay them out to investors, or use them as a substitute for outside capital which, in this case, costs 10 percent. Thus, since these cash flows are expected to save the firm 10 per¬cent, this is their opportunity cost reinvest¬ment rate.<br />The IRR method assumes reinvestment at the internal rate of return itself, which is an incorrect assumption, given a constant expected future cost of capital, and ready access to capital markets.<br /><br />10-22 a. The project’s expected cash flows are as follows (in millions of dollars):<br /><br />Time Net Cash Flow<br />0 ($ 2.0)<br />1 13.0<br />2 (12.0)<br /><br />We can construct the following NPV profile:<br />k NPV<br />0% ($1,000,000)<br />10 (99,174)<br />50 1,333,333<br />80 1,518,519<br />100 1,500,000<br />200 1,000,000<br />300 500,000<br />400 120,000<br />410 87,659<br />420 56,213<br />430 25,632<br />450 (33,058)<br /><br />b. If k = 10%, reject the project since NPV < $0. Its NPV at k = 10% is equal to -$99,174. But if k = 20%, accept the project because NPV > $0. Its NPV at k = 20% is $500,000.<br /><br />c. Other possible projects with multiple rates of return could be nuclear power plants where disposal of radioactive wastes is required at the end of the project’s life.<br /><br />d. MIRR @ k = 10%:<br /><br />PV costs = $2,000,000 + $12,000,000/(1.10)2 = $11,917,355.<br />FV inflows = $13,000,000 1.10 = $14,300,000.<br />MIRR = 9.54%. (Reject the project since MIRR < k =" 20%:" costs =" $2,000,000" 2 =" $10,333,333." inflows =" $13,000,000" 20 =" $15,600,000." mirr =" 22.87%."> k.)<br /><br />Looking at the results, this project’s MIRR calculations lead to the same decisions as the NPV calculations. However, the MIRR method will not always lead to the same accept/reject decision as the NPV method. Decisions in which two mutually exclusive projects are involved and differ in scale (size), MIRR can conflict with NPV. In those situations, the NPV method should be used.<br /><br /><br />10-23 a. Payback A (cash flows in thousands):<br /><br />Annual<br />Period Cash Flows Cumulative<br />0 ($25,000) ($25,000)<br />1 5,000 (20,000)<br />2 10,000 (10,000)<br />3 15,000 5,000<br />4 20,000 25,000<br /><br />PaybackA = 2 + $10,000/$15,000 = 2.67 years.<br /><br />Payback B (cash flows in thousands):<br /><br />Annual<br />Period Cash Flows Cumulative<br />0 ($25,000) ($25,000)<br />1 20,000 (5,000)<br />2 10,000 5,000<br />3 8,000 13,000<br />4 6,000 19,000<br /><br />PaybackB = 1 + $5,000/$10,000 = 1.50 years.<br /><br />b. Discounted payback A (cash flows in thousands):<br /><br />Annual Discounted @10%<br />Period Cash Flows Cash Flows Cumulative<br />0 ($25,000) ($25,000.00) ($25,000.00)<br />1 5,000 4,545.45 (20,454.55)<br />2 10,000 8,264.46 (12,190.09)<br />3 15,000 11,269.72 (920.37)<br />4 20,000 13,660.27 12,739.90<br /><br />Discounted PaybackA = 3 + $920.37/$13,660.27 = 3.07 years.<br /><br />Discounted payback B (cash flows in thousands):<br /><br />Annual Discounted @10%<br />Period Cash Flows Cash Flows Cumulative<br />0 ($25,000) ($25,000.00) ($25,000.00)<br />1 20,000 18,181.82 (6,818.18)<br />2 10,000 8,264.46 1,446.28<br />3 8,000 6,010.52 7,456.80<br />4 6,000 4,098.08 11,554.88<br /><br />Discounted PaybackB = 1 + $6,818.18/$8,264.46 = 1.825 years.<br /><br />c. NPVA = $12,739,908; IRRA = 27.27%.<br />NPVB = $11,554,880; IRRB = 36.15%.<br /><br />Both projects have positive NPVs, so both projects should be undertaken.<br /><br />d. At a discount rate of 5 percent, NPVA = $18,243,813.<br />At a discount rate of 5 percent, NPVB = $14,964,829.<br /><br />At a discount rate of 5 percent, Project A has the higher NPV; consequently, it should be accepted.<br /><br />e. At a discount rate of 15 percent, NPVA = $8,207,071.<br />At a discount rate of 15 percent, NPVB = $8,643,390.<br /><br />At a discount rate of 15 percent, Project B has the higher NPV; consequently, it should be accepted.<br /><br />f. Project =<br />Year CFA - CFB<br />0 $ 0<br />1 (15)<br />2 0<br />3 7<br />4 14<br /><br />IRR = Crossover rate = 13.5254% 13.53%.<br /><br />g. Use 3 steps to calculate MIRRA @ k = 10%:<br /><br />Step 1: Calculate the NPV of the uneven cash flow stream, so its FV can then be calculated. With a financial calculator, enter the cash flow stream into the cash flow registers, then enter I = 10, and solve for NPV = $37,739,908.<br /><br />Step 2: Calculate the FV of the cash flow stream as follows:<br />Enter N = 4, I = 10, PV = -37739908, and PMT = 0 to solve for FV = $55,255,000.<br /><br />Step 3: Calculate MIRRA as follows:<br /><br />Enter N = 4, PV = -25000000, PMT = 0, and FV = 55255000 to solve for I = 21.93%.<br /><br />Use 3 steps to calculate MIRRB @ k = 10%:<br /><br />Step 1: Calculate the NPV of the uneven cash flow stream, so its FV can then be calculated. With a financial calculator, enter the cash flow stream into the cash flow registers, then enter I = 10, and solve for NPV = $36,554,880.<br /><br />Step 2: Calculate the FV of the cash flow stream as follows:<br />Enter N = 4, I = 10, PV = -36554880, and PMT = 0 to solve for FV = $53,520,000.<br /><br />Step 3: Calculate MIRRB as follows:<br />Enter N = 4, PV = -25000000, PMT = 0, and FV = 53520000 to solve for I = 20.96%.<br /><br />According to the MIRR approach, if the 2 projects were mutually exclusive, Project A would be chosen because it has the higher MIRR. This is consistent with the NPV approach. Note: Because these two projects are equal in size, we don’t need to worry about a conflict between the MIRR and NPV decisions.saleem shahzadnoreply@blogger.com2tag:blogger.com,1999:blog-3421608066886271296.post-68974292326346635902010-12-14T15:16:00.004+05:002011-01-18T16:04:24.820+05:00Chapter 11Chapter 11<br />Cash Flow Estimation and Risk Analysis<br />SOLUTIONS TO END-OF-CHAPTER PROBLEMS<br /><br /><br /><br />11-1 Equipment $ 9,000,000<br />NOWC Investment 3,000,000<br />Initial investment outlay $12,000,000<br /><br /><br />11-2 Operating Cash Flows: t = 1<br />Sales revenues $10,000,000<br />Operating costs 7,000,000<br />Depreciation 2,000,000<br />Operating income before taxes $ 1,000,000<br />Taxes (40%) 400,000<br />Operating income after taxes $ 600,000<br />Add back depreciation 2,000,000<br />Operating cash flow $ 2,600,000<br /><br /><br />11-3 Equipment’s original cost $20,000,000<br />Depreciation (80%) 16,000,000<br />Book value $ 4,000,000<br /><br />Gain on sale = $5,000,000 - $4,000,000 = $1,000,000.<br />Tax on gain = $1,000,000(0.4) = $400,000.<br />AT net salvage value = $5,000,000 - $400,000 = $4,600,000.<br /><br /><br />11-4 E(NPV) = 0.05(-$70) + 0.20(-$25) + 0.50($12) + 0.20($20) + 0.05($30)<br />= -$3.5 + -$5.0 + $6.0 + $4.0 + $1.5<br />= $3.0 million.<br /><br />NPV = [0.05(-$70 - $3)2 + 0.20(-$25 - $3)2 + 0.50($12 - $3)2 +<br />0.20($20 - $3)2 + 0.05($30 - $3)2]½<br />= $23.622 million.<br /><br /><br /><br /><br /><br />11-5 a. 0 1 2 3 4 5<br />Initial investment ($250,000)<br />Net oper. WC (25,000)<br /><br />Cost savings $ 90,000 $ 90,000 $ 90,000 $ 90,000 $ 90,000<br />Depreciation 82,500 112,500 37,500 17,500 0<br />Oper. inc. before taxes $ 7,500 ($ 22,500) $ 52,500 $ 72,500 $ 90,000<br />Taxes (40%) 3,000 (9,000) 21,000 29,000 36,000<br />Oper. Inc. (AT) $ 4,500 ($ 13,500) $ 31,500 $ 43,500 $ 54,000<br />Add: Depreciation 82,500 112,500 37,500 17,500 0<br />Oper. CF $ 87,000 $ 99,000 $ 69,000 $ 61,000 $ 54,000<br /><br />Return of NOWC $25,000<br />Sale of Machine 23,000<br />Tax on sale (40%) (9,200)<br />Net cash flow ($275,000) $ 87,000 $ 99,000 $ 69,000 $ 61,000 $ 92,800<br /><br />NPV = $37,035.13<br /><br />Notes:<br />a Depreciation Schedule, Basis = $250,000<br /><br />MACRS Rate<br /> Basis =<br />Year Beg. Bk. Value MACRS Rate Depreciation Ending BV<br />1 $250,000 0.33 $ 82,500 $167,500<br />2 167,500 0.45 112,500 55,000<br />3 55,000 0.15 37,500 17,500<br />4 17,500 0.07 17,500 0<br />$250,000<br /><br />b. If savings increase by 20 percent, then savings will be (1.2)($90,000)<br />= $108,000.<br /><br />If savings decrease by 20 percent, then savings will be (0.8)($90,000)<br />= $72,000.<br /><br />(1) Savings increase by 20%:<br /><br />0 1 2 3 4 5<br />Initial investment ($250,000)<br />Net oper. WC (25,000)<br /><br />Cost savings $108,000 $108,000 $108,000 $108,000 $108,000<br />Depreciation 82,500 112,500 37,500 17,500 0<br />Oper. inc. before taxes $ 25,500 ($ 4,500) $ 70,500 $ 90,500 $108,000<br />Taxes (40%) 10,200 (1,800) 28,200 36,200 43,200<br />Oper. Inc. (AT) $ 15,300 ($ 2,700) $ 42,300 $ 54,300 $ 64,800<br />Add: Depreciation 82,500 112,500 37,500 17,500 0<br />Oper. CF $ 97,800 $109,800 $ 79,800 $ 71,800 $ 64,800<br /><br />Return of NOWC $25,000<br />Sale of Machine 23,000<br />Tax on sale (40%) (9,200)<br />Net cash flow ($275,000) $ 97,800 $109,800 $ 79,800 $ 71,800 $103,600<br /><br />NPV = $77,975.63<br /><br /><br />(2) Savings decrease by 20%:<br /><br />0 1 2 3 4 5<br />Initial investment ($250,000)<br />Net oper. WC (25,000)<br /><br />Cost savings $ 72,000 $ 72,000 $ 72,000 $ 72,000 $ 72,000<br />Depreciation 82,500 112,500 37,500 17,500 0<br />Oper. inc. before taxes ($ 10,500)($ 40,500) $ 34,500 $ 54,500 $ 72,000<br />Taxes (40%) (4,200) (16,200) 13,800 21,800 28,800<br />Oper. Inc. (AT) ($ 6,300)($ 24,300) $ 20,700 $ 32,700 $ 43,200<br />Add: Depreciation 82,500 112,500 37,500 17,500 0<br />Oper. CF $ 76,200 $ 88,200 $ 58,200 $ 50,200 $ 43,200<br /><br />Return of NOWC $25,000<br />Sale of Machine 23,000<br />Tax on sale (40%) (9,200)<br />Net cash flow ($275,000) $ 76,200 $ 88,200 $ 58,200 $ 50,200 $ 82,000<br /><br />NPV = -$3,905.37<br /><br />c. Worst-case scenario:<br /><br />0 1 2 3 4 5<br />Initial investment ($250,000)<br />Net oper. WC (30,000)<br /><br />Cost savings $ 72,000 $ 72,000 $ 72,000 $ 72,000 $ 72,000<br />Depreciation 82,500 112,500 37,500 17,500 0<br />Oper. inc. before taxes ($ 10,500)($ 40,500) $ 34,500 $ 54,500 $ 72,000<br />Taxes (40%) (4,200) (16,200) 13,800 21,800 28,800<br />Oper. Inc. (AT) ($ 6,300)($ 24,300) $ 20,700 $ 32,700 $ 43,200<br />Add: Depreciation 82,500 112,500 37,500 17,500 0<br />Oper. CF $ 76,200 $ 88,200 $ 58,200 $ 50,200 $ 43,200<br /><br />Return of NOWC $30,000<br />Sale of Machine 18,000<br />Tax on sale (40%) (7,200)<br />Net cash flow ($280,000) $ 76,200 $ 88,200 $ 58,200 $ 50,200 $ 84,000<br /><br />NPV = -$7,663.52<br /><br />Base-case scenario:<br /><br />This was worked out in part a. NPV = $37,035.13.<br /><br />Best-case scenario:<br /><br />0 1 2 3 4 5<br />Initial investment ($250,000)<br />Net oper. WC ( 20,000)<br /><br />Cost savings $108,000 $108,000 $108,000 $108,000 $108,000<br />Depreciation 82,500 112,500 37,500 17,500 0<br />Oper. inc. before taxes $ 25,500 ($ 4,500) $ 70,500 $ 90,500 $108,000<br />Taxes (40%) 10,200 (1,800) 28,200 36,200 43,200<br />Oper. Inc. (AT) $ 15,300 ($ 2,700) $ 42,300 $ 54,300 $ 64,800<br />Add: Depreciation 82,500 112,500 37,500 17,500 0<br />Oper. CF $ 97,800 $109,800 $ 79,800 $ 71,800 $ 64,800<br /><br />Return of NOWC $20,000<br />Sale of Machine 28,000<br />Tax on sale (40%) (11,200)<br />Net cash flow ($270,000) $ 97,800 $109,800 $ 79,800 $ 71,800 $101,600<br /><br />NPV = $81,733.79<br /><br />Prob. NPV Prob. NPV<br />Worst-case 0.35 ($ 7,663.52) ($ 2,682.23)<br />Base-case 0.35 37,035.13 12,962.30<br />Best-case 0.30 81,733.79 24,520.14<br />E(NPV) $34,800.21<br /><br />NPV = [(0.35)(-$7,663.52 - $34,800.21)2 + (0.35)($37,035.13 - $34,800.21)2 + (0.30)($81,733.79 - $34,800.21)2]½<br />NPV = [$631,108,927.93 + $1,748,203.59 + $660,828,279.49]½<br />NPV = $35,967.84.<br /><br />CV = $35,967.84/$34,800.21 = 1.03.<br /><br /><br />11-6 a. The applicable depreciation values are as follows for the two scenarios:<br /><br />Year Scenario 1 (straight-line) Scenario 2 (MACRS)<br />1 $200,000 $264,000<br />2 200,000 360,000<br />3 200,000 120,000<br />4 200,000 56,000<br /><br />b. To find the difference in net present values under these two methods, we must determine the difference in incremental cash flows each method provides. The depreciation expenses can not simply be subtracted from each other, as there are tax ramifications due to depreciation expense. The full depreciation expense is subtracted from Revenues to get operating income, and then taxes due are computed Then, depreciation is added to after-tax operating income to get the project’s operating cash flow. Therefore, if the tax rate is 40%, only 60% of the depreciation expense is actually subtracted out during the after-tax operating income calculation and the full depreciation expense is added back to get operating income. So, there is a tax benefit associated with the depreciation expense that amounts to 40% of the depreciation expense. Therefore, the differences between depreciation expenses under each scenario should be computed and multiplied by 0.4 to determine the benefit provided by the depreciation expense.<br /><br />Year Depr. Exp. Difference (2 – 1) Depr. Exp. Diff. 0.4 (MACRS)<br />1 $64,000 $25,600<br />2 160,000 64,000<br />3 -80,000 -32,000<br />4 -144,000 -57,600<br /><br />Now to find the difference in NPV to be generated under these scenarios, just enter the cash flows that represent the benefit from depreciation expense and solve for net present value based upon a WACC of 10%.<br /><br /><br />CF0 = 0<br />CF1 = 25600<br />CF2 = 64000<br />CF3 = -32000<br />CF4 = -57600<br /><br />I = 10<br />NPV = $12,781.64<br /><br />So, all else equal the use of the accelerated depreciation method will result in a higher NPV (by $12,781.64) than would the use of a straight-line depreciation method.<br /><br /><br />11-7 a. The net cost is $178,000:<br /><br />Cost of investment at t = 0:<br /><br />Base price ($140,000)<br />Modification (30,000)<br />Increase in NOWC (8,000)<br />Cash outlay for new machine ($178,000)<br /><br />b. The operating cash flows follow:<br /><br />Year 1 Year 2 Year 3<br />After-tax savings $30,000 $30,000 $30,000<br />Depreciation tax savings 22,440 30,600 10,200<br />Net operating cash flow $52,440 $60,600 $40,200<br /><br />Notes:<br /><br />1. The after-tax cost savings is $50,000(1 — T) = $50,000(0.6) = $30,000.<br /><br />2. The depreciation expense in each year is the depreciable basis, $170,000, times the MACRS allowance percentages of 0.33, 0.45, and 0.15 for Years 1, 2, and 3, respectively. Depreciation expense in Years 1, 2, and 3 is $56,100, $76,500, and $25,500. The depreciation tax savings is calculated as the tax rate (40 percent) times the depreciation expense in each year.<br /><br />c. The terminal cash flow is $48,760:<br /><br />Salvage value $60,000<br />Tax on SV* (19,240)<br />Return of NOWC 8,000<br />$48,760<br /><br />Remaining BV in Year 4 = $170,000(0.07) = $11,900.<br /><br />*Tax on SV = ($60,000 - $11,900)(0.4) = $19,240.<br /><br /><br />d. The project has an NPV of ($19,549). Thus, it should not be accepted.<br /><br />Year Net Cash Flow PV @ 12%<br />0 ($178,000) ($178,000)<br />1 52,440 46,821<br />2 60,600 48,310<br />3 88,960 63,320<br />NPV = ($ 19,549)<br /><br />Alternatively, place the cash flows on a time line:<br /><br />0 1 2 3<br /> <br />-178,000 52,440 60,600 40,200<br />48,760<br />88,960<br /><br />With a financial calculator, input the appropriate cash flows into the cash flow register, input I = 12, and then solve for NPV = -$19,548.65 -$19,549.<br /><br /><br />11-8 a. The net cost is $126,000:<br /><br />Price ($108,000)<br />Modification (12,500)<br />Increase in NOWC (5,500)<br />Cash outlay for new machine ($126,000)<br /><br />b. The operating cash flows follow:<br /><br />Year 1 Year 2 Year 3<br />1. After-tax savings $28,600 $28,600 $28,600<br />2. Depreciation tax savings 13,918 18,979 6,326<br />Net cash flow $42,518 $47,579 $34,926<br /><br />Notes:<br /><br />1. The after-tax cost savings is $44,000(1 - T) = $44,000(0.65)<br />= $28,600.<br /><br />2. The depreciation expense in each year is the depreci¬able basis, $120,500, times the MACRS allowance percentages of 0.33, 0.45, and 0.15 for Years 1, 2, and 3, respectively. Depreciation expense in Years 1, 2, and 3 is $39,765, $54,225, and $18,075. The depreciation tax savings is calculated as the tax rate (35 percent) times the depreciation expense in each year.<br /><br /><br />c. The terminal cash flow is $50,702:<br /><br />Salvage value $65,000<br />Tax on SV* (19,798)<br />Return of NOWC 5,500<br />$50,702<br /><br />BV in Year 4 = $120,500(0.07) = $8,435.<br /><br />*Tax on SV = ($65,000 - $8,435)(0.35) = $19,798.<br /><br />d. The project has an NPV of $10,841; thus, it should be accepted.<br /><br />Year Net Cash Flow PV @ 12%<br />0 ($126,000) ($126,000)<br />1 42,518 37,963<br />2 47,579 37,930<br />3 85,628 60,948<br />NPV = $ 10,841<br /><br />Alternatively, place the cash flows on a time line:<br /><br />0 1 2 3<br /> <br />-126,000 42,518 47,579 34,926<br />50,702<br />85,628<br /><br />With a financial calculator, input the appropriate cash flows into the cash flow register, input I = 12, and then solve for NPV = $10,840.51 $10,841.<br /><br /><br />11-9 a. Expected annual cash flows:<br /><br />Project A: Probable<br />Probability × Cash Flow = Cash Flow<br />0.2 $6,000 $1,200<br />0.6 6,750 4,050<br />0.2 7,500 1,500<br />Expected annual cash flow = $6,750<br />Project B: Probable<br />Probability × Cash Flow = Cash Flow<br />0.2 $ 0 $ 0<br />0.6 6,750 4,050<br />0.2 18,000 3,600<br />Expected annual cash flow = $7,650<br /><br /><br />Coefficient of variation:<br /><br /><br /><br /><br /><br />Project A:<br /><br /><br /><br /><br />Project B:<br /><br /><br /><br />CVA = $474.34/$6,750 = 0.0703.<br />CVB = $5,797.84/$7,650 = 0.7579.<br /><br />b. Project B is the riskier project because it has the greater variability in its probable cash flows, whether measured by the standard deviation or the coefficient of variation. Hence, Project B is evaluated at the 12 percent cost of capital, while Project A requires only a 10 percent cost of capital.<br /><br />Using a financial calculator, input the appropriate expected annual cash flows for Project A into the cash flow register, input I = 10, and then solve for NPVA = $10,036.25.<br /><br />Using a financial calculator, input the appropriate expected annual cash flows for Project B into the cash flow register, input I = 12, and then solve for NPVB = $11,624.01.<br /><br />Project B has the higher NPV; therefore, the firm should accept Project B.<br /><br />c. The portfolio effects from Project B would tend to make it less risky than otherwise. This would tend to reinforce the decision to accept Project B. Again, if Project B were negatively correlated with the GDP (Project B is profitable when the economy is down), then it is less risky and Project B's acceptance is reinforced.<br /><br /><br /><br />11-10 If actual life is 5 years:<br /><br />Using a time line approach:<br /><br />0 1 2 3 4 5<br /> <br />Investment outlay (36,000)<br />Operating cash flows<br />excl. deprec. (AT) 7,200 7,200 7,200 7,200 7,200<br />Depreciation savings 2,880 2,880 2,880 2,880 2,880<br />Net cash flow (36,000) 10,080 10,080 10,080 10,080 10,080<br /><br />NPV10% = $2,211.13.<br /><br />If actual life is 4 years:<br /><br /><br />Using a time line approach:<br /><br />0 1 2 3 4<br /> <br />Investment outlay (36,000)<br />Operating cash flows<br />excl. deprec. (AT) 7,200 7,200 7,200 7,200<br />Depreciation savings 2,880 2,880 2,880 2,880<br />Tax savings on loss 2,880<br />Net cash flow (36,000) 10,080 10,080 10,080 12,960<br /><br />NPV10% = -$2,080.68.<br /><br />If actual life is 8 years:<br /><br /><br />Using a time line approach:<br /><br />0 1 5 6 7 8<br /> • • • <br />Investment outlay (36,000)<br />Operating cash flows<br />excl. deprec. (AT) 7,200 7,200 7,200 7,200 7,200<br />Depreciation savings 2,880 2,880<br />Net cash flow (36,000) 10,080 10,080 7,200 7,200 7,200<br /><br />NPV10% = $13,328.93.<br /><br />If the life is as low as 4 years (an unlikely event), the investment will not be desirable. But, if the investment life is longer than 4 years, the investment will be a good one. Therefore, the decision will depend on the directors' confidence in the life of the tractor. Given the low proba-bility of the tractor's life being only 4 years, it is likely that the directors will decide to purchase the tractor.saleem shahzadnoreply@blogger.com0tag:blogger.com,1999:blog-3421608066886271296.post-17720524933275037842010-12-14T15:17:00.007+05:002011-01-18T16:02:07.105+05:00Chapter 12Chapter 12<br />Other Topics in Capital Budgeting<br />SOLUTIONS TO END-OF-CHAPTER PROBLEMS<br /><br /><br />12-1 a. Project A: 0 1 2<br /> <br />-10,000 6,000 8,000<br /><br />Using a financial calculator, input the following data: CF0 = -10000, CF1 = 6000, CF2 = 8000, I = 10, and then solve for NPVA = $2,066.12.<br /><br />Project B: 0 1 2 3 4<br /> <br />-10,000 4,000 4,000 4,000 4,000<br /><br />Using a financial calculator, input the following data: CF0 = -10000, CF1-4 = 4000, I = 10, and then solve for NPVB = $2,679.46.<br /><br />Since neither project can be repeated, Project B should be selected because it has a higher NPV than Project A.<br /><br />b. To determine the answer to part b, we must use the replacement chain (common life) approach to calculate the extended NPV for Project A. Project B already extends out to 4 years, so its NPV is $2,679.46.<br /><br />Project A: 0 1 2 3 4<br /> <br />-10,000 6,000 8,000 6,000 8,000<br />-10,000<br />-2,000<br /><br />Using a financial calculator, input the following data: CF0 = -10000, CF1 = 6000, CF2 = -2000, CF3 = 6000, CF4 = 8000, I = 10, and then solve for NPVA = $3,773.65.<br /><br />Since Project A’s extended NPV = $3,773.65, it should be selected over Project B with an NPV = $2,679.46.<br /><br /><br />12-2 WACC1 = 12%; WACC2 = 12.5%.<br /><br />Since each project is independent and of average risk, all projects whose IRR > WACC will be accepted. Consequently, Projects A, B, C, D, and E will be accepted and the optimal capital budget is $5,250,000.<br /><br /><br />12-3 Since Projects C and D are now mutually exclusive only one of them can be accepted. The project with the higher NPV should now be chosen. Therefore, Project D should be selected over Project C. The projects now selected are A, B, D, and E with an optimal capital budget of $4 million.<br />12-4 Risk-adjusted<br />Projects Risk WACC IRR Decision<br />A High 14.5% 14.0% Reject<br />B Average 12.5 13.5 Accept<br />C Average 12.5 13.2 Accept<br />D Average 12.5 13.0 Accept<br />E Average 12.5 12.7 Accept<br />F Low 10.5 12.3 Accept<br />G Low 10.5 12.2 Accept<br /><br />On the basis of a risk-adjusted WACC, Projects B, C, D, E, F, and G will be accepted and only Project A will be rejected. The firm’s optimal capital budget is $6 million.<br /><br /><br />12-5 NPV190-3 = $11,982 (for 3 years).<br />Extended NPV190-3 = $11,982 + $11,982/(1.14)3 = $20,070.<br />NPV360-6 = $22,256 (for 6 years).<br /><br />Both new machines have positive NPVs; hence the old machine should be replaced. Further, since its NPV is greater, choose Model 360-6.<br /><br /><br />12-6 Plane A: Expected life = 5 years; Cost = $100 million; NCF = $30 million; COC = 12%.<br />Plane B: Expected life = 10 years; Cost = $132 million; NCF = $25 million; COC = 12%.<br /><br />A: 0 1 2 3 4 5 6 7 8 9 10<br /> <br />-100 30 30 30 30 30 30 30 30 30 30<br />-100<br />-70<br /><br />Enter these values into the cash flow register: CF0 = -100; CF1-4 = 30;<br />CF5 = -70; CF6-10 = 30. Then enter I = 12, and press the NPV key to get NPVA = $12.764 $12.76 million.<br /><br />B: 0 1 2 3 4 5 6 7 8 9 10<br /> <br />-132 25 25 25 25 25 25 25 25 25 25<br /><br />Enter these cash flows into the cash flow register, along with the interest rate, and press the NPV key to get NPVB = $9.256 $9.26 million.<br />Project A is the better project and will increase the company's value by $12.76 million.<br /><br /><br />12-7 A: 0 1 2 3 4 5 6 7 8<br /> <br />-10 4 4 4 4 4 4 4 4<br />-10<br />-6<br />Machine A’s simple NPV is calculated as follows: Enter CF0 = -10 and<br />CF1-4 = 4. Then enter I = 10, and press the NPV key to get NPVA = $2.679 million. However, this does not consider the fact that the project can be repeated again. Enter these values into the cash flow register: CF0 = -10; CF1-3 = 4; CF4 = -6; CF5-8 = 4. Then enter I = 10, and press the NPV key to get Extended NPVA = $4.5096 $4.51 million.<br /><br />B: 0 1 2 3 4 5 6 7 8<br /> <br />-15 3.5 3.5 3.5 3.5 3.5 3.5 3.5 3.5<br /><br />Enter these cash flows into the cash flow register, along with the interest rate, and press the NPV key to get NPVB = $3.672 $3.67 million.<br />Machine A is the better project and will increase the company's value by $4.51 million.<br /><br /><br />12-8 a. 0 1 2 20<br /> • • • <br />-20 3 3 3<br /><br />NPV = $2.4083 million.<br /><br />b. Wait 1 year:<br /><br />NPV @<br />0 1 2 3 21 Yr. 0<br />Tax imposed • • • <br />25% Prob. 0 -20 2.4 2.4 2.4 -$1.8512<br /><br />Tax not imposed • • • <br />75% Prob. 0 -20 3.2 3.2 3.2 3.2 3.4841<br /><br />Note though, that if the tax is imposed, the NPV of the project is negative and therefore would not be undertaken. The value of this option of waiting one year is evaluated as 0.25($0) + (0.75)($3.4841) = $2.6131 million.<br />Since the NPV of waiting one year is greater than going ahead and proceeding with the project today, it makes sense to wait.<br /><br /><br />12-9 a. NPV of abandonment after Year t:<br /><br />Using a financial calculator, input the following: CF0 = -22500,<br />CF1 = 23750, and I = 10 to solve for NPV1 = -$909.09 -$909.<br /><br />Using a financial calculator, input the following: CF0 = -22500,<br />CF1 = 6250, CF2 = 20250, and I = 10 to solve for NPV2 = -$82.64 -$83.<br /><br />Using a financial calculator, input the following: CF0 = -22500,<br />CF1 = 6250, Nj = 2, CF3 = 17250, and I = 10 to solve for NPV3 = $1,307.29 $1,307.<br /><br />Using a financial calculator, input the following: CF0 = -22500,<br />CF1 = 6250, Nj = 3, CF4 = 11250, and I = 10 to solve for NPV4 = $726.73 $727.<br /><br />Using a financial calculator, input the following: CF0 = -22500,<br />CF1 = 6250, Nj = 5, and I = 10 to solve for NPV5 = $1,192.42 $1,192.<br /><br />The firm should operate the truck for 3 years, NPV3 = $1,307.<br /><br />b. No. Abandonment possibilities could only raise NPV and IRR. The value of the firm is maximized by abandoning the project after Year 3.<br /><br /><br />12-10 a. 0 1 2 3 4<br /> <br />-8 4 4 4 4<br /><br />NPV = $4.6795 million.<br /><br />b. Wait 2 years:<br /><br />NPV @<br />0 1 2 3 4 5 6 Yr. 0<br /> <br />10% Prob. 0 0 -9 2.2 2.2 2.2 2.2 -$1.6746<br /><br /> <br />90% Prob. 0 0 -9 4.2 4.2 4.2 4.2 3.5648<br /><br />If the cash flows are only $2.2 million, the NPV of the project is negative and, thus, would not be undertaken. The value of the option of waiting two years is evaluated as 0.10($0) + 0.90($3.5648) = $3.2083 million.<br />Since the NPV of waiting two years is less than going ahead and proceeding with the project today, it makes sense to drill today.<br /><br /><br />12-11 a. 0 1 14 15<br /> • • • <br />-6,200,000 600,000 600,000 600,000<br /><br />Using a financial calculator, input the following data: CF0 = -6200000; CF1-15 = 600000; I = 12; and then solve for NPV = -$2,113,481.31.<br /><br /><br /><br />b. 0 1 14 15<br /> • • • <br />-6,200,000 1,200,000 1,200,000 1,200,000<br /><br />Using a financial calculator, input the following data: CF0 =<br />-6200000; CF1-15 = 1200000; I = 12; and then solve for NPV = $1,973,037.39.<br /><br />c. If they proceed with the project today, the project’s expected NPV = (0.5 -$2,113,481.31) + (0.5 $1,973,037.39) = -$70,221.96. So, Nevada Enterprises would not do it.<br /><br />d. Since the project’s NPV with the tax is negative, if the tax were imposed the firm would abandon the project. Thus, the decision tree looks like this:<br />NPV @<br />0 1 2 15 Yr. 0<br />50% Prob. • • • <br />Taxes -6,200,000 6,000,000 0 0 -$ 842,857.14<br /><br />No Taxes • • • <br />50% Prob. -6,200,000 1,200,000 1,200,000 1,200,000 1,973,037.39<br />Expected NPV $ 565,090.13<br /><br />Yes, the existence of the abandonment option changes the expected NPV of the project from negative to positive. Given this option the firm would take on the project because its expected NPV is $565,090.13.<br /><br />e. NPV @<br />0 1 Yr. 0<br />50% Prob. <br />Taxes NPV = ? -1,500,000 $ 0.00<br />+300,000 = NPV @ t = 1<br /><br />No Taxes <br />50% Prob. NPV = ? -1,500,000 2,232,142.86<br />+4,000,000 = NPV @ t = 1 Expected NPV $1,116,071.43<br /><br />If the firm pays $1,116,071.43 for the option to purchase the land, then the NPV of the project is exactly equal to zero. So the firm would not pay any more than this for the option.saleem shahzadnoreply@blogger.com0tag:blogger.com,1999:blog-3421608066886271296.post-53774083259176396592010-12-14T15:17:00.006+05:002011-01-18T16:00:03.144+05:00Chapter 13Chapter 13<br />Capital Structure and Leverage<br />SOLUTIONS TO END-OF-CHAPTER PROBLEMS<br /><br />13-1 QBE =<br />QBE =<br />QBE = 500,000 units.<br /><br /><br />13-2 The optimal capital structure is that capital structure where WACC is minimized and stock price is maximized. Since Jackson’s stock price is maximized at a 30 percent debt ratio, the firm’s optimal capital structure is 30 percent debt and 70 percent equity. This is also the debt level where the firm’s WACC is minimized.<br /><br /><br />13-3 From the Hamada Equation, b = bU[1 + (1 – T)(D/E)], we can calculate bU as bU = b/[1 + (1 – T)(D/E)].<br /><br />bU = 1.2/[1 + (1 – 0.4)($2,000,000/$8,000,000)]<br />bU = 1.2/[1 + 0.15]<br />bU = 1.0435.<br /><br /><br />13-4 a. 8,000 units 18,000 units<br />Sales $200,000 $450,000<br />Fixed costs 140,000 140,000<br />Variable costs 120,000 270,000<br />Total costs $260,000 $410,000<br />Gain (loss) ($ 60,000) $ 40,000<br /><br />b. QBE = = = 14,000 units.<br /><br />SBE = QBE(P) = (14,000)($25) = $350,000.<br /><br /><br /><br />c. If the selling price rises to $31, while the variable cost per unit remains fixed, P - V rises to $16. The end result is that the breakeven point is lowered.<br /><br />QBE = = = 8,750 units.<br /><br />SBE = QBE(P) = (8,750)($31) = $271,250.<br /><br />The breakeven point drops to 8,750 units. The contribution margin per each unit sold has been increased; thus the variability in the firm’s profit stream has been increased, but the opportunity for magnified profits has also been increased.