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Fundamentals of Corporate Finance 3rd ed Jonathan Berk Ch17

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Chapter 17 Payout Policy

Note: All problems in this chapter are available in MyFinanceLab. An asterisk (*)

indicates problems with a higher level of difficulty.

1. Plan: Determine the ex-dividend day and the last day that an investor can purchase the stock and receive the dividend. The last day to buy and still get the dividend must be three business days before the record date. The record date is Monday, April 5, 2010. The ex-dividend day is the first day that buying the stock will not entitle you to the dividend.

Execute:

a. April 1

b. March 31

Evaluate: An investor who purchases the stock on April 1 will receive the dividend; an investor who purchases the stock on April 2 will not receive the dividend.

2. Plan: Calculate the first ex-dividend day price.

Chapter 17 Payout Policy 211

Execute: Assuming perfect markets, the first ex-dividend price should drop by exactly the dividend payment. Thus, the first ex-dividend price should be $49 per share.

Evaluate: In a perfect capital market, the first price of the stock on the ex-dividend day should be the closing price on the previous day less the amount of the dividend.

3. Plan: ECB has a market capitalization of $20 million ($20  1 million shares). If it repurchases shares at the market price, it will need to pay $20  100,000 $2 million.

Execute:

Its new market capitalization will be $18 million. (It started with $20 million and distributed $2 million through the repurchase.)

Its share price will stay at $20 ($18 million/900,000 shares).

Evaluate: As long as the company repurchases its shares at the market price, the price will not change after the repurchase. This is because buying shares at the market price is a zero-NPV investment—it has neither created nor destroyed value.

4. Plan: Compute the changes in the balance sheet and determine the new leverage ratio.

212 Berk/DeMarzo/Harford • Fundamentals of Corporate Finance, Third Edition, Global Edition

Execute:

a. Both the cash balance and shareholder equity will drop by $20 million.

b. After the repurchase, equity will be $280 million, and debt is still $200 million.

The debt-to-equity ratio will be 200/280 71.4%.

Evaluate: Cash and shareholder equity will both decline by $20 million on the balance sheet. The new leverage ratio will be 71.4%.

5. Plan: Determine the present value of the annuity of dividends.

Execute: The present value of the perpetuity should be $20 million with a discount rate of 10%.

Evaluate: The dividend payments should be ($20 million/0.10) $2.00 million per year in perpetuity.

X0.10X$2 million

$20 million6. Plan: Make the calculations requested in the problem.

Execute:

Chapter 17 Payout Policy 213

a. $1 billion/20 million shares $50 per share

b. $100 million/$50 per share 2 million shares

c. If markets are perfect, then the price right after the repurchase should be the

same as the price immediately before the repurchase. Thus, the price will be $50 per share.

Evaluate: What will the price per share of EJH be right before the repurchase? $50 per share

How many shares will be repurchased? 2 million shares

What will the price per share of EJH be right after the repurchase? $50 per share

7. Plan: Make the calculations requested in the problem.

Execute:

a. The dividend payoff is $250/$500 $0.50 on a per share basis. In a perfect

capital market the price of the shares will drop by this amount to $14.50.

b. $15

214 Berk/DeMarzo/Harford • Fundamentals of Corporate Finance, Third Edition, Global Edition

c. Both are the same.

Evaluate: What is the ex-dividend price of a share in a perfect capital market? $14.50

If the board instead decided to use the cash to do a one-time share repurchase, in a perfect capital market what is the price of the shares once the repurchase is complete? $15.00

In a perfect capital market, which policy (in part [a] or [b]) makes investors in the firm better off? Both policies would leave the firm equally well off.

8. Plan: Determine what you have to do to maintain your same position in a firm that decides to do a share repurchase.

Execute: If you sell 0.5/15 of one share, you receive $0.50, and your remaining shares will be worth $14.50, leaving you in the same position as if the firm had paid a dividend.

Evaluate: If you sell $0.50 of stock, you would be in the same position as having received a dividend.

9. Plan: Determine the price of HNH stock with a $2.00 dividend. Then compute

Chapter 17 Payout Policy 215

the stock price

if HNH suspends the dividend payments and instead repurchases shares.

Execute:

a. P $1.60/0.12 $13.33 P $2/0.12 $16.67

Evaluate: HNH with a dividend will sell for $13.33. If HNH suspends the dividend and uses the $2.00 per share to repurchase shares, the stock will sell for $16.67. The increased value of the repurchase policy comes from the fact that dividends are taxed and capital gains are not.

