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Corporate Finance

Stephen Ross, Randolph Westerfield, Jeffrey Jaffe

Chapter 16

Capital Structure: Basic Concepts - all with Video Answers

Educators

Chapter Questions

Problem 1

EBIT and Leverage Money, Inc., has no debt outstanding and a total market value of $\$ 275,000$. Earnings before interest and taxes, EBIT, are projected to be $\$ 21,000$ if economic conditions are normal. If there is strong expansion in the economy, then EBIT will be 25 percent higher. If there is a recession, then EBIT will be 40 percent lower. Money is considering a $\$ 99,000$ debt issue with an interest rate of 8 percent. The proceeds will be used to repurchase shares of stock. There are currently 5,000 shares outstanding. Ignore taxes for this problem.
a. Calculate earnings per share, EPS, under each of the three economic scenarios before any debt is issued. Also calculate the percentage changes in EPS when the economy expands or enters a recession.
b. Repeat part (a) assuming that Money goes through with recapitalization. What do you observe?

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Problem 2

EBIT, Taxes, and Leverage Repeat parts (a) and (b) in Problem 1 assuming Money has a tax rate of 35 percent.

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Problem 3

ROE and Leverage Suppose the company in Problem 1 has a market-to-book ratio of 1.0.
a. Calculate return on equity, ROE, under each of the three economic scenarios before any debt is issued. Also calculate the percentage changes in ROE for economic expansion and recession, assuming no taxes.
b. Repeat part (a) assuming the firm goes through with the proposed recapitalization. c. Repeat parts (a) and (b) of this problem assuming the firm has a tax rate of 35 percent.

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Problem 4

Break-Even EBIT Rolston Corporation is comparing two different capital structures, an all-equity plan (Plan I) and a levered plan (Plan II). Under Plan I, Rolston would have 265,000 shares of stock outstanding. Under Plan II, there would be 185,000 shares of stock outstanding and $\$ 2.8$ million in debt outstanding. The interest rate on the debt is 10 percent and there are no taxes.
a. If EBIT is $\$ 750,000$, which plan will result in the higher EPS?
b. If EBIT is $\$ 1,500,000$, which plan will result in the higher EPS?
c. What is the break-even EBIT?

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Problem 5

MM and Stock Value In Problem 4, use MM Proposition I to find the price per share of equity under each of the two proposed plans. What is the value of the firm?

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Problem 6

Break-Even EBIT and Leverage Kolby Corp. is comparing two different capital structures. Plan I would result in 900 shares of stock and \$65,700 in debt. Plan II would result in 1,900 shares of stock and $\$ 29,200$ in debt. The interest rate on the debt is 10 percent.
a. Ignoring taxes, compare both of these plans to an all-equity plan assuming that EBIT will be $\$ 8,500$. The all-equity plan would result in 2,700 shares of stock outstanding. Which of the three plans has the highest EPS? The lowest?
b. In part (a) what are the break-even levels of EBIT for each plan as compared to that for an all-equity plan? Is one higher than the other? Why?
c. Ignoring taxes, when will EPS be identical for Plans I and II?
d. Repeat parts (a), (b), and (c) assuming that the corporate tax rate is 40 percent. Are the break-even levels of EBIT different from before? Why or why not?

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Problem 7

Leverage and Stock Value Ignoring taxes in Problem 6, what is the price per share of equity under Plan I? Plan II? What principle is illustrated by your answers?

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Problem 8

Homemade Leverage Star, Inc., a prominent consumer products firm, is debating whether or not to convert its all-equity capital structure to one that is 35 percent debt. Currently there are 6,000 shares outstanding and the price per share is $\$ 58$. EBIT is expected to remain at $\$ 33,000$ per year forever. The interest rate on new debt is 8 percent, and there are no taxes.
a. Ms. Brown, a shareholder of the firm, owns 100 shares of stock. What is her cash flow under the current capital structure, assuming the firm has a dividend payout rate of 100 percent?
b. What will Ms. Brown's cash flow be under the proposed capital structure of the firm? Assume that she keeps all 100 of her shares.
c. Suppose Star does convert, but Ms. Brown prefers the current all-equity capital structure. Show how she could unlever her shares of stock to recreate the original capital structure.
d. Using your answer to part (c), explain why Star's choice of capital structure is irrelevant.