<br /><br />d. If the selling price rises to $31 and the variable cost per unit rises to $23, P - V falls to $8. The end result is that the breakeven point increases.<br /><br />QBE = = = 17,500 units.<br /><br />SBE = QBE(P) = (17,500)($31) = $542,500.<br />The breakeven point increases to 17,500 units because the contribution margin per each unit sold has decreased.<br /><br /><br /><br />13-5 a. The current dividend per share, D0, = $400,000/200,000 = $2.00. D1 = $2.00 (1.05) = $2.10. Therefore, P0 = D1/(ks - g) = $2.10/(0.134 - 0.05) = $25.00.<br /><br />b. Step 1: Calculate EBIT before the recapitalization:<br />EBIT = $1,000,000/(1 - T) = $1,000,000/0.6 = $1,666,667.<br />Note: The firm is 100% equity financed, so there is no interest expense.<br /><br />Step 2: Calculate net income after the recapitalization:<br />[$1,666,667 - 0.11($1,000,000)]0.6 = $934,000.<br /><br />Step 3: Calculate the number of shares outstanding after the recapi-talization:<br />200,000 - ($1,000,000/$25) = 160,000 shares.<br /><br />Step 4: Calculate D1 after the recapitalization:<br />D0 = 0.4($934,000/160,000) = $2.335.<br />D1 = $2.335(1.05) = $2.4518.<br /><br />Step 5: Calculate P0 after the recapitalization:<br />P0 = D1/(ks - g) = $2.4518/(0.145 - 0.05) = $25.8079 $25.81.<br /><br /><br />13-6 a. LL: D/TA = 30%.<br />EBIT $4,000,000<br />Interest ($6,000,000 0.10) 600,000<br />EBT $3,400,000<br />Tax (40%) 1,360,000<br />Net income $2,040,000<br /><br />Return on equity = $2,040,000/$14,000,000 = 14.6%.<br /><br /><br />HL: D/TA = 50%.<br />EBIT $4,000,000<br />Interest ($10,000,000 0.12) 1,200,000<br />EBT $2,800,000<br />Tax (40%) 1,120,000<br />Net income $1,680,000<br /><br />Return on equity = $1,680,000/$10,000,000 = 16.8%.<br /><br />b. LL: D/TA = 60%.<br />EBIT $4,000,000<br />Interest ($12,000,000 0.15) 1,800,000<br />EBT $2,200,000<br />Tax (40%) 880,000<br />Net income $1,320,000<br /><br />Return on equity = $1,320,000/$8,000,000 = 16.5%.<br /><br />Although LL’s return on equity is higher than it was at the 30 percent leverage ratio, it is lower than the 16.8 percent return of HL.<br />Initially, as leverage is increased, the return on equity also increases. But, the interest rate rises when leverage is increased. Therefore, the return on equity will reach a maximum and then decline.<br /><br /><br />13-7 No leverage: D = 0 (debt); E = $14,000,000.<br /><br />State Ps EBIT (EBIT - kdD)(1-T) ROEs Ps(ROE) Ps(ROEs-RÔE)2<br />1 0.2 $4,200,000 $2,520,000 0.18 0.036 0.00113<br />2 0.5 2,800,000 1,680,000 0.12 0.060 0.00011<br />3 0.3 700,000 420,000 0.03 0.009 0.00169<br />RÔE = 0.105<br />Variance = 0.00293<br />Standard deviation = 0.054<br />RÔE = 10.5%.<br />2 = 0.00293.<br /> = 5.4%.<br />CV = /RÔE = 5.4%/10.5% = 0.514.<br /><br />Leverage ratio = 10%: D = $1,400,000; E = $12,600,000; kd = 9%.<br /><br />State Ps EBIT (EBIT - kdD)(1-T) ROEs Ps(ROE) Ps(ROEs-RÔE)2<br />1 0.2 $4,200,000 $2,444,400 0.194 0.039 0.00138<br />2 0.5 2,800,000 1,604,400 0.127 0.064 0.00013<br />3 0.3 700,000 344,400 0.027 0.008 0.00212<br />RÔE = 0.111<br />Variance = 0.00363<br />Standard deviation = 0.060<br />RÔE = 11.1%.<br />2 = 0.00363.<br /> = 6%.<br />CV = 6%/11.1% = 0.541.<br /><br />Leverage ratio = 50%: D = $7,000,000; E = $7,000,000; kd = 11%.<br /><br />State Ps EBIT (EBIT - kdD)(1-T) ROEs Ps(ROE) Ps(ROEs-RÔE)2<br />1 0.2 $4,200,000 $2,058,000 0.294 0.059 0.00450<br />2 0.5 2,800,000 1,218,000 0.174 0.087 0.00045<br />3 0.3 700,000 (42,000) (0.006) (0.002) 0.00675<br />RÔE = 0.144<br />Variance = 0.01170<br />Standard deviation = 0.108<br />RÔE = 14.4%.<br />2 = 0.01170.<br /> = 10.8%.<br />CV = 10.8%/14.4% = 0.750.<br /><br />Leverage ratio = 60%: D = $8,400,000; E = $5,600,000; kd = 14%.<br /><br />State Ps EBIT (EBIT - kdD)(1-T) ROEs Ps(ROE) Ps(ROEs-RÔE)2<br />1 0.2 $4,200,000 $1,814,400 0.324 0.065 0.00699<br />2 0.5 2,800,000 974,400 0.174 0.087 0.00068<br />3 0.3 700,000 (285,600) (0.051) (0.015) 0.01060<br />RÔE = 0.137<br />Variance = 0.01827<br />Standard deviation = 0.135<br />RÔE = 13.7%.<br />2 = 0.01827.<br /> = 13.5%.<br />CV = 13.5%/13.7% = 0.985 0.99.<br /><br />As leverage increases, the expected return on equity rises up to a point. But as the risk increases with increased leverage, the cost of debt rises. So after the return on equity peaks, it then begins to fall. As leverage increases, the measures of risk (both the standard deviation and the coefficient of variation of the return on equity) rise with each increase in leverage.<br /><br /><br />13-8 Facts as given: Current capital structure: 25%D, 75%E; kRF = 5%; kM – kRF = 6%; T = 40%; ks = 14%.<br /><br />Step 1: Determine the firm’s current beta.<br />ks = kRF + (kM – kRF)b<br />14% = 5% + (6%)b<br />9% = 6%b<br />1.5 = b.<br /><br />Step 2: Determine the firm’s unlevered beta, bU.<br />bU = bL/[1 + (1 – T)(D/E)]<br />bU = 1.5/[1 + (1 – 0.4)(0.25/0.75)]<br />bU = 1.5/1.20<br />bU = 1.25.<br /><br /><br />Step 3: Determine the firm’s beta under the new capital structure.<br />bL = bU(1 + (1 – T)(D/E))<br />bL = 1.25[1 + (1 – 0.4)(0.5/0.5)]<br />bL = 1.25(1.6)<br />bL = 2.<br /><br />Step 4: Determine the firm’s new cost of equity under the changed capital structure.<br />ks = kRF + (kM – kRF)b<br />ks = 5% + (6%)2<br />ks = 17%.<br /><br /><br />13-9 a. Using the standard formula for the weighted average cost of capital, we find:<br /><br />WACC = wdkd(1 - T) + wcks<br />WACC = (0.2)(8%)(1 - 0.4) + (0.8)(12.5%)<br />WACC = 10.96%.<br /><br />b. The firm's current levered beta at 20% debt can be found using the CAPM formula.<br /><br />ks = kRF + (kM - kRF)b<br />12.5% = 5% + (6%)b<br />b = 1.25.<br /><br />c. To “unlever” the firm's beta, the Hamada Equation is used.<br /><br />bL = bU[1 + (1 – T)(D/E)]<br />1.25 = bU[1 + (1 - 0.4)(0.2/0.8)]<br />1.25 = bU(1.15)<br />bU = 1.086957.<br /><br />d. To determine the firm’s new cost of common equity, one must find the firm’s new beta under its new capital structure. Consequently, you must “relever” the firm's beta using the Hamada Equation:<br /><br />bL,40% = bU[1 + (1 – T)(D/E)]<br />bL,40% = 1.086957 [1 + (1 - 0.4)(0.4/0.6)]<br />bL,40% = 1.086957(1.4)<br />bU = 1.521739.<br /><br />The firm's cost of equity, as stated in the problem, is derived using the CAPM equation.<br /><br />ks = kRF + (kM - kRF)b<br />ks = 5% + (6%)1.521739<br />ks = 14.13%.<br /><br />e. Again, the standard formula for the weighted average cost of capital is used. Remember, the WACC is a marginal, after-tax cost of capital and hence the relevant before-tax cost of debt is now 9.5% and the cost of equity is 14.13%.<br /><br />WACC = wdkd(1 - T) + wcks<br />WACC = (0.4)(9.5%)(1 - 0.4) + (0.6)(14.13%)<br />WACC = 10.76%.<br /><br />f. The firm should be advised to proceed with the recapitalization as it causes the WACC to decrease from 10.96% to 10.76%. As a result, the recapitalization would lead to an increase in firm value.<br /><br /><br />13-10 a. Expected EPS for Firm C:<br /><br />E(EPSC) = 0.1(-$2.40) + 0.2($1.35) + 0.4($5.10) + 0.2($8.85) + 0.1($12.60)<br />= -$0.24 + $0.27 + $2.04 + $1.77 + $1.26 = $5.10.<br /><br />(Note that the table values and probabilities are dispersed in a symmetric manner such that the answer to this problem could have been obtained by simple inspection.)<br /><br />b. According to the standard deviations of EPS, Firm B is the least risky, while C is the riskiest. However, this analysis does not take account of portfolio effects--if C’s earnings go up when most other companies’ decline (that is, its beta is low), its apparent riskiness would be reduced. Also, standard deviation is related to size, or scale, and to correct for scale we could calculate a coefficient of variation (/mean):<br /><br />E(EPS) CV = /E(EPS)<br />A $5.10 $3.61 0.71<br />B 4.20 2.96 0.70<br />C 5.10 4.11 0.81<br /><br />By this criterion, C is still the most risky.<br /><br /><br />13-11 a. Without new investment<br />Sales $12,960,000<br />VC 10,200,000<br />FC 1,560,000<br />EBIT $ 1,200,000<br />Interest 384,000*<br />EBT $ 816,000<br />Tax (40%) 326,400<br />Net income $ 489,600<br /><br />*Interest = 0.08($4,800,000) = $384,000.<br /><br /><br />1. EPSOld = $489,600/240,000 = $2.04.<br /><br />With new investment Debt Stock<br />Sales $12,960,000 $12,960,000<br />VC (0.8)($10,200,000) 8,160,000 8,160,000<br />FC 1,800,000 1,800,000<br />EBIT $ 3,000,000 $ 3,000,000<br />Interest 1,104,000** 384,000<br />EBT $ 1,896,000 $ 2,616,000<br />Tax (40%) 758,400 1,046,400<br />Net income $ 1,137,600 $ 1,569,600<br /><br />**Interest = 0.08($4,800,000) + 0.10($7,200,000) = $1,104,000.<br /><br />2. EPSD = $1,137,600/240,000 = $4.74.<br /><br />3. EPSS = $1,569,600/480,000 = $3.27.<br />EPS should improve, but expected EPS is significantly higher if financial leverage is used.<br /><br />b. EPS =<br />= .<br /><br />EPSDebt =<br />= .<br /><br />EPSStock = .<br /><br />Therefore,<br /><br />=<br />$10.667Q = $3,624,000<br />Q = 339,750 units.<br /><br />This is the “indifference” sales level, where EPSdebt = EPSstock.<br /><br />c. EPSOld = = 0<br />$6.133Q = $1,944,000<br />Q = 316,957 units.<br /><br />This is the QBE considering interest charges.<br /><br /><br />EPSNew,Debt = = 0<br />$10.667Q = $2,904,000<br />Q = 272,250 units.<br /><br />EPSNew,Stock = = 0<br />$10.667Q = $2,184,000<br />Q = 204,750 units.<br /><br />d. At the expected sales level, 450,000 units, we have these EPS values:<br /><br />EPSOld Setup = $2.04. EPSNew,Debt = $4.74. EPSNew,Stock = $3.27.<br /><br />We are given that operating leverage is lower under the new setup. Accordingly, this suggests that the new production setup is less risky than the old one--variable costs drop very sharply, while fixed costs rise less, so the firm has lower costs at “reasonable” sales levels.<br />In view of both risk and profit considerations, the new production setup seems better. Therefore, the question that remains is how to finance the investment.<br />The indifference sales level, where EPSdebt = EPSstock, is 339,750 units. This is well below the 450,000 expected sales level. If sales fall as low as 250,000 units, these EPS figures would result:<br /><br />EPSDebt = = -$0.59.<br /><br />EPSStock = = $0.60.<br /><br />These calculations assume that P and V remain constant, and that the company can obtain tax credits on losses. Of course, if sales rose above the expected 450,000 level, EPS would soar if the firm used debt financing.<br />In the “real world” we would have more information on which to base the decision--coverage ratios of other companies in the industry and better estimates of the likely range of unit sales. On the basis of the information at hand, we would probably use equity financing, but the decision is really not obvious.<br /><br /><br /><br />13-12 Use of debt (millions of dollars):<br /><br />Probability 0.3 0.4 0.3<br />Sales $2,250.0 $2,700.0 $3,150.0<br />EBIT (10%) 225.0 270.0 315.0<br />Interest* 77.4 77.4 77.4<br />EBT $ 147.6 $ 192.6 $ 237.6<br />Taxes (40%) 59.0 77.0 95.0<br />Net income $ 88.6 $ 115.6 $ 142.6<br /><br />Earnings per share (20 million shares) $ 4.43 $ 5.78 $ 7.13<br /><br />*Interest on debt = ($270 0.12) + Current interest expense<br />= $32.4 + $45 = $77.4.<br />Expected EPS = (0.30)($4.43) + (0.40)($5.78) + (0.30)($7.13)<br />= $5.78 if debt is used.<br /><br />2Debt = (0.30)($4.43 - $5.78)2 + (0.40)($5.78 - $5.78)2<br />+ (0.30)($7.13 - $5.78)2 = 1.094.<br /><br />Debt = = $1.05<br />= Standard deviation of EPS if debt financing is used.<br /><br />CV = = 0.18.<br /><br />E(TIEDebt) = = = 3.49.<br />Debt/Assets = ($652.50 + $300 + $270)/($1,350 + $270) = 75.5%.<br /><br />Use of stock (millions of dollars):<br /><br />Probability 0.3 0.4 0.3<br />Sales $2,250.0 $2,700.0 $3,150.0<br />EBIT 225.0 270.0 315.0<br />Interest 45.0 45.0 45.0<br />EBT $ 180.0 $ 225.0 $ 270.0<br />Taxes (40%) 72.0 90.0 108.0<br />Net income $ 108.0 $ 135.0 $ 162.0<br /><br />Earnings per share<br />(24.5 million shares)* $ 4.41 $ 5.51 $ 6.61<br /><br />*Number of shares = ($270 million/$60) + 20 million<br />= 4.5 million + 20 million = 24.5 million.<br /><br />EPSEquity = (0.30)($4.41) + (0.40)($5.51) + (0.30)($6.61) = $5.51.<br /><br />2Equity = (0.30)($4.41 - $5.51)2 + (0.40)($5.51 - $5.51)2<br />+ (0.30)($6.61 - $5.51)2 = 0.7260.<br /><br />Equity = = $0.85.<br /><br />CV = = 0.15.<br /><br />E(TIE) = = 6.00.<br /><br />= = 58.8%.<br /><br />Under debt financing the expected EPS is $5.78, the standard deviation is $1.05, the CV is 0.18, and the debt ratio increases to 75.5 percent. (The debt ratio had been 70.6 percent.) Under equity financing the expected EPS is $5.51, the standard deviation is $0.85, the CV is 0.15, and the debt ratio decreases to 58.8 percent. At this interest rate, debt financing provides a higher expected EPS than equity financing; however, the debt ratio is significantly higher under the debt financing situation as compared with the equity financing situation. Because EPS is not significantly greater under debt financing, while the risk is noticeably greater, equity financing should be recommended.<br /><br /><br />13-13 a. Firm A<br /><br />1. Fixed costs = $80,000.<br /><br />2. Variable cost/unit =<br />=<br /><br />3. Selling price/unit =<br /><br />Firm B<br /><br />1. Fixed costs = $120,000.<br /><br />2. Variable cost/unit =<br />= = $4.00/unit.<br /><br />3. Selling price/unit = = = $8.00/unit.<br /><br />b. Firm B has the higher operating leverage due to its larger amount of fixed costs.<br /><br />c. Operating profit = (Selling price)(Units sold) - Fixed costs<br />- (Variable costs/unit)(Units sold).<br /><br />Firm A’s operating profit = $8X - $80,000 - $4.80X.<br />Firm B’s operating profit = $8X - $120,000 - $4.00X.<br /><br />Set the two equations equal to each other:<br /><br />$8X - $80,000 - $4.80X = $8X - $120,000 - $4.00X<br />-$0.8X = -$40,000<br />X = $40,000/$0.80 = 50,000 units.<br /><br />Sales level = (Selling price)(Units) = $8(50,000) = $400,000.<br /><br />At this sales level, both firms earn $80,000:<br /><br />ProfitA = $8(50,000) - $80,000 - $4.80(50,000)<br />= $400,000 - $80,000 - $240,000 = $80,000.<br /><br />ProfitB = $8(50,000) - $120,000 - $4.00(50,000)<br />= $400,000 - $120,000 - $200,000 = $80,000.<br /><br /><br />13-14 Tax rate = 40% kRF = 5.0%<br />bU = 1.2 kM – kRF = 6.0%<br /><br />From data given in the problem and table we can develop the following table:<br /><br />Leveraged<br />D/A E/A D/E kd kd(1 – T) betaa ksb WACCc<br />0.00 1.00 0.0000 7.00% 4.20% 1.20 12.20% 12.20%<br />0.20 0.80 0.2500 8.00 4.80 1.38 13.28 11.58<br />0.40 0.60 0.6667 10.00 6.00 1.68 15.08 11.45<br />0.60 0.40 1.5000 12.00 7.20 2.28 18.68 11.79<br />0.80 0.20 4.0000 15.00 9.00 4.08 29.48 13.10<br /><br />Notes:<br />a These beta estimates were calculated using the Hamada equation, bL =<br />bU[1 + (1 – T)(D/E)].<br />b These ks estimates were calculated using the CAPM, ks = kRF + (kM – kRF)b.<br />c These WACC estimates were calculated with the following equation: WACC = wd(kd)(1 – T) + (wc)(ks).<br /><br />The firm’s optimal capital structure is that capital structure which minimizes the firm’s WACC. Elliott’s WACC is minimized at a capital structure consisting of 40% debt and 60% equity. At that capital structure, the firm’s WACC is 11.45%.saleem shahzadnoreply@blogger.com0tag:blogger.com,1999:blog-3421608066886271296.post-90791632313710807952010-12-14T15:17:00.005+05:002011-01-18T15:56:10.867+05:00Chapter 14Chapter 14<br />Distributions to Shareholders:<br />Dividends and Share Repurchases<br />SOLUTIONS TO END-OF-CHAPTER PROBLEMS<br /><br />14-1 70% Debt; 30% Equity; Capital Budget = $3,000,000; NI = $2,000,000; PO = ?<br /><br />Equity retained = 0.3($3,000,000) = $900,000.<br /><br />NI $2,000,000<br />-Additions to RE 900,000<br />Earnings Remaining $1,100,000<br /><br />Payout =<br /><br /><br />14-2 P0 = $90; Split = 3 for 2; New P0 = ?<br /><br /><br /><br /><br />14-3 NI = $2,000,000; Shares = 1,000,000; P0 = $32; Repurchase = 20%; New P0 = ?<br /><br />Repurchase = 0.2 1,000,000 = 200,000 shares.<br />Repurchase amount = 200,000 $32 = $6,400,000.<br /><br />EPSOld = = = $2.00.<br /><br />P/E = = 16.<br /><br />EPSNew = = = $2.50.<br /><br />PriceNew = EPSnew P/E = $2.50(16) = $40.<br /><br /><br />14-4 Retained earnings = Net income (1 - Payout ratio)<br />= $5,000,000(0.55) = $2,750,000.<br /><br />External equity needed:<br /><br />Total equity required = (New investment)(1 - Debt ratio)<br />= $10,000,000(0.60) = $6,000,000.<br /><br />New external equity needed = $6,000,000 - $2,750,000 = $3,250,000.<br />14-5 DPS after split = $0.75.<br /><br />Equivalent pre-split dividend = $0.75(5) = $3.75.<br /><br />New equivalent dividend = Last year’s dividend(1.09)<br />$3.75 = Last year’s dividend(1.09)<br />Last year’s dividend = $3.75/1.09 = $3.44.<br /><br /><br />14-6 Step 1: Determine the capital budget by selecting those projects whose returns are greater than the project’s risk-adjusted cost of capital.<br />Projects H and L should be chosen because IRR > k, so the firm’s capital budget = $10 million.<br /><br />Step 2: Determine how much of the capital budget will be financed with equity.<br /><br />Capital Budget Equity % = Equity Required.<br />$10,000,000 0.5 = $5,000,000.<br /><br />Step 3: Determine dividends through residual model.<br /><br />$7,287,500 - $5,000,000 = $2,287,500.<br /><br />Step 4: Calculate payout ratio.<br /><br />$2,287,500/$7,287,500 = 0.3139 = 31.39%.<br /><br /><br />14-7 a. Before finding the long-run growth rate, the dividend payout ratio must be determined.<br /><br />Dividend payout ratio = DPS/EPS = $0.75/$2.25 = 0.3333.<br /><br />The firm's long-run growth rate can be found by multiplying the portion of a firm's earnings that are retained times the firm's return on equity.<br /><br />g = ROE Retention ratio<br />= (Net Income/Equity Capital) (1 - Dividend payout ratio)<br />= 18% (1 - 0.3333) = 12%.<br /><br />b. The required return can be calculated using the DCF approach.<br /><br />ks = D1/P0 + g<br />ks = $0.75/$15.00 + 0.12<br />ks = 0.17 or 17%.<br /><br /><br />c. The new payout ratio can be calculated as:<br /><br />$1.50/$2.25 = 0.6667.<br /><br />The new long-run growth rate can now be calculated as:<br /><br />g = ROE (1 - Dividend payout ratio)<br />g = 18% (1 - 0.6667) = 6%.<br /><br />The firm's required return would be:<br /><br />ks = D1/P0 + g<br />ks = $1.50/$15.00 + 0.06<br />ks = 0.16 or 16%.<br /><br />d. The firm's original plan was to issue a dividend equal to $0.75 per share, which equates to a total dividend of $0.75 times the number of shares outstanding. So, first the number of shares outstanding must be determined from the EPS.<br /><br />Amount of equity capital = Total assets Equity ratio<br />= $10 million 0.6 = $6 million.<br /><br />Net income = Equity capital ROE = $6 million 0.18 = $1.08 million.<br /><br />EPS = Net income/Number of shares<br />$2.25 = $1.08 million/Number of shares<br />Number of shares = 480,000.<br /><br />With 480,000 shares outstanding, the total dividend that would be paid would be $0.75 480,000 shares = $360,000. The firm's current market capitalization is $7.2 million, determined by 480,000 shares at $15 per share. If the stock dividend is implemented, it shall account for 5% of the firm's current market capitalization<br />($360,000/$7,200,000 = 0.05).<br /><br />e. If the total amount of value to be distributed to shareholders is $360,000, at a price of $15 per share, then the number of new shares issued would be:<br /><br />Number of new shares = Dividend value/Price per share<br />Number of new shares = $360,000/$15<br />Number of new shares = 24,000 shares.<br /><br />The stock dividend will leave the firm's net income unchanged, therefore the firm's new EPS is its net income divided by the new total number of shares outstanding.<br /><br />New EPS = Net income/(Old shares outstanding + New shares outstanding)<br />New EPS = $1,080,000/(480,000 + 24,000)<br />New EPS = $2.1429.<br /><br />The dilution of earnings per share is the difference between old EPS and new EPS.<br /><br /><br />Dilution of EPS = Old EPS - New EPS<br />Dilution of EPS = $2.25 - $2.1429<br />Dilution of EPS = $0.1071 ≈ $0.11 per share.<br /><br /><br />14-8 a. Total dividends03 = Net income Payout ratio<br />= $1,800,000 0.40<br />= $720,000.<br /><br />DPS03 = Dividends03/Shares outstanding<br />= $720,000/500,000<br />= $1.44.<br /><br />b. Dividend yield = DPS/P0<br />= $1.44/$48.00<br />= 3%.<br /><br />c. Total dividends02 = Net income02 Payout ratio<br />= $1,500,000 0.4<br />= $600,000.<br /><br />DPS02 = Dividends02/Shares outstanding<br />= $600,000/500,000<br />= $1.20.<br /><br />d. Payout ratio = Dividends/Net income<br />= $600,000/$1,800,000<br />= 0.3333 = 331/3%.<br /><br />e. Since the company would like to avoid transactions costs involved in issuing new equity, it would be best for the firm to maintain the same per-share dividend. This will provide a stable dividend to investors, yet allow the firm to expand operations without significantly affecting the dividend. A constant dividend payout ratio would cause serious fluctuations to the dividend depending on the level of earnings. If earnings were high, then dividends would be high. However, if earnings were low, then dividends would be low. This would cause great uncertainty for investors regarding dividends and would cause the firm’s stock price to decline (because investors prefer a more stable dividend policy).<br /><br /><br />14-9 a. 1. 2003 Dividends = (1.10)(2002 Dividends)<br />= (1.10)($3,600,000) = $3,960,000.<br /><br />2. 2002 Payout = $3,600,000/$10,800,000 = 0.3333 = 331/3%.<br /><br />2003 Dividends = (0.3333)(2003 Net income)<br />= (0.3333)($14,400,000) = $4,800,000.<br /><br />(Note: If the payout ratio is rounded off to 33 percent, 2003 dividends are then calculated as $4,752,000.)<br /><br />3. Equity financing = $8,400,000(0.60) = $5,040,000.<br /><br />2003 Dividends = Net income - Equity financing<br />= $14,400,000 - $5,040,000 = $9,360,000.<br />All of the equity financing is done with retained earnings as long as they are available.<br /><br />4. The regular dividends would be 10 percent above the 2002 dividends:<br /><br />Regular dividends = (1.10)($3,600,000) = $3,960,000.<br /><br />The residual policy calls for dividends of $9,360,000. Therefore, the extra dividend, which would be stated as such, would be<br /><br />Extra dividend = $9,360,000 - $3,960,000 = $5,400,000.<br /><br />An even better use of the surplus funds might be a stock repurchase.<br /><br />b. Policy 4, based on the regular dividend with an extra, seems most logical. Implemented properly, it would lead to the correct capital budget and the correct financing of that budget, and it would give correct signals to investors.<br /><br />c. ks = + g = + 10% = 15%.<br /><br />d. g = Retention rate(ROE)<br />0.10 = [1 – ($3,600,000/$10,800,000)](ROE)<br />ROE = 0.10/0.6667 = 0.15 = 15%.<br /><br />e. A 2003 dividend of $9,000,000 may be a little low. The cost of equity is 15 percent, and the average return on equity is 15 percent. However, with an average return on equity of 15 percent, the marginal return is lower yet. That suggests that the capital budget is too large, and that more dividends should be paid out. Of course, we really cannot be sure of this--the company could be earning low returns (say 10 percent) on existing assets yet have extremely profitable investment opportuni¬ties this year (say averaging 30 percent) for an expected overall average ROE of 15 percent. Still, if this year’s projects are like those of past years, then the payout appears to be slightly low.<br /><br /><br />14-10 a. Capital budget = $10,000,000; Capital structure = 60% equity, 40% debt; Common shares outstanding = 1,000,000.<br /><br />Retained earnings needed = $10,000,000(0.6) = $6,000,000.<br /><br />b. According to the residual dividend model, only $2 million is available for dividends.<br /><br />NI - Retained earnings needed for capital projects = Residual dividend<br />$8,000,000 - $6,000,000 = $2,000,000.<br /><br />DPS = $2,000,000/1,000,000 = $2.00.<br /><br />Payout ratio = $2,000,000/$8,000,000 = 25%.<br /><br />c. Retained earnings available = $8,000,000 - $3.00(1,000,000)<br />Retained earnings available = $5,000,000.<br /><br />d. No. If the company maintains its $3.00 DPS, only $5 million of retained earnings will be available for capital projects. However, if the firm is to maintain its current capital structure $6 million of equity is required. This would necessitate the company having to issue $1 million of new common stock.<br /><br />e. Capital budget = $10 million; Dividends = $3 million; NI = $8 million;<br />Capital structure = ?<br /><br />RE available = $8,000,000 - $3,000,000<br />= $5,000,000.<br /><br />Percentage of cap. budget financed with RE = = 50%.<br /><br />Percentage of cap. budget financed with debt = = 50%.<br /><br />f. Dividends = $3 million; Capital budget = $10 million; 60% equity, 40% debt; NI = $8 million.<br /><br />Equity needed = $10,000,000(0.6) = $6,000.000.<br /><br />RE available = $8,000,000 - $3.00(1,000,000)<br />= $5,000,000.<br /><br />External (New) equity needed = $6,000,000 - $5,000,000<br />= $1,000,000.<br /><br />g. Dividends = $3 million; NI = $8 million; Capital structure = 60% equity, 40% debt.<br /><br />RE available = $8,000,000 - $3,000,000<br />= 5,000,000.<br /><br />We’re forcing the RE available = Required equity to fund the new capital budget.<br /><br />Required equity = Capital budget (Target equity ratio)<br />$5,000,000 = Capital budget(0.6)<br />Capital budget = $8,333,333.<br /><br />Therefore, if Buena Terra cuts its capital budget from $10 million to $8.33 million, it can maintain its $3.00 DPS, its current capital structure, and still follow the residual dividend policy.<br /><br />h. The firm can do one of four things:<br /><br />(1) Cut dividends.<br />(2) Change capital structure, that is, use more debt.<br />(3) Cut its capital budget.<br />(4) Issue new common stock.<br /><br />Realize that each of these actions is not without consequences to the company’s cost of capital, stock price, or both.saleem shahzadnoreply@blogger.com1tag:blogger.com,1999:blog-3421608066886271296.post-49022298970545446392010-12-14T15:18:00.004+05:002011-01-18T15:54:39.999+05:00Chapter 15Chapter 15<br />Managing Current Assets<br />SOLUTIONS TO END-OF-CHAPTER PROBLEMS<br /><br />15-1 Net Float = Disbursement float - Collections float<br />= (4 $10,000) - (3 $10,000)<br />= $10,000.<br /><br /><br />15-2 Sales = $10,000,000; S/I = 2.<br /><br />Inventory = S/2<br />= = $5,000,000.<br /><br />If S/I = 5, how much cash is freed up?<br /><br />Inventory = S/5<br />= = $2,000,000.<br /><br />Cash freed = $5,000,000 - $2,000,000 = $3,000,000.<br /><br /><br />15-3 DSO = 17; Credit sales/Day = $3,500; A/R = ?<br /><br />DSO =<br />17 =<br />A/R = 17 $3,500 = $59,500.<br /><br /><br />15-4 a. Cost = (Number of locations)(Number of transfers)(Cost per transfer)<br />+ (Monthly cost)(12)<br />= (10)(260)($9.75) + ($6,500)(12) = $25,350 + $78,000<br />= $103,350.<br /><br />b. Reduction in days of float = 3 days.<br /><br />Benefit =<br />= (3)($325,000)(0.10) = $97,500.<br /><br />c. Net gain (loss) = $97,500 - $103,350 = -$5,850.<br /><br />Malitz should not initiate the lockbox system since it will cost the firm $5,850 more than it will earn on the freed funds.<br />15-5 a. 0.4(10) + 0.6(40) = 28 days.<br /><br />b. $912,500/365 = $2,500 sales per day.<br /><br />$2,500(28) = $70,000 = Average receivables.<br /><br />c. 0.4(10) + 0.6(30) = 22 days. $912,500/365 = $2,500 sales per day.<br /><br />$2,500(22) = $55,000 = Average receivables.<br /><br />Sales may also decline as a result of the tighter credit. This would further reduce receivables. Also, some customers may now take discounts further reducing receivables.<br /><br /><br />15-6 a. Setting up the formula for the cash conversion cycle, sales can be calculated.<br /><br />CCC =<br />16.79 = ($47,000/ADS) + ($66,000/ADS) - ($72,000/0.8ADS)<br />16.79 = ($47,000/ADS) + ($66,000/ADS) - ($90,000/ADS)<br />16.79 = $23,000/ADS<br />16.79ADS = $23,000<br />ADS = $1,369.863.<br /><br />Therefore, annual sales equal $500,000 ($1,369.863 365 = $500,000).<br /><br />b. Based upon the given information, the firm's current assets equal $148,750 ($35,750 + $47,000 + $66,000). Therefore, for its current ratio to increase to 2.0, it must reduce accounts payable to a level such that current liabilities total $74,375 ($148,750/2). If accrued liabilities on the balance sheet equal $13,000, accounts payable must be reduced to $61,375 ($74,375 - $13,000). The firm's new average daily cost of goods sold would equal $1,369.863 0.70 = $958.90. Combined with the original information, the new CCC can be determined as follows:<br /><br />CCC = (AR/Avg. Daily Sales) + (Inv/Avg. Daily Sales) - (AP/Avg. Daily COGS)<br />CCC = ($47,000/$1,369.863) + ($66,000/$1,369.863) - ($61,375/$958.90)<br />CCC = 34.31 + 48.18 - 64.01<br />CCC = 18.48 days.<br /><br /><br />15-7 a. Cash conversion cycle = 22 + 40 - 30 = 32 days.<br /><br />b. Working capital financing = 1,500 32 $6 = $288,000.<br /><br />c. If the payables deferral period was increased by 5 days, then its cash conversion cycle would decrease by 5 days, so its working capital financing needs would decrease by<br /><br />Decrease in working capital financing = 1,500 5 $6 = $45,000.<br />d. Cash conversion cycle = 20 + 40 - 30 = 30 days.<br />Working capital financing = 1,800 30 $7 = $378,000.<br /><br /><br />15-8 a. CCC =<br />= 75 + 38 - 30 = 83 days.<br /><br />b. Average sales per day = $3,421,875/365 = $9,375.<br />Investment in receivables = $9,375 38 = $356,250.<br /><br />c. Inventory turnover = 365/75 = 4.87.<br /><br /><br />15-9 a. Inventory conversion period = 365/Inventory turnover ratio<br />= 365/6 = 60.83 days.<br /><br />Receivables collection period = DSO = 36.5 days.<br /><br />CCC =<br />= 60.83 + 36.5 - 40 = 57.33 days.<br /><br />b. Total assets = Inventory + Receivables + Fixed assets<br />= $150,000/6 + [($150,000/365) 36.5] + $35,000<br />= $25,000 + $15,000 + $35,000 = $75,000.<br /><br />Total assets turnover = Sales/Total assets<br />= $150,000/$75,000 = 2.<br /><br />ROA = Profit margin Total assets turnover<br />= 0.06 2 = 0.12 = 12%.<br /><br />c. Inventory conversion period = 365/7.3 = 50 days.