Chapter 20

Hybrid Financing: Preferred Stock, Leasing,

Warrants, and Convertibles

SOLUTIONS TO END-OF-CHAPTER PROBLEMS

20-1 If the company purchased the equipment its balance sheet would look like:

Current assets $300 Debt $500

Fixed assets 600 Equity 400

Total assets $900 Total claims $900

Therefore, the company’s debt ratio = $500/$900 = 55.6%.

If the company leases the asset and does not capitalize the lease, its debt ratio = $400/$800 = 50%.

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.

20-2 First issue: 20-year straight bonds with an 8 percent annual coupon.

Second issue: 20-year bonds with 6 percent annual coupon with warrants. Both bonds issued at par $1,000. Value of warrants = ?

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%.)

Second issue: $1,000 = Bond + Warrants.

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.

N = 20; I = kd = 8; PMT = 60, FV = 1000, and solve for PV = $803.64.

Value of warrants = $1,000 - $803.64 = $196.36.

20-3 Convertible Bond’s Par value = $1,000; Conversion price, Pc = $40; CR = ?

CR =

20-4 a. Year

0 1 2 3 4

I. Cost of Owning:

Net purchase price ($1,500,000)

Depr. tax savingsa $198,000 $270,000 $ 90,000 $ 42,000

Net cash flow ($1,500,000) $198,000 $270,000 $ 90,000 $ 42,000

PV cost of owning

at 9% ($ 991,845)

II. Cost of Leasing:

Lease payment (AT) (240,000) (240,000) (240,000) (240,000)

Purch. option priceb (250,000)

Net cash flow $ 0 ($240,000) ($240,000) ($240,000) ($490,000)

PV cost of leasing

at 9% ($ 954,639)

III. Cost Comparison

Net advantage to leasing (NAL) = PV cost of owning - PV cost of leasing

= $991,845 - $954,639

= $37,206.

a Cost of new machinery: $1,500,000.

b Cost of purchasing the machinery after the lease expires.

MACRS Deprec. Tax Savings

Year Allowance Factor Depreciation T(Depreciation)

1 0.33 $495,000 $198,000

2 0.45 675,000 270,000

3 0.15 225,000 90,000

4 0.07 105,000 42,000

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.

b. We assume that Morris-Meyer will buy the equipment at the end of

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.)

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.

20-5 a. Exercise value = Current price - Striking price.

Ps = $18: Exercise Value = -$3 which is considered $0.

Ps = $21: Exercise Value = $0.

Ps = $25: Exercise Value = $4.

Ps = $70: Exercise Value = $49.

b. No precise answers are possible, but some “reasonable” war¬rant prices are as follows:

Ps = $18: Warrant = $1.50; Premium = $4.50.

Ps = $21: Warrant = $3.00; Premium = $3.00.

Ps = $25: Warrant = $5.50; Premium = $1.50.

Ps = $70: Warrant = $50.00; Premium = $1.00.

c. 1. The longer the life, the higher the warrant value.

2. The less variable the stock price, the lower the warrant value.

3. The higher the expected EPS growth rate, the higher the warrant price.

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.

d. Vpackage = $1,000

=

= VB + 50($1.50) = VB = $1,000 - $75 = $925.

Using a financial calculator, input the following: N = 20, I = 10,

PV = -925, FV = 1000, PMT = ? PMT = $91.19 ≈ $90. Consequently, the coupon interest rate = $90/$1,000 = 9%.

20-6 a. Balance sheets before lease is capitalized:

McDaniel-Edwards Balance Sheet (thousands of dollars):

Debt $400

Equity 200

Total liabilities

Total assets $600 and equity $600

Debt/assets ratio = $400/$600 = 67%.

Jordan-Hocking Balance Sheet (thousands of dollars):

Debt $200

Equity 200

Total liabilities

Total assets $400 and equity $400

Debt/assets ratio = $200/$400 = 50%.

b. Balance sheet after lease is capitalized:

Jordan-Hocking Balance Sheet (thousands of dollars):

Assets $400 Debt $200

Value of leased asset 200 PV of lease payments 200

Equity 200

Total liabilities

Total assets $600 and equity $600

Debt/assets ratio = $400/$600 = 67%.

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.

20-7 a. 0 1 2 3 4

Net purchase price (250,000)

Depr’n tax savingsa 20,000 32,000 19,000 12,000

Maintenance (AT) (12,000) (12,000) (12,000) (12,000)

Salvage value 42,500

Net cash flow (250,000) 8,000 20,000 7,000 42,500

PV cost of owning at 6% = -$185,112.

