Additional Practice Questions (Week 1) -merged PDF

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Q1.

Acort Industries owns assets that will have an 80% probability of having a market value of $50 million in one year. There is a 20% chance that the assets will be worth only $20 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 $20 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? a. E[Value in one year] = 0.8 ( 50) + 0.2( 20) = 44. E =

44 = $40m. 1.10

b. D = 20 = 19.048 . Therefore, E = 40 −19.048 = $20.952m. 1.05

Q2.

c. Without leverage, r =

44 − 1 = 10% , 40

with leverage, r =

44 − 20 −1 =14.55%. 20.952

d. Without leverage, r =

20 − 1 = −50% 40

, with leverage, r =

0 − 1 = − 100%. 20.952

Suppose there are no taxes. Firm ABC has no debt, and firm XYZ has debt of $5000 on which it pays interest of 10% each year. Both companies have identical projects that generate free cash flows of $800 or $1000 each year. After paying any interest on debt, both companies use all remaining free cash flows to pay dividends each year. a. Fill in the table below showing the payments debt and equity holders of each firm will receive given each of the two possible levels of free cash flows.

b. Suppose you hold 10% of the equity of ABC. What is another portfolio you could hold that would provide the same cash flows? c. Suppose you hold 10% of the equity of XYZ. If you can borrow at 10%, what is an alternative strategy that would provide the same cash flows? a. ABC FCF

Debt Payments

XYZ Equity Dividends

Debt Payments

Equity Dividends 1

$800 $1,000

0 0

800 1000

500 500

300 500

b. Unlevered Equity = Debt + Levered Equity. Buy 10% of XYZ debt and 10% of XYZ Equity, get 50 + (30, 50) = (80,100) c. Levered Equity = Unlevered Equity + Borrowing. Borrow $500, buy 10% of ABC, receive (80,100) – 50 = (30, 50) Q3.

Suppose Alpha Industries and Omega Technology have identical assets that generate identical cash flows. Alpha Industries is an all-equity firm, with 10 million shares outstanding that trade for a price of $22 per share. Omega Technology has 20 million shares outstanding as well as debt of $60 million. a. According to MM Proposition I, what is the stock price for Omega Technology? b. Suppose Omega Technology stock currently trades for $11 per share. What arbitrage opportunity is available? What assumptions are necessary to exploit this opportunity? a. V(Alpha) = 10 × 22 = 220m = V(Omega) = D + E ⇒ E = 220 – 60 = 160m ⇒ p = $8 per share. b. Omega is overpriced. Sell 20 Omega, buy 10 Alpha, and borrow 60. Initial = 220 – 220 + 60 = 60. Assumes 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).

Q4.

Cisoft is a highly profitable technology firm that currently has $2 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 2 billion shares outstanding. These shares currently trade for $20 per share. Cisoft has issued no other securities except for stock options given to its employees. The current market value of these options is $6 billion. a. What is the market value of Cisoft’s non-cash assets? b. With perfect capital markets, what is the market value of Cisoft’s equity after the share repurchase? What is the value per share? a. Total value of Cisoft = (2 billion shares x $20 per share) + $6 billion = $46 billion. Market value of Cisoft’s non-cash assets = $46 billion - $2 billion = $44 billion. $2 ฀฀฀฀฀฀฀฀฀฀฀฀ b. ฀฀฀฀฀฀฀฀฀฀฀฀ ฀฀฀฀ ฀฀ℎ฀฀฀฀฀฀฀฀ ฀฀฀฀฀฀฀฀฀฀฀฀ℎ฀฀฀฀฀฀฀฀ = = 0.1 ฀฀฀฀฀฀฀฀฀฀฀฀฀฀ ฀฀ℎ฀฀฀฀฀฀฀฀ $20 ฀฀฀฀฀฀ ฀฀ℎ฀฀฀฀฀฀