10. Plan: Compute the after-tax income from each and compare.

Execute:

a. Table 17.2 shows that in 2010, the capital gains tax rate was 15%, and the

dividend tax rate was 15%. At those rates, tax on a $10 capital gain is $1.50, and the tax on a $10 special dividend is $1.50. The after-tax income for both will be $8.50.

b. If the capital gains tax rate is 20%, the tax on a $10 capital gain is $2.00, and

216 Berk/DeMarzo/Harford • Fundamentals of Corporate Finance, Third Edition, Global Edition

the after-tax income is $8.00. If the dividends tax rate is 40%, then the tax on a $10 special dividend is $4.00, and the after-tax income is $6.00. The difference in after-tax income is $2.00.

Evaluate: There is no difference in after-tax income when the tax rates on capital gains and dividends are the same. There is a $2.00 difference in after-tax income if the capital gains tax rate is 20% and the dividend tax rate is 40%.

11. a. 1985: Yes, dividends were taxed at 50% relative to 20% for capital gains.

b. 19: No, dividends were not tax-disadvantaged (they were not advantaged

either): Dividends and capital gains were both taxed at 28%.

c. 1995: Yes, dividends were taxed at 40% relative to 28% for capital gains.

d. 1999: Yes, dividends were taxed at 40% relative to 20% for capital gains.

e. 2005: No, dividends were not tax-disadvantaged (they were not advantaged

either): Dividends and capital gains were both taxed at 15%.

12. a. Invest the $5 special dividend, and earn interest of $0.50 per year.

b. Borrow $5 today, and use the increase in the regular dividend to pay the

Chapter 17 Payout Policy 217

interest of $0.50 per year on the loan.

13. Plan: Determine the values of Kay stock at various times regarding the decision to pay or not pay a one-time dividend.

Execute:

a. The value of Kay will remain the same.

b. The value of Kay will fall by $100 million.

c. It will neither benefit nor hurt investors.

Evaluate: If the board went ahead with this plan, what would happen to the value of Kay stock upon the announcement of a change in policy? The value of Kay will remain the same.

What would happen to the value of Kay stock on the ex-dividend date of the one-time dividend? The value of Kay will fall by $100 million.

Given these price reactions, will this decision benefit investors? It will neither benefit nor hurt investors.

14. Plan: Recalculate Problem 10 assuming a 35% corporate tax rate.

218 Berk/DeMarzo/Harford • Fundamentals of Corporate Finance, Third Edition, Global Edition

Execute:

a. The value of Kay will rise by $35 million.

b. The value of Kay will fall by $100 million.

c. It will benefit investors.

Evaluate: If the board went ahead with this plan, what would happen to the value of Kay stock upon the announcement of a change in policy? What would happen to the value of Kay stock on the ex-dividend date of the one-time dividend? The value of Kay will rise by $35 million.

The value of Kay will fall by $100 million.

Given these price reactions, will this decision benefit investors? It will benefit investors.

15. Plan: Recalculate Problem 10 assuming investors pay a 15% tax on

dividends but no capital gains tax. Kay does not pay corporate taxes.

Execute: Assume investors pay a 15% tax on dividends but no capital gains taxes nor taxes on interest income, and Kay does not pay corporate taxes:

Chapter 17 Payout Policy 219

a. The value of Kay will remain the same.

b. The value of Kay will fall by $85 million.

c. It will neither benefit nor hurt investors.

The value of Kay will fall by $85 million.

Given these price reactions, will this decision benefit investors? It will neither benefit nor hurt investors.

Use the following information to answer Questions 16 through 20.

AMC Corporation currently has an enterprise value of $400 million and $100 million in excess cash. The firm has 10 million shares outstanding and no debt. Suppose AMC uses its excess cash to repurchase shares. After the share repurchase, news will come out that will change AMC’s enterprise value to either $600 million or $200 million.

220 Berk/DeMarzo/Harford • Fundamentals of Corporate Finance, Third Edition, Global Edition

16. Plan: Calculate AMC’s share price prior to share repurchase.

Execute: Because Enterprise Value is:

Equity Debt Cash, AMC’s equity value

Equity EV Cash $500 million

Therefore,

Share price ($500 million)/(10 million shares) $50 per share.

Evaluate: AMC’s share price would be $50.00 before share repurchase.

17. Plan: Calculate the values of AMC’s share price assuming AMC’s

enterprise value goes up and then declines.