<br /><br />Cash conversion cycle = 50 + 36.5 - 40 = 46.5 days.<br /><br />Total assets = Inventory + Receivables + Fixed assets<br />= $150,000/7.3 + $15,000 + $35,000<br />= $20,548 + $15,000 + $35,000 = $70,548.<br /><br />Total assets turnover = $150,000/$70,548 = 2.1262.<br /><br />ROA = $9,000/$70,548 = 12.76%.<br /><br /><br /><br />15-10 a. Return on equity may be computed as follows:<br /><br />Tight Moderate Relaxed<br />Current assets<br />(% of sales Sales) $ 900,000 $1,000,000 $1,200,000<br />Fixed assets 1,000,000 1,000,000 1,000,000<br />Total assets $1,900,000 $2,000,000 $2,200,000<br /><br />Debt (60% of assets) $1,140,000 $1,200,000 $1,320,000<br />Equity 760,000 800,000 880,000<br />Total liab./equity $1,900,000 $2,000,000 $2,200,000<br /><br />EBIT (12% $2 million) $ 240,000 $ 240,000 $ 240,000<br />Interest (8%) 91,200 96,000 105,600<br />Earnings before taxes $ 148,800 $ 144,000 $ 134,400<br />Taxes (40%) 59,520 57,600 53,760<br />Net income $ 89,280 $ 86,400 $ 80,640<br />Return on equity 11.75% 10.80% 9.16%<br /><br />b. No, this assumption would probably not be valid in a real world situation. A firm’s current asset policies, particularly with regard to accounts receivable, such as discounts, collection period, and collection policy, may have a significant effect on sales. The exact nature of this function may be difficult to quantify, however, and determining an “optimal” current asset level may not be possible in actuality.<br /><br />c. As the answers to Part a indicate, the tighter policy leads to a higher expected return. However, as the current asset level is decreased, presumably some of this reduction comes from accounts receivable. This can be accomplished only through higher discounts, a shorter collection period, and/or tougher collection policies. As outlined above, this would in turn have some effect on sales, possibly lowering profits. More restrictive receivable policies might involve some additional costs (collection, and so forth) but would also probably reduce bad debt expenses. Lower current assets would also imply lower liquid assets; thus, the firm’s ability to handle contingencies would be impaired. Higher risk of inadequate liquidity would increase the firm’s risk of insolvency and thus increase its chance of failing to meet fixed charges. Also, lower inventories might mean lost sales and/or expensive production stoppages. Attempting to attach numerical values to these potential losses and probabilities would be extremely difficult.<br /><br /><br /><br />15-11 a. Firm’s Bank’s<br />checkbook records<br />Day 1 Deposit $1,200,000;<br />write check for<br />$1,600,000. -$ 400,000 $1,200,000<br /><br />Day 2 Write check<br />for $1,600,000. -$2,000,000 $1,200,000<br /><br />Day 3 Write check<br />for $1,600,000. -$3,600,000 $1,200,000<br /><br />Day 4 Write check<br />for $1,600,000. -$5,200,000 $1,200,000<br /><br />Day 5 Write check for<br />$1,600,000; deposit<br />$1,600,000. -$5,200,000 $1,200,000<br /><br />After the firm has reached a steady state, it must deposit $1,600,000 each day to cover the checks written four days earlier.<br /><br />b. The firm has four days of float.<br /><br />c. The firm should try to maintain a balance on the bank’s records of $1,200,000. On its own books it will have a balance of minus $5,200,000.<br /><br />d. For any level of sales, the firm will probably have a higher rate of return on assets and equity if it can reduce its total assets. By using float, SSC can reduce its cash account, by (4 $1,600,000)<br />- $1,200,000 = $5,200,000. However, they actually can reduce equity and debt by $6,000,000 as the firm has gross float of $6,400,000 - $400,000 (increase in the amount deposited in the bank) = $6,000,000, so earnings per share will be higher. In terms of the Du Pont equation, the rate of return on equity will be higher because of the reduction in total assets.<br /><br /><br />15-12 a. Presently, HGC has 5 days of collection float; under the lockbox system, this would drop to 2 days.<br /><br />$1,400,000 5 days = $7,000,000<br />$1,400,000 2 days = 2,800,000<br />$4,200,000<br /><br />HGC can reduce its cash balances by the $4,200,000 reduction in negative float.<br /><br />b. 0.10($4,200,000) = $420,000 = the value of the lockbox system on an annual basis.<br /><br />c. $420,000/12 = $35,000 = maximum monthly charge HGC can pay for the lockbox system.<br />15-13 a. Helen’s Fashion Designs<br />Cash Budget, July-December 2003<br /><br />I. Collections and Payments:<br /><br />May June July August September October November December January<br />Sales $180,000 $180,000 $360,000 $540,000 $720,000 $360,000 $360,000 $ 90,000 $180,000<br /><br />Collections:<br />1st month 18,000 18,000 36,000 54,000 72,000 36,000 36,000 9,000<br />2nd month 0 135,000 135,000 270,000 405,000 540,000 270,000 270,000<br />3rd month 0 0 27,000 27,000 54,000 81,000 108,000 54,000<br />Total collections $198,000 $351,000 $531,000 $657,000 $414,000 $333,000<br /><br />Purchases 90,000 90,000 126,000 882,000 306,000 234,000 162,000 90,000<br /><br />Payments<br />(1-mo. lag) 90,000 90,000 126,000 882,000 306,000 234,000 162,000<br /><br />II. Gain or Loss for Month:<br /><br />July August September October November December<br />Receipts:<br />Collections $198,000 $351,000 $531,000 $657,000 $414,000 $333,000<br /><br />Payments:<br />Labor and raw materials 90,000 126,000 882,000 306,000 234,000 162,000<br />Administrative salaries 27,000 27,000 27,000 27,000 27,000 27,000<br />Lease payment 9,000 9,000 9,000 9,000 9,000 9,000<br />Misc. expenses 2,700 2,700 2,700 2,700 2,700 2,700<br />Income tax 0 0 63,000 0 0 63,000<br />Progress payment 0 0 0 180,000 0 0<br />Total payments $128,700 $164,700 $983,700 $524,700 $272,700 $263,700<br /><br />Net cash gain (loss) $ 69,300 $186,300 ($452,700) $132,300 $141,300 $ 69,300<br /><br />III. Cash Surplus or Loan Requirements:<br /><br />July August September October November December<br />Cash at start of month w/o loans $132,000 $201,300 $387,600 ($ 65,100) $ 67,200 $208,500<br /><br />Cumulative cash 201,300 387,600 (65,100) 67,200 208,500 277,800<br />Less: Target cash balance 90,000 90,000 90,000 90,000 90,000 90,000<br />Cumulative surplus cash or total<br />loans outstanding to maintain<br />target balance $111,300 $297,600 ($155,100) ($22,800) $118,500 $187,800<br /><br />b. The cash budget indicates that Helen will have surplus funds available during July, August, November, and December. During September the company will need to borrow $155,100. The cash surplus that accrues during October will enable Helen to reduce the loan balance outstanding to $22,800 by the end of October.<br /><br />c. In a situation such as this, where inflows and outflows are not synchronized during the month, it may not be possible to use a cash budget centered on the end of the month. The cash budget should be set up to show the cash positions of the firm on the 5th of each month. In this way the company could establish its maximum cash requirement and use these maximum figures to estimate its required line of credit.<br />The table below shows the status of the cash account on selected dates within the month of July. It shows how the inflows accumulate steadily throughout the month and how the requirement of paying all the outflows on the 5th of the month requires that the firm obtain external financing. By July 14, however, the firm reaches the point where the inflows have offset the outflows, and by July 30 we see that the monthly totals agree with the cash budget developed earlier in Part a.<br /><br />7/2/03 7/4/03 7/5/03 7/6/03 7/14/03 7/30/03<br />Opening balance $132,000 $132,000 $132,000 $132,000 $132,000 $132,000<br /><br />Cumulative inflows<br />(1/30 receipts<br /> no. of days) 13,200 26,400 33,000 39,600 92,400 198,000<br /><br />Total cash available $145,200 $158,400 $165,000 $171,600 $224,400 $330,000<br /><br />Outflow 0 0 128,700 128,700 128,700 128,700<br /><br />Net cash position $145,200 $158,400 $ 36,300 $ 42,900 $ 95,700 $201,300<br /><br />Target cash balance 90,000 90,000 90,000 90,000 90,000 90,000<br /><br />Cash above minimum needs<br />(borrowing needs) $ 55,200 $ 68,400 ($ 53,700)($ 47,100) $ 5,700 $111,300<br /><br />d. The months preceding peak sales would show a decreased current ratio and an increased debt ratio due to additional short-term bank loans. In the following months as receipts are collected from sales, the current ratio would increase and the debt ratio would decline. Abnormal changes in these ratios would affect the firm’s ability to obtain bank credit.saleem shahzadnoreply@blogger.com0tag:blogger.com,1999:blog-3421608066886271296.post-43719646737115746582010-12-14T15:18:00.003+05:002011-01-18T15:53:21.347+05:00Chapter 16Chapter 16<br />Financing Current Assets<br />SOLUTIONS TO END-OF-CHAPTER PROBLEMS<br /><br />16-1 Nominal cost of trade credit =<br />= 0.0309 24.33 = 0.7526 = 75.26%.<br /><br />Effective cost of trade credit = (1.0309)24.33 - 1.0 = 1.0984 = 109.84%.<br /><br /><br />16-2 Effective cost of trade credit = (1 + 1/99)8.11 - 1.0<br />= 0.0849 = 8.49%.<br /><br /><br />16-3 Net purchase price of inventory = $500,000/day.<br /><br />Credit terms = 2/15, net 40.<br /><br />$500,000 15 = $7,500,000.<br /><br /><br />16-4 $25,000 interest-only loan, 11 percent nominal rate. Interest calculated as simple interest based on 365-day year. Interest for 1st month = ?<br /><br />Interest rate per day = 0.11/365 = 0.000301.<br /><br />Interest charge for period = (31)(0.11/365)($25,000)<br />= $233.56.<br /><br /><br />16-5 $15,000 installment loan, 11 percent nominal rate.<br />Effective annual rate, assuming a 365-day year = ?<br /><br />Add-on interest = 0.11($15,000) = $1,650.<br /><br />Monthly Payment = = $1,387.50.<br /><br />0 1 2 11 12<br /> • • • <br />15,000 -1,387.50 -1,387.50 -1,387.50 -1,387.50<br /><br />With a financial calculator, enter N = 12, PV = 15000, PMT = -1387.50,<br />FV = 0, and then press I to obtain 1.6432%. However, this is a monthly rate.<br /><br /><br />Effective annual rateAdd-on = (1 + kd)n - 1.0<br />= (1.016432)12 - 1.0<br />= 1.2160 - 1.0 = 0.2160 = 21.60%.<br /><br /><br />16-6 a. = 73.74%.<br /><br />b. = 14.90%.<br /><br />c. = 32.25%.<br /><br />d. = 21.28%.<br /><br />e. = 29.80%.<br /><br /><br />16-7 a. = 45.15%.<br /><br />Because the firm still takes the discount on Day 20, 20 is used as the discount period in calculating the cost of nonfree trade credit.<br /><br />b. Paying after the discount period, but still taking the discount gives the firm more credit than it would receive if it paid within 15 days.<br /><br /><br />16-8 a. Effective rate = 12%.<br /><br />b. 0 1<br /> <br />50,000 -50,000<br />- 4,500<br />-10,000 (compensating balance) 10,000<br />40,000 -44,500<br /><br />With a financial calculator, enter N = 1, PV = 40000, PMT = 0, and FV = -44500 to solve for I = 11.25%.<br /><br />Note that, if Hawley actually needs $50,000 of funds, he will have to borrow = $62,500. The effective interest rate will still be 11.25 percent.<br /><br /><br />c. 0 1<br /> <br />50,000 -50,000<br />-4,375 (discount interest) 7,500<br />-7,500 (compensating balance) -42,500<br />38,125<br /><br />With a financial calculator, enter N = 1, PV = 38125, PMT = 0, and FV = -42500 to solve for I = 11.4754% 11.48%.<br /><br />Note that, if Hawley actually needs $50,000 of funds, he will have to borrow = $65,573.77. The effective interest rate will still be 11.48 percent.<br /><br />d. Approximate annual rate = = = 16%.<br /><br />Effective Annual Rate:<br /><br />$50,000 =<br /><br />kd, the monthly interest rate, is 1.1326 percent, found with a financial calculator. Input N = 12; PV = 50000; PMT = -4166.67; FV = -4000; and I = ?. The precise effective annual rate is (1.011326)12 - 1.0 = 14.47%.<br /><br />Alternative b has the lowest effective interest rate.<br /><br /><br />16-9 Accounts payable:<br /><br />Nominal cost =<br /><br />EAR cost = (1.03093)4.5625 - 1.0 = 14.91%.<br /><br />Bank loan:<br /><br />0 1<br /> <br />500,000 -500,000<br />-60,000 (discount interest)<br />440,000<br /><br />With a financial calculator, enter N = 1, PV = 440000, PMT = 0, and FV =<br />-500000 to solve for I = 13.636% 13.64%.<br /><br />Note that, if Masson actually needs $500,000 of funds, he will have to borrow = $568,181.82. The effective interest rate will still be 13.64 percent.<br /><br />The bank loan has the lowest cost to D.J. Masson at 13.64 percent.<br /><br /><br />16-10 a. Simple interest: 12%.<br /><br />b. 3-months: (1 + 0.115/4)4 - 1 = 12.0055%, or use the interest conversion feature of your calculator as follows:<br /><br />NOM% = 11.5; P/YR = 4; EFF% = ? EFF% = 12.0055%.<br /><br />c. Add-on: Interest = Funds needed(kd).<br />Loan = Funds needed(1 + kd).<br />PMT = Loan/12.<br /><br />Assume you borrowed $100. Then, Loan = $100(1.06) = $106.<br />PMT = $106/12 = $8.8333.<br /><br />$100 = .<br /><br />Enter N = 12, PV = 100, PMT = -8.8333, FV = 0, and press I to get<br />I = 0.908032% = kd. This is a monthly periodic rate, so the effective annual rate = (1.00908032)12 - 1 = 0.1146 = 11.46%.<br /><br />d. Trade credit: 1/99 = 1.01% on discount if pay in 15 days, otherwise pay 45 days later. So, get 60 - 15 = 45 days of credit at a cost of 1/99 = 1.01%. There are 365/45 = 8.1111 periods, so the effective cost rate is:<br /><br />(1 + 1/99)8.11 - 1 = (1.0101)8.11 - 1 = 8.4934%.<br /><br />Thus, the least expensive type of credit for Yonge is trade credit with an effective cost of 8.4934%.<br /><br /><br />16-11 a. = 10 days = $10,000 10 = $100,000.<br /><br />b. There is no cost of trade credit at this point. The firm is using “free” trade credit.<br /><br />c. = 30 = $10,000 30 = $300,000.<br /><br />Nominal cost = (2/98)(365/20) = 37.24%,<br />or $74,490/($300,000 - $100,000) = 37.25%.<br /><br />Effective cost = (1 + 2/98)365/20 - 1 = 0.4459 = 44.59%.<br /><br />d. Nominal rate =<br /><br />Effective cost = (1 + 2/98)365/30 - 1 = 0.2786 = 27.86%.<br /><br /><br />16-12 a. Bank Loan<br /><br />Terms: 13 percent, discount interest<br /><br />0 1<br /> <br />300,000 -300,000<br />-39,000 (discount interest)<br />261,000<br /><br />With a financial calculator, enter N = 1, PV = 261000, PMT = 0, and<br />FV = -300000 to solve for I = 14.9425% 14.94%.<br />Note that, if Thompson actually needs $300,000 of funds, it will have to borrow = $344,827.59. The effective interest rate will still be 14.9425% 14.94%.<br /><br />Trade Credit<br /><br />Terms: 2/10, net 30. But the firm plans delaying payments 35 additional days, which is the equivalent of 2/10, net 65.<br /><br />Nominal cost =<br />= .<br /><br />Effective cost = (1 + 2/98)365/55 - 1 = 14.35%.<br /><br />Comparing effective interest costs, the Thompson Corporation might be tempted to obtain financing from a bank. (For reason see solution to Part b.)<br /><br />b. The interest rate comparison had favored trade credit, but Thompson Corporation should take into account how its trade creditors would look upon a 35-day delay in making payments. Thompson would become a “slow pay” account, and in times when suppliers were operating at full capacity, Thompson would be given poor service and would also be forced to pay on time.<br />16-13 a. Size of bank loan = (Purchases/Day)(Days late)<br />=<br />= ($600,000/60)(60 - 30) = $10,000(30) = $300,000.<br /><br />Alternatively, one could simply recognize that accounts payable must be cut to half of its existing level, because 30 days is half of 60 days.<br /><br />b. Given the limited information, the decision must be based on the rule-of-thumb comparisons, such as the following:<br /><br />1. Debt ratio = ($1,500,000 + $700,000)/$3,000,000 = 73%.<br />Raattama’s debt ratio is 73 percent, as compared to a typical debt ratio of 50 percent. The firm appears to be undercapitalized.<br /><br />2. Current ratio = $1,800,000/$1,500,000 = 1.20.<br /><br />The current ratio appears to be low, but current assets could cover current liabilities if all accounts receivable can be collected and if the inventory can be liquidated at its book value.<br /><br />The company appears to be carrying excess current assets and financing extensively with debt. Bank borrowings are already high, and the liquidity situation is poor. On the basis of these observations, the loan should be denied, and the treasurer should be advised to seek permanent capital, especially equity capital.<br /><br /><br />16-14 a. The quarterly interest rate is equal to 11.25%/4 = 2.8125%.<br /><br />Effective annual rate = (1 + 0.028125)4 - 1<br />= 1.117336 - 1 = 0.117336 = 11.73%.<br /><br />b. 0 1<br /> <br />1,500,000 -1,500,000<br />-33,750 (discount interest) 300,000<br />-300,000 (compensating balance) -1,200,000<br />1,166,250<br /><br />With a financial calculator, enter N = 1, PV = 1166250, PMT = 0, and<br />FV = -1200000 to solve for I = 2.89389% 2.89%. However, this is a periodic rate.<br /><br />Effective annual rate = (1 + 0.0289389)4 - 1 = 12.088% 12.09%.<br /><br />Note that, if Gifts Galore actually needs $1,500,000 of funds, it will have to borrow = = $1,929,260.45. The effective interest rate will still be 12.088% 12.09%.<br /><br />c. Installment loan:<br /><br />Nominal quarterly rate = = = 4.5%.<br /><br />Nominal annual rate = 4.5% 4 = 18%.<br /><br /><br />16-15 a. Malone’s current accounts payable balance represents 60 days purchases. Daily purchases can be calculated as = $8.33.<br />If Malone takes discounts then the accounts payable balance would include only 10 days purchases, so the A/P balance would be $8.33 10 = $83.33.<br /><br />If Malone doesn’t take discounts but pays in 30 days, its A/P balance would be $8.33 30 = $250.<br /><br />b. Takes Discounts:<br />If Malone takes discounts its A/P balance would be $83.33. The cash it would need to be loaned is $500 - $83.33 = $416.67.<br /><br />Since the loan is a discount loan with compensating balances, Malone would require more than a $416.67 loan.<br /><br />Face amount of loan = = $641.03.<br /><br />Doesn’t Take Discounts:<br />If Malone doesn’t take discounts, its A/P balance would be $250. The cash needed from the bank is $500 - $250 = $250.<br /><br />Face amount of loan = = $384.62.<br /><br />c. Nonfree Trade Credit:<br />Nominal annual cost:<br />= = 18.43%.<br /><br />Effective cost:<br /><br /><br />Bank Loan: 15% Discount Loan with 20% compensating balance.<br />Assume the firm doesn’t take discounts so it needs $250 and borrows $384.62. (The cost will be the same regardless of how much the firm borrows.)<br /><br />0 1<br /> <br />384.62 -384.62<br />-57.69 Discount interest +76.92<br />-76.92 Compensating balance -307.70<br />250.00<br /><br />With a financial calculator, input the following data, N = 1, PV = 250, PMT = 0, FV = -307.70, and then solve for I = 23.08%.<br /><br />Just to show you that it doesn’t matter how much the firm borrows, assume the firm takes discounts and it reduces A/P to $83.33 so it needs $416.67 cash and borrows $641.03.<br /><br />0 1<br /> <br />641.03 -641.03<br />-96.15 Discount interest +128.21<br />-128.21 Compensating balance -512.82<br />416.67<br /><br />With a financial calculator, input the following data, N = 1, PV = 416.67, PMT = 0, FV = -512.82, and then solve for I = 23.08%.<br /><br />Because the cost of nonfree trade credit is less than the cost of the bank loan, Malone should forge discounts and reduce its payables only to $250,000.<br /><br />d. Pro Forma Balance Sheet (Thousands of Dollars):<br /><br />Casha $ 126.9 Accounts payable $ 250.0<br />Accounts receivable 450.0 Notes payableb 434.6<br />Inventory 750.0 Accrued liabilities 50.0<br />Prepaid interest 57.7<br />Total current Total current<br />assets $1,384.6 liabilities $ 734.6<br />Fixed assets 750.0 Long-term debt 150.0<br />Common equity 1,250.0<br />Total assets $2,134.6 Total claims $2,134.6<br /><br />a $384,615(0.2) = $76,923 = Compensating balance.<br />Cash = $50 + $76.923 = $126.9.<br />b Notes payable = $50 + $384.6 = $434.6.<br /><br />e. To reduce the accounts payable by $250,000, which reflects the 1% discount, Malone must pay the full cost of the payables, which is $250,000/0.99 = $252,525.25. The lost discount is the difference between the full cost of the payables and the amount that is reported net of discount: Lost discount = $252,525.25 - $250,000.00 = $2,525.25. The after-tax cost of the lost discount is $2,525.25(1 - 0.40) = $1,515.15. Notice that this provides a tax shield in the amount of $2,525.25(0.40) = $1,010.10. The total amount of cash that Malone needs to pay down $250,000 of accounts payable is the gross amount minus the tax shield: $252,525.25 - $1,010.10 = $251,515.15.<br /><br />Face amount of loan = = $386,946.38.<br /><br />Pro Forma Balance Sheet (Thousands of Dollars:<br /><br />Casha $ 127.4 Accounts payable $ 250.0<br />Accounts receivable 450.0 Notes payableb 436.9<br />Inventory 750.0 Accrued liabilities 50.0<br />Prepaid interest 58.0<br />Total current Total current<br />assets $1,385.4 liabilities $ 736.9<br />Fixed assets 750.0 Long-term debt 150.0<br />Common equityc 1,248.5<br />Total assets $2,135.4 Total claims $2,135.4<br /><br />a $386,946.38(0.2) = $77,389.27 = Compensating balance.<br />Cash = $50 + $77.4 = $127.4.<br />b Notes payable = $50 + $386.9 = $436.9.<br />c Common equity = Previous common equity - after-tax discount<br />= $1,250 - $1.5 = $1,248.5.<br /><br /><br />16-16 a. 1. Line of credit:<br />Commitment fee = (0.005)($2,000,000)(335/365) = $ 9,178<br />Interest = (0.11)(30/365)($2,000,000) = 18,082<br />Total $27,260<br /><br />2. Trade discount:<br />a. = = 24.83% 24.8%.<br /><br />Total cost = 0.2483($2,000,000)(30/365) = $40,816.<br /><br />b. Effective cost = (1 + 2/98)365/30 - 1 = 0.2786 = 27.86%.<br /><br />Total cost = 0.2786($2,000,000)(30/365) = $45,804.<br /><br />3. 30-day commercial paper:<br />Interest = (0.095)($2,000,000)(30/365) = $15,616<br />Transaction fee = (0.005)($2,000,000) = 10,000<br />$25,616<br /><br /><br />4. 60-day commercial paper:<br />Interest = (0.09)($2,000,000)(60/365) = $29,589<br />Transaction fee = (0.005)($2,000,000) = 10,000<br />$39,589<br /><br />Marketable securities interest received<br />= (0.094)($2,000,000)(30/365) = -15,452<br /><br />Transactions cost, marketable securities<br />= (0.004)($2,000,000) = +8,000<br />$32,137<br /><br />The 30-day commercial paper has the lowest cost.<br /><br />b. The lowest cost of financing is not necessarily the best. The use of 30-day commercial paper is the cheapest; however, sometimes the commercial paper market is tight and funds are not available. This market also is impersonal. A banking arrangement may provide financial counseling and a long-run relationship in which the bank performs almost as a “partner and counselor” to the firm. Note also that while the use of 60-day commercial paper is more expensive than the use of 30-day paper, it provides more flexibility in the event the money is needed for more than 30 days. However, the line of credit provides even more flexibility than the 60-day commercial paper and at a lower cost.saleem shahzadnoreply@blogger.com0tag:blogger.com,1999:blog-3421608066886271296.post-66407364048123363262010-12-14T15:19:00.001+05:002011-01-18T15:51:58.679+05:00Chapter 17Chapter 17<br />Financial Planning and Forecasting<br />SOLUTIONS TO END-OF-CHAPTER PROBLEMS<br /><br />17-1 AFN = (A*/S0)S - (L*/S0)S - MS1(RR)<br />= $1,000,000 - $1,000,000<br />- 0.05($6,000,000)(0.3)<br />= (0.6)($1,000,000) - (0.1)($1,000,000) - ($300,000)(0.3)<br />= $600,000 - $100,000 - $90,000<br />= $410,000.<br /><br /><br />17-2 AFN =<br />= (0.8)($1,000,000) - $100,000 - $90,000<br />= $800,000 - $190,000<br />= $610,000.<br /><br />The capital intensity ratio is measured as A*/S0. This firm’s capital intensity ratio is higher than that of the firm in Problem 17-1; therefore, this firm is more capital intensive--it would require a large increase in total assets to support the increase in sales.<br /><br /><br />17-3 AFN = (0.6)($1,000,000) - (0.1)($1,000,000) - 0.05($6,000,000)(1)<br />= $600,000 - $100,000 - $300,000<br />= $200,000.<br /><br />Under this scenario the company would have a higher level of retained earnings, which would reduce the amount of additional funds needed.<br /><br /><br />17-4 Sales = $300,000,000; gSales = 12%; Inv. = $25 + 0.125(Sales).<br /><br />S1 = $300,000,000 1.12 = $336,000,000.<br /><br />Inv. = $25 + 0.125($336)<br />= $67 million.<br /><br />Sales/Inv. = $336,000,000/$67,000,000 5.0149 = 5.01.<br /><br /><br />17-5 Sales = $5,000,000,000; FA = $1,700,000,000; FA are operated at 90% capacity.<br /><br />a. Full capacity sales = $5,000,000,000/0.90 = $5,555,555,556.<br /><br />b. Target FA/S ratio = $1,700,000,000/$5,555,555,556 = 30.6%.<br /><br />c. Sales increase 12%; FA = ?<br /><br />S1 = $5,000,000,000 1.12 = $5,600,000,000.<br /><br />No increase in FA up to $5,555,555,556.<br /><br />FA = 0.306 ($5,600,000,000 - $5,555,555,556)<br />= 0.306 ($44,444,444)<br />= $13,600,000.<br /><br /><br />17-6 a. 2002 Forecast Basis 2003<br />Sales $700 1.25 $875.00<br />Oper. costs 500 0.70 Sales 612.50<br />EBIT $200 $262.50<br />Interest 40 40.00<br />EBT $160 $222.50<br />Taxes (40%) 64 89.00<br />Net income $ 96 $133.50<br /><br />Dividends (33.33%) $ 32 $ 44.50<br />Addit. to R/E $ 64 $ 89.00<br /><br />b. Dividends = ($44.50 - $32.00)/$32.00 = 39.06%.<br /><br /><br />17-7 Actual Forecast Basis Pro Forma<br />Sales $3,000 1.10 $3,300<br />Oper.costs excluding<br />depreciation 2,450 0.80 Sales 2,640<br />EBITDA $ 550 $ 660<br />Depreciation 250 0.0833 Sales 275<br />EBIT $ 300 $ 385<br />Interest 125 125<br />EBT $ 175 $ 260<br />Taxes (40%) 70 104<br />Net income $ 105 $ 156<br /><br /><br />17-8 a. = .<br /><br />$1,200,000 = $375,000 + Long-term debt + $425,000 + $295,000<br />Long-term debt = $105,000.<br /><br />Total debt = Accounts payable + Long-term debt<br />= $375,000 + $105,000 = $480,000.<br /><br />Alternatively,<br /><br />Total debt = - Common stock – Retained earnings<br />= $1,200,000 - $425,000 - $295,000 = $480,000.<br /><br /><br />b. Assets/Sales (A*/S0) = $1,200,000/$2,500,000 = 48%.<br />L*/Sales (L*/S0) = $375,000/$2,500,000 = 15%.<br />2003 Sales = (1.25)($2,500,000) = $3,125,000.<br /><br />S = $3,125,000 - $2,500,000 = $625,000.<br /><br />AFN = (A*/S0)(S) - (L*/S0)(S) - MS1(RR) - New common stock<br />= (0.48)($625,000) - (0.15)($625,000)<br />- (0.06)($3,125,000)(0.6) - $75,000<br />= $300,000 - $93,750 - $112,500 - $75,000 = $18,750.<br /><br />Alternatively, using the percent of sales method:<br /><br />Forecast<br />Basis Additions (New 2003<br />2002 2003 Sales Financing, R/E) Pro Forma<br />Total assets $1,200,000 0.48 $1,500,000<br /><br />Current liabilities $ 375,000 0.15 $ 468,750<br />Long-term debt 105,000 105,000<br />Total debt $ 480,000 $ 573,750<br />Common stock 425,000 75,000* 500,000<br />Retained earnings 295,000 112,500** 407,500<br />Total common equity $ 720,000 $ 907,500<br />Total liabilities<br />and equity $1,200,000 $1,481,250<br /><br />AFN = New long-term debt = $ 18,750<br /><br />*Given in problem that firm will sell new common stock = $75,000.<br /><br />**PM = 6%; RR = 60%; NI2003 = $2,500,000 1.25 0.06 = $187,500.<br />Addition to RE = NI RR = $187,500 0.6 = $112,500.<br /><br /><br />17-9 S2002 = $2,000,000; A2002 = $1,500,000; CL2002 = $500,000;<br />NP2002 = $200,000; A/P2002 = $200,000; Accrued liabilities2002 = $100,000;<br />A*/S0 = 0.75; PM = 5%; RR = 40%; S?<br /><br />AFN = (A*/S0)S - (L*/S0)S - MS1(RR)<br />= (0.75)S - S -(0.05)(S1)(0.4)<br />= (0.75)S - (0.15)S - (0.02)S1<br />= (0.6)S - (0.02)S1<br />= 0.6(S1 - S0) - (0.02)S1<br />= 0.6(S1 - $2,000,000) - (0.02)S1<br />= 0.6S1 - $1,200,000 - 0.02S1<br />$1,200,000 = 0.58S1<br />$2,068,965.52 = S1.<br /><br />Sales can increase by $2,068,965.52 - $2,000,000 = $68,965.52 without additional funds being needed.<br /><br /><br /><br />17-10 Sales = $320,000,000; gSales = 12%; Rec. = $9.25 + 0.07(Sales).<br /><br />S1 = $320,000,000 1.12 = $358,400,000.<br /><br />Rec. = $9.25 + 0.07($358.4)<br />= $34.338 million.<br /><br />DSO = Rec./(Sales/365)<br />= $34,338,000/($358,400,000/365)<br />= 34.97 days 35 days.<br /><br /><br />17-11 Sales = $110,000,000; gSales = 5%; Inv. = $9 + 0.0875(Sales).<br /><br />S1 = $110,000,000 1.05 = $115,500,000.<br /><br />Inv. = $9 + 0.0875($115.5)<br />= $19.10625 million.<br /><br />Sales/Inv. = $115,500,000/$19,106,250<br />= 6.0451.<br /><br /><br />17-12 a. Sales = $2,000,000,000; FA = $600,000,000; FA are operated at 80 capacity.<br /><br />= Actual sales/(% of capacity at which FA are operated)<br />= $2,000,000,000/0.80<br />= $2,500,000,000.<br /><br />b. Target FA/Sales ratio = $600,000,000/$2,500,000,000<br />= 0.24 = 24.0%.<br /><br />c. Sales increase 30%; FA = ?<br />S1 = $2,000,000,000 1.30 = $2,600,000,000.<br />No increase in FA up to $2,500,000,000.<br /><br />FA = 0.24 ($2,600,000,000 $2,500,000,000)<br />= 0.24 $100,000,000<br />= $24,000,000.<br /><br /><br />17-13 a. Forecast<br />2002 Basis 2003<br />Sales $1,528 1.20 $1,833.60<br />Operating costs 933 0.60 Sales 1,100.16<br />EBIT $ 595 $ 733.44<br />Interest 95 95.00<br />EBT $ 500 $ 638.44<br />Taxes (40%) 200 255.38<br />Net income $ 300 $ 383.06<br /><br />Dividends (25%) $ 75 $ 95.77<br />Addition to retained earnings $ 225 $ 287.29<br />b. From the first question we know that the new dividend amount is $95.77.<br />Dividends = ($95.77 $75.00)/$75.00 = 0.2769 = 27.69%.<br /><br /><br />17-14 a. AFN = (A*/S0)(S) - (L*/S0)(S) - MS1(RR)<br />= = $13.44 million.<br /><br />b. Tozer Computers<br />Pro Forma Balance Sheet<br />December 31, 2003<br />(Millions of Dollars)<br /><br />2003<br />Forecast Pro Forma<br />Basis 2003 after<br />2002 2003 Sales Additions Pro Forma Financing Financing<br />Cash $ 3.5 0.01 $ 4.20 $ 4.20<br />Receivables 26.0 0.0743 31.20 31.20<br />Inventories 58.0 0.1657 69.60 69.60<br />Total current<br />assets $ 87.5 $105.00 $105.00<br />Net fixed assets 35.0 0.1000 42.00 42.00<br />Total assets $122.5 $147.00 $147.00<br /><br />Accounts payable $ 9.0 0.0257 $ 10.80 $ 10.80<br />Notes payable 18.0 18.00 +13.44 31.44<br />Accrued liab. 8.5 0.0243 10.20 10.20<br />Total current<br />liabilities $ 35.5 $ 39.00 $ 52.44<br />Mortgage loan 6.0 6.00 6.00<br />Common stock 15.0 15.00 15.00<br />Retained earnings 66.0 7.56* 73.56 73.56<br />Total liab.