฀฀฀฀฀฀฀฀฀฀฀฀ ฀฀฀฀ ฀฀ℎ฀฀฀฀฀฀฀฀ ฀฀฀฀฀฀฀฀฀฀฀฀฀฀฀฀฀฀฀฀฀฀ ฀฀฀฀฀฀฀฀฀฀ ฀฀฀฀฀฀฀฀฀฀฀฀฀฀ℎ฀฀฀฀ = 2 ฀฀฀฀฀฀฀฀฀฀฀฀฀฀ − 0.1 ฀฀฀฀฀฀฀฀฀฀฀฀฀฀ = 1.9 ฀฀฀฀฀฀฀฀฀฀฀฀฀฀ ฀฀฀฀฀฀฀฀฀฀฀฀ ฀฀฀฀฀฀฀฀฀฀ ฀฀฀฀ ฀฀฀฀฀฀฀฀฀฀฀฀ ฀฀฀฀฀฀฀฀฀฀ ฀฀฀฀฀฀฀฀฀฀฀฀ℎ฀฀฀฀฀฀ = $40 ฀฀฀฀฀฀฀฀฀฀฀฀฀฀ − $2 ฀฀฀฀฀฀ $38 ฀฀฀฀฀฀฀฀฀฀฀฀฀฀

2

฀฀฀฀฀฀฀฀฀฀ ฀฀฀฀฀฀ ฀฀ℎ฀฀฀฀฀฀ =

$38 ฀฀฀฀฀฀฀฀฀฀฀฀฀฀

1.9 ฀฀฀฀฀฀฀฀฀฀฀฀฀฀

Q5.

= $20 ฀฀฀฀฀฀ ฀฀ℎ฀฀฀฀฀฀

Zetatron is an all-equity firm with 100 million shares outstanding, which are currently trading for $7.50 per share. A month ago, Zetatron announced it will change its capital structure by borrowing $100 million in short-term debt, borrowing $100 million in long-term debt, and issuing $100 million of preferred stock. The $300 million raised by these issues, plus another $50 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 for Zetatron 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? a. i.

A = 50 cash + 700 non-cash L = 750 equity

ii. A = 350 cash + 700 non-cash L = 750 equity + 100 short-term debt + 100 long-term debt + 100 preferred stock

iii. A = 700 non-cash L = 400 equity + 100 short-term debt + 100 long-term debt + 100 preferred stock

b. Repurchase Q6.

350 400 = 46.67 shares ⇒ 53.33 remain. Value is = 7.50. 7.50 53.33

Suppose Paypal (PYPL) has no debt and an equity cost of capital of 9.2%. The average debt-to-value ratio for the credit services industry is 15%. 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%? At a cost of debt of 6%:

Q7.

Hubbard Industries is an all-equity firm whose shares have an expected return of 10.2%. Hubbard does a leveraged recapitalization, issuing debt and repurchasing stock, until its debtequity ratio is 0.58. Due to the increased risk, 3

shareholders now expect a return of 15.2%. Assuming there are no taxes and Hubbard’s debt is risk free, what is the interest rate on the debt? ฀฀ ฀฀ ฀฀฀฀฀฀฀฀฀฀ = ฀฀฀ ฀ = ฀฀ + ฀฀ ฀฀+฀฀ ฀ ฀ ฀฀+฀฀ ฀฀ 1

0.58

฀฀฀฀฀฀฀฀฀฀ = 10.2% =1+0.58 (15.2%) + 1+0.58 ฀฀฀฀ 10.2% = 0.6329(15.2%) + 0.3671฀฀฀฀ 10.2% = 9.62% + 0.3671฀฀฀฀ 0.58% = 0.3671฀฀฀฀ 0.58% ฀฀฀ ฀ = = 1.58% 0.3671

Q8.

Hartford Mining has 50 million shares that are currently trading for $4 per share and $200 million worth of debt. The debt is risk free and has an interest rate of 5%, and the expected return of Hartford stock is 11%. Suppose a mining strike causes the price of Hartford stock to fall 25% to $3 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? ru = wacc =

Q9.

1 1 200 (11) + (5) = 8% . re = 8% + ( 8% − 5%) = 12% 2 2 150

Paul Rosenzweig is founder and CEO of OpenStart, an innovative software company. The company is all equity financed, with 100 million shares outstanding. The shares are trading at a price of $1. Campbell currently owns 20 million shares. There are two possible states in one year. Either the new version of their software is a hit, and the company will be worth $180 million, or it will be a disappointment, in which case the value of the company will drop to $75 million. The current risk free rate is 3%. Rosenzweig is considering taking the company private by repurchasing the rest of the outstanding equity by issuing debt due in one year. Assume the debt is zero-coupon and will pay its face value in one year. a. What is the market value of the new debt that must be issued? b. Suppose OpenStart issues risk-free debt with a face value of $75 million. How much of its outstanding equity could it repurchase with the proceeds from the debt? What fraction of the remaining equity would Jim still not own? c. Combine the fraction of the equity Jim does not own with the risk-free debt. What are the payoffs of this combined portfolio? What is the value of this portfolio? d. What face value of risky debt would have the same payoffs as the portfolio in (c)? e. What is the yield on the risky debt in (d) that will be required to take the company private? f. If the two outcomes are equally likely, what is OpenStart’s current WACC (before the transaction)? g. What is OpenStart’s debt and equity cost of capital after the transaction? Show that the WACC is unchanged by the new leverage. 4

