Tutorial 3 Solutions PDF

Preview

Summary

Download Tutorial 3 Solutions PDF

Description

Tutorial Solution 3. Capital Structure in a Perfect Market Note: This topic has more questions than can be covered in a 2 hour session. The questions to be covered by your tutor are indicated by an asterisk (*); the rest should be viewed as extra practice problems. MMI: 14-1*.

Consider a project with free cash flows in one year of $137,022 or $188,017, with each outcome being equally likely. The initial investment required for the project is $100,655, and the project’s cost of capital is 20%. The risk-free interest rate is 5%. a.

What is the NPV of this project?

b.

Suppose that to raise the funds for the initial investment, the project is sold to investors as an allequity firm. The equity holders will receive the cash flows of the project in one year. How much money can be raised in this way—that is, what is the initial market value of the unlevered equity?

c.

Suppose the initial $100,655 is instead raised by borrowing at the risk-free interest rate. What are the cash flows of the levered equity in one year, and what is its initial value according to MM?

Solution: a.

E[ C] (0.5 137, 022) (0.5 188, 017) 162, 519.50

NPV= -100,655 + 162,519.5/1.2=34,777.92 b. c.

162,519.50 135, 432.92 Equity value  PV ( C)  1.20 Cash flows in one year: Cash flows of debt = 100,655*1.05=105,687.75 Cash flows of levered equity either 188,017-105,687.75=82,329.25 or 137,022-105,687.75 = 31334.25 Initial value of levered equity, by MM, is 135,432.92 – 100,655 = $34,777.92.

14-3*.

Acort Industries owns assets that will have a 75% probability of having a market value of $48 million one year from now. There is a 25% chance that the assets will be worth only $18 million. The current risk-free rate is 5%, and Acort’s assets have a cost of capital of 10%. a.

If Acort is unlevered, what is the current market value of its equity?

b.

Suppose instead that Acort has debt with a face value of $18 million due in one year. According to MM, what is the value of Acort’s equity in this case?

c.

What is the expected return of Acort’s equity without leverage? What is the expected return of Acort’s equity with leverage?

d.

What is the lowest possible realized return of Acort’s equity with and without leverage?

Solution:

a.

Current market value of unlevered equity = [0.75 (48) + 0.25 (18)]/1.10 = $36.82m

b.

D=

c.

Without leverage (unlevered equity), r = 10%=(0.75*48+0.25*18)/36.82-1=10%

18 1.05

17.143 . Therefore, levered equity: E = 36.82 – 17.143 = $19.677m

With leverage (levered equity): Cash flows of levered equity in one year = cash flows of assets – cash flows of debt So it will be either 48-18=30 or 18-18=0 => Expected cash flows of levered equity in one year = 0.75*30+0.25*0=22.5 Return of levered equity is: 22.5/19.677-1= 14.36% d. With leverage, the lowest cash flows of levered equity in one year is 0 => r=0/19.677-1=-100% Without leverage, the lowest cash flows of unlevered equity in one year is 18 => r = 18/36.82-1=-51.11% 14-4.

Wolfrum Technology (WT) has no debt. Its assets will be worth $444 million in one year if the economy is strong, but only $226 million in one year if the economy is weak. Both events are equally likely. The market value today of its assets is $257 million. a.

What is the expected return of WT stock without leverage?

b.

Suppose the risk-free interest rate is 5%. If WT borrows $52 million today at this rate and uses the proceeds to pay an immediate cash dividend, what will be the market value of its equity just after the dividend is paid, according to MM?

c.

What is the expected return of WT stock after the dividend is paid in part (b)?

Solution:

14-6*.

a.

(0.5  444 + 0.5  226)/257 = 1.303  30%

b.

E + D = 257, D = 52  E = 205

c.

(0.5  (444 – 52  1.05) + 0.5  (226 – 52  1.05))/205 = 1.3678  36.78%

Suppose Alpha Industries and Omega Technology have identical assets that generate identical cash flows. Alpha Industries is an all-equity firm, with 14 million shares outstanding that trade for a price of $24 per share. Omega Technology has 22 million shares outstanding as well as debt of $100 million. a.