<br />and equity $122.5 $133.56 $147.00<br /><br />AFN = $ 13.44<br />*PM = $10.5/$350 = 3%.<br />RR = = 60%.<br />NI = $350 1.2 0.03 = $12.6.<br />Addition to RE = NI RR<br />= $12.6 0.6 = $7.56.<br /><br />c. Current ratio = $105/$52.44 = 2.00.<br /><br />The current ratio is poor compared to 2.5 in 2002 and the industry average of 3.<br /><br />Debt/Total assets = $58.44/$147 = 39.8%.<br /><br />The debt-to-total assets ratio is too high compared to 33.9 percent in 2002 and a 30 percent industry average.<br /><br />=<br />=<br />The rate of return on equity is good compared to 13 percent in 2002 and a 12 percent industry average.<br /><br />d. 1. =<br />= - (0.03)(0.6)($364 + $378 + $392 + $406 + $420)<br />= $24.5 - $3.5 - $35.28<br />= -$14.28 million surplus funds.<br /><br />2. Tozer Computers<br />Pro Forma Balance Sheet<br />December 31, 2007<br />(Millions of Dollars)<br /><br />2007<br />Forecast Pro Forma<br />Basis 2007 after<br />2002 2007 Sales Additions Pro Forma Financing Financing<br />Total curr. assets $ 87.50 0.25 $105.00 $105.00<br />Net fixed assets 35.00 0.10 42.00 42.00<br />Total assets $122.50 $147.00 $147.00<br /><br />Accounts payable $ 9.00 0.0257 $ 10.80 $ 10.80<br />Notes payable 18.00 18.00 -14.28 3.72<br />Accrued liab. 8.50 0.0243 10.20 10.20<br />Total current<br />liabilities $ 35.50 $ 39.00 $ 24.72<br />Mortgage loan 6.00 6.00 6.00<br />Common stock 15.00 15.00 15.00<br />Retained earnings 66.00 $35.28* 101.28 101.28<br />Total liab.<br />and equity $122.50 $161.28 $147.00<br /><br />AFN = -$14.28<br /><br />*PM = 3%; Payout = 40%.<br />NI = 0.03 ($364 + $378 + $392 + $406 + $420) = $58.8.<br />Addition to RE = NI RR = $58.8 0.6 = $35.28.<br /><br />3. Current ratio = $105/$24.72 = 4.25 (good).<br /><br />Debt/Total assets = $30.72/$147 = 20.9% (good).<br /><br />Return on equity = $12.6/$116.28 = 10.84% (low).*<br /><br />*The rate of return declines because of the decrease in the debt/assets ratio. The firm might, with this slow growth, consider a dividend increase. A dividend increase would reduce future increases in retained earnings, and in turn, common equity, which would help boost the ROE.<br /><br />e. Tozer probably could carry out either the slow growth or fast growth plan, but under the fast growth plan (20 percent per year), the risk ratios would deteriorate, indicating that the company might have trouble with its bankers and would be increasing the odds of bankruptcy.<br /><br /><br /><br />17-15 a. = = = $48,000.<br /><br />% increase = = = 0.33 = 33%.<br /><br />Therefore, sales could expand by 33 percent before the firm would need to add fixed assets.<br /><br />b. Krogh Lumber<br />Pro Forma Income Statement<br />December 31, 2003<br />(Thousands of Dollars)<br /><br />Forecast 2003<br />2002 Basis Pro Forma<br />Sales $36,000 1.25 $45,000<br />Operating costs 30,783 0.8551 38,479<br />EBIT $ 5,217 $ 6,521<br />Interest 1,017 1,017<br />EBT $ 4,200 $ 5,504<br />Taxes (40%) 1,680 2,202<br />Net income $ 2,520 $ 3,302<br /><br />Dividends (60%) $ 1,512 $ 1,981<br />Addition to RE $ 1,008 $ 1,321<br /><br />Krogh Lumber<br />Pro Forma Balance Sheet<br />December 31, 2003<br />(Thousands of Dollars)<br /><br />Forecast 2003 2003<br />Basis 1st 2nd<br />2002 2003 Sales Additions Pass AFN Pass<br />Cash $ 1,800 0.05 $ 2,250 $ 2,250<br />Receivables 10,800 0.30 13,500 13,500<br />Inventories 12,600 0.35 15,750 15,750<br />Total current<br />assets $25,200 $31,500 $31,500<br />Net fixed assets 21,600 21,600* 21,600<br />Total assets $46,800 $53,100 $53,100<br /><br />Accounts payable $ 7,200 0.20 $ 9,000 $ 9,000<br />Notes payable 3,472 3,472 +2,549 6,021<br />Accrued liab. 2,520 0.07 3,150 3,150<br />Total current<br />liabilities $13,192 $15,622 $18,171<br />Mortgage bonds 5,000 5,000 5,000<br />Common stock 2,000 2,000 2,000<br />Retained earnings 26,608 1,321** 27,929 27,929<br />Total liabilities<br />and equity $46,800 $50,551 $53,100<br /><br />AFN = $ 2,549<br />*From Part a we know that sales can increase by 33% before additions to fixed assets are needed.<br /><br />**See income statement.<br />c. The rate of return projected for 2003 under the conditions in Part b is (calculations in thousands):<br /><br />ROE = = 11.03%.<br /><br />If the firm attained the industry average DSO and inventory turn¬over ratio, this would mean a reduction in finan¬cial requirements of:<br /><br />Receivables: = 90<br />New A/R = $11,096.<br /><br /> in A/R = $13,500 - $11,096 = $2,404.<br /><br />Inventory: = 3.33; Inv. = $13,500.<br /><br /> in Inv. = $15,750 - $13,500 = $2,250.<br /><br />Total in assets = $2,404 + $2,250 = $4,654.<br /><br />If this freed-up capital was used to reduce equity, then common equity would be $29,929 - $4,654 = $25,275. Assuming no change in net income, the new ROE would be:<br /><br />ROE = = 13.06%.<br /><br />One would, in a real analysis, want to consider both the feasibility of maintaining sales if receivables and inven¬tories were reduced and also other possible effects on the profit margin. Also, note that the current ratio was $25,200/$13,192 = 1.91 in 2002. It is projected to decline in Part b to $31,500/$18,171 = 1.73, and the latest change would cause a further reduction to ($31,500 - $4,654)/$18,171 = 1.48. Creditors might not tolerate such a reduction in liquidity and might insist that at least some of the freed-up capital be used to reduce notes payable. Still, this would reduce interest charges, which would increase the profit margin, which would in turn increase the ROE. Management should always consider the possibility of changing ratios as part of financial projections.<br /><br /><br /><br />17-16 a. Morrissey Technologies Inc.<br />Pro Forma Income Statement<br />December 31, 2003<br /><br />Forecast 2003<br />2002 Basis Pro Forma<br />Sales $3,600,000 1.10 $3,960,000<br />Operating Costs 3,279,720 0.9110 3,607,692<br />EBIT $ 320,280 $ 352,308<br />Interest 20,280 20,280<br />EBT $ 300,000 $ 332,028<br />Taxes (40%) 120,000 132,811<br />Net income $ 180,000 $ 199,217<br /><br />Dividends: $1.08 100,000 = $ 108,000 $ 112,000*<br />Addition to RE: $ 72,000 $ 87,217<br /><br />*2003 Dividends = $1.12 100,000 = $112,000.<br /><br />Morrissey Technologies Inc.<br />Pro Forma Balance Statement<br />December 31, 2003<br /><br />Forecast<br />Basis 2003<br />2002 2003 Sales Additions Pro Forma<br />Cash $ 180,000 0.05 $ 198,000<br />Receivables 360,000 0.10 396,000<br />Inventories 720,000 0.20 792,000<br />Total current<br />assets $1,260,000 $1,386,000<br />Fixed assets 1,440,000 0.40 1,584,000<br />Total assets $2,700,000 $2,970,000<br /><br />Accounts payable $ 360,000 0.10 $ 396,000<br />Notes payable 156,000 156,000<br />Accrued liab. 180,000 0.05 198,000<br />Total current<br />liabilities $ 696,000 $ 750,000<br />Common stock 1,800,000 1,800,000<br />Retained earnings 204,000 87,217* 291,217<br />Total liab.<br />and equity $2,700,000 $2,841,217<br /><br />AFN = $ 128,783<br /><br />*See income statement.<br /><br /><br />b. AFN = $2,700,000/$3,600,000(Sales)<br />- ($360,000 + $180,000)/$3,600,000(Sales)<br />- (0.05)($3,600,000 + Sales)0.4<br />$0 = 0.75(Sales) - 0.15(Sales) - 0.02(Sales) - $72,000<br />$0 = 0.58(Sales) - $72,000<br />$72,000 = 0.58(Sales)<br />Sales = $124,138.<br /><br />Growth rate in sales =<br /><br /><br />17-17 a. & b. Lewis Company<br />Pro Forma Income Statement<br />December 31, 2003<br />(Thousands of Dollars)<br /><br />2002 Forecast Basis 2003 Pro Forma<br />Sales $8,000 1.2 $9,600<br />Operating costs 7,450 0.9313 8,940<br />EBIT $ 550 $ 660<br />Interest 150 150<br />EBT $ 400 $ 510<br />Taxes (40%) 160 204<br />Net income $ 240 $ 306<br /><br />Dividends: $1.04 150 = $ 156 $1.10 150 = $ 165<br />Addition to R.E.: $ 84 $ 141<br /><br /><br />Lewis Company<br />Pro Forma Balance Sheet<br />December 31, 2003<br />(Thousands of Dollars)<br /><br />Forecast 1st 2nd<br />Basis Pass AFN Pass<br />2002 2003 Sales Additions 2003 Effects 2003<br />Cash $ 80 0.010 $ 96 $ 96<br />Receivables 240 0.030 288 288<br />Inventories 720 0.090 864 864<br />Total current<br />assets $1,040 $1,248 $1,248<br />Fixed assets 3,200 0.400 3,840 3,840<br />Total assets $4,240 $5,088 $5,088<br /><br />Accounts payable 160 0.020 $ 192 $ 192<br />Accrued liab. 40 0.005 48 48<br />Notes payable 252 252 + 51** 303<br />Total current<br />liabilities $ 452 $ 492 $ 543<br />Long-term debt 1,244 1,244 +248** 1,492<br />Total debt $1,696 $1,736 $2,035<br />Common stock 1,605 1,605 +368** 1,973<br />Retained earnings 939 141* 1,080 1,080<br />Total liabilities<br />and equity $4,240 $4,421 $5,088<br /><br />AFN = $ 667<br /><br />*See income statement.<br /><br />**CA/CL = 2.3; D/A = 40%.<br />Maximum total debt = 0.4 $5,088 = $2,035.<br />Maximum increase in debt = $2,035 - $1,736 = $299.<br />Maximum current liabilities = $1,248/2.3 = $543.<br />Increase in notes payable = $543 - $492 = $51.<br />Increase in long-term debt = $299 - $51 = $248.<br />Increase in common stock = $667 - $299 = $368.saleem shahzadnoreply@blogger.com0tag:blogger.com,1999:blog-3421608066886271296.post-56099327207797942842010-12-14T15:21:00.001+05:002011-01-18T15:50:09.663+05:00Chapter 18Chapter 18<br />Derivatives and Risk Management<br />SOLUTIONS TO END-OF-CHAPTER PROBLEMS<br /><br />18-1 Call option’s market price = $7; Stock’s price = $30; Option exercise price = $25.<br /><br />a. Exercise value = Current stock price - Exercise price<br />= $30 - $25<br />= $5.00.<br /><br />b. Premium value = Option’s market price - Exercise value<br />= $7 - $5<br />= $2.00.<br /><br /><br />18-2 a. The value of an option increases as the stock price increases, but by less than the stock price increase.<br /><br />b. An increase in the volatility of the stock price increases the value of an option. The riskier the underlying security, the more valuable the option.<br /><br />c. As the risk-free rate increases, the option’s value increases.<br /><br />d. The shorter the time to expiration of the option, the lower the value of the option. The option’s value depends on the chances for an increase in the price of the underlying stock, and the longer the option has to go, the higher the stock price may climb.<br /><br />Therefore, conditions a, b, and c will cause an option’s market value to increase.<br /><br /><br />18-3 P = $15; X = $15; t = 0.5; kRF = 0.10; 2 = 0.12; d1 = 0.32660;<br />d2 = 0.08165; N(d1) = 0.62795; N(d2) = 0.53252; V = ?<br /><br />Using the Black-Scholes Option Pricing Model, you calculate the option’s value as:<br /><br />V = P[N(d1)] - [N(d2)]<br />= $15(0.62795) - $15e(-0.10)(0.5)(0.53252)<br />= $9.4193 - $15(0.9512)(0.53252)<br />= $9.4193 - $7.5982<br />= $1.8211 $1.82.<br /><br /><br />18-4 Option’s exercise price = $15; Exercise value = $22; Premium value = $5;<br />V = ? P0 = ?<br /><br />Premium = Market price - Exercise value<br />$5 = V - $22<br />V = $27.<br /><br />Exercise value = P0 - Exercise price<br />$22 = P0 - $15<br />P0 = $37.<br /><br /><br />18-5 Futures contract settled at 100 16/32 percent of $100,000 contract value, so PV = 1.005 $1,000 = $1,005 100 bonds = $100,500. Using a financial calculator, we can solve for kd as follows:<br /><br />N = 40; PV = -1005; PMT = 30; FV = 1000; solve for I = kd = 2.9784% 2 = 5.9569% 5.96%.<br /><br />If interest rates increase to 6.96 percent, then we would solve for PV as follows:<br /><br />N = 40; I = 6.96/2 = 3.48; PMT = 30; FV = 1000; solve for PV = $897.1769 100 = $89,717.69. Thus, the contract’s value has decreased from $105,000 to $89,717.69.<br /><br /><br />18-6 a. In this situation, the firm would be hurt if interest rates were to rise by December, so it would use a short hedge, or sell futures contracts. Since futures contracts are for $100,000 in Treasury bonds, the firm must sell 200 contracts to cover its planned $20,000,000 December bond issue. Since futures maturing in December are selling for 108 28/32 of par, the value of Zinn’s futures is about $21,775,000. Should interest rates rise by December, Zinn Company will be able to repurchase the futures contracts at a lower cost, which will help offset their loss from financing at the higher interest rate. Thus, the firm has hedged against rising interest rates.<br /><br />b. The firm would now pay 13 percent on the bonds. With an 11 percent coupon rate, the bond issue would bring in only $17,796,299, so the firm would lose $20,000,000 - $17,796,299 = $2,203,701:<br /><br />N = 20; I = 6.5; PMT = 1100000; FV = 20000000; and solve for PV = $17,796,299.<br /><br />However, the value of the short futures position began at $21,775,000:<br /><br />108 28/32 of $20,000,000 = 1.08875($20,000,000) = $21,775,000, or roughly N = 40; PMT = 600000; FV = 20000000; and PV = -21775000; and solve for I/2 = 2.638177.<br /><br />I = 2.638177% 2 = 5.276354% 5.3%.<br /><br />(Note that the future contracts are on hypothetical 20-year, 6 percent semiannual coupon bonds that are yielding about 5.3 percent.)<br />Now, if interest rates increased by 200 basis points, to 7.3 percent, the value of the futures contract will drop to $17,287,299:<br /><br />N = 40; I = 7.3/2 = 3.65; PMT = 600000; FV = 20000000; and solve for PV = $17,287,299.<br /><br />Since Zinn Company sold the futures contracts for $21,775,000, and will, in effect, buy them back at $17,287,299, the firm would make a $21,775,000 - $17,287,299 = $4,487,701 profit on the transaction ignoring transaction costs.<br />Thus, the firm gained $4,487,701 on its futures position, but lost $2,203,701 on its underlying bond issue. On net, it gained $4,487,701 - $2,203,701 = $2,284,000.<br /><br />c. In a perfect hedge, the gains on futures contracts exactly offset losses due to rising interest rates. For a perfect hedge to exist, the underlying asset must be identical to the futures asset. Using the Zinn Company example, a futures contract must have existed on Zinn’s own debt (it existed on Treasury bonds) for the company to have an opportunity to create a perfect hedge. In reality, it is virtually impossible to create a perfect hedge, since in most cases the underlying asset is not identical to the futures asset.<br /><br /><br />18-7 a. The current exercise value of the call option is max(0, $60 - $55) = $5. Since the market value of the option is $9.29, the premium associated with the call is $4.29. The current exercise value of the put option is max(0, $55 - $60) = $0. Since the market value of the option is $3.06, the premium associated with the put is $3.06.<br /><br />b. Remember, that the options will only be exercised if they yield a positive payoff. In this case, the put option will not be exercised. In addition, the initial investments for the options will be the market values of the options. The returns under each of the scenarios are summarized below:<br /><br />Investment Returns<br />Own stock [($70 - $60)/$60] = 16.67%.<br />Buy call option [($70 - $55)/$9.29] - 1 = 61.46%.<br />Buy put option [($0)/$3.06] - 1 = -100%.<br /><br />c. In this case, the call option will not be exercised. The returns under each of the scenarios are summarized below:<br /><br />Investment Returns<br />Own stock [($50 - $60)/$60] = -16.67%.<br />Buy call option [($0)/$9.29] - 1 = -100%.<br />Buy put option [($55 - $50)/$3.06] - 1 = 63.40%.<br /><br /><br />d. Recall, that the stock price is expected to be either $50 or $70, with equal probability. If Audrey buys 0.6 shares of stock and sells one call option, her expected payoffs are:<br /><br />Ending price 0.60 = Ending stock value Ending option value<br />$50 0.60 = $30 $ 0<br />$70 0.60 = $42 $15<br /><br />Audrey’s investment strategy would yield a payoff of $30 - $0 = $30, if the ending stock price is $50. Her strategy has a payoff of $42 - $15 = $27, if the ending stock price is $70. This is not a riskless hedged portfolio.<br /><br />e. Recall, that the stock price is expected to be either $50 or $70, with equal probability. If Audrey buys 0.75 shares of stock and sells one call option, her expected payoffs are:<br /><br />Ending price 0.75 = Ending stock value Ending option value<br />$50 0.75 = $37.50 $ 0<br />$70 0.75 = $52.50 $15<br /><br />Audrey’s investment strategy would yield a payoff of $37.50 - $0 = $37.50, if the ending stock price is $50. Her strategy has a payoff of $52.50 - $15 = $37.50, if the ending stock price is $70. Since her payoff is guaranteed to be $37.50, regardless of the ending stock price, this is a riskless hedged portfolio.saleem shahzadnoreply@blogger.com0tag:blogger.com,1999:blog-3421608066886271296.post-91790092127893885672010-12-14T13:27:00.003+05:002011-01-12T16:25:58.887+05:00Chapter 5<div align="center">Chapter 5<br />Risk and Rates of Return<br />SOLUTIONS TO END-OF-CHAPTER PROBLEMS<br /><br /><br /><br />5-1 = (0.1)(-50%) + (0.2)(-5%) + (0.4)(16%) + (0.2)(25%) + (0.1)(60%)<br />= 11.40%.<br /><br />2 = (-50% - 11.40%)2(0.1) + (-5% - 11.40%)2(0.2) + (16% - 11.40%)2(0.4)<br />+ (25% - 11.40%)2(0.2) + (60% - 11.40%)2(0.1)<br /><br />2 = 712.44; = 26.69%.<br /><br />CV = = 2.34.<br /><br /><br />5-2 Investment Beta<br />$35,000 0.8<br />40,000 1.4<br />Total $75,000<br /><br />bp = ($35,000/$75,000)(0.8) + ($40,000/$75,000)(1.4) = 1.12.<br /><br /><br />5-3 kRF = 5%; RPM = 6%; kM = ?<br /><br />kM = 5% + (6%)1 = 11%.<br /><br />k when b = 1.2 = ?<br /><br />k = 5% + 6%(1.2) = 12.2%.<br /><br /><br />5-4 kRF = 6%; kM = 13%; b = 0.7; k = ?<br /><br />k = kRF + (kM - kRF)b<br />= 6% + (13% - 6%)0.7<br />= 10.9%.<br /><br /><br />5-5 a. k = 11%; kRF = 7%; RPM = 4%.<br /><br />k = kRF + (kM – kRF)b<br />11% = 7% + 4%b<br />4% = 4%b<br />b = 1.<br /><br /><br />b. kRF = 7%; RPM = 6%; b = 1.<br /><br />k = kRF + (kM – kRF)b<br />k = 7% + (6%)1<br />k = 13%.<br /><br /><br />5-6 a. .<br /><br />= 0.1(-35%) + 0.2(0%) + 0.4(20%) + 0.2(25%) + 0.1(45%)<br />= 14% versus 12% for X.<br /><br />b. = .<br /><br />= (-10% - 12%)2(0.1) + (2% - 12%)2(0.2) + (12% - 12%)2(0.4)<br />+ (20% - 12%)2(0.2) + (38% - 12%)2(0.1) = 148.8%.<br /><br />X = 12.20% versus 20.35% for Y.<br /><br />CVX = X/ X = 12.20%/12% = 1.02, while<br /><br />CVY = 20.35%/14% = 1.45.<br /><br />If Stock Y is less highly correlated with the market than X, then it might have a lower beta than Stock X, and hence be less risky in a portfolio sense.<br /><br /><br />5-7 a. ki = kRF + (kM - kRF)bi = 9% + (14% - 9%)1.3 = 15.5%.<br /><br />b. 1. kRF increases to 10%:<br /><br />kM increases by 1 percentage point, from 14% to 15%.<br /><br />ki = kRF + (kM - kRF)bi = 10% + (15% - 10%)1.3 = 16.5%.<br /><br />2. kRF decreases to 8%:<br /><br />kM decreases by 1%, from 14% to 13%.<br /><br />ki = kRF + (kM - kRF)bi = 8% + (13% - 8%)1.3 = 14.5%.<br /><br />c. 1. kM increases to 16%:<br /><br />ki = kRF + (kM - kRF)bi = 9% + (16% - 9%)1.3 = 18.1%.<br /><br /><br />2. kM decreases to 13%:<br /><br />ki = kRF + (kM - kRF)bi = 9% + (13% - 9%)1.3 = 14.2%.<br /><br /><br />5-8 Old portfolio beta = (b) + (1.00)<br />1.12 = 0.95b + 0.05<br />1.07 = 0.95b<br />1.1263 = b.<br /><br />New portfolio beta = 0.95(1.1263) + 0.05(1.75) = 1.1575 1.16.<br /><br />Alternative Solutions:<br /><br />1. Old portfolio beta = 1.12 = (0.05)b1 + (0.05)b2 + ... + (0.05)b20<br /><br />1.12 = (0.05)<br />= 1.12/0.05 = 22.4.<br /><br />New portfolio beta = (22.4 - 1.0 + 1.75)(0.05) = 1.1575 1.16.<br /><br />2. excluding the stock with the beta equal to 1.0 is 22.4 - 1.0 =<br />21.4, so the beta of the portfolio excluding this stock is b = 21.4/19 = 1.1263. The beta of the new portfolio is:<br /><br />1.1263(0.95) + 1.75(0.05) = 1.1575 1.16.<br /><br /><br />5-9 Portfolio beta = (1.50) + (-0.50)<br />+ (1.25) + (0.75)<br />bp = (0.1)(1.5) + (0.15)(-0.50) + (0.25)(1.25) + (0.5)(0.75)<br />= 0.15 - 0.075 + 0.3125 + 0.375 = 0.7625.<br /><br />kp = kRF + (kM - kRF)(bp) = 6% + (14% - 6%)(0.7625) = 12.1%.<br /><br />Alternative solution: First, calculate the return for each stock using the CAPM equation [kRF + (kM - kRF)b], and then calculate the weighted average of these returns.<br /><br />kRF = 6% and (kM - kRF) = 8%.<br /><br /><br />Stock Investment Beta k = kRF + (kM - kRF)b Weight<br />A $ 400,000 1.50 18% 0.10<br />B 600,000 (0.50) 2 0.15<br />C 1,000,000 1.25 16 0.25<br />D 2,000,000 0.75 12 0.50<br />Total $4,000,000 1.00<br /><br />kp = 18%(0.10) + 2%(0.15) + 16%(0.25) + 12%(0.50) = 12.1%.<br /><br /><br />5-10 We know that bR = 1.50, bS = 0.75, kM = 13%, kRF = 7%.<br /><br />ki = kRF + (kM - kRF)bi = 7% + (13% - 7%)bi.<br /><br />kR = 7% + 6%(1.50) = 16.0%<br />kS = 7% + 6%(0.75) = 11.5<br />4.5%<br /><br /><br />5-11 = 10%; bX = 0.9; X = 35%.<br />= 12.5%; bY = 1.2; Y = 25%.<br />kRF = 6%; RPM = 5%.<br /><br />a. CVX = 35%/10% = 3.5. CVY = 25%/12.5% = 2.0.<br /><br />b. For diversified investors the relevant risk is measured by beta. Therefore, the stock with the higher beta is more risky. Stock Y has the higher beta so it is more risky than Stock X.<br /><br />c. kX = 6% + 5%(0.9)<br />kX = 10.5%.<br /><br />kY = 6% + 5%(1.2)<br />kY = 12%.<br /><br />d. kX = 10.5%; = 10%.<br />kY = 12%; = 12.5%.<br /><br />Stock Y would be most attractive to a diversified investor since its expected return of 12.5% is greater than its required return of 12%.<br /><br />e. bp = ($7,500/$10,000)0.9 + ($2,500/$10,000)1.2<br />= 0.6750 + 0.30<br />= 0.9750.<br /><br />kp = 6% + 5%(0.975)<br />kp = 10.875%.<br /><br />f. If RPM increases from 5% to 6%, the stock with the highest beta will have the largest increase in its required return. Therefore, Stock Y will have the greatest increase.<br />Check:<br />kX = 6% + 6%(0.9)<br />= 11.4%. Increase 10.5% to 11.4%.<br /><br />kY = 6% + 6%(1.2)<br />= 13.2%. Increase 12% to 13.2%.<br /><br /><br />5-12 kRF = k* + IP = 2.5% + 3.5% = 6%.<br /><br />ks = 6% + (6.5%)1.7 = 17.05%.<br /><br /><br />5-13 Using Stock X (or any stock):<br />9% = kRF + (kM – kRF)bX<br />9% = 5.5% + (kM – kRF)0.8<br />(kM – kRF) = 4.375%.<br /><br /><br />5-14 In equilibrium:<br />kJ = = 12.5%.<br />kJ = kRF + (kM - kRF)b<br />12.5% = 4.5% + (10.5% - 4.5%)b<br />b = 1.33.<br /><br /><br />5-15 bHRI = 1.8; bLRI = 0.6. No changes occur.<br /><br />kRF = 6%. Decreases by 1.5% to 4.5%.<br /><br />kM = 13%. Falls to 10.5%.<br /><br />Now SML: ki = kRF + (kM - kRF)bi.<br /><br />kHRI = 4.5% + (10.5% - 4.5%)1.8 = 4.5% + 6%(1.8) = 15.3%<br />kLRI = 4.5% + (10.5% - 4.5%)0.6 = 4.5% + 6%(0.6) = 8.1%<br />Difference 7.2%<br /><br /><br />5-16 An index fund will have a beta of 1.0. If kM is 12.5 percent (given in the problem) and the risk-free rate is 5 percent, you can calculate the market risk premium (RPM) calculated as kM - kRF as follows:<br /><br />k = kRF + (RPM)b<br />12.5% = 5% + (RPM)1.0<br />7.5% = RPM.<br /><br />Now, you can use the RPM, the kRF, and the two stocks’ betas to calculate their required returns.<br /><br /><br />Bradford:<br />kB = kRF + (RPM)b<br />= 5% + (7.5%)1.45<br />= 5% + 10.875%<br />= 15.875%.<br /><br />Farley:<br />kF = kRF + (RPM)b<br />= 5% + (7.5%)0.85<br />= 5% + 6.375%<br />= 11.375%.<br /><br />The difference in their required returns is:<br />15.875% - 11.375% = 4.5%.<br /><br /><br />5-17 Step 1: Determine the market risk premium from the CAPM:<br />0.12 = 0.0525 + (kM - kRF)1.25<br />(kM - kRF) = 0.054.<br /><br />Step 2: Calculate the beta of the new portfolio:<br />The beta of the new portfolio is ($500,000/$5,500,000)(0.75) + ($5,000,000/$5,500,000)(1.25) = 1.2045.<br /><br />Step 3: Calculate the required return on the new portfolio:<br />The required return on the new portfolio is:<br />5.25% + (5.4%)(1.2045) = 11.75%.<br /><br /><br />5-18 After additional investments are made, for the entire fund to have an expected return of 13%, the portfolio must have a beta of 1.5455 as shown below:<br /><br />13% = 4.5% + (5.5%)b<br />b = 1.5455.<br /><br />Since the fund’s beta is a weighted average of the betas of all the individual investments, we can calculate the required beta on the additional investment as follows:<br /><br />1.5455 = +<br />1.5455 = 1.2 + 0.2X<br />0.3455 = 0.2X<br />X = 1.7275.<br /><br /><br />5-19 a. ($1 million)(0.5) + ($0)(0.5) = $0.5 million.<br /><br />b. You would probably take the sure $0.5 million.<br /><br />c. Risk averter.<br />d. 1. ($1.15 million)(0.5) + ($0)(0.5) = $575,000, or an expected profit of $75,000.<br /><br />2. $75,000/$500,000 = 15%.<br /><br />3. This depends on the individual’s degree of risk aversion.<br /><br />4. Again, this depends on the individual.<br /><br />5. The situation would be unchanged if the stocks’ returns were perfectly positively correlated. Otherwise, the stock portfolio would have the same expected return as the single stock (15 percent) but a lower standard deviation. If the correlation coefficient between each pair of stocks was a negative one, the portfolio would be virtually risk¬less. Since r for stocks is generally in the range of +0.6 to +0.7, investing in a portfolio of stocks would definitely be an improvement over investing in the single stock.<br /><br /><br />5-20 a. M = 0.1(7%) + 0.2(9%) + 0.4(11%) + 0.2(13%) + 0.1(15%) = 11%.<br /><br />kRF = 6%. (given)<br /><br />Therefore, the SML equation is<br /><br />ki = kRF + (kM - kRF)bi = 6% + (11% - 6%)bi = 6% + (5%)bi.<br /><br />b. First, determine the fund’s beta, bF. The weights are the percentage of funds invested in each stock.<br /><br />A = $160/$500 = 0.32<br />B = $120/$500 = 0.24<br />C = $80/$500 = 0.16<br />D = $80/$500 = 0.16<br />E = $60/$500 = 0.12<br /><br />bF = 0.32(0.5) + 0.24(2.0) + 0.16(4.0) + 0.16(1.0) + 0.12(3.0)<br />= 0.16 + 0.48 + 0.64 + 0.16 + 0.36 = 1.8.<br /><br />Next, use bF = 1.8 in the SML determined in Part a:<br /><br />= 6% + (11% - 6%)1.8 = 6% + 9% = 15%.<br /><br />c. kN = Required rate of return on new stock = 6% + (5%)2.0 = 16%.<br /><br />An expected return of 15 percent on the new stock is below the 16 percent required rate of return on an investment with a risk of b = 2.0. Since kN = 16% > N = 15%, the new stock should not be purchased. The expected rate of return that would make the fund indifferent to purchasing the stock is 16 percent.<br /><br />5-21 The answers to a, b, c, and d are given below:<br /><br />kA kB Portfolio<br />1998 (18.00%) (14.50%) (16.25%)<br />1999 33.00 21.80 27.40<br />2000 15.00 30.50 22.75<br />2001 (0.50) (7.60) (4.05)<br />2002 27.00 26.30 26.65<br /><br />Mean 11.30 11.30 11.30<br />Std. Dev. 20.79 20.78 20.13<br />Coef. Var. 1.84 1.84 1.78<br /><br />e. A risk-averse investor would choose the portfolio over either Stock A or Stock B alone, since the portfolio offers the same expected return but with less risk. This result occurs because returns on A and B are not perfectly positively correlated (rAB = 0.88).<br /><br /><br /><br /><br />SPREADSHEET PROBLEM<br /><br /><br /><br />5-22 The detailed solution for the spreadsheet problem is available both on the instructor’s resource CD-ROM and on the instructor’s side of South-Western’s web site, http://brigham.swlearning.com.<br /><br /><br /><br /><br /><br /><br /><br /><br />INTEGRATED CASE<br /><br /><br /><br />Merrill Finch Inc.<br />Risk and Return<br /><br />5-23 ASSUME THAT YOU RECENTLY GRADUATED WITH A MAJOR IN FINANCE, AND YOU JUST LANDED A JOB AS A FINANCIAL PLANNER WITH MERRILL FINCH INC., A LARGE FINANCIAL SERVICES CORPORATION. YOUR FIRST ASSIGNMENT IS TO INVEST $100,000 FOR A CLIENT. BECAUSE THE FUNDS ARE TO BE INVESTED IN A BUSINESS AT THE END OF ONE YEAR, YOU HAVE BEEN INSTRUCTED TO PLAN FOR A ONE-YEAR HOLDING PERIOD. FURTHER, YOUR BOSS HAS RESTRICTED YOU TO THE FOLLOWING INVESTMENT ALTERNATIVES IN THE TABLE BELOW, SHOWN WITH THEIR PROBABILITIES AND ASSOCIATED OUTCOMES. (DISREGARD FOR NOW THE ITEMS AT THE BOTTOM OF THE DATA; YOU WILL FILL IN THE BLANKS LATER.)<br /><br />RETURNS ON ALTERNATIVE INVESTMENTS<br />ESTIMATED RATE OF RETURN<br />STATE OF THE T- HIGH COLLEC- U.S. MARKET 2-STOCK<br />ECONOMY PROB. BILLS TECH TIONS RUBBER PORTFOLIO PORTFOLIO<br />RECESSION 0.1 8.0% -22.0% 28.0% 10.0%* -13.0% 3.0%<br />BELOW AVG 0.2 8.0 -2.0 14.7 -10.0 1.0<br />AVERAGE 0.4 8.0 20.0 0.0 7.0 15.0 10.0<br />ABOVE AVG 0.2 8.0 35.0 -10.0 45.0 29.0<br />BOOM 0.1 8.0 50.0 -20.0 30.0 43.0 15.0<br /><br />k-HAT ( ) 1.7% 13.8% 15.0%<br />STD DEV () 0.0 13.4 18.8 15.3 3.3<br />COEF OF VAR (CV) 7.9 1.4 1.0 0.3<br />BETA (b) -0.87 0.89<br /><br />*NOTE THAT THE ESTIMATED RETURNS OF U.S. RUBBER DO NOT ALWAYS MOVE IN THE SAME DIRECTION AS THE OVERALL ECONOMY. FOR EXAMPLE, WHEN THE ECONOMY IS BELOW AVERAGE, CONSUMERS PURCHASE FEWER TIRES THAN THEY WOULD IF THE ECONOMY WAS STRONGER. HOWEVER, IF THE ECONOMY IS IN A FLAT-OUT RECESSION, A LARGE NUMBER OF CONSUMERS WHO WERE PLANNING TO PURCHASE A NEW CAR MAY CHOOSE TO WAIT AND INSTEAD PURCHASE NEW TIRES FOR THE CAR THEY CURRENTLY OWN. UNDER THESE CIRCUMSTANCES, WE WOULD EXPECT U.S. RUBBER’S STOCK PRICE TO BE HIGHER IF THERE IS A RECESSION THAN IF THE ECONOMY WAS JUST BELOW AVERAGE.<br /><br /><br />MERRILL FINCH’S ECONOMIC FORECASTING STAFF HAS DEVELOPED PROBABILITY ESTIMATES FOR THE STATE OF THE ECONOMY, AND ITS SECURITY ANALYSTS HAVE DEVELOPED A SOPHISTICATED COMPUTER PROGRAM, WHICH WAS USED TO ESTIMATE THE RATE OF RETURN ON EACH ALTERNATIVE UNDER EACH STATE OF THE ECONOMY. HIGH TECH INC. IS AN ELECTRONICS FIRM; COLLECTIONS INC. COLLECTS PAST-DUE DEBTS; AND U.S. RUBBER MANUFACTURES TIRES AND VARIOUS OTHER RUBBER AND PLASTICS PRODUCTS. MERRILL FINCH ALSO MAINTAINS A “MARKET PORTFOLIO” THAT OWNS A MARKET-WEIGHTED FRACTION OF ALL PUBLICLY TRADED STOCKS; YOU CAN INVEST IN THAT PORTFOLIO, AND THUS OBTAIN AVERAGE STOCK MARKET RESULTS. GIVEN THE SITUATION AS DESCRIBED, ANSWER THE FOLLOWING QUESTIONS.<br /><br />A. 1. WHY IS THE T-BILL’S RETURN INDEPENDENT OF THE STATE OF THE ECONOMY?<br />DO T-BILLS PROMISE A COMPLETELY RISK-FREE RETURN?<br /><br />ANSWER: [SHOW S5-1 THROUGH S5-7 HERE.] THE 8 PERCENT T-BILL RETURN DOES NOT DEPEND ON THE STATE OF THE ECONOMY BECAUSE THE TREASURY MUST (AND WILL) REDEEM THE BILLS AT PAR REGARDLESS OF THE STATE OF THE ECONOMY.<br />THE T-BILLS ARE RISK-FREE IN THE DEFAULT RISK SENSE BECAUSE THE<br />8 PERCENT RETURN WILL BE REALIZED IN ALL POSSIBLE ECONOMIC STATES. HOWEVER, REMEMBER THAT THIS RETURN IS COMPOSED OF THE REAL RISK-FREE RATE, SAY 3 PERCENT, PLUS AN INFLATION PREMIUM, SAY 5 PERCENT. SINCE THERE IS UNCERTAINTY ABOUT INFLATION, IT IS UNLIKELY THAT THE REALIZED REAL RATE OF RETURN WOULD EQUAL THE EXPECTED 3 PERCENT. FOR EXAMPLE, IF INFLATION AVERAGED 6 PERCENT OVER THE YEAR, THEN THE REALIZED REAL RETURN WOULD ONLY BE 8% - 6% = 2%, NOT THE EXPECTED 3 PERCENT. THUS, IN TERMS OF PURCHASING POWER, T-BILLS ARE NOT RISKLESS.