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Problem 9

Homemade Leverage and WACC $\mathrm{ABC}$ Co. and $\mathrm{XYZ}$ Co. are identical firms in all respects except for their capital structure. $\mathrm{ABC}$ is all equity financed with $\$ 750,000$ in stock. XYZ uses both stock and perpetual debt; its stock is worth $\$ 375,000$ and the interest rate on its debt is 8 percent. Both firms expect EBIT to be $\$ 86,000$. Ignore taxes.
a. Richard owns $\$ 30,000$ worth of XYZ's stock. What rate of return is he expecting?
b. Show how Richard could generate exactly the same cash flows and rate of return by investing in $\mathrm{ABC}$ and using homemade leverage.
c. What is the cost of equity for $\mathrm{ABC}$ ? What is it for $X Y Z$ ?
d. What is the WACC for $A B C$ ? For $X Y Z$ ? What principle have you illustrated?

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Problem 10

MM Nina Corp. uses no debt. The weighted average cost of capital is 9 percent. If the current market value of the equity is $\$ 37$ million and there are no taxes, what is EBIT?

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Problem 11

MM and Taxes In the previous question, suppose the corporate tax rate is 35 percent. What is EBIT in this case? What is the WACC? Explain.

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03:05

Problem 12

Calculating WACC Weston Industries has a debt-equity ratio of 1.5. Its WACC is 11 percent, and its cost of debt is 7 percent. The corporate tax rate is 35 percent.
a. What is Weston's cost of equity capital?
b. What is Weston's unlevered cost of equity capital?
c. What would the cost of equity be if the debt-equity ratio were 2 ? What if it were 1.0 ? What if it were zero?

Breanna Ollech
Breanna Ollech
Numerade Educator
03:05

Problem 13

Calculating WACC Shadow Corp. has no debt but can borrow at 8 percent. The firm's WACC is currently 11 percent, and the tax rate is 35 percent.
a. What is Shadow's cost of equity?
b. If the firm converts to 25 percent debt, what will its cost of equity be?
c. If the firm converts to 50 percent debt, what will its cost of equity be?
d. What is Shadow's WACC in part (b)? In part (c)?

Breanna Ollech
Breanna Ollech
Numerade Educator

Problem 14

MM and Taxes Bruce \& Co. expects its EBIT to be $\$ 185,000$ every year forever. The firm can borrow at 9 percent. Bruce currently has no debt, and its cost of equity is 16 percent. If the tax rate is 35 percent, what is the value of the firm? What will the value be if Bruce borrows $\$ 135,000$ and uses the proceeds to repurchase shares?

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Problem 15

MM and Taxes In Problem 14, what is the cost of equity after recapitalization? What is the WACC? What are the implications for the firm's capital structure decision?

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Problem 16

MM Proposition I Levered, Inc., and Unlevered, Inc., are identical in every way except their capital structures. Each company expects to earn $\$ 29$ million before interest per year in perpetuity, with each company distributing all its earnings as dividends. Levered's perpetual debt has a market value of $\$ 91$ million and costs 8 percent per year. Levered has 2.3 million shares outstanding, currently worth $\$ 105$ per share. Unlevered has no debt and 4.5 million shares outstanding, currently worth $\$ 80$ per share. Neither firm pays taxes. Is Levered's stock a better buy than Unlevered's stock?

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Problem 17

MM Tool Manufacturing has an expected EBIT of $\$ 57,000$ in perpetuity and a tax rate of 35 percent. The firm has $\$ 90,000$ in outstanding debt at an interest rate of 8 percent, and its unlevered cost of capital is 15 percent. What is the value of the firm according to MM Proposition I with taxes? Should Tool change its debt-equity ratio if the goal is to maximize the value of the firm? Explain.