a. The market value of the 80 million shares Rosenzweig does not own is $80 million. b. Value of the debt: $75 million/1.03 = $72.82 million. Because the unlevered value of equity is $100 million, the value of the unlevered equity would be $100 – $72.82 = $27.18 million. c. To raise a total of $80 million, after raising $72.82 million in risk-free debt you would need to raise an additional $7.18 million, which is equivalent to 26.42% of the levered equity. d. The payoff is $75 million if the software is not a hit. If the software is a hit, the payoff is $75 + (7.18/27.18) x ($180 - $75) = $102.74 million. The value of this portfolio is the market value of the debt plus the value of the remaining equity: $72.82 + $7.18 = $80 million. e. With a face value of $102.74 million and a market value of $80 million, the yield is 102.74/80 – 1 = 28.43% f. Without leverage, the return on equity is 180/100 – 1 = 80% or 75/100 – 1 = 25%, for an expected return of (80% - 25%)/2 = 27.5%. As the company is currently all equity, this is its initial WACC. g. OpenStart’s debt return is 28.43% in the good state, and 75/80 – 1 = -6.25% in the bad state, for an expected return of (28.43% - 6.25%)/2 = 11.09%. OpenStart’s remaining equity is worth $20 million and has a payoff of $180 – $102.74 = $77.26 million or zero, or an expected payoff of $77.26/2 = $38.63 million. This corresponds to an expected return of 38.63/20 – 1 = 94.15%. The WACC is therefore (20/100)(93.15%) + (80/100)(11.09%) = 27.5%, just as in (f).

Q10. Suppose Levered Bank is funded with 1.6% equity and 98.4% debt. Its current market capitalization is $10.62 billion, and its market to book ratio is 0.9. Levered Bank earns a 4.21% expected return on its assets (the loans it makes), and pays 3.7% on its debt. New capital requirements will necessitate that Levered Bank increase its equity to 3.2% of its capital structure. It will issue new equity and use the funds to retire existing debt. The interest rate on its debt is expected to remain at 3.7%. a. What is Levered Bank’s expected ROE with 1.6% equity? b. Assuming perfect capital markets, what will Levered Bank’s expected ROE be after it increases its equity to 3.2%? c. Consider the difference between Levered Bank’s ROE and its cost of debt. How does this “premium” compare before and after the Bank’s increase in leverage? d. Suppose the return on Levered Bank’s assets has a volatility of 0.29%. What is the volatility of Levered Bank’s ROE before and after the increase in equity? e. Does the reduction in Levered Bank’s ROE after the increase in equity reduce its attractiveness to shareholders? Explain. 5

a. Assets = $10.62/0.016 = $663.75 market value, with E = $10.62 and D = $653.13 Assets = $663.75/0.90 = $737.5 book value, with E = $84.37 and D = $653.13 $737.5 × 4.21% – ($653.13) × 3.7% = $6.88 6.88 10.62 6.88 84.37

= 0.6481 = 64.81% ROE (market value) = 0.015 = 8.15%

b. In market value, Equity → $10.62 billion x 2 = $21.24 billion Earnings = 64.81% × 10.62 + 3.7% × 10.62 = 68.51% × 10.62 ROE = 68.51% × 10.62/21.24 = 0.3426 = 34.26% c. 64.81 – 3.7 = 61.11% 34.26 – 3.7 = 30.56% — premium drops in half (rounded) d. Vol = 663.75 × 0.29%/10.62 = 18.13% before, vs. 663.75 × 0.29%/21.24 = 9.06% after. e. No, premium and risk both fall by half.

6

Q1.

Grommit Engineering expects to have net income next year of $20.75 million and free cash flow of $22.15 million. Grommit’s marginal corporate tax rate is 20%. a. If Grommit increases leverage so that its interest expense rises by $1 million, how will its net income change? b. For the same increase in interest expense, how will free cash flow change? a. Net income will fall by the after-tax interest expense to million. b. Free cash flow is not affected by interest expenses.