<br />ALSO, IF YOU INVESTED IN A PORTFOLIO OF T-BILLS, AND RATES THEN DECLINED, YOUR NOMINAL INCOME WOULD FALL; THAT IS, T-BILLS ARE EXPOSED TO REINVESTMENT RATE RISK. SO, WE CONCLUDE THAT THERE ARE NO TRULY RISK-FREE SECURITIES IN THE UNITED STATES. IF THE TREASURY SOLD INFLATION-INDEXED, TAX-EXEMPT BONDS, THEY WOULD BE TRULY RISKLESS, BUT ALL ACTUAL SECURITIES ARE EXPOSED TO SOME TYPE OF RISK.<br /><br /><br />A. 2. WHY ARE HIGH TECH’S RETURNS EXPECTED TO MOVE WITH THE ECONOMY WHEREAS COLLECTIONS’ ARE EXPECTED TO MOVE COUNTER TO THE ECONOMY?<br /><br />ANSWER: [SHOW S5-8 HERE.] HIGH TECH’S RETURNS MOVE WITH, HENCE ARE POSITIVELY CORRELATED WITH, THE ECONOMY, BECAUSE THE FIRM’S SALES, AND HENCE PROFITS, WILL GENERALLY EXPERIENCE THE SAME TYPE OF UPS AND DOWNS AS THE ECONOMY. IF THE ECONOMY IS BOOMING, SO WILL HIGH TECH. ON THE OTHER HAND, COLLECTIONS IS CONSIDERED BY MANY INVESTORS TO BE A HEDGE AGAINST BOTH BAD TIMES AND HIGH INFLATION, SO IF THE STOCK MARKET CRASHES, INVESTORS IN THIS STOCK SHOULD DO RELATIVELY WELL. STOCKS SUCH AS COLLECTIONS ARE THUS NEGATIVELY CORRELATED WITH (MOVE COUNTER TO) THE ECONOMY. (NOTE: IN ACTUALITY, IT IS ALMOST IMPOSSIBLE TO FIND STOCKS THAT ARE EXPECTED TO MOVE COUNTER TO THE ECONOMY. EVEN COLLECTIONS SHARES HAVE POSITIVE (BUT LOW) CORRELATION WITH THE MARKET.)<br /><br /><br />B. CALCULATE THE EXPECTED RATE OF RETURN ON EACH ALTERNATIVE AND FILL IN THE BLANKS ON THE ROW FOR IN THE TABLE ABOVE.<br /><br />ANSWER: [SHOW S5-9 AND S5-10 HERE.] THE EXPECTED RATE OF RETURN, , IS EXPRESSED AS FOLLOWS:<br /><br />.<br /><br />HERE Pi IS THE PROBABILITY OF OCCURRENCE OF THE iTH STATE, ki IS THE ESTIMATED RATE OF RETURN FOR THAT STATE, AND n IS THE NUMBER OF STATES. HERE IS THE CALCULATION FOR HIGH TECH:<br /><br />HIGH TECH = 0.1(-22.0%) + 0.2(-2.0%) + 0.4(20.0%) + 0.2(35.0%) + 0.1(50.0%)<br />= 17.4%.<br /><br />WE USE THE SAME FORMULA TO CALCULATE k’S FOR THE OTHER ALTERNATIVES:<br /><br />T-BILLS = 8.0%.<br /><br />COLLECTIONS = 1.7%.<br /><br />U.S.RUBBER = 13.8%.<br /><br />M = 15.0%.<br /><br /><br />C. YOU SHOULD RECOGNIZE THAT BASING A DECISION SOLELY ON EXPECTED RETURNS IS ONLY APPROPRIATE FOR RISK-NEUTRAL INDIVIDUALS. SINCE YOUR CLIENT, LIKE VIRTUALLY EVERYONE, IS RISK AVERSE, THE RISKINESS OF EACH ALTERNATIVE IS AN IMPORTANT ASPECT OF THE DECISION. ONE POSSIBLE MEASURE OF RISK IS THE STANDARD DEVIATION OF RETURNS.<br /><br />1. CALCULATE THIS VALUE FOR EACH ALTERNATIVE, AND FILL IN THE BLANK ON THE ROW FOR IN THE TABLE ABOVE.<br /><br />ANSWER: [SHOW S5-11 THROUGH S5-13 HERE.] THE STANDARD DEVIATION IS CALCULATED AS FOLLOWS:<br /><br /> = .<br /><br />HIGH TECH = [(-22.0 - 17.4)2(0.1) + (-2.0 - 17.4)2(0.2) + (20.0 - 17.4)2(0.4)<br />+ (35.0 - 17.4)2(0.2) + (50.0 - 17.4)2(0.1)]½<br />= = 20.0%.<br /><br />HERE ARE THE STANDARD DEVIATIONS FOR THE OTHER ALTERNATIVES:<br /><br />T-BILLS = 0.0%.<br /><br />COLLECTIONS = 13.4%.<br /><br />U.S. RUBBER = 18.8%.<br /><br />M = 15.3%.<br /><br /><br />C. 2. WHAT TYPE OF RISK IS MEASURED BY THE STANDARD DEVIATION?<br /><br />ANSWER: [SHOW S5-14 AND S5-15 HERE.] THE STANDARD DEVIATION IS A MEASURE OF A SECURITY’S (OR A PORTFOLIO’S) STAND-ALONE RISK. THE LARGER THE STANDARD DEVIATION, THE HIGHER THE PROBABILITY THAT ACTUAL REALIZED RETURNS WILL FALL FAR BELOW THE EXPECTED RETURN, AND THAT LOSSES RATHER THAN PROFITS WILL BE INCURRED.<br /><br /><br />C. 3. DRAW A GRAPH THAT SHOWS ROUGHLY THE SHAPE OF THE PROBABILITY DISTRIBUTIONS FOR HIGH TECH, U.S. RUBBER, AND T-BILLS.<br /><br /><br />ANSWER:<br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br />ON THE BASIS OF THESE DATA, HIGH TECH IS THE MOST RISKY INVESTMENT,<br />T-BILLS THE LEAST RISKY.<br /><br /><br />D. SUPPOSE YOU SUDDENLY REMEMBERED THAT THE COEFFICIENT OF VARIATION (CV) IS GENERALLY REGARDED AS BEING A BETTER MEASURE OF STAND-ALONE RISK THAN THE STANDARD DEVIATION WHEN THE ALTERNATIVES BEING CONSIDERED HAVE WIDELY DIFFERING EXPECTED RETURNS. CALCULATE THE MISSING CVs, AND FILL IN THE BLANKS ON THE ROW FOR CV IN THE TABLE ABOVE. DOES THE CV PRODUCE THE SAME RISK RANKINGS AS THE STANDARD DEVIATION?<br /><br />ANSWER: [SHOW S5-16 THROUGH S5-19 HERE.] THE COEFFICIENT OF VARIATION (CV) IS A STANDARDIZED MEASURE OF DISPERSION ABOUT THE EXPECTED VALUE; IT SHOWS THE AMOUNT OF RISK PER UNIT OF RETURN.<br /><br />CV = .<br /><br />CVT-BILLS = 0.0%/8.0% = 0.0.<br /><br />CVHIGH TECH = 20.0%/17.4% = 1.1.<br /><br />CVCOLLECTIONS = 13.4%/1.7% = 7.9.<br /><br />CVU.S. RUBBER = 18.8%/13.8% = 1.4.<br /><br />CVM = 15.3%/15.0% = 1.0.<br /><br />WHEN WE MEASURE RISK PER UNIT OF RETURN, COLLECTIONS, WITH ITS LOW EXPECTED RETURN, BECOMES THE MOST RISKY STOCK. THE CV IS A BETTER MEASURE OF AN ASSET’S STAND-ALONE RISK THAN BECAUSE CV CONSIDERS BOTH THE EXPECTED VALUE AND THE DISPERSION OF A DISTRIBUTION--A SECURITY WITH A LOW EXPECTED RETURN AND A LOW STANDARD DEVIATION COULD HAVE A HIGHER CHANCE OF A LOSS THAN ONE WITH A HIGH BUT A HIGH .<br /><br /><br />E. SUPPOSE YOU CREATED A 2-STOCK PORTFOLIO BY INVESTING $50,000 IN HIGH TECH AND $50,000 IN COLLECTIONS.<br /><br />1. CALCULATE THE EXPECTED RETURN ( ), THE STANDARD DEVIATION (p), AND THE COEFFICIENT OF VARIATION (CVp) FOR THIS PORTFOLIO AND FILL IN THE APPROPRIATE BLANKS IN THE TABLE ABOVE.<br /><br />ANSWER: [SHOW S5-20 THROUGH S5-23 HERE.] TO FIND THE EXPECTED RATE OF RETURN ON THE TWO-STOCK PORTFOLIO, WE FIRST CALCULATE THE RATE OF RETURN ON THE PORTFOLIO IN EACH STATE OF THE ECONOMY. SINCE WE HAVE HALF OF OUR MONEY IN EACH STOCK, THE PORTFOLIO’S RETURN WILL BE A WEIGHTED AVERAGE IN EACH TYPE OF ECONOMY. FOR A RECESSION, WE HAVE: kp = 0.5(-22%) + 0.5(28%) = 3%. WE WOULD DO SIMILAR CALCULATIONS FOR THE OTHER STATES OF THE ECONOMY, AND GET THESE RESULTS:<br /><br />STATE PORTFOLIO<br />RECESSION 3.0%<br />BELOW AVERAGE 6.4<br />AVERAGE 10.0<br />ABOVE AVERAGE 12.5<br />BOOM 15.0<br /><br />NOW WE CAN MULTIPLY PROBABILITIES TIMES OUTCOMES IN EACH STATE TO GET THE EXPECTED RETURN ON THIS TWO-STOCK PORTFOLIO, 9.6 PERCENT.<br />ALTERNATIVELY, WE COULD APPLY THIS FORMULA,<br /><br />k = wi ki = 0.5(17.4%) + 0.5(1.7%) = 9.6%,<br /><br />WHICH FINDS k AS THE WEIGHTED AVERAGE OF THE EXPECTED RETURNS OF THE INDIVIDUAL SECURITIES IN THE PORTFOLIO.<br />IT IS TEMPTING TO FIND THE STANDARD DEVIATION OF THE PORTFOLIO AS THE WEIGHTED AVERAGE OF THE STANDARD DEVIATIONS OF THE INDIVIDUAL SECURITIES, AS FOLLOWS:<br /><br />p wi(i) + wj(j) = 0.5(20%) + 0.5(13.4%) = 16.7%.<br /><br />HOWEVER, THIS IS NOT CORRECT--IT IS NECESSARY TO USE A DIFFERENT FORMULA, THE ONE FOR THAT WE USED EARLIER, APPLIED TO THE TWO-STOCK PORTFOLIO’S RETURNS.<br />THE PORTFOLIO’S DEPENDS JOINTLY ON (1) EACH SECURITY’S AND<br />(2) THE CORRELATION BETWEEN THE SECURITIES’ RETURNS. THE BEST WAY TO APPROACH THE PROBLEM IS TO ESTIMATE THE PORTFOLIO’S RISK AND RETURN IN EACH STATE OF THE ECONOMY, AND THEN TO ESTIMATE p WITH THE FORMULA. GIVEN THE DISTRIBUTION OF RETURNS FOR THE PORTFOLIO, WE CAN CALCULATE THE PORTFOLIO’S AND CV AS SHOWN BELOW:<br /><br />p = [(3.0 - 9.6)2(0.1) + (6.4 - 9.6)2(0.2) + (10.0 - 9.6)2(0.4)<br />+ (12.5 - 9.6)2(0.2) + (15.0 - 9.6)2(0.1)]½ = 3.3%.<br /><br />CVp = 3.3%/9.6% = 0.34.<br /><br /><br />E. 2. HOW DOES THE RISKINESS OF THIS 2-STOCK PORTFOLIO COMPARE WITH THE RISKINESS OF THE INDIVIDUAL STOCKS IF THEY WERE HELD IN ISOLATION?<br /><br />ANSWER: [SHOW S5-24 THROUGH S5-27 HERE.] USING EITHER OR CV AS OUR STAND-ALONE RISK MEASURE, THE STAND-ALONE RISK OF THE PORTFOLIO IS SIGNIFICANTLY LESS THAN THE STAND-ALONE RISK OF THE INDIVIDUAL STOCKS. THIS IS BECAUSE THE TWO STOCKS ARE NEGATIVELY CORRELATED--WHEN HIGH TECH IS DOING POORLY, COLLECTIONS IS DOING WELL, AND VICE VERSA. COMBINING THE TWO STOCKS DIVERSIFIES AWAY SOME OF THE RISK INHERENT IN EACH STOCK IF IT WERE HELD IN ISOLATION, i.e., IN A 1-STOCK PORTFOLIO.<br /><br /><br />OPTIONAL QUESTION<br /><br />DOES THE EXPECTED RATE OF RETURN ON THE PORTFOLIO DEPEND ON THE PERCENTAGE OF THE PORTFOLIO INVESTED IN EACH STOCK? WHAT ABOUT THE RISKINESS OF THE PORTFOLIO?<br /><br />ANSWER: USING A SPREADSHEET MODEL, IT’S EASY TO VARY THE COMPOSITION OF THE PORTFOLIO TO SHOW THE EFFECT ON THE PORTFOLIO’S EXPECTED RATE OF RETURN AND STANDARD DEVIATION:<br /><br />HIGH TECH PLUS COLLECTIONS<br />% IN HIGH TECH p p<br />0% 1.7% 13.4%<br />10 3.3 10.0<br />20 4.9 6.7<br />30 6.4 3.3<br />40 8.0 0.0<br />50 9.6 3.3<br />60 11.1 6.7<br />70 12.7 10.0<br />80 14.3 13.4<br />90 15.8 16.7<br />100 17.4 20.0<br /><br />THE EXPECTED RATE OF RETURN ON THE PORTFOLIO IS MERELY A LINEAR COMBINATION OF THE TWO STOCK’S EXPECTED RATES OF RETURN. HOWEVER, PORTFOLIO RISK IS ANOTHER MATTER. p BEGINS TO FALL AS HIGH TECH AND COLLECTIONS ARE COMBINED; IT REACHES ZERO AT 40 PERCENT HIGH TECH; AND THEN IT BEGINS TO RISE. HIGH TECH AND COLLECTIONS CAN BE COMBINED TO FORM A NEAR ZERO RISK PORTFOLIO BECAUSE THEY ARE VERY CLOSE TO BEING PERFECTLY NEGATIVELY CORRELATED; THEIR CORRELATION COEFFICIENT IS<br />-0.9998. (NOTE: UNFORTUNATELY, WE CANNOT FIND ANY ACTUAL STOCKS WITH r = -1.0.)<br /><br /><br />F. SUPPOSE AN INVESTOR STARTS WITH A PORTFOLIO CONSISTING OF ONE RANDOMLY SELECTED STOCK. WHAT WOULD HAPPEN (1) TO THE RISKINESS AND (2) TO THE EXPECTED RETURN OF THE PORTFOLIO AS MORE AND MORE RANDOMLY SELECTED STOCKS WERE ADDED TO THE PORTFOLIO? WHAT IS THE IMPLICATION FOR INVESTORS? DRAW A GRAPH OF THE TWO PORTFOLIOS TO ILLUSTRATE YOUR ANSWER.<br /><br /><br />ANSWER: [SHOW S5-28 AND S5-29 HERE.]<br /><br /><br /><br />THE STANDARD DEVIATION GETS SMALLER AS MORE STOCKS ARE COMBINED IN THE PORTFOLIO, WHILE kp (THE PORTFOLIO’S RETURN) REMAINS CONSTANT. THUS, BY ADDING STOCKS TO YOUR PORTFOLIO, WHICH INITIALLY STARTED AS A<br />1-STOCK PORTFOLIO, RISK HAS BEEN REDUCED.<br />IN THE REAL WORLD, STOCKS ARE POSITIVELY CORRELATED WITH ONE ANOTHER--IF THE ECONOMY DOES WELL, SO DO STOCKS IN GENERAL, AND VICE VERSA. CORRELATION COEFFICIENTS BETWEEN STOCKS GENERALLY RANGE FROM +0.5 TO +0.7. A SINGLE STOCK SELECTED AT RANDOM WOULD ON AVERAGE HAVE A STANDARD DEVIATION OF ABOUT 35 PERCENT. AS ADDITIONAL STOCKS ARE ADDED TO THE PORTFOLIO, THE PORTFOLIO’S STANDARD DEVIATION DECREASES BECAUSE THE ADDED STOCKS ARE NOT PERFECTLY POSITIVELY CORRELATED. HOWEVER, AS MORE AND MORE STOCKS ARE ADDED, EACH NEW STOCK HAS LESS OF A RISK-REDUCING IMPACT, AND EVENTUALLY ADDING ADDITIONAL STOCKS HAS VIRTUALLY NO EFFECT ON THE PORTFOLIO’S RISK AS MEASURED BY . IN FACT, STABILIZES AT ABOUT 20.4 PERCENT WHEN 40 OR MORE RANDOMLY SELECTED STOCKS ARE ADDED. THUS, BY COMBINING STOCKS INTO WELL-DIVERSIFIED PORTFOLIOS, INVESTORS CAN ELIMINATE ALMOST ONE-HALF THE RISKINESS OF HOLDING INDIVIDUAL STOCKS. (NOTE: IT IS NOT COMPLETELY COSTLESS TO DIVERSIFY, SO EVEN THE LARGEST INSTITUTIONAL INVESTORS HOLD LESS THAN ALL STOCKS. EVEN INDEX FUNDS GENERALLY HOLD A SMALLER PORTFOLIO THAT IS HIGHLY CORRELATED WITH AN INDEX SUCH AS THE S&P 500 RATHER THAN HOLD ALL THE STOCKS IN THE INDEX.)<br />THE IMPLICATION IS CLEAR: INVESTORS SHOULD HOLD WELL-DIVERSIFIED PORTFOLIOS OF STOCKS RATHER THAN INDIVIDUAL STOCKS. (IN FACT, INDIVIDUALS CAN HOLD DIVERSIFIED PORTFOLIOS THROUGH MUTUAL FUND INVESTMENTS.) BY DOING SO, THEY CAN ELIMINATE ABOUT HALF OF THE RISKINESS INHERENT IN INDIVIDUAL STOCKS.<br /><br /><br />G. 1. SHOULD PORTFOLIO EFFECTS IMPACT THE WAY INVESTORS THINK ABOUT THE RISKINESS OF INDIVIDUAL STOCKS?<br /><br />ANSWER: [SHOW S5-30 HERE.] PORTFOLIO DIVERSIFICATION DOES AFFECT INVESTORS’ VIEWS OF RISK. A STOCK’S STAND-ALONE RISK AS MEASURED BY ITS OR CV, MAY BE IMPORTANT TO AN UNDIVERSIFIED INVESTOR, BUT IT IS NOT RELEVANT TO A WELL-DIVERSIFIED INVESTOR. A RATIONAL, RISK-AVERSE INVESTOR IS MORE INTERESTED IN THE IMPACT THAT THE STOCK HAS ON THE RISKINESS OF HIS OR HER PORTFOLIO THAN ON THE STOCK’S STAND-ALONE RISK. STAND-ALONE RISK IS COMPOSED OF DIVERSIFIABLE RISK, WHICH CAN BE ELIMINATED BY HOLDING THE STOCK IN A WELL-DIVERSIFIED PORTFOLIO, AND THE RISK THAT REMAINS IS CALLED MARKET RISK BECAUSE IT IS PRESENT EVEN WHEN THE ENTIRE MARKET PORTFOLIO IS HELD.<br /><br /><br />G. 2. IF YOU DECIDED TO HOLD A 1-STOCK PORTFOLIO, AND CONSEQUENTLY WERE EXPOSED TO MORE RISK THAN DIVERSIFIED INVESTORS, COULD YOU EXPECT TO BE COMPENSATED FOR ALL OF YOUR RISK; THAT IS, COULD YOU EARN A RISK PREMIUM ON THAT PART OF YOUR RISK THAT YOU COULD HAVE ELIMINATED BY DIVERSIFYING?<br /><br />ANSWER: [SHOW S5-31 HERE.] IF YOU HOLD A ONE-STOCK PORTFOLIO, YOU WILL BE EXPOSED TO A HIGH DEGREE OF RISK, BUT YOU WON’T BE COMPENSATED FOR IT. IF THE RETURN WERE HIGH ENOUGH TO COMPENSATE YOU FOR YOUR HIGH RISK, IT WOULD BE A BARGAIN FOR MORE RATIONAL, DIVERSIFIED INVESTORS. THEY WOULD START BUYING IT, AND THESE BUY ORDERS WOULD DRIVE THE PRICE UP AND THE RETURN DOWN. THUS, YOU SIMPLY COULD NOT FIND STOCKS IN THE MARKET WITH RETURNS HIGH ENOUGH TO COMPENSATE YOU FOR THE STOCK’S DIVERSIFIABLE RISK.<br /><br /><br />H. THE EXPECTED RATES OF RETURN AND THE BETA COEFFICIENTS OF THE ALTERNATIVES AS SUPPLIED BY MERRILL FINCH’S COMPUTER PROGRAM ARE AS FOLLOWS:<br /><br />SECURITY RETURN ( ) RISK (BETA)<br />HIGH TECH 17.4% 1.30<br />MARKET 15.0 1.00<br />U.S. RUBBER 13.8 0.89<br />T-BILLS 8.0 0.00<br />COLLECTIONS 1.7 (0.87)<br /><br />(1) WHAT IS A BETA COEFFICIENT, AND HOW ARE BETAS USED IN RISK ANALYSIS? (2) DO THE EXPECTED RETURNS APPEAR TO BE RELATED TO EACH ALTERNATIVE’S MARKET RISK? (3) IS IT POSSIBLE TO CHOOSE AMONG THE ALTERNATIVES ON THE BASIS OF THE INFORMATION DEVELOPED THUS FAR? USE THE DATA GIVEN AT THE START OF THE PROBLEM TO CONSTRUCT A GRAPH THAT SHOWS HOW THE T-BILL’S, HIGH TECH’S, AND THE MARKET’S BETA COEFFICIENTS ARE CALCULATED. THEN DISCUSS WHAT BETAS MEASURE AND HOW THEY ARE USED IN RISK ANALYSIS.<br /><br />ANSWER: [SHOW S5-32 THROUGH S5-39 HERE.]<br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br />(DRAW THE FRAMEWORK OF THE GRAPH, PUT UP THE DATA, THEN PLOT THE POINTS FOR THE MARKET (45 LINE) AND CONNECT THEM, AND THEN GET THE SLOPE AS Y/X = 1.0.) STATE THAT AN AVERAGE STOCK, BY DEFINITION, MOVES WITH THE MARKET. THEN DO THE SAME WITH HIGH TECH AND T-BILLS. BETA COEFFICIENTS MEASURE THE RELATIVE VOLATILITY OF A GIVEN STOCK VIS-A-VIS AN AVERAGE STOCK. THE AVERAGE STOCK’S BETA IS 1.0. MOST STOCKS HAVE BETAS IN THE RANGE OF 0.5 TO 1.5. THEORETICALLY, BETAS CAN BE NEGATIVE, BUT IN THE REAL WORLD THEY ARE GENERALLY POSITIVE.<br />BETAS ARE CALCULATED AS THE SLOPE OF THE “CHARACTERISTIC” LINE, WHICH IS THE REGRESSION LINE SHOWING THE RELATIONSHIP BETWEEN A GIVEN STOCK AND THE GENERAL STOCK MARKET.<br />AS EXPLAINED IN WEB APPENDIX 5A, WE COULD ESTIMATE THE SLOPES, AND THEN USE THE SLOPES AS THE BETAS. IN PRACTICE, 5 YEARS OF MONTHLY DATA, WITH 60 OBSERVATIONS, WOULD GENERALLY BE USED, AND A COMPUTER WOULD BE USED TO OBTAIN A LEAST SQUARES REGRESSION LINE.<br />THE EXPECTED RETURNS ARE RELATED TO EACH ALTERNATIVE’S MARKET RISK--THAT IS, THE HIGHER THE ALTERNATIVE’S RATE OF RETURN THE HIGHER ITS BETA. ALSO, NOTE THAT T-BILLS HAVE ZERO RISK.<br />WE DO NOT YET HAVE ENOUGH INFORMATION TO CHOOSE AMONG THE VARIOUS ALTERNATIVES. WE NEED TO KNOW THE REQUIRED RATES OF RETURN ON THESE ALTERNATIVES AND COMPARE THEM WITH THEIR EXPECTED RETURNS.<br /><br /><br />I. THE YIELD CURVE IS CURRENTLY FLAT, THAT IS, LONG-TERM TREASURY BONDS ALSO HAVE AN 8 PERCENT YIELD. CONSEQUENTLY, MERRILL FINCH ASSUMES THAT THE RISK-FREE RATE IS 8 PERCENT.<br /><br />1. WRITE OUT THE SECURITY MARKET LINE (SML) EQUATION, USE IT TO CALCULATE THE REQUIRED RATE OF RETURN ON EACH ALTERNATIVE, AND THEN GRAPH THE RELATIONSHIP BETWEEN THE EXPECTED AND REQUIRED RATES OF RETURN.<br /><br />ANSWER: [SHOW S5-40 THROUGH S5-44 HERE.] HERE IS THE SML EQUATION:<br /><br />ki = kRF + (kM – kRF)bi.<br /><br />MERRILL FINCH HAS ESTIMATED THE RISK-FREE RATE TO BE kRF = 8%. FURTHER, OUR ESTIMATE OF kM = M IS 15 PERCENT. THUS, THE REQUIRED RATES OF RETURN FOR THE ALTERNATIVES ARE AS FOLLOWS:<br /><br />HIGH TECH: 8% + (15% - 8%)1.30 = 17.10%.<br />MARKET: 8% + (15% - 8%)1.00 = 15.0%.<br />U.S. RUBBER: 8% + (15% - 8%)0.89 = 14.23%.<br />T-BILLS: 8% + (15% - 8%)0 = 8.0%.<br />COLLECTIONS: 8% + (15% - 8%)-0.87 = 1.91%.<br />I. 2. HOW DO THE EXPECTED RATES OF RETURN COMPARE WITH THE REQUIRED RATES OF RETURN?<br /><br />ANSWER: WE HAVE THE FOLLOWING RELATIONSHIPS:<br /><br />EXPECTED REQUIRED<br />RETURN RETURN<br />SECURITY ( ) (k) CONDITION<br />HIGH TECH 17.4% 17.1% UNDERVALUED: > k<br />MARKET 15.0 15.0 FAIRLY VALUED (MARKET EQUILIBRIUM)<br />U.S. RUBBER 13.8 14.2 OVERVALUED: k ><br />T-BILLS 8.0 8.0 FAIRLY VALUED<br />COLLECTIONS 1.7 1.9 OVERVALUED: k ><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br />(NOTE: THE PLOT LOOKS SOMEWHAT UNUSUAL IN THAT THE X-AXIS EXTENDS TO THE LEFT OF ZERO. WE HAVE A NEGATIVE BETA STOCK, HENCE A REQUIRED RETURN THAT IS LESS THAN THE RISK-FREE RATE.) THE T-BILLS AND MARKET PORTFOLIO PLOT ON THE SML, HIGH TECH PLOTS ABOVE IT, AND COLLECTIONS AND U.S. RUBBER PLOT BELOW IT. THUS, THE T-BILLS AND THE MARKET PORTFOLIO PROMISE A FAIR RETURN, HIGH TECH IS A GOOD DEAL BECAUSE ITS EXPECTED RETURN IS ABOVE ITS REQUIRED RETURN, AND COLLECTIONS AND U.S. RUBBER HAVE EXPECTED RETURNS BELOW THEIR REQUIRED RETURNS.<br /><br /><br />I. 3. DOES THE FACT THAT COLLECTIONS HAS AN EXPECTED RETURN THAT IS LESS THAN THE T-BILL RATE MAKE ANY SENSE?<br />ANSWER: COLLECTIONS IS AN INTERESTING STOCK. ITS NEGATIVE BETA INDICATES NEGATIVE MARKET RISK--INCLUDING IT IN A PORTFOLIO OF “NORMAL” STOCKS WILL LOWER THE PORTFOLIO’S RISK. THEREFORE, ITS REQUIRED RATE OF RETURN IS BELOW THE RISK-FREE RATE. BASICALLY, THIS MEANS THAT COLLECTIONS IS A VALUABLE SECURITY TO RATIONAL, WELL-DIVERSIFIED INVESTORS. TO SEE WHY, CONSIDER THIS QUESTION: WOULD ANY RATIONAL INVESTOR EVER MAKE AN INVESTMENT THAT HAS A NEGATIVE EXPECTED RETURN? THE ANSWER IS “YES”--JUST THINK OF THE PURCHASE OF A LIFE OR FIRE INSURANCE POLICY. THE FIRE INSURANCE POLICY HAS A NEGATIVE EXPECTED RETURN BECAUSE OF COMMISSIONS AND INSURANCE COMPANY PROFITS, BUT BUSINESSES BUY FIRE INSURANCE BECAUSE THEY PAY OFF AT A TIME WHEN NORMAL OPERATIONS ARE IN BAD SHAPE. LIFE INSURANCE IS SIMILAR--IT HAS A HIGH RETURN WHEN WORK INCOME CEASES. A NEGATIVE BETA STOCK IS CONCEPTUALLY SIMILAR TO AN INSURANCE POLICY.<br /><br /><br />I. 4. WHAT WOULD BE THE MARKET RISK AND THE REQUIRED RETURN OF A 50-50 PORTFOLIO OF HIGH TECH AND COLLECTIONS? OF HIGH TECH AND U.S. RUBBER?<br /><br />ANSWER: [SHOW S5-45 AND S5-46 HERE.] NOTE THAT THE BETA OF A PORTFOLIO IS SIMPLY THE WEIGHTED AVERAGE OF THE BETAS OF THE STOCKS IN THE PORTFOLIO. THUS, THE BETA OF A PORTFOLIO WITH 50 PERCENT HIGH TECH AND 50 PERCENT COLLECTIONS IS:<br /><br />.<br /><br />bp = 0.5(bHIGH TECH) + 0.5(bCOLLECTIONS) = 0.5(1.30) + 0.5(–0.87)<br />= 0.215,<br /><br />kp = kRF + (kM - kRF)bp = 8.0% + (15.0% - 8.0%)(0.215)<br />= 8.0% + 7%(0.215) = 9.51% 9.5%.<br /><br />FOR A PORTFOLIO CONSISTING OF 50 PERCENT HIGH TECH PLUS 50 PERCENT<br />U.S. RUBBER, THE REQUIRED RETURN WOULD BE 15.7 PERCENT:<br /><br />bp = 0.5(1.30) + 0.5(0.89) = 1.095.<br /><br />kp = 8.0% + 7%(1.095) = 15.665% 15.7%.<br /><br />J. 1. SUPPOSE INVESTORS RAISED THEIR INFLATION EXPECTATIONS BY 3 PERCENTAGE POINTS OVER CURRENT ESTIMATES AS REFLECTED IN THE 8 PERCENT RISK-FREE RATE. WHAT EFFECT WOULD HIGHER INFLATION HAVE ON THE SML AND ON THE RETURNS REQUIRED ON HIGH- AND LOW-RISK SECURITIES?<br /><br />ANSWER: [SHOW S5-47 HERE.]<br />HERE WE HAVE PLOTTED THE SML FOR BETAS RANGING FROM 0 TO 2.0. THE BASE CASE SML IS BASED ON kRF = 8% AND = 15%. IF INFLATION EXPECTATIONS INCREASE BY 3 PERCENTAGE POINTS, WITH NO CHANGE IN RISK AVERSION, THEN THE ENTIRE SML IS SHIFTED UPWARD (PARALLEL TO THE BASE CASE SML) BY<br />3 PERCENTAGE POINTS. NOW, kRF = 11%, kM = 18%, AND ALL SECURITIES’ REQUIRED RETURNS RISE BY 3 PERCENTAGE POINTS. NOTE THAT THE MARKET RISK PREMIUM, kM - kRF, REMAINS AT 7 PERCENTAGE POINTS.<br /><br /><br />J. 2. SUPPOSE INSTEAD THAT INVESTORS’ RISK AVERSION INCREASED ENOUGH TO CAUSE THE MARKET RISK PREMIUM TO INCREASE BY 3 PERCENTAGE POINTS. (INFLATION REMAINS CONSTANT.) WHAT EFFECT WOULD THIS HAVE ON THE SML AND ON RETURNS OF HIGH- AND LOW-RISK SECURITIES?<br /><br />ANSWER: [SHOW S5-48 THROUGH S5-50 HERE.] WHEN INVESTORS’ RISK AVERSION INCREASES, THE SML IS ROTATED UPWARD ABOUT THE Y-INTERCEPT (kRF). kRF REMAINS AT 8 PERCENT, BUT NOW kM INCREASES TO 18 PERCENT, SO THE MARKET RISK PREMIUM INCREASES TO 10 PERCENT. THE REQUIRED RATE OF RETURN WILL RISE SHARPLY ON HIGH-RISK (HIGH-BETA) STOCKS, BUT NOT MUCH ON LOW-BETA SECURITIES.<br /><br /><br />OPTIONAL QUESTION<br /><br />FINANCIAL MANAGERS ARE MORE CONCERNED WITH INVESTMENT DECISIONS RELATING TO REAL ASSETS SUCH AS PLANT AND EQUIPMENT THAN WITH INVESTMENTS IN FINANCIAL ASSETS SUCH AS SECURITIES. HOW DOES THE ANALYSIS THAT WE HAVE GONE THROUGH RELATE TO REAL ASSET INVESTMENT DECISIONS, ESPECIALLY CORPORATE CAPITAL BUDGETING DECISIONS?<br /><br />ANSWER: THERE IS A GREAT DEAL OF SIMILARITY BETWEEN YOUR FINANCIAL ASSET DECISIONS AND A FIRM’S CAPITAL BUDGETING DECISIONS. HERE IS THE LINKAGE:<br /><br />1. A COMPANY MAY BE THOUGHT OF AS A PORTFOLIO OF ASSETS. IF THE COMPANY DIVERSIFIES ITS ASSETS, AND ESPECIALLY IF IT INVESTS IN SOME PROJECTS THAT TEND TO DO WELL WHEN OTHERS ARE DOING BADLY, IT CAN LOWER THE VARIABILITY OF ITS RETURNS.<br /><br />2. COMPANIES OBTAIN THEIR INVESTMENT FUNDS FROM INVESTORS, WHO BUY THE FIRM’S STOCKS AND BONDS. WHEN INVESTORS BUY THESE SECURITIES, THEY REQUIRE A RISK PREMIUM THAT IS BASED ON THE COMPANY’S RISK AS THEY (INVESTORS) SEE IT. FURTHER, SINCE INVESTORS IN GENERAL HOLD WELL-DIVERSIFIED PORTFOLIOS OF STOCKS AND BONDS, THE RISK THAT IS RELEVANT TO THEM IS THE SECURITY’S MARKET RISK, NOT ITS STAND-ALONE RISK. THUS, INVESTORS VIEW THE FIRM’S RISK FROM A MARKET RISK PERSPECTIVE.<br /><br />3. THEREFORE, WHEN A MANAGER MAKES A DECISION TO BUILD A NEW PLANT, THE RISKINESS OF THE INVESTMENT IN THE PLANT THAT IS RELEVANT TO THE FIRM’S INVESTORS (ITS OWNERS) IS ITS MARKET RISK, NOT ITS STAND-ALONE RISK. ACCORDINGLY, MANAGERS NEED TO KNOW HOW PHYSICAL ASSET INVESTMENT DECISIONS AFFECT THEIR FIRM’S BETA COEFFICIENT. A PARTICULAR ASSET MAY LOOK QUITE RISKY WHEN VIEWED IN ISOLATION, BUT IF ITS RETURNS ARE NEGATIVELY CORRELATED WITH RETURNS ON MOST OTHER STOCKS, THE ASSET MAY REALLY HAVE LOW RISK. WE WILL DISCUSS ALL THIS IN MORE DETAIL IN OUR CAPITAL BUDGETING DISCUSSION. </div>saleem shahzadnoreply@blogger.com0tag:blogger.com,1999:blog-3421608066886271296.post-14691559579564174252010-12-14T13:25:00.002+05:002011-01-12T16:25:17.247+05:00Chapter 4Chapter 4<br /> The Financial Environment:<br /> Markets, Institutions, and Interest Rates<br /> <br /> <br />SOLUTIONS TO END-OF-CHAPTER PROBLEMS<br /><br /><br /><br />4-1 k* = 3%; I1 = 2%; I2 = 4%; I3 = 4%; MRP = 0; kT2 = ?; kT3 = ?<br /><br />k = k* + IP + DRP + LP + MRP.<br /><br />Since these are Treasury securities, DRP = LP = 0.<br /><br />kT2 = k* + IP2.<br />IP2 = (2% + 4%)/2 = 3%.<br />kT2 = 3% + 3% = 6%.<br /><br />kT3 = k* + IP3.<br />IP3 = (2% + 4% + 4%)/3 = 3.33%.<br />kT3 = 3% + 3.33% = 6.33%.<br /><br /><br />4-2 kT10 = 6%; kC10 = 8%; LP = 0.5%; DRP = ?<br /><br />k = k* + IP + DRP + LP + MRP.<br /><br />kT10 = 6% = k* + IP + MRP; DRP = LP = 0.<br /><br />kC10 = 8% = k* + IP + DRP + 0.5% + MRP.<br /><br />Because both bonds are 10-year bonds the inflation premium and maturity risk premium on both bonds are equal. The only difference between them is the liquidity and default risk premiums.<br /><br />kC10 = 8% = k* + IP + MRP + 0.5% + DRP. But we know from above that k* + IP + MRP = 6%; therefore,<br /><br />kC10 = 8% = 6% + 0.5% + DRP<br />1.5% = DRP.<br /><br /><br />4-3 kT1 = 5%; 1kT1 = 6%; kT2 = ?<br /><br />kT2 = = 5.5%.<br /><br /><br />4-4 k* = 3%; IP = 3%; kT2 = 6.2%; MRP2 = ?<br /><br />kT2 = k* + IP + MRP = 6.2%<br />kT2 = 3% + 3% + MRP = 6.2%<br />MRP = 0.2%.<br /> <br />4-5 Let x equal the yield on 2-year securities 4 years from now:<br /><br />7.5% = [(4)(7%) + 2x]/6<br />0.45 = 0.28 + 2x<br /> x = 0.085 or 8.5%.<br /><br /><br />4-6 k = k* + IP + MRP + DRP + LP.<br />k* = 0.03.<br />IP = [0.03 + 0.04 + (5)(0.035)]/7 = 0.035.<br />MRP = 0.0005(6) = 0.003.<br />DRP = 0.<br />LP = 0.<br /><br />kT7 = 0.03 + 0.035 + 0.003 = 0.068 = 6.8%.<br /><br /><br />4-7 a. k1 = 3%, and<br /><br />k2 = = 4.5%,<br /><br />Solving for k1 in Year 2, 1k1, we obtain<br /><br />1k1 = (4.5% × 2) - 3% = 6%.<br /><br />b. For riskless bonds under the expectations theory, the interest rate for a bond of any maturity is kn = k* + average inflation over n years. If k* = 1%, we can solve for IPn:<br /><br />Year 1: k1 = 1% + I1 = 3%;<br />I1 = expected inflation = 3% - 1% = 2%.<br /><br />Year 2: k1 = 1% + I2 = 6%;<br />I2 = expected inflation = 6% - 1% = 5%.<br /><br />Note also that the average inflation rate is (2% + 5%)/2 = 3.5%, which, when added to k* = 1%, produces the yield on a 2-year bond, 4.5 percent. Therefore, all of our results are consistent.<br /><br />Alternative solution: Solve for the inflation rates in Year 1 and Year 2 first:<br /><br />kRF = k* + IP.<br /> <br />Year 1: 3% = 1% + IP1; IP1 = 2%, thus I1 = 2%.<br /><br />Year 2: 4.5% = 1% + IP2; IP2 = 3.5%.<br /><br /> IP2 = (I1 + I2)/2<br />3.5% = (2% + I2)/2<br /> I2 = 5%.<br /><br />Then solve for the yield on the one-year bond in the second year:<br />Year 2: k1 = 1% + 5% = 6%.<br /><br /><br />4-8 k* = 2%; MRP = 0%; k1 = 5%; k2 = 7%; 1k1 = ?<br /><br />1k1 represents the one-year rate on a bond one year from now (Year 2).<br /><br />k2 = <br />7% = <br />9% = 1k1.<br /><br />1k1 = k* + I2<br />9% = 2% + I2<br />7% = I2.<br /><br />The average interest rate during the 2-year period differs from the 1-year interest rate expected for Year 2 because of the inflation rate reflected in the two interest rates. The inflation rate reflected in the interest rate on any security is the average rate of inflation expected over the security’s life.<br /><br /><br />4-9 Basic relevant equations:<br /><br />kt = k* + IPt + DRPt + MRPt + LPt.<br /><br />But here IP is the only premium, so kt = k* + IPt.<br /><br />IPt = Avg. inflation = (I1 + I2 + ...)/N.<br /><br />We know that I1 = IP1 = 3% and k* = 2%. Therefore,<br /><br />kT1 = 2% + 3% = 5%. kT3 = k1 + 2% = 5% + 2% = 7%. But,<br /><br />kT3 = k* + IP3 = 2% + IP3 = 7%, so<br /><br />IP3 = 7% - 2% = 5%.<br /><br />We also know that It = Constant after t = 1.<br /><br />We can set up this table:<br /><br /> k* I Avg. I = IPt k = k* + IPt<br />1 2 3 3%/1 = 3% 5%<br />2 2 I (3% + I)/2 = IP2<br />3 2 I (3% + I + I)/3 = IP3 k3 = 7%, so IP3 = 7% - 2% = 5%.<br /><br />IP3 = (3% + 2I)/3 = 5%<br /> 2I = 12%<br /> I = 6%.<br /><br /><br />4-10 kC8 = k* + IP8 + MRP8 + DRP8 + LP8<br />8.3% = 2.5% + (2.8% 4 + 3.75% 4)/8 + 0.0% + DRP8 + 0.75%<br />8.3% = 2.5% + 3.275% + 0.0% + DRP8 + 0.75%<br />8.3% = 6.525% + DRP8<br />DRP8 = 1.775%.<br /><br /><br />4-11 T-bill rate = k* + IP<br /> 5.5% = k* + 3.25%<br /> k* = 2.25%.<br /><br /><br />4-12 We’re given all the components to determine the yield on the Cartwright bonds except the default risk premium (DRP) and MRP. Calculate the MRP as 0.1%(5 - 1) = 0.4%. Now, we can solve for the DRP as follows:<br />7.75% = 2.3% + 2.5% + 0.4% + 1.0% + DRP, or DRP = 1.55%.<br /><br /><br />4-13 First, calculate the inflation premiums for the next three and five years, respectively. They are IP3 = (2.5% + 3.2% + 3.6%)/3 = 3.1% and IP5 = (2.5% + 3.2% + 3.6% + 3.6% + 3.6%)/5 = 3.3%. The real risk-free rate is given as 2.75%. Since the default and liquidity premiums are zero on Treasury bonds, we can now solve for the default risk premium. Thus, 6.25% = 2.75% + 3.1% + MRP3, or MRP3 = 0.4%. Similarly, 6.8% = 2.75% + 3.3% + MRP5, or MRP5 = 0.75%. Thus, MRP5 – MRP3 = 0.75% - 0.40% = 0.35%.<br /><br /><br />4-14 a. Real<br />Years to Risk-Free<br />Maturity Rate (k*) IP** MRP kT = k* + IP + MRP<br /> 1 2% 7.00% 0.2% 9.20%<br /> 2 2 6.00 0.4 8.40<br /> 3 2 5.00 0.6 7.60<br /> 4 2 4.50 0.8 7.30<br /> 5 2 4.20 1.0 7.20<br /> 10 2 3.60 1.0 6.60<br /> 20 2 3.30 1.0 6.30<br /><br /> <br />**The computation of the inflation premium is as follows:<br /><br /> <br /> Expected Average<br />Year Inflation Expected Inflation<br /> 1 7% 7.00%<br /> 2 5 6.00 <br /> 3 3 5.00 <br /> 4 3 4.50 <br /> 5 3 4.20 <br /> 10 3 3.60 <br /> 20 3 3.30 <br /><br />For example, the calculation for 3 years is as follows:<br /><br /> <br /><br />Thus, the yield curve would be as follows:<br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br />b. The interest rate on the Exxon Mobil bonds has the same components as the Treasury securities, except that the Exxon Mobil bonds have default risk, so a default risk premium must be included. Therefore,<br /><br />kExxon Mobil = k* + IP + MRP + DRP.<br /><br /> <br />For a strong company such as Exxon Mobil, the default risk premium is virtually zero for short-term bonds. However, as time to maturity increases, the probability of default, although still small, is suffi-cient to warrant a default premium. Thus, the yield risk curve for the Exxon Mobil bonds will rise above the yield curve for the Treasury securities. In the graph, the default risk premium was assumed to be 1.0 percentage point on the 20-year Exxon Mobil bonds. The return should equal 6.3% + 1% = 7.3%.<br /><br />c. Exelon bonds would have significantly more default risk than either Treasury securities or Exxon Mobil bonds, and the risk of default would increase over time due to possible financial deterioration. In this example, the default risk premium was assumed to be 1.0 percentage point on the 1-year Exelon bonds and 2.0 percentage points on the <br />20-year bonds. The 20-year return should equal 6.3% + 2% = 8.3%.<br /><br /><br />4-15 Term Rate<br /> 6 months 5.1%<br /> 1 year 5.5<br /> 2 years 5.6<br /> 3 years 5.7<br /> 4 years 5.8<br /> 5 years 6.0<br />10 years 6.1<br />20 years 6.5<br />30 years 6.3<br /><br /><br /><br /><br /><br />4-16 a. The average rate of inflation for the 5-year period is calculated as:<br /><br /> = (0.13 + 0.09 + 0.07 + 0.06 + 0.06)/5 = 8.20%.<br /><br />b. k = k* + IPAvg. = 2% + 8.2% = 10.20%.<br /><br /> <br />c. Here is the general situation:<br /><br /> Arithmetic<br /> 1-Year Average Maturity Estimated<br /> Expected Expected Risk Interest<br /> Year Inflation Inflation k* Premium Rates <br /> 1 13% 13.0% 2% 0.1% 15.1%<br /> 2 9 11.0 2 0.2 13.2<br /> 3 7 9.7 2 0.3 12.0<br /> 5 6 8.2 2 0.5 10.7<br /> . . . . . .<br /> . . . . . .<br /> . . . . . .