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Problem 18

Firm Value Cavo Corporation expects an EBIT of $\$ 19,750$ every year forever. The company currently has no debt, and its cost of equity is 15 percent.
a. What is the current value of the company?
b. Suppose the company can borrow at 10 percent. If the corporate tax rate is 35 percent, what will the value of the firm be if the company takes on debt equal to 50 percent of its unlevered value? What if it takes on debt equal to 100 percent of its unlevered value?
c. What will the value of the firm be if the company takes on debt equal to 50 percent of its levered value? What if the company takes on debt equal to 100 percent of its levered value?

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Problem 19

MM Proposition I with Taxes The Maxwell Company is financed entirely with equity. The company is considering a loan of $\$ 1.8$ million. The loan will be repaid in equal installments over the next two years, and it has an interest rate of 8 percent. The company's tax rate is 35 percent. According to MM Proposition I with taxes, what would be the increase in the value of the company after the loan?

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Problem 20

MM Proposition I without Taxes Alpha Corporation and Beta Corporation are identical in every way except their capital structures. Alpha Corporation, an allequity firm, has 15,000 shares of stock outstanding, currently worth $\$ 30$ per share. Beta Corporation uses leverage in its capital structure. The market value of Beta's debt is $\$ 65,000$, and its cost of debt is 9 percent. Each firm is expected to have earnings before interest of $\$ 75,000$ in perpetuity. Neither firm pays taxes. Assume that every investor can borrow at 9 percent per year.
a. What is the value of Alpha Corporation?
b. What is the value of Beta Corporation?
c. What is the market value of Beta Corporation's equity?
d. How much will it cost to purchase 20 percent of each firm's equity?
e. Assuming each firm meets its earnings estimates, what will be the dollar return to each position in part (d) over the next year?
f. Construct an investment strategy in which an investor purchases 20 percent of Alpha's equity and replicates both the cost and dollar return of purchasing 20 percent of Beta's equity.
g. Is Alpha's equity more or less risky than Beta's equity? Explain.

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03:05

Problem 21

Cost of Capital Acetate, Inc., has equity with a market value of $\$ 23$ million and debt with a market value of $\$ 7$ million. Treasury bills that mature in one year yield 5 percent per year, and the expected return on the market portfolio is 12 percent. The beta of Acetate's equity is 1.15 . The firm pays no taxes.
a. What is Acetate's debt-equity ratio?
b. What is the firm's weighted average cost of capital?
c. What is the cost of capital for an otherwise identical all-equity firm?

Breanna Ollech
Breanna Ollech
Numerade Educator

Problem 22

Homemade Leverage The Veblen Company and the Knight Company are identical in every respect except that Veblen is not levered. The market value of Knight Company's 6 percent bonds is $\$ 1.4$ million. Financial information for the two firms appears here. All earnings streams are perpetuities. Neither firm pays taxes. Both firms distribute all earnings available to common stockholders immediately.
\begin{tabular}{lrr|}
& \multicolumn{1}{cr}{ Veblen } & Knight \\
\hline Projected operating income & $\$ 550,000$ & $\$ 550,000$ \\
Year-end interest on debt & - & 84,000 \\
Market value of stock & $4,300,000$ & $3,140,000$ \\
Market value of debt & - & $1,400,000$
\end{tabular}
a. An investor who can borrow at 6 percent per year wishes to purchase 5 percent of Knight's equity. Can he increase his dollar return by purchasing 5 percent of Veblen's equity if he borrows so that the initial net costs of the two strategies are the same?
b. Given the two investment strategies in (a), which will investors choose? When will this process cease?