Execute: AMC repurchases $100 million/($50 per share) 2 million shares. With 8

million remaining shares outstanding (and no excess cash), its share price if its EV goes up to $600 million is:

Share price $600/8 $75 per share

And if EV goes down to $200 million:

Chapter 17 Payout Policy 221

Share price $200/8 $25 per share

Evaluate: AMC’s share price would rise to $75.00 if enterprise value rose. It would fall to $25.00 if enterprise value were to fall.

*18. Plan: Calculate the values of AMC’s share price assuming AMC’s

enterprise value goes up and declines and AMC waits until after the news comes out to execute the repurchase.

Execute: If EV rises to $600 million prior to repurchase, given its $100 million in cash and

10 million shares outstanding, AMC’s share price will rise to:

Share price (600 100)/10 $70 per share

If EV falls to $200 million:

Share price (200 100)/10 $30 per share

The share price after the repurchase will also be $70 or $30 because the share repurchase itself does not change the stock price.

Evaluate: AMC’s share price would rise to $70.00 if enterprise value rose. It would

222 Berk/DeMarzo/Harford • Fundamentals of Corporate Finance, Third Edition, Global Edition

fall to $30.00 if enterprise value were to fall.

Note: The differences in the outcomes for Problem 17 versus Problem 18 arise

because by holding cash (a risk-free asset), AMC reduces the volatility of its share price.

19. If management expects good news to come out, they would prefer to do

the repurchase first, so that the stock price would rise to $75 rather than $70. On the other hand, if they expect bad news to come out, they would prefer to do the repurchase after the news comes out, for a stock price of $30 rather than $25. (Intuitively, management prefers to do a repurchase if the stock is undervalued—they expect good news to come out—but not when it is overvalued because they expect bad news to come out.)

*20. Based on Problem 17, we expect managers to do a share repurchase before

good news comes out and after any bad news has already come out. Therefore, if investors believe managers are better informed about the firm’s future prospects, and that they are timing their share repurchases accordingly, a share repurchase announcement would lead to an increase in the stock price.

21. Plan: A 10% stock dividend means one new share for every 10, so FCF will

distribute 2,000 new shares.

Execute:

Chapter 17 Payout Policy 223

a. Before the dividend, FCF’s stock price is $700,000/20,000 = $35.

b. Because the stock dividend does not bring in or disgorge any money, FCF’s

total market capitalization does not change—only the shares outstanding change:

$700,000/22,000 = $31.8182

The investor’s 1,000 shares becomes 1,100 shares, so the total value of his or her investment before is 1,000($35) $35,000 and after is 1,100($31.8182) $35,000.

Evaluate: The stock dividend does not leave the investor any better or worse off because he or she received new shares in proportion to how many he or she held before the stock dividend.

22. Plan: Calculate the value of Host’s shares assuming a 20% stock dividend

and a 3:2 stock split.

Execute:

a. With a 20% stock dividend, an investor holding 100 shares receives 20

additional shares. However, because the total value of the firm’s shares is unchanged, the stock price should fall to:

224 Berk/DeMarzo/Harford • Fundamentals of Corporate Finance, Third Edition, Global Edition

Share price $20  100/120 $20/1.20 $16.67 per share

b. A 3:2 stock split means for every two shares currently held, the investor

receives a third share. This split is therefore equivalent to a 50% stock dividend. The share price will fall to:

Share price $20  2/3 $20/1.50 $13.33 per share

Evaluate: A 20% stock dividend should produce a stock price of $16.67, while a 3:2 stock split should produce a share price of $13.33.

23. Plan: Determine the stock split ratio required to produce a Berkshire

Hathaway A share worth $50.00.

Execute: To bring its stock price down to $50 per share, Berkshire Hathaway would need a split ratio of:

$120,0002,400$50 to 1

Evaluate: A 2,400 to 1 stock split will reduce a Berkshire Hathaway A share to $50.00.

24. Plan: Calculate the value of an Adaptec share after the stock dividend.

Chapter 17 Payout Policy 225

Execute: The value of the dividend paid per Adaptec share was (0.16 shares of Roxio)  ($14.23 per share of Roxio)

$2.34 per share. Therefore, ignoring tax effects

or other news that might come out, we would expect Adaptec’s stock price to fall to $10.55 2.34 $8.21 per share once it goes ex-dividend.

Evaluate: Adaptec’s shares should sell for $8.21 once it goes ex-dividend. (Note: In fact, Adaptec stock opened on Monday, May 14, 2001—the next trading day—at a price of $8.45 per share.)

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