<br /> 10 6 7.1 2 1.0 10.1<br /> 20 6 6.6 2 2.0 10.6<br /> <br /><br />d. The “normal” yield curve is upward sloping because, in “normal” times, inflation is not expected to trend either up or down, so IP is the same for debt of all maturities, but the MRP increases with years, so the yield curve slopes up. During a recession, the yield curve typically slopes up especially steeply, because inflation and consequently short-term interest rates are currently low, yet people expect inflation and interest rates to rise as the economy comes out of the recession.<br /><br />e. If inflation rates are expected to be constant, then the expectations theory holds that the yield curve should be hori¬zontal. However, in this event it is likely that maturity risk premiums would be applied to long-term bonds because of the greater risks of holding long-term rather than short-term bonds:<br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /> <br />If maturity risk premiums were added to the yield curve in Part e above, then the yield curve would be more nearly normal; that is, the long-term end of the curve would be raised. (The yield curve shown in this answer is upward sloping; the yield curve shown in Part c is downward sloping.)<br /> <br />SPREADSHEET PROBLEM<br /><br /><br /><br />4-17 The detailed solution for the spreadsheet problem is available both on the instructor’s resource CD-ROM and on the instructor’s side of South-Western’s web site, http://brigham.swlearning.com.<br /><br /> <br />INTEGRATED CASE<br /><br /><br /><br />Smyth Barry & Company<br />Financial Markets, Institutions, and Interest Rates<br /><br />4-18 ASSUME THAT YOU RECENTLY GRADUATED WITH A DEGREE IN FINANCE AND HAVE JUST REPORTED TO WORK AS AN INVESTMENT ADVISOR AT THE BROKERAGE FIRM OF SMYTH BARRY & CO. YOUR FIRST ASSIGNMENT IS TO EXPLAIN THE NATURE OF THE U.S. FINANCIAL MARKETS TO MICHELLE VARGA, A PROFESSIONAL TENNIS PLAYER WHO HAS JUST COME TO THE UNITED STATES FROM MEXICO. VARGA IS A HIGHLY RANKED TENNIS PLAYER WHO EXPECTS TO INVEST SUBSTANTIAL AMOUNTS OF MONEY THROUGH SMYTH BARRY. SHE IS ALSO VERY BRIGHT, AND, THEREFORE, SHE WOULD LIKE TO UNDERSTAND IN GENERAL TERMS WHAT WILL HAPPEN TO HER MONEY. YOUR BOSS HAS DEVELOPED THE FOLLOWING SET OF QUESTIONS THAT YOU MUST ASK AND ANSWER TO EXPLAIN THE U.S. FINANCIAL SYSTEM TO VARGA.<br /><br />A. WHAT IS A MARKET? DIFFERENTIATE BETWEEN THE FOLLOWING TYPES OF MARKETS: PHYSICAL ASSET VS. FINANCIAL MARKETS, SPOT VS. FUTURES MARKETS, MONEY VS. CAPITAL MARKETS, PRIMARY VS. SECONDARY MARKETS, AND PUBLIC VS. PRIVATE MARKETS.<br /><br />ANSWER: [SHOW S4-1 THROUGH S4-3 HERE.] A MARKET IS ONE IN WHICH ASSETS ARE BOUGHT AND SOLD. THERE ARE MANY DIFFERENT TYPES OF FINANCIAL MARKETS, EACH ONE DEALING WITH A DIFFERENT TYPE OF FINANCIAL ASSET, SERVING A DIFFERENT SET OF CUSTOMERS, OR OPERATING IN A DIFFERENT PART OF THE COUNTRY. FINANCIAL MARKETS DIFFER FROM PHYSICAL ASSET MARKETS IN THAT REAL, OR TANGIBLE, ASSETS SUCH AS MACHINERY, REAL ESTATE, AND AGRICULTURAL PRODUCTS ARE TRADED IN THE PHYSICAL ASSET MARKETS, BUT FINANCIAL SECURITIES REPRESENTING CLAIMS ON ASSETS ARE TRADED IN THE FINANCIAL MARKETS. SPOT MARKETS ARE MARKETS IN WHICH ASSETS ARE BOUGHT OR SOLD FOR “ON-THE-SPOT” DELIVERY, WHILE FUTURES MARKETS ARE MARKETS IN WHICH PARTICIPANTS AGREE TODAY TO BUY OR SELL AN ASSET AT SOME FUTURE DATE.<br />MONEY MARKETS ARE THE MARKETS IN WHICH DEBT SECURITIES WITH MATURITIES OF LESS THAN ONE YEAR ARE TRADED. NEW YORK, LONDON, AND TOKYO ARE MAJOR MONEY MARKET CENTERS. LONGER-TERM SECURITIES, INCLUDING STOCKS AND BONDS, ARE TRADED IN THE CAPITAL MARKETS. THE NEW YORK STOCK EXCHANGE IS AN EXAMPLE OF A CAPITAL MARKET, WHILE THE NEW YORK COMMERCIAL PAPER AND TREASURY BILL MARKETS ARE MONEY MARKETS.<br />PRIMARY MARKETS ARE MARKETS IN WHICH CORPORATIONS RAISE CAPITAL BY ISSUING NEW SECURITIES, WHILE SECONDARY MARKETS ARE MARKETS IN WHICH SECURITIES AND OTHER FINANCIAL ASSETS ARE TRADED AMONG INVESTORS AFTER THEY HAVE BEEN ISSUED BY CORPORATIONS. PRIVATE MARKETS, WHERE TRANSACTIONS ARE WORKED OUT DIRECTLY BETWEEN TWO PARTIES, ARE DIFFERENTIATED FROM PUBLIC MARKETS, WHERE STANDARDIZED CONTRACTS ARE TRADED ON ORGANIZED EXCHANGES.<br /><br /><br />B. WHAT IS AN INITIAL PUBLIC OFFERING (IPO) MARKET?<br /><br />ANSWER: THE INITIAL PUBLIC OFFERING (IPO) MARKET IS A SUBSET OF THE PRIMARY MARKET. HERE FIRMS “GO PUBLIC” BY OFFERING SHARES TO THE PUBLIC FOR THE FIRST TIME.<br /><br /><br /> <br />C. IF APPLE COMPUTER DECIDED TO ISSUE ADDITIONAL COMMON STOCK, AND VARGA PURCHASED 100 SHARES OF THIS STOCK FROM MERRILL LYNCH, THE UNDERWRITER, WOULD THIS TRANSACTION BE A PRIMARY MARKET TRANSACTION OR A SECONDARY MARKET TRANSACTION? WOULD IT MAKE A DIFFERENCE IF VARGA PURCHASED PREVIOUSLY OUTSTANDING APPLE STOCK IN THE DEALER MARKET?<br /><br />ANSWER: IF VARGA PURCHASED NEWLY ISSUED APPLE STOCK, THIS WOULD CONSTITUTE A PRIMARY MARKET TRANSACTION, WITH MERRILL LYNCH ACTING AS AN INVESTMENT BANKER IN THE TRANSACTION. IF VARGA PURCHASED “USED” STOCK, THEN THE TRANSACTION WOULD BE IN THE SECONDARY MARKET.<br /><br /><br />D. DESCRIBE THE THREE PRIMARY WAYS IN WHICH CAPITAL IS TRANSFERRED BETWEEN SAVERS AND BORROWERS.<br /><br />ANSWER: [SHOW S4-4 AND S4-5 HERE.] TRANSFERS OF CAPITAL CAN BE MADE (1) BY DIRECT TRANSFER OF MONEY AND SECURITIES, (2) THROUGH AN INVESTMENT BANKING HOUSE, OR (3) THROUGH A FINANCIAL INTERMEDIARY. IN A DIRECT TRANSFER, A BUSINESS SELLS ITS STOCKS OR BONDS DIRECTLY TO INVESTORS (SAVERS), WITHOUT GOING THROUGH ANY TYPE OF INSTITUTION. THE BUSINESS BORROWER RECEIVES DOLLARS FROM THE SAVERS, AND THE SAVERS RECEIVE SECURITIES (BONDS OR STOCK) IN RETURN.<br />IF THE TRANSFER IS MADE THROUGH AN INVESTMENT BANKING HOUSE, THE INVESTMENT BANK SERVES AS A MIDDLEMAN. THE BUSINESS SELLS ITS SECURITIES TO THE INVESTMENT BANK, WHICH IN TURN SELLS THEM TO THE SAVERS. ALTHOUGH THE SECURITIES ARE SOLD TWICE, THE TWO SALES CONSTITUTE ONE COMPLETE TRANSACTION IN THE PRIMARY MARKET.<br />IF THE TRANSFER IS MADE THROUGH A FINANCIAL INTERMEDIARY, SAVERS INVEST FUNDS WITH THE INTERMEDIARY, WHICH THEN ISSUES ITS OWN SECURITIES IN EXCHANGE. BANKS ARE ONE TYPE OF INTERMEDIARY, RECEIVING DOLLARS FROM MANY SMALL SAVERS AND THEN LENDING THESE DOLLARS TO BORROWERS TO PURCHASE HOMES, AUTOMOBILES, VACATIONS, AND SO ON, AND ALSO TO BUSINESSES AND GOVERNMENT UNITS. THE SAVERS RECEIVE A CERTIFICATE OF DEPOSIT OR SOME OTHER INSTRUMENT IN EXCHANGE FOR THE FUNDS DEPOSITED WITH THE BANK. MUTUAL FUNDS, INSURANCE COMPANIES, AND PENSION FUNDS ARE OTHER TYPES OF INTERMEDIARIES.<br /><br /><br /> <br />E. WHAT ARE THE TWO LEADING STOCK MARKETS? DESCRIBE THE TWO BASIC TYPES OF STOCK MARKETS.<br /><br />ANSWER: [SHOW S4-6 HERE.] THE TWO LEADING STOCK MARKETS TODAY ARE THE NEW YORK STOCK EXCHANGE AND THE NASDAQ STOCK MARKET. THERE ARE JUST TWO BASIC TYPES OF STOCK MARKETS: (1) PHYSICAL LOCATION EXCHANGES, WHICH INCLUDE THE NEW YORK STOCK EXCHANGE (NYSE), THE AMERICAN STOCK EXCHANGE (AMEX), AND SEVERAL REGIONAL STOCK EXCHANGES, AND (2) ELECTRONIC DEALER-BASED MARKETS THAT INCLUDE THE NASDAQ STOCK MARKET, THE LESS FORMAL OVER-THE-COUNTER MARKET, AND THE RECENTLY DEVELOPED ELECTRONIC COMMUNICATIONS NETWORKS (ECNs).<br /> THE PHYSICAL LOCATION EXCHANGES ARE FORMAL ORGANIZATIONS HAVING TANGIBLE, PHYSICAL LOCATIONS AND TRADING IN DESIGNATED SECURITIES. THERE ARE EXCHANGES FOR STOCKS, BONDS, COMMODITIES, FUTURES, AND OPTIONS. THE PHYSICAL LOCATION EXCHANGES ARE CONDUCTED AS AUCTION MARKETS WITH SECURITIES GOING TO THE HIGHEST BIDDER. BUYERS AND SELLERS PLACE ORDERS WITH THEIR BROKERS WHO THEN EXECUTE THOSE ORDERS BY MATCHING BUYERS AND SELLERS, ALTHOUGH SPECIALISTS ASSIST IN PROVIDING CONTINUITY TO THE MARKETS.<br />THE ELECTRONIC DEALER-BASED MARKET IS MADE UP OF HUNDREDS OF BROKERS AND DEALERS AROUND THE COUNTRY WHO ARE CONNECTED ELECTRONICALLY BY TELEPHONES AND COMPUTERS. THE DEALER-BASED MARKET FACILITATES TRADING OF SECURITIES THAT ARE NOT LISTED ON A PHYSICAL LOCATION EXCHANGE. A DEALER MARKET IS DEFINED TO INCLUDE ALL FACILITIES THAT ARE NEEDED TO CONDUCT SECURITY TRANSACTIONS NOT MADE ON THE PHYSICAL LOCATION EXCHANGES. THESE FACILITIES INCLUDE (1) THE RELATIVELY FEW DEALERS WHO HOLD INVENTORIES OF THESE SECURITIES AND WHO ARE SAID TO MAKE A MARKET IN THESE SECURITIES; (2) THE THOUSANDS OF BROKERS WHO ACT AS AGENTS IN BRINGING THE DEALERS TOGETHER WITH INVESTORS; AND (3) THE COMPUTERS, TERMINALS, AND ELECTRONIC NETWORKS THAT PROVIDE A COMMUNICATION LINK BETWEEN DEALERS AND BROKERS. DEALERS CONTINUOUSLY POST A PRICE AT WHICH THEY ARE WILLING TO BUY THE STOCK (THE BID PRICE) AND A PRICE AT WHICH THEY ARE WILLING TO SELL THE STOCK (THE ASK PRICE). THE ASK PRICE IS ALWAYS HIGHER THAN THE BID PRICE, AND THE DIFFERENCE (OR “BID-ASK SPREAD”) REPRESENTS THE DEALER’S MARKUP, OR PROFIT.<br /><br /><br />F. WHAT DO WE CALL THE PRICE THAT A BORROWER MUST PAY FOR DEBT CAPITAL? WHAT IS THE PRICE OF EQUITY CAPITAL? WHAT ARE THE FOUR MOST FUNDAMENTAL FACTORS THAT AFFECT THE COST OF MONEY, OR THE GENERAL LEVEL OF INTEREST RATES, IN THE ECONOMY?<br /><br />ANSWER: [SHOW S4-7 AND S4-8 HERE.] THE INTEREST RATE IS THE PRICE PAID FOR BORROWED CAPITAL, WHILE THE RETURN ON EQUITY CAPITAL COMES IN THE FORM OF DIVIDENDS PLUS CAPITAL GAINS. THE RETURN THAT INVESTORS REQUIRE ON CAPITAL DEPENDS ON (1) PRODUCTION OPPORTUNITIES, (2) TIME PREFERENCES FOR CONSUMPTION, (3) RISK, AND (4) INFLATION.<br />PRODUCTION OPPORTUNITIES REFER TO THE RETURNS THAT ARE AVAILABLE FROM INVESTMENT IN PRODUCTIVE ASSETS: THE MORE PRODUCTIVE A PRODUCER FIRM BELIEVES ITS ASSETS WILL BE, THE MORE IT WILL BE WILLING TO PAY FOR THE CAPITAL NECESSARY TO ACQUIRE THOSE ASSETS.<br />TIME PREFERENCE FOR CONSUMPTION REFERS TO CONSUMERS’ PREFERENCES FOR CURRENT CONSUMPTION VERSUS SAVINGS FOR FUTURE CONSUMPTION: CONSUMERS WITH LOW PREFERENCES FOR CURRENT CONSUMPTION WILL BE WILLING TO LEND AT A LOWER RATE THAN CONSUMERS WITH A HIGH PREFERENCE FOR CURRENT CONSUMPTION.<br />INFLATION REFERS TO THE TENDENCY OF PRICES TO RISE, AND THE HIGHER THE EXPECTED RATE OF INFLATION, THE LARGER THE REQUIRED RATE OF RETURN.<br />RISK, IN A MONEY AND CAPITAL MARKET CONTEXT, REFERS TO THE CHANCE THAT A LOAN WILL NOT BE REPAID AS PROMISED--THE HIGHER THE PERCEIVED DEFAULT RISK, THE HIGHER THE REQUIRED RATE OF RETURN.<br />RISK IS ALSO LINKED TO THE MATURITY AND LIQUIDITY OF A SECURITY. THE LONGER THE MATURITY AND THE LESS LIQUID (MARKETABLE) THE SECURITY, THE HIGHER THE REQUIRED RATE OF RETURN, OTHER THINGS CONSTANT.<br />THE PRECEDING DISCUSSION RELATED TO THE GENERAL LEVEL OF MONEY COSTS, BUT THE LEVEL OF INTEREST RATES WILL ALSO BE INFLUENCED BY SUCH THINGS AS FED POLICY, FISCAL AND FOREIGN TRADE DEFICITS, AND THE LEVEL OF ECONOMIC ACTIVITY. ALSO, INDIVIDUAL SECURITIES WILL HAVE HIGHER YIELDS THAN THE RISK-FREE RATE BECAUSE OF THE ADDITION OF VARIOUS PREMIUMS AS DISCUSSED BELOW.<br /><br /><br />G. WHAT IS THE REAL RISK-FREE RATE OF INTEREST (k*) AND THE NOMINAL RISK-FREE RATE (kRF)? HOW ARE THESE TWO RATES MEASURED?<br /><br />ANSWER: [SHOW S4-9 AND S4-10 HERE.] KEEP THESE EQUATIONS IN MIND AS WE DISCUSS INTEREST RATES. WE WILL DEFINE THE TERMS AS WE GO ALONG:<br /><br />k = k* + IP + DRP + LP + MRP.<br /><br />kRF = k* + IP.<br /><br />THE REAL RISK-FREE RATE, k*, IS THE RATE THAT WOULD EXIST ON DEFAULT-FREE SECURITIES IN THE ABSENCE OF INFLATION.<br />THE NOMINAL RISK-FREE RATE, kRF, IS EQUAL TO THE REAL RISK-FREE RATE PLUS AN INFLATION PREMIUM, WHICH IS EQUAL TO THE AVERAGE RATE OF INFLATION EXPECTED OVER THE LIFE OF THE SECURITY.<br /> <br />THERE IS NO TRULY RISKLESS SECURITY, BUT THE CLOSEST THING IS A SHORT-TERM U.S. TREASURY BILL (T-BILL), WHICH IS FREE OF MOST RISKS. THE REAL RISK-FREE RATE, k*, IS ESTIMATED BY SUBTRACTING THE EXPECTED RATE OF INFLATION FROM THE RATE ON SHORT-TERM TREASURY SECURITIES. IT IS GENERALLY ASSUMED THAT k* IS IN THE RANGE OF 1 TO 4 PERCENTAGE POINTS. THE T-BOND RATE IS USED AS A PROXY FOR THE LONG-TERM RISK-FREE RATE. HOWEVER, WE KNOW THAT ALL LONG-TERM BONDS CONTAIN INTEREST RATE RISK, SO THE T-BOND RATE IS NOT REALLY RISKLESS. IT IS, HOWEVER, FREE OF DEFAULT RISK.<br /><br /><br />H. DEFINE THE TERMS INFLATION PREMIUM (IP), DEFAULT RISK PREMIUM (DRP), LIQUIDITY PREMIUM (LP), AND MATURITY RISK PREMIUM (MRP). WHICH OF THESE PREMIUMS IS INCLUDED WHEN DETERMINING THE INTEREST RATE ON <br />(1) SHORT-TERM U.S. TREASURY SECURITIES, (2) LONG-TERM U.S. TREASURY SECURITIES, (3) SHORT-TERM CORPORATE SECURITIES, AND (4) LONG-TERM CORPORATE SECURITIES? EXPLAIN HOW THE PREMIUMS WOULD VARY OVER TIME AND AMONG THE DIFFERENT SECURITIES LISTED ABOVE.<br /><br />ANSWER: [SHOW S4-11 HERE.] THE INFLATION PREMIUM (IP) IS A PREMIUM ADDED TO THE REAL RISK-FREE RATE OF INTEREST TO COMPENSATE FOR EXPECTED INFLATION.<br />THE DEFAULT RISK PREMIUM (DRP) IS A PREMIUM BASED ON THE PROBABILITY THAT THE ISSUER WILL DEFAULT ON THE LOAN, AND IT IS MEASURED BY THE DIFFERENCE BETWEEN THE INTEREST RATE ON A U.S. TREASURY BOND AND A CORPORATE BOND OF EQUAL MATURITY AND MARKETABILITY.<br />A LIQUID ASSET IS ONE THAT CAN BE SOLD AT A PREDICTABLE PRICE ON SHORT NOTICE; A LIQUIDITY PREMIUM IS ADDED TO THE RATE OF INTEREST ON SECURITIES THAT ARE NOT LIQUID.<br />THE MATURITY RISK PREMIUM (MRP) IS A PREMIUM THAT REFLECTS INTEREST RATE RISK; LONGER-TERM SECURITIES HAVE MORE INTEREST RATE RISK (THE RISK OF CAPITAL LOSS DUE TO RISING INTEREST RATES) THAN DO SHORTER-TERM SECURITIES, AND THE MRP IS ADDED TO REFLECT THIS RISK.<br /><br />1. SHORT-TERM TREASURY SECURITIES INCLUDE ONLY AN INFLATION PREMIUM.<br /><br />2. LONG-TERM TREASURY SECURITIES CONTAIN AN INFLATION PREMIUM PLUS A MATURITY RISK PREMIUM. NOTE THAT THE INFLATION PREMIUM ADDED TO LONG-TERM SECURITIES WILL DIFFER FROM THAT FOR SHORT-TERM SECURITIES UNLESS THE RATE OF INFLATION IS EXPECTED TO REMAIN CONSTANT.<br /><br /> <br />3. THE RATE ON SHORT-TERM CORPORATE SECURITIES IS EQUAL TO THE REAL RISK-FREE RATE PLUS PREMIUMS FOR INFLATION, DEFAULT RISK, AND LIQUIDITY. THE SIZE OF THE DEFAULT AND LIQUIDITY PREMIUMS WILL VARY DEPENDING ON THE FINANCIAL STRENGTH OF THE ISSUING CORPORATION AND ITS DEGREE OF LIQUIDITY, WITH LARGER CORPORATIONS GENERALLY HAVING GREATER LIQUIDITY BECAUSE OF MORE ACTIVE TRADING.<br /><br />4. THE RATE FOR LONG-TERM CORPORATE SECURITIES ALSO INCLUDES A PREMIUM FOR MATURITY RISK. THUS, LONG-TERM CORPORATE SECURITIES GENERALLY CARRY THE HIGHEST YIELDS OF THESE FOUR TYPES OF SECURITIES.<br /><br /><br />I. WHAT IS THE TERM STRUCTURE OF INTEREST RATES? WHAT IS A YIELD CURVE?<br /><br />ANSWER: [SHOW S4-12 HERE. S4-12 SHOWS A RECENT (OCTOBER 2002) TREASURY YIELD CURVE.] THE TERM STRUCTURE OF INTEREST RATES IS THE RELATIONSHIP BETWEEN INTEREST RATES, OR YIELDS, AND MATURITIES OF SECURITIES. WHEN THIS RELATIONSHIP IS GRAPHED, THE RESULTING CURVE IS CALLED A YIELD CURVE. (SKETCH OUT A YIELD CURVE ON THE BOARD.)<br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br />J. SUPPOSE MOST INVESTORS EXPECT THE INFLATION RATE TO BE 5 PERCENT NEXT YEAR, 6 PERCENT THE FOLLOWING YEAR, AND 8 PERCENT THEREAFTER. THE REAL RISK-FREE RATE IS 3 PERCENT. THE MATURITY RISK PREMIUM IS ZERO FOR BONDS THAT MATURE IN 1 YEAR OR LESS, 0.1 PERCENT FOR 2-YEAR BONDS, AND THEN THE MRP INCREASES BY 0.1 PERCENT PER YEAR THEREAFTER FOR 20 YEARS, AFTER WHICH IT IS STABLE. WHAT IS THE INTEREST RATE ON 1-YEAR, 10-YEAR, AND 20-YEAR TREASURY BONDS? DRAW A YIELD CURVE WITH THESE DATA. WHAT FACTORS CAN EXPLAIN WHY THIS CONSTRUCTED YIELD CURVE IS UPWARD SLOPING?<br /><br />ANSWER: [SHOW S4-13 THROUGH S4-18 HERE.]<br /><br />STEP 1: FIND THE AVERAGE EXPECTED INFLATION RATE OVER YEARS 1 TO 20:<br /><br />YR 1: IP = 5.0%.<br /><br />YR 10: IP = (5 + 6 + 8 + 8 + 8 + ... + 8)/10 = 7.5%.<br /><br />YR 20: IP = (5 + 6 + 8 + 8 + ... + 8)/20 = 7.75%.<br /><br />STEP 2: FIND THE MATURITY RISK PREMIUM IN EACH YEAR:<br /><br />YR 1: MRP = 0.0%.<br /><br />YR 10: MRP = 0.1% 9 = 0.9%.<br /><br />YR 20: MRP = 0.1% 19 = 1.9%.<br /><br />STEP 3: SUM THE IPs AND MRPs, AND ADD k* = 3%:<br /><br />YR 1: kRF = 3% + 5.0% + 0.0% = 8.0%.<br /><br />YR 10: kRF = 3% + 7.5% + 0.9% = 11.4%.<br /><br />YR 20: kRF = 3% + 7.75% + 1.9% = 12.65%.<br /><br />THE SHAPE OF THE YIELD CURVE DEPENDS PRIMARILY ON TWO FACTORS: <br />(1) EXPECTATIONS ABOUT FUTURE INFLATION AND (2) THE RELATIVE RISKINESS OF SECURITIES WITH DIFFERENT MATURITIES.<br />THE CONSTRUCTED YIELD CURVE IS UPWARD SLOPING. THIS IS DUE TO INCREASING EXPECTED INFLATION AND AN INCREASING MATURITY RISK PREMIUM.<br /><br /><br />K. AT ANY GIVEN TIME, HOW WOULD THE YIELD CURVE FACING AN AAA-RATED COMPANY COMPARE WITH THE YIELD CURVE FOR U.S. TREASURY SECURITIES? AT ANY GIVEN TIME, HOW WOULD THE YIELD CURVE FACING A BB-RATED COMPANY COMPARE WITH THE YIELD CURVE FOR U.S. TREASURY SECURITIES? DRAW A GRAPH TO ILLUSTRATE YOUR ANSWER.<br /><br /> <br />ANSWER: [SHOW S4-19 THROUGH S4-20 HERE.] (CURVES FOR AAA-RATED AND BB-RATED SECURITIES HAVE BEEN ADDED TO DEMONSTRATE THAT RISKIER SECURITIES REQUIRE HIGHER RETURNS.) THE YIELD CURVE NORMALLY SLOPES UPWARD, INDICATING THAT SHORT-TERM INTEREST RATES ARE LOWER THAN LONG-TERM INTEREST RATES. YIELD CURVES CAN BE DRAWN FOR GOVERNMENT SECURITIES OR FOR THE SECURITIES OF ANY CORPORATION, BUT CORPORATE YIELD CURVES WILL ALWAYS LIE ABOVE GOVERNMENT YIELD CURVES, AND THE RISKIER THE CORPORATION, THE HIGHER ITS YIELD CURVE. THE SPREAD BETWEEN A CORPORATE YIELD CURVE AND THE TREASURY CURVE WIDENS AS THE CORPORATE BOND RATING DECREASES.<br /><br /><br />L. WHAT IS THE PURE EXPECTATIONS THEORY? WHAT DOES THE PURE EXPECTATIONS THEORY IMPLY ABOUT THE TERM STRUCTURE OF INTEREST RATES?<br /><br />ANSWER: [SHOW S4-21 AND S4-22 HERE.] THE PURE EXPECTATIONS THEORY ASSUMES THAT INVESTORS ESTABLISH BOND PRICES AND INTEREST RATES STRICTLY ON THE BASIS OF EXPECTATIONS FOR INTEREST RATES. THIS MEANS THAT THEY ARE INDIFFERENT WITH RESPECT TO MATURITY IN THE SENSE THAT THEY DO NOT VIEW LONG-TERM BONDS AS BEING RISKIER THAN SHORT-TERM BONDS. IF THIS WERE TRUE, THEN THE MATURITY RISK PREMIUM WOULD BE ZERO, AND LONG-TERM INTEREST RATES WOULD SIMPLY BE A WEIGHTED AVERAGE OF CURRENT AND EXPECTED FUTURE SHORT-TERM INTEREST RATES. IF THE PURE EXPECTATIONS THEORY IS CORRECT, YOU CAN USE THE YIELD CURVE TO “BACK OUT” EXPECTED FUTURE INTEREST RATES.<br /><br /><br />M. SUPPOSE THAT YOU OBSERVE THE FOLLOWING TERM STRUCTURE FOR TREASURY SECURITIES:<br /><br /> MATURITY YIELD<br /> 1 YEAR 6.0%<br /> 2 YEARS 6.2<br /> 3 YEARS 6.4<br /> 4 YEARS 6.5<br /> 5 YEARS 6.5<br /><br />ASSUME THAT THE PURE EXPECTATIONS THEORY OF THE TERM STRUCTURE IS CORRECT. (THIS IMPLIES THAT YOU CAN USE THE YIELD CURVE GIVEN ABOVE TO “BACK OUT” THE MARKET’S EXPECTATIONS ABOUT FUTURE INTEREST RATES.) <br />WHAT DOES THE MARKET EXPECT WILL BE THE INTEREST RATE ON 1-YEAR SECURITIES ONE YEAR FROM NOW? WHAT DOES THE MARKET EXPECT WILL BE THE INTEREST RATE ON 3-YEAR SECURITIES TWO YEARS FROM NOW?<br /><br />ANSWER: [SHOW S4-23 THROUGH S4-27 HERE.] CALCULATION FOR k ON 1-YEAR SECURITIES ONE YEAR FROM NOW:<br /><br /> 6.2% = <br />12.4% = 6.0% + X<br /> 6.4% = X.<br /><br />ONE YEAR FROM NOW, 1-YEAR SECURITIES WILL YIELD 6.4%.<br />CALCULATION FOR k ON 3-YEAR SECURITIES TWO YEARS FROM NOW:<br /><br /> 6.5% = <br />32.5% = 12.4% + 3X<br />20.1% = 3X<br /> 6.7% = X.<br /><br />TWO YEARS FROM NOW, 3-YEAR SECURITIES WILL YIELD 6.7%.<br /><br /><br />N. FINALLY, VARGA IS ALSO INTERESTED IN INVESTING IN COUNTRIES OTHER THAN THE UNITED STATES. DESCRIBE THE VARIOUS TYPES OF RISKS THAT ARISE WHEN INVESTING OVERSEAS.<br /><br />ANSWER: [SHOW S4-28 AND S4-29 HERE.] FIRST, VARGA SHOULD CONSIDER COUNTRY RISK, WHICH REFERS TO THE RISK THAT ARISES FROM INVESTING OR DOING BUSINESS IN A PARTICULAR COUNTRY. THIS RISK DEPENDS ON THE COUNTRY’S ECONOMIC, POLITICAL, AND SOCIAL ENVIRONMENT. COUNTRY RISK ALSO INCLUDES THE RISK THAT PROPERTY WILL BE EXPROPRIATED WITHOUT ADEQUATE COMPENSATION, AS WELL AS NEW HOST COUNTRY STIPULATIONS ABOUT LOCAL PRODUCTION, SOURCING OR HIRING PRACTICES, AND DAMAGE OR DESTRUCTION OF FACILITIES DUE TO INTERNAL STRIFE.<br />SECOND, VARGA SHOULD CONSIDER EXCHANGE RATE RISK. VARGA NEEDS TO KEEP IN MIND WHEN INVESTING OVERSEAS THAT MORE OFTEN THAN NOT THE SECURITY WILL BE DENOMINATED IN A CURRENCY OTHER THAN THE DOLLAR, WHICH MEANS THAT THE VALUE OF THE INVESTMENT WILL DEPEND ON WHAT HAPPENS TO EXCHANGE RATES. TWO FACTORS CAN LEAD TO EXCHANGE RATE FLUCTUATIONS. (1) CHANGES IN RELATIVE INFLATION WILL LEAD TO CHANGES IN EXCHANGE RATES. (2) AN INCREASE IN COUNTRY RISK WILL ALSO CAUSE THE COUNTRY’S CURRENCY TO FALL. CONSEQUENTLY, INFLATION RISK, COUNTRY RISK, AND EXCHANGE RATE RISK ARE ALL INTERRELATED.saleem shahzadnoreply@blogger.com0tag:blogger.com,1999:blog-3421608066886271296.post-20966494740424298092010-12-14T13:23:00.002+05:002011-01-12T16:24:47.701+05:00Chapter 3 Chapter 3
<br /> Analysis of Financial Statements
<br />
<br />
<br />SOLUTIONS TO END-OF-CHAPTER PROBLEMS
<br />
<br />
<br />
<br />3-1 DSO = 40 days; S = $7,300,000; AR = ?
<br />
<br />DSO =
<br />40 =
<br />40 = AR/$20,000
<br />AR = $800,000.
<br />
<br />
<br />3-2 A/E = 2.4; D/A = ?
<br />
<br />
<br />
<br />
<br />3-3 ROA = 10%; PM = 2%; ROE = 15%; S/TA = ?; TA/E = ?
<br />ROA = NI/A; PM = NI/S; ROE = NI/E.
<br />
<br />ROA = PM S/TA
<br />NI/A = NI/S S/TA
<br />10% = 2% S/TA
<br />S/TA = 5.
<br />
<br />ROE = PM S/TA TA/E
<br />NI/E = NI/S S/TA TA/E
<br />15% = 2% 5 TA/E
<br />15% = 10% TA/E
<br />TA/E = 1.5.
<br />
<br />
<br />3-4 TA = $10,000,000,000; CL = $1,000,000,000; LT debt = $3,000,000,000; CE = $6,000,000,000; Shares outstanding = 800,000,000; P0 = $32; M/B = ?
<br />
<br />Book value = = $7.50.
<br />
<br />M/B = = 4.2667.
<br />
<br />
<br />3-5 TA = $12,000,000,000; T = 40%; EBIT/TA = 15%; ROA = 5%; TIE = ?
<br />
<br />= 0.15
<br />EBIT = $1,800,000,000.
<br />
<br />= 0.05
<br />NI = $600,000,000.
<br />
<br />Now use the income statement format to determine interest so you can calculate the firm’s TIE ratio.
<br />
<br />EBIT $1,800,000,000 See above.
<br />INT 800,000,000
<br />EBT $1,000,000,000 EBT = $600,000,000/0.6
<br />Taxes (40%) 400,000,000
<br />NI $ 600,000,000 See above.
<br />
<br />TIE = EBIT/INT
<br />= $1,800,000,000/$800,000,000
<br />= 2.25.
<br />
<br />
<br />3-6 We are given ROA = 3% and Sales/Total assets = 1.5.
<br />
<br />From Du Pont equation: ROA = Profit margin Total assets turnover
<br />3% = Profit margin(1.5)
<br />Profit margin = 3%/1.5 = 2%.
<br />
<br />We can also calculate the company’s debt ratio in a similar manner, given the facts of the problem. We are given ROA(NI/A) and ROE(NI/E); if we use the reciprocal of ROE we have the following equation:
<br />
<br />
<br />
<br />
<br />Alternatively,
<br />
<br />ROE = ROA EM
<br />5% = 3% EM
<br />EM = 5%/3% = 5/3 = TA/E.
<br />
<br />Take reciprocal:
<br />
<br />E/TA = 3/5 = 60%;
<br />
<br />therefore, D/A = 1 - 0.60 = 0.40 = 40%.
<br />
<br />Thus, the firm’s profit margin = 2% and its debt ratio = 40%.
<br />
<br />
<br />3-7 Present current ratio = = 2.5.
<br />
<br />Minimum current ratio = = 2.0.
<br />
<br />$1,312,500 + NP = $1,050,000 + 2NP
<br />NP = $262,500.
<br />
<br />Short-term debt can increase by a maximum of $262,500 without violating a 2 to 1 current ratio, assuming that the entire increase in notes payable is used to increase current assets. Since we assumed that the additional funds would be used to increase inventory, the inventory account will increase to $637,500 and current assets will total $1,575,000.
<br />
<br />
<br />3-8 TIE = EBIT/INT, so find EBIT and INT.
<br />Interest = $500,000 0.1 = $50,000.
<br />
<br />Net income = $2,000,000 0.05 = $100,000.
<br />Pre-tax income (EBT) = $100,000/(1 - T) = $100,000/0.7 = $142,857.
<br />EBIT = EBT + Interest = $142,857 + $50,000 = $192,857.
<br />
<br />TIE = $192,857/$50,000 = 3.86.
<br />
<br />
<br />3-9 TA = $30,000,000,000; EBIT/TA = 20%; TIE = 8; DA = $3,200,000,000; Lease payments = $2,000,000,000; Principal payments = $1,000,000,000; EBITDA coverage = ?
<br />
<br />EBIT/$30,000,000,000 = 0.2
<br />EBIT = $6,000,000,000.
<br />
<br />
<br />8 = EBIT/INT
<br />8 = $6,000,000,000/INT
<br />INT = $750,000,000.
<br />
<br />EBITDA = EBIT + DA
<br />= $6,000,000,000 + $3,200,000,000
<br />= $9,200,000,000.
<br />
<br />EBITDA coverage ratio =
<br />=
<br />= = 2.9867.
<br />
<br />
<br />3-10 ROE = Profit margin TA turnover Equity multiplier
<br />= NI/Sales Sales/TA TA/Equity.
<br />
<br />Now we need to determine the inputs for the equation from the data that were given. On the left we set up an income statement, and we put numbers in it on the right:
<br />
<br />Sales (given) $10,000,000
<br />- Cost na
<br />EBIT (given) $ 1,000,000
<br />- INT (given) 300,000
<br />EBT $ 700,000
<br />- Taxes (34%) 238,000
<br />NI $ 462,000
<br />
<br />Now we can use some ratios to get some more data:
<br />Total assets turnover = 2 = S/TA; TA = S/2 = $10,000,000/2 = $5,000,000.
<br />
<br />D/A = 60%; so E/A = 40%; and, therefore,
<br />Equity multiplier = TA/E = 1/(E/A) = 1/0.4 = 2.5.
<br />
<br />Now we can complete the Du Pont equation to determine ROE:
<br />ROE = $462,000/$10,000,000 $10,000,000/$5,000,000 2.5 = 0.231 = 23.1%.
<br />
<br />
<br />
<br />3-11 Known data:
<br />
<br />TA = $1,000,000; kd = 8%; T = 40%; BEP = 0.2 = EBIT/Total assets, so EBIT = 0.2($1,000,000) = $200,000; D/A = 0.5 = 50%, so Equity = $500,000.
<br />
<br />D/A = 0% D/A = 50%
<br />EBIT $200,000 $200,000
<br />Interest 0 40,000*
<br />EBT $200,000 $160,000
<br />Tax (40%) 80,000 64,000
<br />NI $120,000 $ 96,000
<br />
<br />ROE = = = 12% = 19.2%
<br />Difference in ROE = 19.2% - 12.0% = 7.2%.
<br />
<br />*If D/A = 50%, then half of the assets are financed by debt, so Debt = $500,000. At an 8 percent interest rate, INT = $40,000.
<br />
<br />
<br />3-12 Statement a is correct. Refer to the solution setup for Problem 3-11 and think about it this way: (1) Adding assets will not affect common equity if the assets are financed with debt. (2) Adding assets will cause expected EBIT to increase by the amount EBIT = BEP(added assets). (3) Interest expense will increase by the amount kd(added assets). (4) Pre-tax income will rise by the amount (added assets)(BEP - kd). Assuming BEP > kd, if pre-tax income increases so will net income. (5) If expected net income increases but common equity is held constant, then the expected ROE will also increase. Note that if kd > BEP, then adding assets financed by debt would lower net income and thus the ROE. Therefore, Statement a is true--if assets financed by debt are added, and if the expected BEP on those assets exceeds the cost of debt, then the firm’s ROE will increase.
<br />Statements b, c, and d are false, because the BEP ratio uses EBIT, which is calculated before the effects of taxes or interest charges are felt. Of course, Statement e is also false.
<br />
<br />
<br />3-13 a. Currently, ROE is ROE1 = $15,000/$200,000 = 7.5%.
<br />The current ratio will be set such that 2.5 = CA/CL. CL is $50,000, and it will not change, so we can solve to find the new level of current assets: CA = 2.5(CL) = 2.5($50,000) = $125,000. This is the level of current assets that will produce a current ratio of 2.5.
<br />At present, current assets amount to $210,000, so they can be reduced by $210,000 - $125,000 = $85,000. If the $85,000 generated is used to retire common equity, then the new common equity balance will be $200,000 - $85,000 = $115,000.
<br />Assuming that net income is unchanged, the new ROE will be ROE2 = $15,000/$115,000 = 13.04%. Therefore, ROE will increase by 13.04% - 7.50% = 5.54%.
<br />
<br />b. 1. Doubling the dollar amounts would not affect the answer; it would still be 5.54%.
<br />2. Common equity would increase by $25,000 from the Part a scenario, which would mean a new ROE of $15,000/$140,000 = 10.71%, which would mean a difference of 10.71% - 7.50% = 3.21%.
<br />
<br />3. An inventory turnover of 2 would mean inventories of $100,000, down $50,000 from the current level. That would mean an ROE of $15,000/$150,000 = 10.00%, so the change in ROE would be 10.00% - 7.5% = 2.5%.
<br />
<br />4. If the company had 10,000 shares outstanding, then its EPS would be $15,000/10,000 = $1.50. The stock has a book value of $200,000/10,000 = $20, so the shares retired would be $85,000/$20 = 4,250, leaving 10,000 - 4,250 = 5,750 shares. The new EPS would be $15,000/5,750 = $2.6087, so the increase in EPS would be $2.6087 - $1.50 = $1.1087, which is a 73.91 percent increase, the same as the increase in ROE.
<br />
<br />5. If the stock was selling for twice book value, or 2 $20 = $40, then only half as many shares could be retired ($85,000/$40 = 2,125), so the remaining shares would be 10,000 - 2,125 = 7,875, and the new EPS would be $15,000/7,875 = $1.9048, for an increase of $1.9048 - $1.5000 = $0.4048.
<br />
<br />c. We could have started with lower inventory and higher accounts receivable, then had you calculate the DSO, then move to a lower DSO that would require a reduction in receivables, and then determine the effects on ROE and EPS under different conditions. Similarly, we could have focused on fixed assets and the FA turnover ratio. In any of these cases, we could have had you use the funds generated to retire debt, which would have lowered interest charges and consequently increased net income and EPS.
<br />If we had to increase assets, then we would have had to finance this increase by adding either debt or equity, which would have lowered ROE and EPS, other things held constant.
<br />Finally, note that we could have asked some conceptual questions about the problem, either as a part of the problem or without any reference to the problem. For example, “If funds are generated by reducing assets, and if those funds are used to retire common stock, will EPS and/or ROE be affected by whether or not the stock sells above, at, or below book value?”
<br />
<br />
<br />3-14 TA = $7,500,000,000; EBIT/TA = 10%; TIE = 2.5; DA = $1,250,000,000; Lease payments = $775,000,000; Principal payments = $500,000,000; EBITDA coverage = ?
<br />
<br />EBIT/$7,500,000,000 = 0.10
<br />EBIT = $750,000,000.
<br />
<br />2.5 = EBIT/INT
<br />2.5 = $750,000,000/INT
<br />INT = $300,000,000.
<br />
<br />
<br />EBITDA = EBIT + DA
<br />= $750,000,000 + $1,250,000,000
<br />= $2,000,000,000.
<br />
<br />EBITDA coverage ratio =
<br />=
<br />= = 1.7619 1.76.
<br />
<br />
<br />3-15 TA = $5,000,000,000; T = 40%; EBIT/TA = 10%; ROA = 5%; TIE ?
<br />
<br />
<br />
<br />
<br />
<br />Now use the income statement format to determine interest so you can calculate the firm’s TIE ratio.
<br />
<br />EBIT $500,000,000 See above.
