Tuesday, December 14, 2010

Chapter 14

Chapter 14
Distributions to Shareholders:
Dividends and Share Repurchases
SOLUTIONS TO END-OF-CHAPTER PROBLEMS

14-1 70% Debt; 30% Equity; Capital Budget = $3,000,000; NI = $2,000,000; PO = ?

Equity retained = 0.3($3,000,000) = $900,000.

NI $2,000,000
-Additions to RE 900,000
Earnings Remaining $1,100,000

Payout =


14-2 P0 = $90; Split = 3 for 2; New P0 = ?




14-3 NI = $2,000,000; Shares = 1,000,000; P0 = $32; Repurchase = 20%; New P0 = ?

Repurchase = 0.2  1,000,000 = 200,000 shares.
Repurchase amount = 200,000  $32 = $6,400,000.

EPSOld = = = $2.00.

P/E = = 16.

EPSNew = = = $2.50.

PriceNew = EPSnew  P/E = $2.50(16) = $40.


14-4 Retained earnings = Net income (1 - Payout ratio)
= $5,000,000(0.55) = $2,750,000.

External equity needed:

Total equity required = (New investment)(1 - Debt ratio)
= $10,000,000(0.60) = $6,000,000.

New external equity needed = $6,000,000 - $2,750,000 = $3,250,000.
14-5 DPS after split = $0.75.

Equivalent pre-split dividend = $0.75(5) = $3.75.

New equivalent dividend = Last year’s dividend(1.09)
$3.75 = Last year’s dividend(1.09)
Last year’s dividend = $3.75/1.09 = $3.44.


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.
Projects H and L should be chosen because IRR > k, so the firm’s capital budget = $10 million.

Step 2: Determine how much of the capital budget will be financed with equity.

Capital Budget  Equity % = Equity Required.
$10,000,000  0.5 = $5,000,000.

Step 3: Determine dividends through residual model.

$7,287,500 - $5,000,000 = $2,287,500.

Step 4: Calculate payout ratio.

$2,287,500/$7,287,500 = 0.3139 = 31.39%.


14-7 a. Before finding the long-run growth rate, the dividend payout ratio must be determined.

Dividend payout ratio = DPS/EPS = $0.75/$2.25 = 0.3333.

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.

g = ROE  Retention ratio
= (Net Income/Equity Capital)  (1 - Dividend payout ratio)
= 18%  (1 - 0.3333) = 12%.

b. The required return can be calculated using the DCF approach.

ks = D1/P0 + g
ks = $0.75/$15.00 + 0.12
ks = 0.17 or 17%.


c. The new payout ratio can be calculated as:

$1.50/$2.25 = 0.6667.

The new long-run growth rate can now be calculated as:

g = ROE  (1 - Dividend payout ratio)
g = 18%  (1 - 0.6667) = 6%.

The firm's required return would be:

ks = D1/P0 + g
ks = $1.50/$15.00 + 0.06
ks = 0.16 or 16%.

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.

Amount of equity capital = Total assets  Equity ratio
= $10 million  0.6 = $6 million.

Net income = Equity capital  ROE = $6 million  0.18 = $1.08 million.

EPS = Net income/Number of shares
$2.25 = $1.08 million/Number of shares
Number of shares = 480,000.

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
($360,000/$7,200,000 = 0.05).

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:

Number of new shares = Dividend value/Price per share
Number of new shares = $360,000/$15
Number of new shares = 24,000 shares.

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.

New EPS = Net income/(Old shares outstanding + New shares outstanding)
New EPS = $1,080,000/(480,000 + 24,000)
New EPS = $2.1429.

The dilution of earnings per share is the difference between old EPS and new EPS.


Dilution of EPS = Old EPS - New EPS
Dilution of EPS = $2.25 - $2.1429
Dilution of EPS = $0.1071 ≈ $0.11 per share.