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Problem 23

MM Propositions Locomotive Corporation is planning to repurchase part of its common stock by issuing corporate debt. As a result, the firm's debt-equity ratio is expected to rise from 35 percent to 50 percent. The firm currently has $\$ 3.6$ million worth of debt outstanding. The cost of this debt is 8 percent per year. Locomotive expects to have an EBIT of $\$ 1.35$ million per year in perpetuity. Locomotive pays no taxes.
a. What is the market value of Locomotive Corporation before and after the repurchase announcement?
b. What is the expected return on the firm's equity before the announcement of the stock repurchase plan?
c. What is the expected return on the equity of an otherwise identical all-equity firm?
d. What is the expected return on the firm's equity after the announcement of the stock repurchase plan?

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Problem 24

Stock Value and Leverage Green Manufacturing, Inc., plans to announce that it will issue $\$ 2$ million of perpetual debt and use the proceeds to repurchase common stock. The bonds will sell at par with a coupon rate of 6 percent. Green is currently an all-equity firm worth $\$ 6.3$ million with 400,000 shares of common stock outstanding. After the sale of the bonds, Green will maintain the new capital structure indefinitely. Green currently generates annual pretax earnings of $\$ 1.5$ million. This level of earnings is expected to remain constant in perpetuity. Green is subject to a corporate tax rate of 40 percent.
a. What is the expected return on Green's equity before the announcement of the debt issue?
b. Construct Green's market value balance sheet before the announcement of the debt issue. What is the price per share of the firm's equity?
c. Construct Green's market value balance sheet immediately after the announcement of the debt issue.
d. What is Green's stock price per share immediately after the repurchase announcement?
e. How many shares will Green repurchase as a result of the debt issue? How many shares of common stock will remain after the repurchase?
f. Construct the market value balance sheet after the restructuring.
g. What is the required return on Green's equity after the restructuring?

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03:05

Problem 25

MM with Taxes Williamson, Inc., has a debt-equity ratio of 2.5. The firm's weighted average cost of capital is 10 percent, and its pretax cost of debt is 6 percent. Williamson is subject to a corporate tax rate of 35 percent.
a. What is Williamson's cost of equity capital?
b. What is Williamson's unlevered cost of equity capital?
c. What would Williamson's weighted average cost of capital be if the firm's debtequity ratio were .75 ? What if it were 1.5 ?

Breanna Ollech
Breanna Ollech
Numerade Educator

Problem 26

Weighted Average Cost of Capital In a world of corporate taxes only, show that the $R_{\text {wACC }}$ can be written as $R_{\text {wACC }}=R_0 \times\left[1-t_C(B / V)\right]$.

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Problem 27

Cost of Equity and Leverage Assuming a world of corporate taxes only, show that the cost of equity, $R_S$, is as given in the chapter by MM Proposition II with corporate taxes.

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Problem 28

Business and Financial Risk Assume a firm's debt is risk-free, so that the cost of debt equals the risk-free rate, $R_f$. Define $\beta_A$ as the firm's asset beta-that is, the systematic risk of the firm's assets. Define $\beta_S$ to be the beta of the firm's equity. Use the capital asset pricing model, CAPM, along with MM Proposition II to show that $\beta_S=\beta_A \times(1+B / S)$, where $B / S$ is the debt-equity ratio. Assume the tax rate is zero.

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02:21

Problem 29

Stockholder Risk Suppose a firm's business operations mirror movements in the economy as a whole very closely - that is, the firm's asset beta is 1.0 . Use the result of previous problem to find the equity beta for this firm for debt-equity ratios of $0,1,5$, and 20 . What does this tell you about the relationship between capital structure and shareholder risk? How is the shareholders' required return on equity affected? Explain.

Sanchit Jain
Sanchit Jain
Numerade Educator

Problem 30

Unlevered Cost of Equity Beginning with the cost of capital equation-that is:
$$
R_{\mathrm{WACC}}=\frac{S}{B+S} R_S+\frac{B}{B+S} R_B
$$
show that the cost of equity capital for a levered firm can be written as follows:
$$
R_S=R_0+\frac{B}{S}\left(R_0-R_B\right)
$$

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