<br />INT 83,333,333
<br />EBT $416,666,667 EBT = $250,000,000/0.6
<br />Taxes (40%) 166,666,667
<br />NI $250,000,000 See above.
<br />
<br />TIE = EBIT/INT
<br />= $500,000,000/$83,333,333
<br />= 6.0.
<br />
<br />
<br />3-16 Total market value = $3,750,000,000(1.9) = $7,125,000,000.
<br />Market value per share = $7,125,000,000/50,000,000 = $142.50.
<br />
<br />Alternative solution:
<br />Book value per share = $3,750,000,000/50,000,000 = $75.
<br />Market value per share = $75(1.9) = $142.50.
<br />
<br />
<br />3-17 Step 1: Solve for current annual sales using the DSO equation:
<br />55 = $750,000/(Sales/365)
<br />55Sales = $273,750,000
<br />Sales = $4,977,272.73.
<br />
<br />Step 2: If sales fall by 15%, the new sales level will be $4,977,272.73(0.85) = $4,230,681.82. Again, using the DSO equation, solve for the new accounts receivable figure as follows:
<br />35 = AR/($4,230,681.82/365)
<br />35 = AR/$11,590.91
<br />AR = $405,681.82 $405,682.
<br />
<br />
<br />3-18 The current EPS is $2,000,000/500,000 shares or $4.00. The current P/E ratio is then $40/$4 = 10.00. The new number of shares outstanding will be 650,000. Thus, the new EPS = $3,250,000/650,000 = $5.00. If the shares are selling for 10 times EPS, then they must be selling for $5.00(10) = $50.
<br />
<br />
<br />3-19 Step 1: Calculate total assets from information given.
<br />Sales = $6 million.
<br />
<br />3.2 = Sales/TA
<br />3.2 =
<br />Assets = $1,875,000.
<br />
<br />Step 2: Calculate net income.
<br />There is 50% debt and 50% equity, so Equity = $1,875,000 0.5 = $937,500.
<br />
<br />ROE = NI/S S/TA TA/E
<br />0.12 = NI/$6,000,000 3.2 $1,875,000/$937,500
<br />0.12 =
<br />$720,000 = 6.4NI
<br />$112,500 = NI.
<br />
<br />
<br />3-20 Given ROA = 8% and net income of $600,000, total assets must be $7,500,000.
<br />
<br />ROA =
<br />8% =
<br />TA = $7,500,000.
<br />
<br />To calculate BEP, we still need EBIT. To calculate EBIT construct a partial income statement:
<br />
<br />EBIT $1,148,077 ($225,000 + $923,077)
<br />Interest 225,000 (Given)
<br />EBT $ 923,077 $600,000/0.65
<br />Taxes (35%) 323,077
<br />NI $ 600,000
<br />
<br />BEP =
<br />=
<br />= 0.1531 = 15.31%.
<br />
<br />
<br />3-21 1. Debt = (0.50)(Total assets) = (0.50)($300,000) = $150,000.
<br />
<br />2. Accounts payable = Debt – Long-term debt = $150,000 - $60,000
<br />= $90,000.
<br />
<br />3. Common stock = - Debt - Retained earnings
<br />= $300,000 - $150,000 - $97,500 = $52,500.
<br />
<br />4. Sales = (1.5)(Total assets) = (1.5)($300,000) = $450,000.
<br />
<br />5. Inventories = Sales/5 = $450,000/5 = $90,000.
<br />
<br />6. Accounts receivable = (Sales/365)(DSO) = ($450,000/365)(36.5)
<br />= $45,000.
<br />
<br />7. Cash + Accounts receivable + Inventories = (1.8)(Accounts payable)
<br />Cash + $45,000 + $90,000 = (1.8)($90,000)
<br />Cash + $135,000 = $162,000
<br />Cash = $27,000.
<br />
<br />8. Fixed assets = Total assets - (Cash + Accts rec. + Inventories)
<br />Fixed assets = $300,000 - ($27,000 + $45,000 + $90,000)
<br />Fixed assets = $138,000.
<br />
<br />9. Cost of goods sold = (Sales)(1 - 0.25) = ($450,000)(0.75) = $337,500.
<br />
<br />
<br />
<br />3-22 a. (Dollar amounts in thousands.)
<br />Industry
<br />Firm Average
<br />
<br />= = 1.98 2.0
<br />
<br />DSO = = = 76.3 days 35 days
<br />
<br />= = 6.66 6.7
<br />
<br />= = 1.70 3.0
<br />
<br />= = 1.7% 1.2%
<br />
<br />= = 2.9% 3.6%
<br />
<br />= = 7.6% 9.0%
<br />
<br />= = 61.9% 60.0%
<br />
<br />b. For the firm,
<br />
<br />ROE = PM T.A. turnover EM = 1.7% 1.7 = 7.6%.
<br />For the industry, ROE = 1.2% 3 2.5 = 9%.
<br />
<br />Note: To find the industry ratio of assets to common equity, recognize that 1 - (total debt/total assets) = common equity/total assets. So, common equity/total assets = 40%, and 1/0.40 = 2.5 = total assets/common equity.
<br />
<br />c. The firm’s days sales outstanding is more than twice as long as the industry average, indicating that the firm should tighten credit or enforce a more stringent collection policy. The total assets turnover ratio is well below the industry average so sales should be increased, assets decreased, or both. While the company’s profit margin is higher than the industry average, its other profitability ratios are low compared to the industry--net income should be higher given the amount of equity and assets. However, the company seems to be in an average liquidity position and financial leverage is similar to others in the industry.
<br />
<br />d. If 2002 represents a period of supernormal growth for the firm, ratios based on this year will be distorted and a comparison between them and industry averages will have little meaning. Potential investors who look only at 2002 ratios will be misled, and a return to normal conditions in 2003 could hurt the firm’s stock price.
<br />
<br />
<br />3-23 a. Industry
<br />Firm Average
<br />
<br />Current ratio = = = 2.73 2
<br />
<br />= = = 30.00% 30.00%
<br />
<br />= = = 11 7
<br />
<br />= = = 9.46 9
<br />
<br />= = = 5 10
<br />
<br />DSO = = = 30.3 days 24 days
<br />
<br />= = = 5.41 6
<br />
<br />= = = 1.77 3
<br />
<br />Profit margin = = = 3.40% 3.00%
<br />
<br />= = = 6.00% 9.00%
<br />
<br />= ROA EM = 6% 1.4286 = 8.57% 12.90%
<br />
<br />Alternatively,
<br />
<br />ROE = = = 8.57% 8.6%.
<br />
<br />
<br />b. ROE = Profit margin Total assets turnover Equity multiplier
<br />
<br />=
<br />
<br />= = 3.4% 1.77 1.4286 = 8.6%.
<br />
<br />Firm Industry Comment
<br />Profit margin 3.4% 3.0% Good
<br />Total assets turnover 1.77 3.0 Poor
<br />Equity multiplier 1.4286 1.43* O.K.
<br />
<br />* 1 - =
<br />1 – 0.30 = 0.7
<br />EM = = = 1.43.
<br />
<br />Alternatively, EM = ROE/ROA = 12.9%/9% = 1.43.
<br />
<br />c. Analysis of the Du Pont equation and the set of ratios shows that the turnover ratio of sales to assets is quite low. Either sales should be increased at the present level of assets, or the current level of assets should be decreased to be more in line with current sales.
<br />
<br />d. The comparison of inventory turnover ratios shows that other firms in the industry seem to be getting along with about half as much inventory per unit of sales as the firm. If the company’s inventory could be reduced, this would generate funds that could be used to retire debt, thus reducing interest charges and improving profits, and strengthening the debt position. There might also be some excess investment in fixed assets, perhaps indicative of excess capacity, as shown by a slightly lower-than-average fixed assets turnover ratio. However, this is not nearly as clear-cut as the overinvestment in inventory.
<br />
<br />e. If the firm had a sharp seasonal sales pattern, or if it grew rapidly during the year, many ratios might be distorted. Ratios involving cash, receivables, inventories, and current liabilities, as well as those based on sales, profits, and common equity, could be biased. It is possible to correct for such problems by using average rather than end-of-period figures.
<br />
<br />
<br />
<br />3-24 a. Here are the firm’s base case ratios and other data as compared to the industry:
<br />
<br />Firm Industry Comment
<br />Current 2.3 2.7 Weak
<br />Inventory turnover 4.8 7.0 Poor
<br />Days sales outstanding 37.4 days 32.0 days Poor
<br />Fixed assets turnover 10.0 13.0 Poor
<br />Total assets turnover 2.3 2.6 Poor
<br />Return on assets 5.9% 9.1% Bad
<br />Return on equity 13.1 18.2 Bad
<br />Debt ratio 54.8 50.0 High
<br />Profit margin on sales 2.5 3.5 Bad
<br />EPS $4.71 n.a. --
<br />Stock Price $23.57 n.a. --
<br />P/E ratio 5.0 6.0 Poor
<br />P/CF ratio 2.0 3.5 Poor
<br />M/B ratio 0.65 n.a. --
<br />
<br />The firm appears to be badly managed--all of its ratios are worse than the industry averages, and the result is low earnings, a low P/E, a low stock price, and a low M/B ratio. The company needs to do something to improve.
<br />
<br />b. A decrease in the inventory level would improve the inventory turnover, total assets turnover, and ROA, all of which are too low. It would have some impact on the current ratio, but it is difficult to say precisely how that ratio would be affected. If the lower inventory level allowed the company to reduce its current liabilities, then the current ratio would improve. The lower cost of goods sold would improve all of the profitability ratios and, if dividends were not increased, would lower the debt ratio through increased retained earnings. All of this should lead to a higher market/book ratio, a higher stock price, a higher price/earnings ratio, and a higher price/cash flow ratio.
<br />
<br />SPREADSHEET PROBLEM
<br />
<br />
<br />
<br />3-25 The detailed solution for the spreadsheet problem is available both on the instructor’s resource CD-ROM and on the instructor’s side of South-Western’s web site, http://brigham.swlearning.com.
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />INTEGRATED CASE
<br />
<br />
<br />
<br />D’Leon Inc., Part II
<br />Financial Statement Analysis
<br />
<br />3-26 PART I OF THIS CASE, PRESENTED IN CHAPTER 2, DISCUSSED THE SITUATION THAT D’LEON INC., A REGIONAL SNACK-FOODS PRODUCER, WAS IN AFTER AN EXPANSION PROGRAM. D’LEON HAD INCREASED PLANT CAPACITY AND UNDERTAKEN A MAJOR MARKETING CAMPAIGN IN AN ATTEMPT TO “GO NATIONAL.” THUS FAR, SALES HAVE NOT BEEN UP TO THE FORECASTED LEVEL, COSTS HAVE BEEN HIGHER THAN WERE PROJECTED, AND A LARGE LOSS OCCURRED IN 2002 RATHER THAN THE EXPECTED PROFIT. AS A RESULT, ITS MANAGERS, DIRECTORS, AND INVESTORS ARE CONCERNED ABOUT THE FIRM’S SURVIVAL.
<br />DONNA JAMISON WAS BROUGHT IN AS ASSISTANT TO FRED CAMPO, D’LEON’S CHAIRMAN, WHO HAD THE TASK OF GETTING THE COMPANY BACK INTO A SOUND FINANCIAL POSITION. D’LEON’S 2001 AND 2002 BALANCE SHEETS AND INCOME STATEMENTS, TOGETHER WITH PROJECTIONS FOR 2003, ARE GIVEN IN TABLES IC3-1 AND IC3-2. IN ADDITION, TABLE IC3-3 GIVES THE COMPANY’S 2001 AND 2002 FINANCIAL RATIOS, TOGETHER WITH INDUSTRY AVERAGE DATA. THE 2003 PROJECTED FINANCIAL STATEMENT DATA REPRESENT JAMISON’S AND CAMPO’S BEST GUESS FOR 2003 RESULTS, ASSUMING THAT SOME NEW FINANCING IS ARRANGED TO GET THE COMPANY “OVER THE HUMP.”
<br />JAMISON EXAMINED MONTHLY DATA FOR 2002 (NOT GIVEN IN THE CASE), AND SHE DETECTED AN IMPROVING PATTERN DURING THE YEAR. MONTHLY SALES WERE RISING, COSTS WERE FALLING, AND LARGE LOSSES IN THE EARLY MONTHS HAD TURNED TO A SMALL PROFIT BY DECEMBER. THUS, THE ANNUAL DATA LOOK SOMEWHAT WORSE THAN FINAL MONTHLY DATA. ALSO, IT APPEARS TO BE TAKING LONGER FOR THE ADVERTISING PROGRAM TO GET THE MESSAGE ACROSS, FOR THE NEW SALES OFFICES TO GENERATE SALES, AND FOR THE NEW MANUFACTURING FACILITIES TO OPERATE EFFICIENTLY. IN OTHER WORDS, THE LAGS BETWEEN SPENDING MONEY AND DERIVING BENEFITS WERE LONGER THAN D’LEON’S MANAGERS HAD ANTICIPATED. FOR THESE REASONS, JAMISON AND CAMPO SEE HOPE FOR THE COMPANY--PROVIDED IT CAN SURVIVE IN THE SHORT RUN.
<br />JAMISON MUST PREPARE AN ANALYSIS OF WHERE THE COMPANY IS NOW, WHAT IT MUST DO TO REGAIN ITS FINANCIAL HEALTH, AND WHAT ACTIONS SHOULD BE TAKEN. YOUR ASSIGNMENT IS TO HELP HER ANSWER THE FOLLOWING QUESTIONS. PROVIDE CLEAR EXPLANATIONS, NOT YES OR NO ANSWERS.
<br />TABLE IC3-1. BALANCE SHEETS
<br />
<br />2003E 2002 2001
<br />ASSETS
<br />CASH $ 85,632 $ 7,282 $ 57,600
<br />ACCOUNTS RECEIVABLE 878,000 632,160 351,200
<br />INVENTORIES 1,716,480 1,287,360 715,200
<br />TOTAL CURRENT ASSETS $2,680,112 $1,926,802 $1,124,000
<br />GROSS FIXED ASSETS 1,197,160 1,202,950 491,000
<br />LESS ACCUMULATED DEPRECIATION 380,120 263,160 146,200
<br />NET FIXED ASSETS $ 817,040 $ 939,790 $ 344,800
<br />TOTAL ASSETS $3,497,152 $2,866,592 $1,468,800
<br />
<br />LIABILITIES AND EQUITY
<br />ACCOUNTS PAYABLE $ 436,800 $ 524,160 $ 145,600
<br />NOTES PAYABLE 300,000 636,808 200,000
<br />ACCRUALS 408,000 489,600 136,000
<br />TOTAL CURRENT LIABILITIES $1,144,800 $1,650,568 $ 481,600
<br />LONG-TERM DEBT 400,000 723,432 323,432
<br />COMMON STOCK 1,721,176 460,000 460,000
<br />RETAINED EARNINGS 231,176 32,592 203,768
<br />TOTAL EQUITY $1,952,352 $ 492,592 $ 663,768
<br />TOTAL LIABILITIES AND EQUITY $3,497,152 $2,866,592 $1,468,800
<br />
<br />NOTE: “E” INDICATES ESTIMATED. THE 2003 DATA ARE FORECASTS.
<br />
<br />
<br />
<br />TABLE IC3-2. INCOME STATEMENTS
<br />
<br />2003E 2002 2001
<br />SALES $7,035,600 $6,034,000 $3,432,000
<br />COST OF GOODS SOLD 5,875,992 5,528,000 2,864,000
<br />OTHER EXPENSES 550,000 519,988 358,672
<br />TOTAL OPERATING COSTS
<br />EXCLUDING DEPRECIATION $6,425,992 $6,047,988 $3,222,672
<br />EBITDA $ 609,608 ($ 13,988) $ 209,328
<br />DEPRECIATION 116,960 116,960 18,900
<br />EBIT $ 492,648 ($ 130,948) $ 190,428
<br />INTEREST EXPENSE 70,008 136,012 43,828
<br />EBT $ 422,640 ($ 266,960) $ 146,600
<br />TAXES (40%) 169,056 (106,784)a 58,640
<br />NET INCOME $ 253,584 ($ 160,176) $ 87,960
<br />
<br />EPS $1.014 ($1.602) $0.880
<br />DPS $0.220 $0.110 $0.220
<br />BOOK VALUE PER SHARE $7.809 $4.926 $6.638
<br />STOCK PRICE $12.17 $2.25 $8.50
<br />SHARES OUTSTANDING 250,000 100,000 100,000
<br />TAX RATE 40.00% 40.00% 40.00%
<br />LEASE PAYMENTS 40,000 40,000 40,000
<br />SINKING FUND PAYMENTS 0 0 0
<br />
<br />NOTE: “E” INDICATES ESTIMATED. THE 2003 DATA ARE FORECASTS.
<br />
<br />aTHE FIRM HAD SUFFICIENT TAXABLE INCOME IN 2000 AND 2001 TO OBTAIN ITS FULL TAX REFUND IN 2002.
<br />
<br />
<br />TABLE IC3-3. RATIO ANALYSIS
<br />
<br />INDUSTRY
<br />2003E 2002 2001 AVERAGE
<br />CURRENT 1.2 2.3 2.7
<br />INVENTORY TURNOVER 4.7 4.8 6.1
<br />DAYS SALES OUTSTANDING (DSO)a 38.2 37.4 32.0
<br />FIXED ASSETS TURNOVER 6.4 10.0 7.0
<br />TOTAL ASSETS TURNOVER 2.1 2.3 2.6
<br />DEBT RATIO 82.8% 54.8% 50.0%
<br />TIE -1.0 4.3 6.2
<br />EBITDA COVERAGE 0.1 3.0 8.0
<br />PROFIT MARGIN -2.7% 2.6% 3.5%
<br />BASIC EARNING POWER -4.6% 13.0% 19.1%
<br />ROA -5.6% 6.0% 9.1%
<br />ROE -32.5% 13.3% 18.2%
<br />PRICE/EARNINGS -1.4 9.7 14.2
<br />PRICE/CASH FLOW -5.2 8.0 11.0
<br />MARKET/BOOK 0.5 1.3 2.4
<br />BOOK VALUE PER SHARE $4.93 $6.64 n.a.
<br />
<br />NOTE: “E” INDICATES ESTIMATED. THE 2003 DATA ARE FORECASTS.
<br />
<br />aCALCULATION IS BASED ON A 365-DAY YEAR.
<br />
<br />
<br />A. WHY ARE RATIOS USEFUL? WHAT ARE THE FIVE MAJOR CATEGORIES OF RATIOS?
<br />
<br />ANSWER: [S3-1 THROUGH S3-5 PROVIDE BACKGROUND INFORMATION. THEN, SHOW S3-6 AND S3-7 HERE.] RATIOS ARE USED BY MANAGERS TO HELP IMPROVE THE FIRM’S PERFORMANCE, BY LENDERS TO HELP EVALUATE THE FIRM’S LIKELIHOOD OF REPAYING DEBTS, AND BY STOCKHOLDERS TO HELP FORECAST FUTURE EARNINGS AND DIVIDENDS. THE FIVE MAJOR CATEGORIES OF RATIOS ARE: LIQUIDITY, ASSET MANAGEMENT, DEBT MANAGEMENT, PROFITABILITY, AND MARKET VALUE.
<br />
<br />
<br />B. CALCULATE D’LEON’S 2003 CURRENT RATIO BASED ON THE PROJECTED BALANCE SHEET AND INCOME STATEMENT DATA. WHAT CAN YOU SAY ABOUT THE COMPANY’S LIQUIDITY POSITION IN 2001, 2002, AND AS PROJECTED FOR 2003? WE OFTEN THINK OF RATIOS AS BEING USEFUL (1) TO MANAGERS TO HELP RUN THE BUSINESS, (2) TO BANKERS FOR CREDIT ANALYSIS, AND (3) TO STOCKHOLDERS FOR STOCK VALUATION. WOULD THESE DIFFERENT TYPES OF ANALYSTS HAVE AN EQUAL INTEREST IN THIS LIQUIDITY RATIO?
<br />
<br />
<br />ANSWER: [SHOW S3-8 AND S3-9 HERE.]
<br />
<br />CURRENT RATIO03 = CURRENT ASSETS/CURRENT LIABILITIES
<br />= $2,680,112/$1,144,800 = 2.34.
<br />
<br />THE COMPANY’S CURRENT RATIO IS IDENTICAL TO ITS 2001 CURRENT RATIO, AND IT HAS IMPROVED FROM ITS 2002 LEVEL. HOWEVER, THE CURRENT RATIO IS WELL BELOW THE INDUSTRY AVERAGE.
<br />
<br />
<br />C. CALCULATE THE 2003 INVENTORY TURNOVER, DAYS SALES OUTSTANDING (DSO), FIXED ASSETS TURNOVER, AND TOTAL ASSETS TURNOVER. HOW DOES D’LEON’S UTILIZATION OF ASSETS STACK UP AGAINST OTHER FIRMS IN ITS INDUSTRY?
<br />
<br />ANSWER: [SHOW S3-10 THROUGH S3-15 HERE.]
<br />
<br />INVENTORY TURNOVER03 = SALES/INVENTORY
<br />= $7,035,600/$1,716,480 = 4.10.
<br />
<br />DSO03 = RECEIVABLES/(SALES/365)
<br />= $878,000/($7,035,600/365) = 45.55 DAYS.
<br />
<br />
<br />FIXED ASSETS TURNOVER03 = SALES/NET FIXED ASSETS
<br />= $7,035,600/$817,040 = 8.61.
<br />
<br />TOTAL ASSETS TURNOVER03 = SALES/TOTAL ASSETS
<br />= $7,035,600/$3,497,152 = 2.01.
<br />
<br />THE FIRM’S INVENTORY TURNOVER AND TOTAL ASSETS TURNOVER RATIOS HAVE BEEN STEADILY DECLINING, WHILE ITS DAYS SALES OUTSTANDING HAS BEEN STEADILY INCREASING (WHICH IS BAD). HOWEVER, THE FIRM’S 2003 TOTAL ASSETS TURNOVER RATIO IS ONLY SLIGHTLY BELOW THE 2002 LEVEL. THE FIRM’S FIXED ASSETS TURNOVER RATIO IS BELOW ITS 2001 LEVEL; HOWEVER, IT IS ABOVE THE 2002 LEVEL.
<br />THE FIRM’S INVENTORY TURNOVER AND TOTAL ASSETS TURNOVER ARE BELOW THE INDUSTRY AVERAGE. THE FIRM’S DAYS SALES OUTSTANDING IS ABOVE THE INDUSTRY AVERAGE (WHICH IS BAD); HOWEVER, THE FIRM’S FIXED ASSETS TURNOVER IS ABOVE THE INDUSTRY AVERAGE. (THIS MIGHT BE DUE TO THE FACT THAT D’LEON IS AN OLDER FIRM THAN MOST OTHER FIRMS IN THE INDUSTRY, IN WHICH CASE, ITS FIXED ASSETS ARE OLDER AND THUS HAVE BEEN DEPRECIATED MORE, OR THAT D’LEON’S COST OF FIXED ASSETS WERE LOWER THAN MOST FIRMS IN THE INDUSTRY.)
<br />
<br />
<br />D. CALCULATE THE 2003 DEBT, TIMES-INTEREST-EARNED, AND EBITDA COVERAGE RATIOS. HOW DOES D’LEON COMPARE WITH THE INDUSTRY WITH RESPECT TO FINANCIAL LEVERAGE? WHAT CAN YOU CONCLUDE FROM THESE RATIOS?
<br />
<br />ANSWER: [SHOW S3-16 THROUGH S3-18 HERE.]
<br />
<br />DEBT RATIO03 = TOTAL DEBT/TOTAL ASSETS
<br />= ($1,144,800 + $400,000)/$3,497,152 = 44.17%.
<br />
<br />TIE03 = EBIT/INTEREST = $492,648/$70,008 = 7.04.
<br />
<br />EBITDA03 = /
<br />= ($609,608 + $40,000)/($70,008 + $40,000)
<br />= $649,608/$110,008 = 5.91.
<br />
<br />THE FIRM’S DEBT RATIO IS MUCH IMPROVED FROM 2002 AND 2001, AND IT IS BELOW THE INDUSTRY AVERAGE (WHICH IS GOOD). THE FIRM’S TIE RATIO IS ALSO GREATLY IMPROVED FROM ITS 2001 AND 2002 LEVELS AND IS ABOVE THE INDUSTRY AVERAGE. WHILE ITS EBITDA COVERAGE RATIO HAS IMPROVED FROM ITS 2001 AND 2002 LEVELS, IT IS STILL BELOW THE INDUSTRY AVERAGE.
<br />
<br />
<br />
<br />E. CALCULATE THE 2003 PROFIT MARGIN, BASIC EARNING POWER (BEP), RETURN ON ASSETS (ROA), AND RETURN ON EQUITY (ROE). WHAT CAN YOU SAY ABOUT THESE RATIOS?
<br />
<br />ANSWER: [SHOW S3-19 THROUGH S3-24 HERE.]
<br />
<br />PROFIT MARGIN03 = NET INCOME/SALES = $253,584/$7,035,600 = 3.60%.
<br />
<br />BASIC EARNING POWER03 = EBIT/TOTAL ASSETS = $492,648/$3,497,152 = 14.09%.
<br />
<br />ROA03 = NET INCOME/TOTAL ASSETS = $253,584/$3,497,152 = 7.25%.
<br />
<br />ROE03 = NET INCOME/COMMON EQUITY = $253,584/$1,952,352 = 12.99% 13.0%.
<br />
<br />THE FIRM’S PROFIT MARGIN IS ABOVE 2001 AND 2002 LEVELS AND SLIGHTLY ABOVE THE INDUSTRY AVERAGE. WHILE THE FIRM’S BASIC EARNING POWER AND ROA RATIOS ARE BOTH ABOVE 2001 AND 2002 LEVELS, THEY ARE STILL BELOW THE INDUSTRY AVERAGE. THE FIRM’S ROE RATIO IS GREATLY IMPROVED OVER ITS 2002 LEVEL; HOWEVER, IT IS SLIGHTLY BELOW ITS 2001 LEVEL AND STILL WELL BELOW THE INDUSTRY AVERAGE.
<br />
<br />
<br />F. CALCULATE THE 2003 PRICE/EARNINGS RATIO, PRICE/CASH FLOW RATIO, AND MARKET/BOOK RATIO. DO THESE RATIOS INDICATE THAT INVESTORS ARE EXPECTED TO HAVE A HIGH OR LOW OPINION OF THE COMPANY?
<br />
<br />ANSWER: [SHOW S3-25 THROUGH S3-27 HERE.]
<br />
<br />EPS03 = NET INCOME/SHARES OUTSTANDING = $253,584/250,000 = $1.0143.
<br />
<br />PRICE/EARNINGS03 = PRICE PER SHARE/EARNINGS PER SHARE
<br />= $12.17/$1.0143 = 12.0.
<br />
<br />CHECK: PRICE = EPS P/E = $1.0143(12.0) = $12.17.
<br />
<br />CASH FLOW/SHARE03 = (NI + DEP)/SHARES = ($253,584 + $116,960)/250,000
<br />= $1.48.
<br />
<br />PRICE/CASH FLOW03 = $12.17/$1.48 = 8.2.
<br />
<br />BVPS03 = COMMON EQUITY/SHARES OUTSTANDING = $1,952,352/250,000 = $7.81.
<br />
<br />MARKET/BOOK03 = MARKET PRICE PER SHARE/BOOK VALUE PER SHARE
<br />= $12.17/$7.81 = 1.56.
<br />
<br />THE P/E, P/CF, AND M/B RATIOS ARE ABOVE THE 2002 AND 2001 LEVELS BUT BELOW THE INDUSTRY AVERAGE.
<br />
<br />
<br />G. USE THE EXTENDED DU PONT EQUATION TO PROVIDE A SUMMARY AND OVERVIEW OF D’LEON’S FINANCIAL CONDITION AS PROJECTED FOR 2003. WHAT ARE THE FIRM’S MAJOR STRENGTHS AND WEAKNESSES?
<br />
<br />
<br />
<br />ANSWER: [SHOW S3-28 AND S3-30 HERE.]
<br />
<br />DU PONT EQUATION =
<br />= 3.60% 2.01 1/(1 - 0.4417) = 12.96% 13.0%.
<br />
<br />STRENGTHS: THE FIRM’S FIXED ASSETS TURNOVER WAS ABOVE THE INDUSTRY AVERAGE. HOWEVER, IF THE FIRM’S ASSETS WERE OLDER THAN OTHER FIRMS IN ITS INDUSTRY THIS COULD POSSIBLY ACCOUNT FOR THE HIGHER RATIO. (D’LEON’S FIXED ASSETS WOULD HAVE A LOWER HISTORICAL COST AND WOULD HAVE BEEN DEPRECIATED FOR LONGER PERIODS OF TIME.) THE FIRM’S PROFIT MARGIN IS SLIGHTLY ABOVE THE INDUSTRY AVERAGE, AND ITS DEBT RATIO HAS BEEN GREATLY REDUCED, SO IT IS NOW BELOW THE INDUSTRY AVERAGE (WHICH IS GOOD). THIS IMPROVED PROFIT MARGIN COULD INDICATE THAT THE FIRM HAS KEPT OPERATING COSTS DOWN AS WELL AS INTEREST EXPENSE (AS SHOWN FROM THE REDUCED DEBT RATIO). INTEREST EXPENSE IS LOWER BECAUSE THE FIRM’S DEBT RATIO HAS BEEN REDUCED, WHICH HAS IMPROVED THE FIRM’S TIE RATIO SO THAT IT IS NOW ABOVE THE INDUSTRY AVERAGE.
<br />
<br />WEAKNESSES: THE FIRM’S CURRENT ASSET RATIO IS LOW; MOST OF ITS ASSET MANAGEMENT RATIOS ARE POOR (EXCEPT FIXED ASSETS TURNOVER); ITS EBITDA COVERAGE RATIO IS LOW; MOST OF ITS PROFITABILITY RATIOS ARE LOW (EXCEPT PROFIT MARGIN); AND ITS MARKET VALUE RATIOS ARE LOW.
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<br />
<br />H. USE THE FOLLOWING SIMPLIFIED 2003 BALANCE SHEET TO SHOW, IN GENERAL TERMS, HOW AN IMPROVEMENT IN THE DSO WOULD TEND TO AFFECT THE STOCK PRICE. FOR EXAMPLE, IF THE COMPANY COULD IMPROVE ITS COLLECTION PROCEDURES AND THEREBY LOWER ITS DSO FROM 45.6 DAYS TO THE 32-DAY INDUSTRY AVERAGE WITHOUT AFFECTING SALES, HOW WOULD THAT CHANGE “RIPPLE THROUGH” THE FINANCIAL STATEMENTS (SHOWN IN THOUSANDS BELOW) AND INFLUENCE THE STOCK PRICE?
<br />
<br />ACCOUNTS RECEIVABLE $ 878 DEBT $1,545
<br />OTHER CURRENT ASSETS 1,802 EQUITY 1,952
<br />NET FIXED ASSETS 817 LIABILITIES PLUS
<br />TOTAL ASSETS $3,497 EQUITY $3,497
<br />
<br />
<br />ANSWER: [SHOW S3-31 THROUGH S3-34 HERE.]
<br />
<br />SALES PER DAY = $7,035,600/365 = $19,275.62.
<br />
<br />ACCOUNTS RECEIVABLE UNDER NEW POLICY = $19,275.62 32 DAYS
<br />= $616,820.
<br />
<br />FREED CASH = OLD A/R - NEW A/R = $878,000 - $616,820 = $261,180.
<br />
<br />
<br />
<br />I. DOES IT APPEAR THAT INVENTORIES COULD BE ADJUSTED, AND, IF SO, HOW SHOULD THAT ADJUSTMENT AFFECT D’LEON’S PROFITABILITY AND STOCK PRICE?
<br />
<br />ANSWER: THE INVENTORY TURNOVER RATIO IS LOW. IT APPEARS THAT THE FIRM EITHER HAS EXCESSIVE INVENTORY OR SOME OF THE INVENTORY IS OBSOLETE. IF INVENTORY WERE REDUCED, THIS WOULD IMPROVE THE CURRENT ASSET RATIO, THE INVENTORY AND TOTAL ASSETS TURNOVER, AND REDUCE THE DEBT RATIO EVEN FURTHER, WHICH SHOULD IMPROVE THE FIRM’S STOCK PRICE AND PROFITABILITY.
<br />
<br />
<br />J. IN 2002, THE COMPANY PAID ITS SUPPLIERS MUCH LATER THAN THE DUE DATES, AND IT WAS NOT MAINTAINING FINANCIAL RATIOS AT LEVELS CALLED FOR IN ITS BANK LOAN AGREEMENTS. THEREFORE, SUPPLIERS COULD CUT THE COMPANY OFF, AND ITS BANK COULD REFUSE TO RENEW THE LOAN WHEN IT COMES DUE IN
<br />90 DAYS. ON THE BASIS OF DATA PROVIDED, WOULD YOU, AS A CREDIT MANAGER, CONTINUE TO SELL TO D’LEON ON CREDIT? (YOU COULD DEMAND CASH ON DELIVERY, THAT IS, SELL ON TERMS OF COD, BUT THAT MIGHT CAUSE D’LEON TO STOP BUYING FROM YOUR COMPANY.) SIMILARLY, IF YOU WERE THE BANK LOAN OFFICER, WOULD YOU RECOMMEND RENEWING THE LOAN OR DEMAND ITS REPAYMENT? WOULD YOUR ACTIONS BE INFLUENCED IF, IN EARLY 2003, D’LEON SHOWED YOU ITS 2003 PROJECTIONS PLUS PROOF THAT IT WAS GOING TO RAISE OVER $1.2 MILLION OF NEW EQUITY CAPITAL?
<br />
<br />ANSWER: WHILE THE FIRM’S RATIOS BASED ON THE PROJECTED DATA APPEAR TO BE IMPROVING, THE FIRM’S CURRENT ASSET RATIO IS LOW. AS A CREDIT MANAGER, I WOULD NOT CONTINUE TO EXTEND CREDIT TO THE FIRM UNDER ITS CURRENT ARRANGEMENT, PARTICULARLY IF I DIDN’T HAVE ANY EXCESS CAPACITY. TERMS OF COD MIGHT BE A LITTLE HARSH AND MIGHT PUSH THE FIRM INTO BANKRUPTCY. LIKEWISE, IF THE BANK DEMANDED REPAYMENT THIS COULD ALSO FORCE THE FIRM INTO BANKRUPTCY.
<br />CREDITORS’ ACTIONS WOULD DEFINITELY BE INFLUENCED BY AN INFUSION OF EQUITY CAPITAL IN THE FIRM. THIS WOULD LOWER THE FIRM’S DEBT RATIO AND CREDITORS’ RISK EXPOSURE.
<br />
<br />
<br />K. IN HINDSIGHT, WHAT SHOULD D’LEON HAVE DONE BACK IN 2001?
<br />
<br />
<br />ANSWER: BEFORE THE COMPANY TOOK ON ITS EXPANSION PLANS, IT SHOULD HAVE DONE AN EXTENSIVE RATIO ANALYSIS TO DETERMINE THE EFFECTS OF ITS PROPOSED EXPANSION ON THE FIRM’S OPERATIONS. HAD THE RATIO ANALYSIS BEEN CONDUCTED, THE COMPANY WOULD HAVE “GOTTEN ITS HOUSE IN ORDER” BEFORE UNDERGOING THE EXPANSION.
<br />
<br />
<br />L. WHAT ARE SOME POTENTIAL PROBLEMS AND LIMITATIONS OF FINANCIAL RATIO ANALYSIS?
<br />
<br />ANSWER: [SHOW S3-35 AND S3-36 HERE.] SOME POTENTIAL PROBLEMS ARE LISTED BELOW:
<br />
<br />1. COMPARISON WITH INDUSTRY AVERAGES IS DIFFICULT IF THE FIRM OPERATES MANY DIFFERENT DIVISIONS.
<br />
<br />2. DIFFERENT OPERATING AND ACCOUNTING PRACTICES DISTORT COMPARISONS.
<br />
<br />3. SOMETIMES HARD TO TELL IF A RATIO IS “GOOD” OR “BAD.”
<br />
<br />4. DIFFICULT TO TELL WHETHER COMPANY IS, ON BALANCE, IN A STRONG OR WEAK POSITION.
<br />
<br />5. “AVERAGE” PERFORMANCE IS NOT NECESSARILY GOOD.
<br />
<br />6. SEASONAL FACTORS CAN DISTORT RATIOS.
<br />
<br />7. “WINDOW DRESSING” TECHNIQUES CAN MAKE STATEMENTS AND RATIOS LOOK BETTER.
<br />
<br />
<br />M. WHAT ARE SOME QUALITATIVE FACTORS ANALYSTS SHOULD CONSIDER WHEN EVALUATING A COMPANY’S LIKELY FUTURE FINANCIAL PERFORMANCE?
<br />
<br />ANSWER: [SHOW S3-37 HERE.] TOP ANALYSTS RECOGNIZE THAT CERTAIN QUALITATIVE FACTORS MUST BE CONSIDERED WHEN EVALUATING A COMPANY. THESE FACTORS, AS SUMMARIZED BY THE AMERICAN ASSOCIATION OF INDIVIDUAL INVESTORS (AAII), ARE AS FOLLOWS:
<br />
<br />1. ARE THE COMPANY’S REVENUES TIED TO ONE KEY CUSTOMER?
<br />
<br />2. TO WHAT EXTENT ARE THE COMPANY’S REVENUES TIED TO ONE KEY PRODUCT?
<br />
<br />3. TO WHAT EXTENT DOES THE COMPANY RELY ON A SINGLE SUPPLIER?
<br />
<br />4. WHAT PERCENTAGE OF THE COMPANY’S BUSINESS IS GENERATED OVERSEAS?
<br />
<br />5. COMPETITION.
<br />
<br />6. FUTURE PROSPECTS.