According to MM Proposition I, what is the stock price for Omega Technology?

b.

Suppose Omega Technology stock currently trades for $15 per share. What arbitrage opportunity is available? What assumptions are necessary to exploit this opportunity?

Solution: a.

V(Alpha) = 14 24 = 336m = V(Omega) = D + E  E = 336 – 100 = 236m  p = $10.73 per share.

b.

Omega is overpriced. - Sell Omega and Buy Alpha - Sell Omega = Sell Levered Equity for 330 (15*22), Borrow 100 - Buy Alpha = Buy Unlevered Equity for 336 (14*24) => Gain=330+100-336= 94 “Homemade leverage” => Assume we can trade shares at current prices and that we can borrow at the same terms as Omega (or own Omega debt and can sell at same price).

14-7*.

Cisoft is a highly profitable technology firm that currently has $5 billion in cash. The firm has decided to use this cash to repurchase shares from investors, and it has already announced these plans to investors. Currently, Cisoft is an all-equity firm with 6 billion shares outstanding. These shares currently trade for $20 per share. Cisoft has also issued debt with the current market value of $10 billion. With perfect capital markets, what is the market value of Cisoft’s equity after the share repurchase? What is the stock price after share repurchase – is it consistent with the MM capital structure theory?

Solution: After repurchasing: 5b 0.25b, shares  6-0.25= 5.750 b shares remain. 20 Price = 115/5.75=20 => share price does not change => consistent with MMI. Equity = 120 – 5 =115. Repurchase

14-9*.

Zetatron is an all-equity firm with 270 million shares outstanding, which are currently trading for $23.64 per share. A month ago, Zetatron announced it will change its capital structure by borrowing $921 million in short-term debt, borrowing $820 million in longterm debt, and issuing $1,015 million of preferred stock. The $2,756 million raised by these issues, plus another $94 million in cash that Zetatron already has, will be used to repurchase existing shares of stock. The transaction is scheduled to occur today. Assume perfect capital markets. a.

What is the market value balance sheet, that is, the market value of assets and the market value of both liabilities and equity for Zetaron: i.

Before this transaction?

ii. After the new securities are issued but before the share repurchase? iii. After the share repurchase? b.

At the conclusion of this transaction, how many shares outstanding will Zetatron have, and what will the value of those shares be?

Solution: a.

i.

A = 94 cash + 6,288.8 non-cash L = 6,382.8 equity

ii. A = 2,850 cash + 6,288.8 non-cash L = 6382.8 equity + 921 short-term debt + 820 long-term debt + 1,015 preferred stock L = 9,138.8 iii. A = 6,288.8 non-cash L = 3,532.8 equity + 921 short-term debt + 820 long-term debt + 1,015 preferred stock L = 6,288.8

b.

Repurchase

2,850 3, 532.8 120.56 shares  270 – 120.6 = 149.44 remain. Value is $23.64. 23.64 149.44

MMII: 14-10.

Explain what is wrong with the following argument: “If a firm issues debt that is risk free, because there is no possibility of default, the risk of the firm’s equity does not change. Therefore, risk-free debt allows the firm to get the benefit of a low cost of capital of debt without raising its cost of capital of equity.” Solution: Any leverage raises the equity cost of capital. In fact, risk-free leverage raises it the most (because it does not share any of the risk).

14-11*. A firm has only one investment project requiring an initial investment of $800 this year, the project will generate cash flows of either $1400 or $900 next year, depending on whether the economy is strong or weak, respectively. Both scenarios are equally likely. The project cash flows depend on the overall economy and thus contain market risk so it has a 10% risk premium over the current risk-free interest rate of 5%. a.

What is the NPV of this project?

b.

If the project is financed using all equity. What is the value of the firm – that is, how much would investors be willing to pay for the firm’ unlevered equity?

c.