Q2.

Your firm currently has $100 million in debt outstanding with a 10% interest rate. The terms of the loan require the firm to repay $25 million of the balance each year. Suppose that the marginal corporate tax rate is 25%, and that the interest tax shields have the same risk as the loan. What is the present value of the interest tax shields from this debt? Year 0 Debt 100 Interest Tax Shield PV $5.19

Q3.

1 75 10 2.50

2 50 7.5 1.88

3 25 5 1.25

4 0 2.5 0.63

5 0 0 0

Bay Transport Systems (BTS) currently has $30 million in debt outstanding. In addition to 6.5% interest, it plans to repay 5% of the remaining balance each year. If BTS has a marginal corporate tax rate of 25%, and if the interest tax shields have the same risk as the loan, what is the present value of the interest tax shield from the debt? Interest tax shield in year 1 = $30 × 6.5% × 25% = $0.49 million. As the outstanding balance declines, so will the interest tax shield. Therefore, we can value the interest tax shield as a growing perpetuity with a growth rate of g = –5% and r = 6.5%: million

Q4.

Rogot Instruments makes fine violins and cellos. It has $1.1 million in debt outstanding, equity valued at $2.2 million, and pays corporate income tax at a rate of 40%. Its cost of equity is 12% and its cost of debt is 6%. a. What is Rogot’s pre-tax WACC? b. What is Rogot’s (effective after-tax) WACC? ฀฀ ฀฀ a. ฀฀฀฀฀฀฀฀฀฀ =฀฀+฀฀ ฀฀฀ ฀ + ฀฀฀฀ ฀฀+฀฀

2.2

1.1

฀฀฀฀฀฀฀฀฀฀ =2.2+1.1 (12%) + 2.2+1.1 (6%) = 10% 1

฀฀

฀฀

b. ฀฀฀฀฀฀฀฀฀฀ =฀฀+฀฀ ฀฀฀ ฀ +฀฀+฀฀ ฀฀฀฀ (1 − ฀฀฀฀ ) 2.2

1.1

฀฀฀฀฀฀฀฀฀฀ =2.2+1.1 (12%) + 2.2+1.1 (6%)(1 − 0.4) = 9.2% Q5.

Summit Builders has a market debt-equity ratio of 0.65 and a corporate tax rate of 25%, and it pays 7% interest on its debt. The interest tax shield from its debt lowers Summit’s WACC by what amount? D 0.65 = = 0.394 . E + D 1.65

Therefore, WACC = Pretax WACC – 0.394(7%)(0.25) = Pretax WACC – 0.69% So, it lowers it by 0.69%. Q6.

NatNah, a builder of acoustic accessories, has no debt and an equity cost of capital of 15%. Suppose NatNah decides to increase its leverage and maintain a market debt-to-value ratio of 0.5. Suppose its debt cost of capital is 9% and its corporate tax rate is 21%. If NatNah’s pretax WACC remains constant, what will its (effective after-tax) WACC be with the increase in leverage?

Q7.

Acme Storage has a market capitalization of $140 million and debt outstanding of $94 million. Acme plans to maintain this same debt-equity ratio in the future. The firm pays an interest rate of 7.8% on its debt and has a corporate tax rate of 38%. a. If Acme’s free cash flow is expected to be $14.04 million next year and is expected to grow at a rate of 6% per year, what is Acme’s WACC? b. What is the value of Acme’s interest tax shield? ฀฀฀฀฀฀ = a. ฀฀฀ ฀ = ฀ ฀ + ฀ ฀ ฀฀฀฀฀฀฀฀−฀฀ ฀฀฀ ฀ = $140 ฀฀฀฀฀฀฀฀฀฀฀฀฀฀ + $94 ฀฀฀฀฀฀฀฀฀฀฀฀฀฀ = $234 ฀฀฀฀฀฀฀฀฀฀฀฀฀฀ 14.04 234 = ฀฀฀฀฀฀฀฀−0.06 234฀฀฀฀฀฀฀฀ − 14.04 = 14.04 234฀฀฀฀฀฀฀฀ = 14.04 + 14.04 234฀฀฀฀฀฀฀฀ = 28.08 28.08 ฀฀฀฀฀฀฀฀ = = 0.12 = 12% 234 ฀฀