14-8 a. Total dividends03 = Net income  Payout ratio
= $1,800,000  0.40
= $720,000.

DPS03 = Dividends03/Shares outstanding
= $720,000/500,000
= $1.44.

b. Dividend yield = DPS/P0
= $1.44/$48.00
= 3%.

c. Total dividends02 = Net income02  Payout ratio
= $1,500,000  0.4
= $600,000.

DPS02 = Dividends02/Shares outstanding
= $600,000/500,000
= $1.20.

d. Payout ratio = Dividends/Net income
= $600,000/$1,800,000
= 0.3333 = 331/3%.

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).


14-9 a. 1. 2003 Dividends = (1.10)(2002 Dividends)
= (1.10)($3,600,000) = $3,960,000.

2. 2002 Payout = $3,600,000/$10,800,000 = 0.3333 = 331/3%.

2003 Dividends = (0.3333)(2003 Net income)
= (0.3333)($14,400,000) = $4,800,000.

(Note: If the payout ratio is rounded off to 33 percent, 2003 dividends are then calculated as $4,752,000.)

3. Equity financing = $8,400,000(0.60) = $5,040,000.

2003 Dividends = Net income - Equity financing
= $14,400,000 - $5,040,000 = $9,360,000.
All of the equity financing is done with retained earnings as long as they are available.

4. The regular dividends would be 10 percent above the 2002 dividends:

Regular dividends = (1.10)($3,600,000) = $3,960,000.

The residual policy calls for dividends of $9,360,000. Therefore, the extra dividend, which would be stated as such, would be

Extra dividend = $9,360,000 - $3,960,000 = $5,400,000.

An even better use of the surplus funds might be a stock repurchase.

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.

c. ks = + g = + 10% = 15%.

d. g = Retention rate(ROE)
0.10 = [1 – ($3,600,000/$10,800,000)](ROE)
ROE = 0.10/0.6667 = 0.15 = 15%.

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.


14-10 a. Capital budget = $10,000,000; Capital structure = 60% equity, 40% debt; Common shares outstanding = 1,000,000.

Retained earnings needed = $10,000,000(0.6) = $6,000,000.

b. According to the residual dividend model, only $2 million is available for dividends.

NI - Retained earnings needed for capital projects = Residual dividend
$8,000,000 - $6,000,000 = $2,000,000.

DPS = $2,000,000/1,000,000 = $2.00.

Payout ratio = $2,000,000/$8,000,000 = 25%.

c. Retained earnings available = $8,000,000 - $3.00(1,000,000)
Retained earnings available = $5,000,000.

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.

e. Capital budget = $10 million; Dividends = $3 million; NI = $8 million;
Capital structure = ?

RE available = $8,000,000 - $3,000,000
= $5,000,000.

Percentage of cap. budget financed with RE = = 50%.

Percentage of cap. budget financed with debt = = 50%.

f. Dividends = $3 million; Capital budget = $10 million; 60% equity, 40% debt; NI = $8 million.

Equity needed = $10,000,000(0.6) = $6,000.000.

RE available = $8,000,000 - $3.00(1,000,000)
= $5,000,000.

External (New) equity needed = $6,000,000 - $5,000,000
= $1,000,000.

g. Dividends = $3 million; NI = $8 million; Capital structure = 60% equity, 40% debt.

RE available = $8,000,000 - $3,000,000
= 5,000,000.

We’re forcing the RE available = Required equity to fund the new capital budget.

Required equity = Capital budget (Target equity ratio)
$5,000,000 = Capital budget(0.6)
Capital budget = $8,333,333.

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.

h. The firm can do one of four things:

(1) Cut dividends.
(2) Change capital structure, that is, use more debt.
(3) Cut its capital budget.
(4) Issue new common stock.

Realize that each of these actions is not without consequences to the company’s cost of capital, stock price, or both.

1 comment:

  1. 14.1 is not complete! but nice efforts.

    ReplyDelete