If the project is financed using both debt and equity where the firm can borrow $750 at the risk-free rate of 5%, what are the cash flows of levered equity in year 1? c1. According to MM Proposition I, what is the value of the equity? What are its cash flows if the economy is strong? What are its cash flows if the economy is weak? c2. What is the return of the equity in each case? What is its expected return? c3. What is the debt-equity ratio of the firm in this case? c4. What is the firm’s WACC in this case?

Solution: a.

200 WACC=10%+5%=15% CF0=-800, E(CF1)=0.5*1400+0.5*900=1150 NPV=-800+1150/1.15=200

b.

Vu=1000 = 800+200 or =E(CF1)/1.15=1000

c1 + c2:

t=0 Levered firm

t=1 Cash flows

Return

Assets Investment NPV Total

Liabilities and Shareholder Equity 800 Debt 750 200 Levered equity 250 1000 Total 1000

Strong 787.5 612.5 1400

Weak 787.5 112.5 900

Strong 5% 145%

Re=0.5*145%+0.5*(-55%) = 45% c3. D/E=750/250=3 c4. RWACC=E/(E+D)*Re+D/(E+D)*Rd=250/100*45% + 750/1000*5% = 15% 14-12*. Hardmon Enterprises is currently an all-equity firm with an expected return of 12%. It is considering a leveraged recapitalization in which it would borrow and repurchase existing shares. a.

Suppose Hardmon borrows to the point that its debt-equity ratio is 0.50. With this amount of debt, the debt cost of capital is 5%. What will the expected return of equity be after this transaction?

b.

Suppose instead Hardmon borrows to the point that its debt-equity ratio is 1.50. With this amount of debt, Hardmon’s debt will be much riskier. As a result, the debt cost of capital will be 7%. What will the expected return of equity be in this case?

c.

A senior manager argues that it is in the best interest of the shareholders to choose the capital structure that leads to the highest expected return for the stock. How would you respond to this argument?

Solution:

14-13.

a.

re = ru + d/e(ru – rd) = 12% + 0.50(12% – 5%) = 15.5%

b.

re = 12% + 1.50(12% – 7%) = 19.5%

c.

Equity returns are higher because the equity risk is higher—the return fairly compensates for the risk. According the MMII in a perfect market, leverage increases the risk of equity but it doesn’t affect firm value - the statement is not convincing in this setting.

Suppose Visa Inc. (V) has no debt and an equity cost of capital of 9.2%. The average debt-to-value ratio for the credit services industry is 13%. What would its cost of equity be if it took on the average amount of debt for its industry at a cost of debt of 6%? Solution: At a cost of debt of 6%: D (r  r ) E U D 0.13 rE 0.092  (0.092  0.06) 0.87 0.0968 rE  rU 

9.68%. 14-14*. Global Pistons (GP) has common stock with a market value of $470 million and debt with a value of $299 million. Investors expect a 13% return on the stock and a 5% return on the debt. Assume perfect capital markets. a.

Suppose GP issues $299 million of new stock to buy back the debt. What is the expected return of the stock after this transaction?

b.

Suppose instead GP issues $71 million of new debt to repurchase stock.

Weak 5% -55%

i.

If the risk of the debt does not change, what is the expected return of the stock after this transaction?

ii. If the risk of the debt increases, would the expected return of the stock be higher or lower than in part (i)? Solution: a.

The firm becomes unlevered firm: Ru=WACC=13%*470/(470+299)+5%*299/(470+299)=9.89%

b.

i.

D=299+71=370; E=470-71=399. The risk of debt does not change => Rd=5% Re=Ru+(D/E)(Ru-Rd)=9.89%+(370/399)*(9.89%-5%)=14.42%

ii. If the risk of debt increases => Rd increases => Re is lower. The debt will share some of the risk. 14-15.