b. ฀฀฀฀฀฀฀฀฀฀฀฀ ฀฀฀฀฀฀฀฀ = ฀฀฀฀฀฀฀฀ + ฀฀฀฀ ฀฀฀฀ ฀฀+฀฀

94

฀฀฀฀฀฀฀฀฀฀฀฀ ฀฀฀฀฀฀฀฀ = 12%140+94 + (7.8%)(0.38) = 13.19% ฀฀฀฀฀฀

$14.04

฀฀฀ ฀ =฀฀฀฀฀฀฀฀฀฀฀฀ ฀฀฀฀฀฀฀฀−฀฀ =0.1319−0.06 = $195.25 ฀฀฀฀ (฀฀฀฀฀฀฀฀฀฀฀฀฀฀฀฀ ฀฀฀฀฀฀ ฀฀ℎ฀฀฀฀฀฀฀฀) $234 ฀฀฀฀฀฀฀฀฀฀฀฀฀฀ − $195.25 ฀฀฀฀฀฀฀฀฀฀฀฀฀฀ = ฀ ฀ − ฀฀ ฀ ฀ = ฀฀ $38.75 ฀฀฀฀฀฀฀฀฀฀฀฀฀฀ 2

Q8.

Suppose Microsoft has 8.15 billion shares outstanding and pays a marginal corporate tax rate of 37%. If Microsoft announces that it will payout $52 billion in cash to investors through a combination of a special dividend and a share repurchase, and if investors had previously assumed Microsoft would retain this excess cash permanently, by how much will Microsoft’s share price change upon the announcement? Reducing cash is equivalent to increasing leverage by $52 billion. PV of tax savings = 37% x $52 billion = $19.24 billion, or $19.24/ 8.15 = $2.36 per share price increase.

Q9.

Suppose the corporate tax rate is 35%, and investors pay a tax rate of 30% on income from dividends or capital gains and a tax rate of 33.1% on interest income. Your firm decides to add debt so it will pay an additional $10 million in interest each year. It will pay this interest expense by cutting its dividend. a. How much will debt holders receive after paying taxes on the interest they earn? b. By how much will the firm need to cut its dividend each year to pay this interest expense? c. By how much will this cut in the dividend reduce equity holders’ annual aftertax income? d. How much less will the government receive in total tax revenues each year? a. $10 × (1 – 0.331) = $6.69 million each year b. Given a corporate tax rate of 35%, an interest expense of $10 million per year reduces net income by $10(1 – 0.35) = $6.5 million after corporate taxes. c. $6.5 million dividend cut -> $6.5 × (1 – 0.3) = $4.55 million per year. d. Interest taxes = 0.331 × $10 = $3.31 million Less corporate taxes = 0.35 × $10 = $3.5 million Less dividend taxes = 0.3 × $6.5 = $2.1 million Government will receive taxes less by = $3.31 - $3.5 - $1.95 = -$2.14 million

Q10. With its current leverage, Impi Corporation will have net income next year of $4.5 million. If Impi’s corporate tax rate is 21% and it pays 8% interest on its debt, how much additional debt can Impi issue this year and still receive the benefit of the interest tax shield next year? Net income of $4.5 million ⇒

million in taxable income.

3

Therefore, Impi can increase its interest expenses by $5.696 million, which corresponds to debt of: million. Q11. Colt Systems will have EBIT this coming year of $15 million. It will also spend $6 million on total capital expenditures and increases in net working capital, and have $3 million in depreciation expenses. Colt is currently an all-equity firm with a corporate tax rate of 21% and a cost of capital of 10%. a. If Colt is expected to grow by 8.5% per year, what is the market value of its equity today? b. If the interest rate on its debt is 8%, how much can Colt borrow now and still have nonnegative net income this coming year? c. Is there a tax incentive for Colt to choose a debt-to-value ratio that exceeds 50%? Explain. a.

b. Interest expense of $15 million ⇒ debt of

15 = $187.5 million. 0.08

c. No. The most they should borrow is 187.5 million; there is no interest tax shield from borrowing more.

4

Q1.

Baruk Industries has no cash and a debt obligation of $39 million that is now due. The market value of Baruk’s assets is $71 million, and the firm has no other liabilities. Assume perfect capital markets. a. Suppose Baruk has 13 million shares outstanding. What is Baruk’s current share price? b. How many new shares must Baruk issue to raise th...