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<br />7. LEGAL AND REGULATORY ENVIRONMENT. </div>saleem shahzadnoreply@blogger.com0tag:blogger.com,1999:blog-3421608066886271296.post-7940051475760080722010-12-14T13:13:00.001+05:002011-01-12T16:23:41.406+05:00Chapter 2Chapter 2<br /> Financial Statements, Cash Flow, and Taxes<br /> <br /><br /><br /> <br />ANSWERS TO END-OF-CHAPTER QUESTIONS<br /><br /><br /><br />2-1 The four financial statements contained in most annual reports are the balance sheet, income statement, statement of retained earnings, and statement of cash flows.<br /><br />2-2 No, because the $20 million of retained earnings would probably not be held as cash. The retained earnings figure represents the reinvestment of earnings by the firm. Consequently, the $20 million would be an investment in all of the firm’s assets.<br /><br />2-3 The balance sheet shows the firm’s financial position on a specific date, for example, December 31, 2002. It shows each account balance at that particular point in time. For example, the cash account shown on the balance sheet would represent the cash the firm has on hand and in the bank on December 31, 2002. The income statement, on the other hand, reports on the firm’s operations over a period of time, for example, over the last 12 months. It reports revenues and expenses that the firm has incurred over that particular time period. For example, the sales figures reported on the income statement for the period ending December 31, 2002, would represent the firm’s sales over the period from January 1, 2002, through December 31, 2002, not just sales for December 31, 2002.<br /><br />2-4 The emphasis in accounting is on the determination of accounting income, or net income, while the emphasis in finance is on net cash flow. Net cash flow is the actual net cash that a firm generates during some specified period. The value of an asset (or firm) is determined by the cash flows generated. Cash is necessary to purchase assets to continue operations and to pay dividends. Thus, financial managers should strive to maximize cash flows available to investors over the long run.<br />Although companies with relatively high accounting profits generally have a relatively high cash flow, the relationship is not precise. A business’s net cash flow generally differs from net income because some of the expenses and revenues listed on the income statement are not paid out or received in cash during the year. The relationship between net cash flow and net income can be expressed as:<br /><br />Net cash flow = Net income + Non-cash charges - Non-cash revenues.<br /><br /> The primary examples of non-cash charges are depreciation and amorti-zation. These items reduce net income but are not paid out in cash, so we add them back to net income when calculating net cash flow. Likewise, some revenues may not be collected in cash during the year, and these items must be subtracted from net income when calculating net cash flow. Typically, depreciation and amortization represent the largest non-cash items, and in many cases the other non-cash items roughly net to zero. For this reason, many analysts assume that net cash flow equals net income plus depreciation and amortization.<br /> <br />2-5 Operating cash flow arises from normal, ongoing operations, whereas net cash flow reflects both operating and financing decisions. Thus, operating cash flow is defined as the difference between sales revenues and operating expenses paid, after taxes on operating income. Operating cash flow can be calculated as follows:<br /><br /> Operating cash flow = EBIT (1 - T) + Depreciation and amortization<br /> = NOPAT + Depreciation and amortization.<br /><br />Note that net cash flow can be calculated as follows:<br /><br />Net cash flow = Net income + Depreciation and amortization.<br /><br />Thus, the difference between the two equations is that net cash flow includes after-tax interest expense.<br /><br />2-6 Accountants translate physical quantities into numbers when they construct the financial statements. The numbers shown on balance sheets generally represent historical costs. When examining a set of financial statements, one should keep in mind the physical reality that lies behind the numbers, and the fact that the translation from physical assets to numbers is far from precise.<br /><br />2-7 Investors (both debt and equity investors) use financial statements to make intelligent decisions about what firms to invest in, managers need financial statements to operate their businesses, and taxing authorities need them to assess taxes.<br /><br />2-8 Operating capital is the amount of investor-supplied capital (interest bearing debt, preferred stock, and common equity) used to acquire the company’s net operating assets. Without this capital a firm cannot exist, as there is no source of funds with which to finance operations.<br /><br />2-9 NOPAT is the amount of net income a company would generate if it had no debt and held no non-operating assets. NOPAT is a better measure of the performance of a company’s operations because debt lowers income. In order to get a true reflection of a company’s operating performance, one would want to take out debt to get a clearer picture of the situation.<br /><br />2-10 Free cash flow is the cash flow actually available for distribution to investors after the company has made all the investments in fixed assets, new products, and operating working capital necessary to sustain ongoing operations. It is defined as net operating profit after taxes (NOPAT) minus the amount of net investment in operating working capital and fixed assets necessary to sustain the business. It is the most important measure of cash flows because it shows the exact amount available to all investors.<br /><br />2-11 Double taxation refers to the fact that corporate income is subject to an income tax, and then stockholders are subject to a further personal tax on dividends received.<br /><br />2-12 Because interest paid is tax deductible but dividend payments are not, the after-tax cost of debt is lower than the after-tax cost of equity. This encourages the use of debt rather than equity. This point is discussed in detail in the chapters titled, “The Cost of Capital” and “Capital Structure and Leverage.”<br /><br />2-13 Accounting net income includes only the cost for debt capital, not the cost of equity capital. Consequently, the cost of equity capital could be so large as to produce a negative EVA.<br /> <br />SOLUTIONS TO END-OF-CHAPTER PROBLEMS<br /><br /><br /><br />2-1 NI = $3,000,000; EBIT = $6,000,000; T = 40%; Interest = ?<br />Need to set up an income statement and work from the bottom up.<br /><br />EBIT $6,000,000<br />Interest 1,000,000<br />EBT $5,000,000 EBT = <br />Taxes (40%) 2,000,000<br />NI $3,000,000<br /><br />Interest = EBIT - EBT = $6,000,000 - $5,000,000 = $1,000,000.<br /><br /><br />2-2 NI = $3,100,000; DEP = $500,000; AMORT = 0; NCF = ?<br />NCF = NI + DEP and AMORT = $3,100,000 + $500,000 = $3,600,000.<br /><br /><br />2-3 EBIT = $170,000; Operating capital = $800,000; kA-T = 11.625%; T = 40%; <br />EVA = ? <br /><br />EVA = EBIT(1 - T) - AT dollar cost of capital<br /> = $170,000(1 - 0.4) – ($800,000 0.11625)<br /> = $102,000 - $93,000<br /> = $9,000.<br /><br /><br />2-4 NI = $50,000,000; R/EY/E = $810,000,000; R/EB/Y = $780,000,000; Dividends = ?<br /><br /> R/EB/Y + NI – Div = R/EY/E<br />$780,000,000 + $50,000,000 – Div = $810,000,000<br /> $830,000,000 – Div = $810,000,000<br /> $20,000,000 = Div.<br /><br /><br />2-5 EBITDA = $7,500,000; NI = $1,800,000; Int = $2,000,000; T = 40%; DA = ?<br /><br />EBITDA $7,500,000<br />DA 2,500,000 EBITDA – DA = EBIT; DA = EBITDA – EBIT<br />EBIT $5,000,000 EBIT = EBT + Int = $3,000,000 + $2,000,000<br />Int 2,000,000 (Given)<br />EBT $3,000,000<br />Taxes (40%) 1,200,000<br />NI $1,800,000 (Given)<br /><br /><br /> <br />2-6 EBIT = $750,000; DEP = $200,000; AMORT = 0; 100% Equity; T = 40%; NI = ?; NCF = ?; OCF = ?<br /><br />First, determine net income by setting up an income statement:<br />EBIT $750,000<br />Interest 0<br />EBT $750,000<br />Taxes (40%) 300,000<br />NI $450,000<br /><br />NCF = NI + DEP and AMORT = $450,000 + $200,000 = $650,000.<br /><br />OCF = EBIT(1 - T) + DEP and AMORT = $750,000(0.6) + $200,000 = $650,000.<br /><br />Note that NCF = OCF because the firm is 100 percent equity financed.<br /><br /><br />2-7 Statements b, c, and d will all decrease the amount of cash on a company’s balance sheet, while Statement a will increase cash through the sale of common stock. This is a source of cash through financing activities.<br /><br /><br />2-8 a. NOPAT = EBIT(1 – T)<br /> = $4,000,000,000(0.6)<br /> = $2,400,000,000.<br /><br /> b. NCF = NI + DEP and AMORT<br /> = $1,500,000,000 + $3,000,000,000<br /> = $4,500,000,000.<br /><br /> c. OCF = NOPAT + DEP and AMORT<br /> = $2,400,000,000 + $3,000,000,000<br /> = $5,400,000,000.<br /><br /> d. FCF = NOPAT – Net Investment in Operating Capital<br /> = $2,400,000,000 - $1,300,000,000<br /> = $1,100,000,000.<br /><br /> e. EVA = NOPAT – <br /> = $2,400,000,000 – [($20,000,000,000)(0.10)]<br /> = $400,000,000.<br /><br /><br />2-9 MVA = (P0 Number of common shares) BV of equity<br />$130,000,000 = $60X $500,000,000<br />$630,000,000 = $60X<br /> X = 10,500,000 common shares.<br /><br /><br /> <br />2-10 First, determine the firm’s total operating capital:<br />Total operating capital = Net operating working capital Net fixed assets<br /> = $5,000,000 $37,000,000<br /> = $42,000,000.<br /><br />Now, you can calculate the firm’s EVA:<br />EVA = EBIT (1 T) (WACC)(Total operating capital)<br /> = $6,375,000 (1 0.40) (0.085)($42,000,000)<br /> = $3,825,000 $3,570,000<br /> = $255,000.<br /><br /><br />2-11 Ending R/E = Beg. R/E Net income Dividends<br />$278,900,000 = $212,300,000 Net income $22,500,000<br />$278,900,000 = $189,800,000 Net income<br /> Net income = $89,100,000.<br /><br /><br />2-12 a. From the statement of cash flows the change in cash must equal cash flow from operating activities plus long-term investing activities plus financing activities. First, we must identify the change in cash as follows:<br /><br />Cash at the end of the year $25,000<br />Cash at the beginning of the year 55,000<br />Change in cash -$30,000<br /><br />The sum of cash flows generated from operations, investment, and financing must equal a negative $30,000. Therefore, we can calculate the cash flow from operations as follows:<br /><br />CF from operations CF from investing CF from financing = in cash<br /> CF from operations $250,000 $170,000 = -$30,000<br /> CF from operations = $50,000.<br /><br />b. To determine the firm’s net income for the current year, you must realize that cash flow from operations is determined by adding sources of cash (such as depreciation and amortization and increases in accrued liabilities) and subtracting uses of cash (such as increases in accounts receivable and inventories) from net income. Since we determined that the firm’s cash flow from operations totaled $50,000 in part a of this problem, we can now calculate the firm’s net income as follows:<br /><br />NI = <br /> NI + $10,000 + $25,000 - $100,000 = $50,000<br /> NI - $65,000 = $50,000<br /> NI = $115,000.<br /><br /> <br />2-13 Working up the income statement you can calculate the new sales level would be $12,681,482.<br /><br />Sales $12,681,482 $5,706,667/(1 0.55)<br />Operating costs (excl. D&A) 6,974,815 $12,681,482 0.55<br />EBITDA $ 5,706,667 $4,826,667 + $880,000<br />Depr. & amort. 880,000 $800,000 1.10<br />EBIT $ 4,826,667 $4,166,667 + $660,000<br />Interest 660,000 $600,000 1.10<br />EBT $ 4,166,667 $2,500,000/(1 0.4)<br />Taxes (40%) 1,666,667 $4,166,667 0.40<br />Net income $ 2,500,000<br /><br /><br />2-14 a. Because we’re interested in net cash flow available to common stockholders, we exclude common dividends paid.<br /><br />CF02 = NI available to common stockholders + Depreciation and amortization<br /> = $364 + $220 = $584 million.<br /><br />The net cash flow number is larger than net income by the current year’s depreciation and amortization expense, which is a noncash charge.<br /><br />b. Balance of RE, December 31, 2001 $1,302<br />Add: NI, 2002 364<br />Less: Div. paid to common stockholders (146)<br />Balance of RE, December 31, 2002 $1,520<br /><br />The RE balance on December 31, 2002 is $1,520 million.<br /><br />c. $1,520 million.<br /><br />d. Cash + Marketable securities = $15 million.<br /><br />e. Total current liabilities = $620 million.<br /><br /><br />2-15 a. Income Statement<br />Sales revenues $12,000,000<br />Costs except deprec. and amort. (75%) 9,000,000<br />EBITDA $ 3,000,000<br />Depreciation and amortization 1,500,000<br />EBT $ 1,500,000<br />Taxes (40%) 600,000<br />Net income $ 900,000<br />Add back deprec. and amort. 1,500,000<br />Net cash flow $ 2,400,000<br /><br />b. If depreciation and amortization doubled, taxable income would fall to zero and taxes would be zero. Thus, net income would decrease to zero, but net cash flow would rise to $3,000,000. Menendez would save $600,000 in taxes, thus increasing its cash flow:<br /><br />CF = T(Depreciation and amortization) = 0.4($1,500,000) = $600,000.<br />c. If depreciation and amortization were halved, taxable income would rise to $2,250,000 and taxes to $900,000. Therefore, net income would rise to $1,350,000, but net cash flow would fall to $2,100,000.<br /><br />d. You should prefer to have higher depreciation and amortization charges and higher cash flows. Net cash flows are the funds that are available to the owners to withdraw from the firm and, therefore, cash flows should be more important to them than net income.<br /><br />e. In the situation where depreciation and amortization doubled, net income fell by 100 percent. Since many of the measures banks and investors use to appraise a firm’s performance depend on net income, a decline in net income could certainly hurt both the firm’s stock price and its ability to borrow. For example, earnings per share is a common number looked at by banks and investors, and it would have declined by 100 percent, even though the firm’s ability to pay dividends and to repay loans would have improved.<br /><br /><br />2-16 This involves setting up the income statement and working from the bottom up.<br /><br />Sales Revenue* $2,500,000<br />Cost of Goods Sold (60%) 1,500,000 2,500,000 0.6<br />EBITDA $1,000,000 EBITDA = EBIT + DEP and AMORT<br />Deprec. and amort. 500,000 (Given)<br />EBIT $ 500,000 EBIT = EBT + Interest<br />Interest 100,000 (Given)<br />EBT $ 400,000 EBT =<br />Taxes (40%) 160,000<br />NI $ 240,000 (Given)<br /><br />* Sales Revenue - COGS = EBITDA<br /> Revenue - 0.6(Revenue) = $1,000,000<br /> 0.4 Revenue = $1,000,000<br /> Revenue = $2,500,000.<br /><br /><br />2-17 a. NOPAT = EBIT(1 - T)<br />= $150,000,000(0.6)<br />= $90,000,000.<br /><br /> b. = Current assets - <br /> = $360,000,000 - ($90,000,000 + $60,000,000)<br /> = $210,000,000.<br /><br /> = $372,000,000 - $180,000,000 = $192,000,000.<br /><br />c. Operating capital01 = <br />= $250,000,000 + $210,000,000<br />= $460,000,000.<br /><br />Operating capital02 = $300,000,000 + $192,000,000<br />= $492,000,000.<br /><br />d. FCF = NOPAT - Net investment in operating capital<br /> = $90,000,000 - ($492,000,000 - $460,000,000)<br /> = $58,000,000.<br /><br />e. The large increase in dividends for 2002 can most likely be attributed to a large increase in free cash flow from 2001 to 2002, since FCF represents the amount of cash available to be paid out to stockholders after the company has made all investments in fixed assets, new products, and operating working capital necessary to sustain the business.<br /><br /><br /><br /> <br />SPREADSHEET PROBLEM<br /><br /><br /><br />2-18 The detailed solution for the spreadsheet problem is available both on the instructor’s resource CD-ROM and on the instructor’s side of South-Western’s web site, http://brigham.swlearning.com.<br /><br /><br /> <br />INTEGRATED CASE<br /><br /><br /><br />D’Leon Inc., Part I<br />Financial Statements and Taxes<br /><br />2-19 DONNA JAMISON, A 1997 GRADUATE OF THE UNIVERSITY OF FLORIDA WITH FOUR YEARS OF BANKING EXPERIENCE, WAS RECENTLY BROUGHT IN AS ASSISTANT TO THE CHAIRMAN OF THE BOARD OF D’LEON INC., A SMALL FOOD PRODUCER THAT OPERATES IN NORTH FLORIDA AND WHOSE SPECIALTY IS HIGH-QUALITY PECAN AND OTHER NUT PRODUCTS SOLD IN THE SNACK-FOODS MARKET. D’LEON’S PRESIDENT, AL WATKINS, DECIDED IN 2001 TO UNDERTAKE A MAJOR EXPANSION AND TO “GO NATIONAL” IN COMPETITION WITH FRITO-LAY, EAGLE, AND OTHER MAJOR SNACK-FOOD COMPANIES. WATKINS FELT THAT D’LEON’S PRODUCTS WERE OF A HIGHER QUALITY THAN THE COMPETITION’S, THAT THIS QUALITY DIFFERENTIAL WOULD ENABLE IT TO CHARGE A PREMIUM PRICE, AND THAT THE END RESULT WOULD BE GREATLY INCREASED SALES, PROFITS, AND STOCK PRICE.<br />THE COMPANY DOUBLED ITS PLANT CAPACITY, OPENED NEW SALES OFFICES OUTSIDE ITS HOME TERRITORY, AND LAUNCHED AN EXPENSIVE ADVERTISING CAMPAIGN. D’LEON’S RESULTS WERE NOT SATISFACTORY, TO PUT IT MILDLY. ITS BOARD OF DIRECTORS, WHICH CONSISTED OF ITS PRESIDENT AND VICE-PRESIDENT PLUS ITS MAJOR STOCKHOLDERS (WHO WERE ALL LOCAL BUSINESS PEOPLE), WAS MOST UPSET WHEN DIRECTORS LEARNED HOW THE EXPANSION WAS GOING. SUPPLIERS WERE BEING PAID LATE AND WERE UNHAPPY, AND THE BANK WAS COMPLAINING ABOUT THE DETERIORATING SITUATION AND THREATENING TO CUT OFF CREDIT. AS A RESULT, WATKINS WAS INFORMED THAT CHANGES WOULD HAVE TO BE MADE, AND QUICKLY, OR HE WOULD BE FIRED. ALSO, AT THE BOARD’S INSISTENCE DONNA JAMISON WAS BROUGHT IN AND GIVEN THE JOB OF ASSISTANT TO FRED CAMPO, A RETIRED BANKER WHO WAS D’LEON’S CHAIRMAN AND LARGEST STOCKHOLDER. CAMPO AGREED TO GIVE UP A FEW OF HIS GOLFING DAYS AND TO HELP NURSE THE COMPANY BACK TO HEALTH, WITH JAMISON’S HELP.<br />JAMISON BEGAN BY GATHERING THE FINANCIAL STATEMENTS AND OTHER DATA GIVEN IN TABLES IC2-1, IC2-2, IC2-3, AND IC2-4. ASSUME THAT YOU ARE JAMISON’S ASSISTANT, AND YOU MUST HELP HER ANSWER THE FOLLOWING QUESTIONS FOR CAMPO. (NOTE: WE WILL CONTINUE WITH THIS CASE IN CHAPTER 3, AND YOU WILL FEEL MORE COMFORTABLE WITH THE ANALYSIS THERE, BUT ANSWERING THESE QUESTIONS WILL HELP PREPARE YOU FOR CHAPTER 3. PROVIDE CLEAR EXPLANATIONS, NOT JUST YES OR NO ANSWERS!)<br />TABLE IC2-1. BALANCE SHEETS<br /><br /> 2002 2001 <br />ASSETS<br />CASH $ 7,282 $ 57,600<br />ACCOUNTS RECEIVABLE 632,160 351,200<br />INVENTORIES 1,287,360 715,200<br /> TOTAL CURRENT ASSETS $1,926,802 $1,124,000<br /><br />GROSS FIXED ASSETS 1,202,950 491,000<br />LESS ACCUMULATED DEPRECIATION 263,160 146,200<br /> NET FIXED ASSETS $ 939,790 $ 344,800<br />TOTAL ASSETS $2,866,592 $1,468,800<br /><br />LIABILITIES AND EQUITY<br />ACCOUNTS PAYABLE $ 524,160 $ 145,600<br />NOTES PAYABLE 636,808 200,000<br />ACCRUALS 489,600 136,000<br /> TOTAL CURRENT LIABILITIES $1,650,568 $ 481,600<br />LONG-TERM DEBT 723,432 323,432<br />COMMON STOCK (100,000 SHARES) 460,000 460,000<br />RETAINED EARNINGS 32,592 203,768<br /> TOTAL EQUITY $ 492,592 $ 663,768<br />TOTAL LIABILITIES AND EQUITY $2,866,592 $1,468,800<br /><br /><br />TABLE IC2-2. INCOME STATEMENTS<br /><br /> 2002 2001 <br />SALES $6,034,000 $3,432,000<br />COST OF GOODS SOLD 5,528,000 2,864,000<br />OTHER EXPENSES 519,988 358,672<br />TOTAL OPERATING COSTS<br /> EXCLUDING DEPRECIATION AND AMORTIZATION $6,047,988 $3,222,672<br />EBITDA ($ 13,988) $ 209,328<br />DEPRECIATION AND AMORTIZATION 116,960 18,900<br />EBIT ($ 130,948) $ 190,428<br />INTEREST EXPENSE 136,012 43,828<br />EBT ($ 266,960) $ 146,600<br />TAXES (40%) (106,784)a 58,640<br />NET INCOME ($ 160,176) $ 87,960<br /><br />EPS ($1.602) $0.880<br />DPS $0.110 $0.220<br />BOOK VALUE PER SHARE $4.926 $6.638<br />STOCK PRICE $2.250 $8.500<br />SHARES OUTSTANDING 100,000 100,000<br />TAX RATE 40.00% 40.00%<br />LEASE PAYMENTS 40,000 40,000<br />SINKING FUND PAYMENTS 0 0<br /><br />NOTE:<br />aTHE FIRM HAD SUFFICIENT TAXABLE INCOME IN 2000 AND 2001 TO OBTAIN ITS FULL TAX REFUND IN 2002.<br /> <br />TABLE IC2-3. STATEMENT OF RETAINED EARNINGS, 2002<br /><br />BALANCE OF RETAINED EARNINGS, 12/31/01 $203,768<br /> ADD: NET INCOME, 2002 (160,176)<br /> LESS: DIVIDENDS PAID (11,000)<br />BALANCE OF RETAINED EARNINGS, 12/31/02 $ 32,592<br /><br /><br />TABLE IC2-4. STATEMENT OF CASH FLOWS, 2002<br /><br />OPERATING ACTIVITIES<br /> NET INCOME ($160,176)<br /> ADDITIONS (SOURCES OF CASH)<br /> DEPRECIATION AND AMORTIZATION 116,960<br /> INCREASE IN ACCOUNTS PAYABLE 378,560<br /> INCREASE IN ACCRUALS 353,600<br /> SUBTRACTIONS (USES OF CASH)<br /> INCREASE IN ACCOUNTS RECEIVABLE (280,960)<br /> INCREASE IN INVENTORIES (572,160)<br />NET CASH PROVIDED BY OPERATING ACTIVITIES ($164,176)<br /><br />LONG-TERM INVESTING ACTIVITIES<br />CASH USED TO ACQUIRE FIXED ASSETS ($711,950)<br /><br />FINANCING ACTIVITIES<br /> INCREASE IN NOTES PAYABLE $436,808<br /> INCREASE IN LONG-TERM DEBT 400,000<br /> PAYMENT OF CASH DIVIDENDS (11,000)<br />NET CASH PROVIDED BY FINANCING ACTIVITIES $825,808<br />SUM: NET DECREASE IN CASH ($ 50,318)<br />PLUS: CASH AT BEGINNING OF YEAR 57,600<br />CASH AT END OF YEAR $ 7,282<br /><br /> <br />A. WHAT EFFECT DID THE EXPANSION HAVE ON SALES, NET OPERATING PROFIT AFTER TAXES (NOPAT), NET OPERATING WORKING CAPITAL (NOWC), TOTAL INVESTOR-SUPPLIED OPERATING CAPITAL, AND NET INCOME?<br /><br />ANSWER: [S2-1 THROUGH S2-9 PROVIDE BACKGROUND INFORMATION. THEN SHOW S2-10 THROUGH S2-14 HERE.] SALES INCREASED BY $2,602,000.<br /><br /> NOPAT02 = EBIT(1 - TAX RATE)<br /> = (-$130,948)(0.6) = ($78,569).<br /><br />NOPAT01 = $190,428(0.6) = $114,257.<br /><br />NOPAT = ($78,569) - $114,257 = ($192,826).<br /><br />NOPAT DECREASED BY $192,826.<br /><br /> NOWC02 = <br /> = ($7,282 + $632,160 + $1,287,360) - ($524,160 + $489,600)<br /> = $913,042.<br /><br /> NOWC01 = ($57,600 + $351,200 + $715,200) - ($145,600 + $136,000)<br /> = $842,400.<br /><br />NOWC = $913,042 - $842,400 = $70,642.<br /><br />NET OPERATING WORKING CAPITAL INCREASED BY $70,642.<br /><br /> OC02 = NET OPERATING WORKING CAPITAL + NET PLANT AND EQUIPMENT<br /> = $913,042 + $939,790 = $1,852,832.<br /><br /> OC01 = $842,400 + $344,800 = $1,187,200.<br /><br />OC = $1,852,832 - $1,187,200 = $665,632.<br /><br />TOTAL INVESTOR-SUPPLIED OPERATING CAPITAL INCREASED SUBSTANTIALLY BY $665,632 FROM 2001 TO 2002.<br /><br /> NI02 – NI01 = ($160,176) - $87,960 = ($248,136).<br /><br />THERE WAS A BIG DROP, -$248,136, IN NET INCOME DURING 2002.<br /><br />B. WHAT EFFECT DID THE COMPANY’S EXPANSION HAVE ON ITS NET CASH FLOW, OPERATING CASH FLOW, AND FREE CASH FLOW?<br /><br />ANSWER: [SHOW S2-15 AND S2-16 HERE.]<br /><br /> NCF02 = NI + DEP AND AMORT = ($160,176) + $116,960 = ($43,216).<br /><br /> NCF01 = $87,960 + $18,900 = $106,860.<br /><br /> OCF02 = EBIT(1 - T) + DEP AND AMORT = (-$130,948)(0.6) + $116,960<br /> = $38,391.<br /><br /> OCF01 = ($190,428)(0.6) + $18,900 = $133,157.<br /><br /> FCF02 = NOPAT - NET INVESTMENT IN OPERATING CAPITAL<br /> = (-$78,569) - ($1,852,832 - $1,187,200)<br /> = (-$78,569) - $665,632 = ($744,201).<br /><br />NCF IS NEGATIVE IN 2002, BUT IT WAS POSITIVE IN 2001. OCF IS POSITIVE IN 2002, BUT IT DECREASED BY OVER 70 PERCENT FROM ITS 2001 LEVEL. FREE CASH FLOW WAS -$744,201 IN 2002.<br /><br /><br />C. JAMISON ALSO HAS ASKED YOU TO ESTIMATE D’LEON’S EVA. SHE ESTIMATES THAT THE AFTER-TAX COST OF CAPITAL WAS 10 PERCENT IN 2001 AND <br />13 PERCENT IN 2002.<br /><br />ANSWER: [SHOW S2-17 THROUGH S2-19 HERE.]<br /><br /> EVA02 = EBIT(1 - T) - AFTER-TAX COST OF OPERATING CAPITAL<br /> = (-$130,948)(0.6) - ($1,852,832)(0.13)<br /> = ($319,437).<br /><br /> EVA01 = EBIT(1 - T) - AFTER-TAX COST OF OPERATING CAPITAL<br /> = ($190,428)(0.6) - ($1,187,200)(0.10)<br /> = ($4,463).<br /><br />IN 2001, EVA WAS SLIGHTLY NEGATIVE; HOWEVER IN 2002 EVA WAS SIGNIFICANTLY NEGATIVE.<br /><br />D. LOOKING AT D’LEON’S STOCK PRICE TODAY, WOULD YOU CONCLUDE THAT THE EXPANSION INCREASED OR DECREASED MVA?<br /><br />ANSWER: [SHOW S2-20 HERE.] DURING THE LAST YEAR, STOCK PRICE HAS DECREASED BY OVER 73 PERCENT, THUS ONE WOULD CONCLUDE THAT THE EXPANSION HAS DECREASED MVA.<br /><br /><br />E. D’LEON PURCHASES MATERIALS ON 30-DAY TERMS, MEANING THAT IT IS SUPPOSED TO PAY FOR PURCHASES WITHIN 30 DAYS OF RECEIPT. JUDGING FROM ITS 2002 BALANCE SHEET, DO YOU THINK D’LEON PAYS SUPPLIERS ON TIME? EXPLAIN. <br />IF NOT, WHAT PROBLEMS MIGHT THIS LEAD TO?<br /><br />ANSWER: [SHOW S2-21 HERE.] D’LEON PROBABLY DOES NOT PAY ITS SUPPLIERS ON TIME JUDGING FROM THE FACT THAT ITS ACCOUNTS PAYABLES BALANCE INCREASED BY 260 PERCENT FROM THE PAST YEAR, WHILE SALES INCREASED BY ONLY 76 PERCENT. COMPANY RECORDS WOULD SHOW IF THEY PAID SUPPLIERS ON TIME. BY NOT PAYING SUPPLIERS ON TIME, D’LEON IS STRAINING ITS RELATIONSHIP WITH THEM. IF D’LEON CONTINUES TO BE LATE, EVENTUALLY SUPPLIERS WILL CUT THE COMPANY OFF AND PUT IT INTO BANKRUPTCY.<br /><br /><br />F. D’LEON SPENDS MONEY FOR LABOR, MATERIALS, AND FIXED ASSETS (DEPRECIATION) TO MAKE PRODUCTS, AND STILL MORE MONEY TO SELL THOSE PRODUCTS. THEN, IT MAKES SALES THAT RESULT IN RECEIVABLES, WHICH EVENTUALLY RESULT IN CASH INFLOWS. DOES IT APPEAR THAT D’LEON’S SALES PRICE EXCEEDS ITS COSTS PER UNIT SOLD? HOW DOES THIS AFFECT THE CASH BALANCE?<br /><br />ANSWER: [SHOW S2-22 HERE.] IT DOES NOT APPEAR THE D’LEON’S SALES PRICE EXCEEDS ITS COSTS PER UNIT SOLD AS INDICATED IN THE INCOME STATEMENT. THE COMPANY IS SPENDING MORE CASH THAN IT IS TAKING IN AND, AS A RESULT, THE CASH ACCOUNT BALANCE HAS DECREASED.<br /><br /><br />G. SUPPOSE D’LEON’S SALES MANAGER TOLD THE SALES STAFF TO START OFFERING 60-DAY CREDIT TERMS RATHER THAN THE 30-DAY TERMS NOW BEING OFFERED. D’LEON’S COMPETITORS REACT BY OFFERING SIMILAR TERMS, SO SALES REMAIN CONSTANT. WHAT EFFECT WOULD THIS HAVE ON THE CASH ACCOUNT? HOW WOULD THE CASH ACCOUNT BE AFFECTED IF SALES DOUBLED AS A RESULT OF THE CREDIT POLICY CHANGE?<br /><br />ANSWER: [SHOW S2-23 HERE.] BY EXTENDING THE SALES CREDIT TERMS, IT WOULD TAKE LONGER FOR D’LEON TO RECEIVE ITS MONEY--ITS CASH ACCOUNT WOULD DECREASE AND ITS ACCOUNTS RECEIVABLE WOULD BUILD UP. BECAUSE COLLECTIONS WOULD SLOW, ACCOUNTS PAYABLE WOULD BUILD UP TOO.<br /> INVENTORY WOULD HAVE TO BE BUILT UP AND POSSIBLY FIXED ASSETS TOO BEFORE SALES COULD BE INCREASED. ACCOUNTS RECEIVABLE WOULD RISE AND CASH WOULD DECLINE. MUCH LATER, WHEN COLLECTIONS INCREASED CASH WOULD RISE. D’LEON WOULD PROBABLY NEED TO BORROW OR SELL STOCK TO FINANCE THE EXPANSION.<br /><br /><br />H. CAN YOU IMAGINE A SITUATION IN WHICH THE SALES PRICE EXCEEDS THE COST OF PRODUCING AND SELLING A UNIT OF OUTPUT, YET A DRAMATIC INCREASE IN SALES VOLUME CAUSES THE CASH BALANCE TO DECLINE?<br /><br />ANSWER: THIS SITUATION IS LIKELY TO OCCUR AS SUGGESTED IN THE SECOND PART OF THE ANSWER TO QUESTION G.<br /><br /><br />I. DID D’LEON FINANCE ITS EXPANSION PROGRAM WITH INTERNALLY GENERATED FUNDS (ADDITIONS TO RETAINED EARNINGS PLUS DEPRECIATION) OR WITH EXTERNAL CAPITAL? HOW DOES THE CHOICE OF FINANCING AFFECT THE COMPANY’S FINANCIAL STRENGTH?<br /><br />ANSWER: [SHOW S2-24 HERE.] D’LEON FINANCED ITS EXPANSION WITH EXTERNAL CAPITAL RATHER THAN INTERNALLY GENERATED FUNDS. IN PARTICULAR, D’LEON ISSUED LONG-TERM DEBT RATHER THAN COMMON STOCK, WHICH REDUCED ITS FINANCIAL STRENGTH AND FLEXIBILITY.<br /><br /><br />J. REFER TO TABLES IC2-2 AND IC2-4. SUPPOSE D’LEON BROKE EVEN IN 2002 IN THE SENSE THAT SALES REVENUES EQUALED TOTAL OPERATING COSTS PLUS INTEREST CHARGES. WOULD THE ASSET EXPANSION HAVE CAUSED THE COMPANY TO EXPERIENCE A CASH SHORTAGE THAT REQUIRED IT TO RAISE EXTERNAL CAPITAL?<br /><br />ANSWER: [SHOW S2-25 HERE.] EVEN IF D’LEON HAD BROKEN EVEN IN 2002, THE FIRM WOULD HAVE HAD TO FINANCE AN INCREASE IN ASSETS.<br />K. IF D’LEON STARTED DEPRECIATING FIXED ASSETS OVER 7 YEARS RATHER THAN <br />10 YEARS, WOULD THAT AFFECT (1) THE PHYSICAL STOCK OF ASSETS, (2) THE BALANCE SHEET ACCOUNT FOR FIXED ASSETS, (3) THE COMPANY’S REPORTED NET INCOME, AND (4) ITS CASH POSITION? ASSUME THE SAME DEPRECIATION METHOD IS USED FOR STOCKHOLDER REPORTING AND FOR TAX CALCULATIONS, AND THE ACCOUNTING CHANGE HAS NO EFFECT ON ASSETS’ PHYSICAL LIVES.<br /><br />ANSWER: [SHOW S2-26 HERE.] THIS WOULD HAVE NO EFFECT ON THE PHYSICAL STOCK OF THE ASSETS; HOWEVER, THE BALANCE SHEET ACCOUNT FOR NET FIXED ASSETS WOULD DECLINE BECAUSE ACCUMULATED DEPRECIATION WOULD INCREASE DUE TO DEPRECIATING ASSETS OVER 7 YEARS VERSUS 10 YEARS. BECAUSE DEPRECIATION EXPENSE WOULD INCREASE, NET INCOME WOULD DECLINE. FINALLY, THE FIRM’S CASH POSITION WOULD INCREASE, BECAUSE ITS TAX PAYMENTS WOULD BE REDUCED.<br /><br /><br />L. EXPLAIN HOW EARNINGS PER SHARE, DIVIDENDS PER SHARE, AND BOOK VALUE PER SHARE ARE CALCULATED, AND WHAT THEY MEAN. WHY DOES THE MARKET PRICE PER SHARE NOT EQUAL THE BOOK VALUE PER SHARE?<br /><br />ANSWER: NET INCOME DIVIDED BY SHARES OUTSTANDING EQUALS EARNINGS PER SHARE. DIVIDENDS DIVIDED BY SHARES OUTSTANDING EQUALS DIVIDENDS PER SHARE, WHILE BOOK VALUE PER SHARE IS CALCULATED AS TOTAL COMMON EQUITY DIVIDED BY SHARES OUTSTANDING.<br />MARKET PRICE PER SHARE DOES NOT EQUAL BOOK VALUE PER SHARE. THE MARKET VALUE OF A STOCK REFLECTS FUTURE PROFITABILITY, WHILE BOOK VALUE PER SHARE REPRESENTS HISTORICAL COST.<br /><br />M. EXPLAIN BRIEFLY THE TAX TREATMENT OF (1) INTEREST AND DIVIDENDS PAID, <br />(2) INTEREST EARNED AND DIVIDENDS RECEIVED, (3) CAPITAL GAINS, AND (4) TAX LOSS CARRY-BACK AND CARRY-FORWARD. HOW MIGHT EACH OF THESE ITEMS IMPACT D’LEON’S TAXES?<br /><br />ANSWER: [SHOW S2-27 THROUGH S2-30 HERE.] FOR A BUSINESS, INTEREST PAID IS CONSIDERED AN EXPENSE AND IS PAID OUT OF PRE-TAX INCOME. THEREFORE, INTEREST PAID IS TAX DEDUCTIBLE FOR BUSINESSES. FOR INDIVIDUALS, INTEREST PAID IS GENERALLY NOT TAX DEDUCTIBLE, WITH THE NOTABLE EXCEPTION BEING LIMITED TAX DEDUCTIBILITY ON HOME MORTGAGE INTEREST. DIVIDENDS PAID BY A BUSINESS ARE PAID OUT OF AFTER-TAX INCOME. INTEREST EARNED, WHETHER BY A BUSINESS OR INDIVIDUAL, IS TAXABLE INCOME AND SUBJECT TO STANDARD INCOME TAXES, EXCEPT FOR SOME STATE AND LOCAL GOVERNMENT DEBT INTEREST. DIVIDENDS RECEIVED ARE FULLY TAXED AS ORDINARY INCOME FOR INDIVIDUALS, CREATING A “DOUBLE TAXATION” OF DIVIDENDS. A PORTION OF DIVIDENDS RECEIVED BY CORPORATIONS IS TAX EXCLUDABLE, IN ORDER TO AVOID “TRIPLE TAXATION.”<br />CAPITAL GAINS ARE DEFINED AS THE PROFITS FROM THE SALE OF AN ASSET NOT USED IN THE NORMAL COURSE OF BUSINESS. FOR INDIVIDUALS, CAPITAL GAINS ON ASSETS ARE TAXED AS ORDINARY INCOME IF HELD FOR LESS THAN A YEAR, AND AT THE CAPITAL GAINS RATE IF HELD FOR MORE THAN A YEAR. CORPORATIONS FACE SOMEWHAT DIFFERENT RULES. CAPITAL GAINS FOR CORPORATIONS ARE TAXED AS ORDINARY INCOME. TAX LOSS CARRY-BACK AND CARRY-FORWARD PROVISIONS ALLOW BUSINESSES TO USE A LOSS IN THE CURRENT YEAR TO OFFSET PROFITS IN PRIOR YEARS (2 YEARS), AND IF LOSSES HAVEN’T BEEN COMPLETELY OFFSET BY PAST PROFITS THEY CAN BE CARRIED FORWARD TO OFFSET PROFITS IN THE FUTURE (20 YEARS).<br />D’LEON PAID INTEREST EXPENSE OF $136,012 WHICH WAS USED TO FURTHER LOWER ITS TAX LIABILITY RESULTING IN A TAX CREDIT OF $106,784 FOR A NET LOSS OF -$160,176. HOWEVER, BECAUSE OF THE TAX LOSS CARRY-BACK AND CARRY-FORWARD PROVISION D’LEON WAS ABLE TO OBTAIN ITS FULL TAX REFUND IN 2002 (AS THE FIRM HAD SUFFICIENT TAXABLE INCOME IN 2000 and 2001).saleem shahzadnoreply@blogger.com0