Hubbard Industries is an all-equity firm whose shares have an expected return of 10.9%. Hubbard does a leveraged recapitalization, issuing debt and repurchasing stock, until its debt-equity ratio is 0.66. Due to the increased risk, shareholders now expect a return of 17.1%. Assuming there are no taxes and Hubbard’s debt is risk-free, what is the interest rate on the debt? Solution:

Re=Ru+(D/E)(Ru-Rd) => 17.1%=10.9%+0.66*(10.9%-Rd)=> Rd=1.51% 14-16.

Hartford Mining has 90 million shares that are currently trading for $2 per share and $160 million worth of debt. The debt is risk free and has an interest rate of 4%, and the expected return of Hartford stock is 11%. Suppose a mining strike causes the price of Hartford stock to fall 25% to $1.50 per share. The value of the risk-free debt is unchanged. Assuming there are no taxes and the risk (unlevered beta) of Hartford’s assets is unchanged, what happens to Hartford’s equity cost of capital? Solution: wacc  ru  re 7.7% 

180 160  11   4 7.7% and New D/E=160/(1.5*90)=160/135 340 340

160  7.7%  4% 12.09% 135

14-17*. Mercer Corp. is a firm with 10 million shares outstanding and $84 million worth of debt outstanding. Its current share price is $73. Mercer’s equity cost of capital is 8.5%. Mercer has just announced that it will issue $354 million worth of debt. It will use the proceeds from this debt to pay off its existing debt, and use the remaining $270 million to pay an immediate dividend. Assume perfect capital markets. a.

Estimate Mercer’s share price just after the recapitalization is announced, but before the transaction occurs.

b.

Estimate Mercer’s share price at the conclusion of the transaction.

c.

Suppose Mercer’s existing debt was risk free with a 4.39% expected return, and its new debt is risky with a 4.93% expected return. Estimate Mercer’s equity cost of capital after the transaction.

Solution:

a.

MM  no change, $73

b.

Firm value = 73  10 + 84 = 814 million

New debt = 354 million E = 814 – 354 = 460 Share price = 460/10 = $46

c.

Ru = (730/814)  8.5% + (84/814)  4.39% = 8.08% Re = 8.08% + 354/460(8.08% – 4.93%) = 10.50%

14-19.

Indell stock has a current market value of $150 million and a beta of 0.70. Indell currently has risk-free debt with a beta=0. The firm decides to change its capital structure by issuing $50 million in additional risk-free debt, and then using this $50 million to repurchase stock. With perfect capital markets, what will be the beta of Indell stock after this transaction?

Solution: E=150, Indell increases its debt by $50 million. Therefore, the value of its equity decreases to E’=150 – 50 = $100 million. However, the firm value, V=D+E, is unchanged according to MMI. If the debt is risk-free: We have:

if

With new level of equity =>

=>

(1)

(2)

Given (1) and (2) we have:

=>

 '  e e

E 150 0.70 1.05. 100 E'

14-22*. You are CEO of a high-growth technology firm. You plan to raise $160 million to fund an expansion by issuing either new shares or new debt. With the expansion, you expect earnings next year of $31 million. The firm currently has 9 million shares outstanding, with a price of $67 per share. Assume perfect capital markets. a.

If you raise the $160 million by selling new shares, what will the forecast for next year’s earnings per share (EPS) be?

b.

If you raise the $160 million by issuing new debt with an interest rate of 8%, what will the forecast for next year’s earnings per share be?

c.

One of your staff argues that “leverage will increase earnings per share”, so EPS in (b) must be higher than EPS in (a). Is your staff correct?

Solution: a.

Issue

160 2.388 million new shares  11.388 million shares outstanding. 67

New EPS 

31 11.388

$2.72 per share.

b.

Interest on new debt = 160 8% = 12.8 million. The interest expense will reduce earnings to 31 – 12.8 = $18.2 million. With 9 million shares outstanding, 18.2/9=2.02 per share.

c.

No, the staff is not correct. Leverage increases the risk of equity, that is, it increases the volatility of equity return or the volatility of earnings per share – it shows that EPS (b) is smaller than that in (a)...