Notes:

1. There is no tax associated with the loom’s salvage value since salvage value equals book value.

2. The appropriate discount rate is the after-tax cost of debt =

kd(1 - T) = 10%(1 - 0.4) = 6%.

a Depreciation tax savings are calculated as follows:

Depreciation Schedule

MACRS

Allowance *Depreciation End of Year Depreciation

Year Factor Expense Book Value Tax Savings

1 0.20 $50,000 $200,000 $20,000

2 0.32 80,000 120,000 32,000

3 0.19 47,500 72,500 19,000

4 0.12 30,000 42,500 12,000

*Note that the loom’s depreciable basis is $250,000.

The cost of leasing can be placed on a time line as follows:

0 1 2 3 4

Lease payment (AT) -42,000 -42,000 -42,000 -42,000 -42,000

PV at 6% = -$187,534.

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.

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

9 percent, the after-tax discount rate (15%(1 - 0.4)):

0 1 2 3 4

($250,000) PVs of all other cash flows

7,547 @ 6%

17,800

5,877

0

30,108 @ 9% $42,500

NPV = (188,668)

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.

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.

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.

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.

20-9 a. Howe Computer Company Balance Sheet:

Alternative 1:

Total current

liabilities $ 50,000

Long-term debt --

Common stock,

par $1 75,000

Paid-in capital 225,000

Retained earnings 25,000

Total liabilities

Total assets $375,000 and equity $375,000

Alternative 2:

Total current

liabilities $ 50,000

Long-term debt --

Common stock,

par $1 70,000

Paid-in capital 230,000

Retained earnings 25,000

Total liabilities

Total assets $375,000 and equity $375,000

Alternative 3:

Total current

liabilities $ 50,000

Long-term debt (10%) 250,000

Common stock,

par $1 70,000

Paid-in capital 230,000

Retained earnings 25,000

Total liabilities

Total assets $625,000 and equity $625,000

b. Original Plan 1 Plan 2 Plan 3

Number of Keith

Howe’s shares 40,000 40,000 40,000 40,000

Total shares 50,000 75,000 70,000 70,000

Percent ownership 80% 53% 57% 57%

c. Original Plan 1 Plan 2 Plan 3

Total assets $275,000 $375,000 $375,000 $625,000

EBIT $ 55,000 $ 75,000 $ 75,000 $125,000

Interest 15,000 0 0 25,000

EBT $ 40,000 $ 75,000 $ 75,000 $100,000

Taxes (40%) 16,000 30,000 30,000 40,000

Net income $ 24,000 $ 45,000 $ 45,000 $ 60,000

Number of shares 50,000 75,000 70,000 70,000

Earnings per share $0.48 $0.60 $0.64 $0.86

d. Total debt $200,000 $ 50,000 $ 50,000 $300,000

Debt/assets ratio 73% 13% 13% 48%

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.

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!)

20-10 Facts and analysis in the problem:

kd = 12%; D0 = $2.46; g = 8%; P0 = $38.

ks = D1/P0 + g = $2.66/$38.00 + 8% = 15%.

Convertible:

Par = $1,000, 20-year; Coupon = 10%; CR = 20 shares.

Call = Five-year deferment; Call price = $1,075 in Year 6, declines by $5 per year.

Will be called when Ct = 1.2(Par) = $1,200.

Find n (number of years) to anticipated call/conversion:

(P0)(CR)(1 + g)n = $1,200

($38)(20)(1 + 0.08)n = $1,200

($760)(1.08)n = $1,200.

Using a financial calculator, input the following:

I = 8, PV = -760, PMT = 0, FV = 1200, N = ? N = 5.93 6.

Straight-debt value of the convertible at t = 0: (Assumes annual payment of coupon)

Using a financial calculator, input the following: N = 20, I = 12, PMT = 100, FV = 1000, PV = ? PV = $850.61 $851.

PV at t = 5 (n = 15): $864. PV at t = 10 (n = 10): $887.

PV at t = 15 (n = 5): $928. PV at t = 20 (n = 0): $1,000.

Conversion value:

Ct = P0(1.08)n(20). C0 = $38(20) = $760. C5 = $38(1.08)5(20) = $1,117.

C6 = $38(1.08)6(20) = $1,206. C10 = $38(1.08)10(20) = $1,641.

a. See the graph to the right.

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%.

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):

VBond = = $855.

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.

20-11 a. The value of the 9% coupon bonds, evaluated at 12%, can be found as follows:

N = 20; I = 12; PMT = 90; and FV = 1000. Solve for PV = $775.92.

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.

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:

Total firm value (t = 10) = $350,000,000 (1.10)10

Total firm value (t = 10) = $907,809,861.

c. With 10 years left to maturity, each of the 100,000 bonds will be worth;

N = 10; I = 12; PMT = 90; and FV = 1000. Solve for PV = $830.49.

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.

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.

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.

Input CF0 = -1000, CF1-9 = 90, CF10 = 964.60, CF11-19 = 90, and CF20 = 1090. Solve for IRR = 12.699%.

The component cost is 12.699%, and the premium associated with the warrants is 12.699% - 12% = 0.699%, or roughly 70 basis points.

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