Chapter 15: Capital Structure Decisions Problems Book Title: Financial Management: Theory and Practice

Chapter 15: Capital Structure Decisions Problems

Book Title: Financial Management: Theory and Practice

Printed By: © 2017 Cengage Learning, Cengage Learning

Chapter Review


Easy Problems 1–6


Break-Even Quantity

Shapland Inc. has fixed operating costs of $500,000 and variable costs of $50 per unit. If it sells the product for $75 per unit, what is the break-even quantity?


Unlevered Beta

Counts Accounting’s beta is 1.15 and its tax rate is 40%. If it is financed with 20% debt, what is its unlevered beta?


Premium for Financial Risk

Ethier Enterprise has an unlevered beta of 1.0. Ethier is financed with 50% debt and has a levered beta of 1.6. If the risk-free rate is 5.5% and the market risk premium is 6%, how much is the additional premium that Ethier’s shareholders require to be compensated for financial risk?


Value of Equity after Recapitalization

Nichols Corporation’s value of operations is equal to $500 million after a recapitalization (the firm had no debt before the recap). It raised $200 million in new debt and used this to buy back stock. Nichols had no short-term investments before or after the recap. After the recap, . What is S (the value of equity after the recap)?

Stock Price after Recapitalization

Lee Manufacturing’s value of operations is equal to $900 million after a recapitalization. (The firm had no debt before the recap.) Lee raised $300 million in new debt and used this to buy back stock. Lee had no short-term investments before or after the recap. After the recap, . The firm had 30 million shares before the recap. What is P (the stock price after the recap)?


Shares Remaining after Recapitalization

Dye Trucking raised $150 million in new debt and used this to buy back stock. After the recap, Dye’s stock price is $7.50. If Dye had 60 million shares of stock before the recap, how many shares does it have after the recap?

Intermediate Problems 7–8


Break-Even Point

Schweser Satellites Inc. produces satellite earth stations that sell for $100,000 each. The firm’s fixed costs, F, are $2 million, 50 earth stations are produced and sold each year, profits total $500,000, and the firm’s assets (all equity financed) are $5 million. The firm estimates that it can change its production process, adding $4 million to assets and $500,000 to fixed operating costs. This change will reduce variable costs per unit by $10,000 and increase output by 20 units. However, the sales price on all units must be lowered to $95,000 to permit sales

of the additional output. The firm has tax loss carryforwards that render its tax rate zero, its cost of equity is 16%, and it uses no debt.

a. What is the incremental profit? To get a rough idea of the project’s profitability, what is the project’s expected rate of return for the next year (defined as the incremental profit divided by the investment)? Should the firm make the investment? Why or why not?

b. Would the firm’s break-even point increase or decrease if it made the change?

c. Would the new situation expose the firm to more or less business risk than the old one?


Capital Structure Analysis

The Rivoli Company has no debt outstanding, and its financial position is given by the following data:

The firm is considering selling bonds and simultaneously repurchasing some of its stock. If it moves to a capital structure with 30% debt based on market values, its cost of equity, , will increase to 11% to reflect the increased risk. Bonds can be sold at a cost, , of 7%. Rivoli is a no-growth firm. Hence, all its earnings are paid out as dividends. Earnings are expected to be constant over time.

a. What effect would this use of leverage have on the value of the firm?

b. What would be the price of Rivoli’s stock?

c. What happens to the firm’s earnings per share after the recapitalization?

d. The $500,000 EBIT given previously is actually the expected value from the following probability distribution:

Determine the times-interest-earned ratio for each probability. What is the

probability of not covering the interest payment at the 30% debt level?

Challenging Problems 9–12


Capital Structure Analysis

Pettit Printing Company has a total market value of $100 million, consisting of 1 million shares selling for $50 per share and $50 million of 10% perpetual bonds now selling at par. The company’s EBIT is $13.24 million, and its tax rate is 15%. Pettit can change its capital structure by either increasing its debt to 70% (based on market values) or decreasing it to 30%. If it decides to increase its use of leverage, it must call its old bonds and issue new ones with a 12% coupon. If it decides to decrease its leverage, it will call its old bonds and replace them with new 8% coupon bonds. The company will sell or repurchase stock at the new equilibrium price to complete the capital structure change.

The firm pays out all earnings as dividends; hence, its stock is a zero-growth stock. Its current cost of equity, , is 14%. If it increases leverage, will be 16%. If it decreases leverage, will be 13%. What is the firm’s WACC and total corporate value under each capital structure?


Optimal Capital Structure with Hamada

Beckman Engineering and Associates (BEA) is considering a change in its capital structure. BEA currently has $20 million in debt carrying a rate of 8%, and its stock price is $40 per share with 2 million shares outstanding. BEA is a zerogrowth firm and pays out all of its earnings as dividends. The firm’s EBIT is $14.933 million, and it faces a 40% federal-plus-state tax rate. The market risk

premium is 4%, and the risk-free rate is 6%. BEA is considering increasing its debt level to a capital structure with 40% debt, based on market values, and repurchasing shares with the extra money that it borrows. BEA will have to retire the old debt in order to issue new debt, and the rate on the new debt will be 9%. BEA has a beta of 1.0.

a. What is BEA’s unlevered beta? Use market value D/S (which is the same as ) when unlevering.

b. What are BEA’s new beta and cost of equity if it has 40% debt?

c. What are BEA’s WACC and total value of the firm with 40% debt?


WACC and Optimal Capital Structure

F. Pierce Products Inc. is considering changing its capital structure. F. Pierce currently has no debt and no preferred stock, but it would like to add some debt to take advantage of low interest rates and the tax shield. Its investment banker has indicated that the pre-tax cost of debt under various possible capital structures would be as follows:

Market Market Market Before-Tax

Debt-to- Equity-to- Debt-to- Cost of

Value Ratio Value Ratio Equity Debt

Ratio (D/S)

0.0 1.0 0.00 6.0%
0.2 0.8 0.25 7.0
0.4 0.6 0.67 8.0
0.6 0.4 1.50 9.0

0.8 0.2 4.00 10.0

F. Pierce uses the CAPM to estimate its cost of common equity, and at the time of the analysis the risk-free rate is 5%, the market risk premium is 6%, and the company’s tax rate is 40%. F. Pierce estimates that its beta now (which is “unlevered” because it currently has no debt) is 0.8. Based on this information, what is the firm’s optimal capital structure, and what would be the weighted average cost of capital at the optimal capital structure?

Equity Viewed as an Option

A. Fethe Inc. is a custom manufacturer of guitars, mandolins, and other stringed instruments and is located near Knoxville, Tennessee. Fethe’s current value of operations, which is also its value of debt plus equity, is estimated to be $5 million. Fethe has $2 million face value, zero coupon debt that is due in 2 years. The risk-free rate is 6%, and the standard deviation of returns for companies similar to Fethe is 50%. Fethe’s owners view their equity investment as an option and they would like to know the value of their investment.

a. Using the Black-Scholes option pricing model, how much is Fethe’s equity worth?

b. How much is the debt worth today? What is its yield?

c. How would the equity value and the yield on the debt change if Fethe’s managers could use risk management techniques to reduce its volatility to 30%? Can you explain this?

Chapter 15: Capital Structure Decisions Problems

Book Title: Financial Management: Theory and Practice

Printed By: Kristina Mack ([email protected]) © 2017 Cengage Learning, Cengage Learning

© 2020 Cengage Learning Inc. All rights reserved. No part of this work may by reproduced or used in any form or by any means graphic, electronic, or mechanical, or in any other manner – without the written permission of the copyright holder.

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