Problem Set
PROBLEM SET: Capital Structure
Exercise 1.
[4]
Establishing a capital structure for a rm is not simple. Although nancial theory guides the process, there is no simple formula. List and explain four main items that one should consider in determining the capital structure.
Exercise 2.
Utility [4]
You want to estimate the total intrinsic value of a large gas and electric utility company. This company has publicly traded shares and has been paying a regular dividend for many years. The company is expected to pay a dividend of e1.25 per share next year and the dividend is expected to grow at a rate of 3% per year thereafter.
You estimate that the appropriate rate for discounting future dividends is 12%. In addition, you know that the company has 46 million shares outstanding and that the market value of its debt is e350 million.
What is the total value of the company?
Exercise 3.
Caterpillar [2]
Suppose Caterpillar, Inc., has 665 million shares outstanding with a share price of $74.77, and $25 billion in debt.
If in three years, Caterpillar has 700 million shares outstanding trading for $83 per share, how much debt will Caterpillar have if it maintains a constant debt-equity ratio?
Exercise 4.
Caterpillar [5]
Suppose Caterpillar, Inc, has 665 million shares outstanding with a share price of $74.77, and $25 billion in debt.
If in three years, Caterpilllar has 700 million shares outstanding trading for $83 per share, how much debt will Caterpillar have if it maintains a constant debt-to-equity ratio?
Exercise 5.
[Medium]
The JumpStart Corporation is unlevered and valued at $500,000. JumpStart has 200,000 shares outstanding.
The company announces that in the near future it will issue $200,000 of debt and buy back $200,000 of stock. If the rm is in the 34% tax bracket, how many shares of stock will be repurchased? Assume MM with taxes.
Exercise 6.
[1]
The dierence between a market value balance sheet and a book value balance sheet is that a market value balance sheet
A) places assets on the right hand side.
B) places liabilities on the left-hand side.
C) does not equate the right hand with the left-hand side.
D) lists items in terms of market values, not historical costs.
E) uses the market rate of return.
Exercise 7.
[3]
A rm has zero debt in its capital structure. Its overall cost of capital is 10%. The rm is considering a new capital structure with 60% debt. The interest rate on the debt would be 8%. Assuming there are no taxes or other imperfections, its cost of equity capital with the new capital structure would be
A) 9%
B) 10%
C) 13%
D) 14%
E) None of the above.
Exercise 8.
[2]
Suppose the risk-free interest rate is 4%. If Nielson borrows $150 million today at this rate and uses the proceeds to pay an immediate cash dividend, then according to MM, the market value of its equity just after the dividend is paid would be closest to:
A) $0 million.
B) $150 million.
C) $250 million.
D) $400 million.
Exercise 9.
[2]
4) Which of the following statements is FALSE?
A) The relative proportions of debt, equity, and other securities that a rm has outstanding constitute its capital structure.
B) The most common choices for nancing a new project are nancing through equity alone and nancing through a combination of debt and equity.
C) The NPV created by a project represents the value to the new investors of the rm.
D) When corporations raise funds from outside investors, they must choose which type of security to issue.
Exercise 10.
[1]
Equity in a rm with debt is called:
A) levered equity.
B) riskless equity.
C) unlevered equity.
D) risky equity.
Exercise 11.
7) Which of the following statements is FALSE?
A) Modigliani and Miller's conclusion veri ed the common view, which stated that even with perfect capital markets, leverage would aect a rm's value.
B) We can evaluate the relationship between risk and return more formally by computing the sensitivity of each security's return to the systematic risk of the economy.
C) Investors in levered equity require a higher expected return to compensate for its increased risk.
D) Leverage increases the risk of equity even when there is no risk that the rm will default.
Exercise 12.
[2]
11) Which of the following is NOT one of Modigliani and Miller's set of conditions referred to as perfect capital markets?
A) All investors hold the e cient portfolio of assets.
B) There are no taxes, transaction costs, or issuance costs associated with security trading.
C) A rm's nancing decisions do not change the cash ows generated by its investments, nor do they reveal new information about them.
D) Investors and rms can trade the same set of securities at competitive market prices equal to the present value of their future cash ows.
Exercise 13.
[2]
Fly by Night Aviation (FBNA) expects to have net income next year of $24 million and interest expense of $3 million. FBNA's corporate tax rate is 21%.
13) FBNA's EBIT is closest to:
A) $33 million.
B) $40 million.
C) $45 million.
D) $60 million.
Exercise 14.
[2]
Fly by Night Aviation (FBNA) expects to have net income next year of $24 million and interest expense of $3 million. FBNA's corporate tax rate is 21%.
14) IF FBNA increases leverage so that its interest expense rises by $1 million, then the amount its net income will change is closest to:
A) -$400,000.
B) -$600,000.
C) $400,000.
D) $600,000.
Exercise 15.
[2]
Fly by Night Aviation (FBNA) expects to have net income next year of $24 million and interest expense of $3 million. FBNA's corporate tax rate is 21%.
15) IF FBNA increases leverage so that its interest expense rises by $1 million, then the amount its unlevered EBIT will change is closest to:
A) $0.
B) -$400,000.
C) $600,000.
D) $400,000.
Exercise 16.
equity value
Suppose the corporate tax rate is 40%. Consider a rm that earns $1000 before interest and taxes each year with no risk. The rm's capital expenditures equal its depreciation expenses each year, and it will have no changes to its net working capital. The risk-free interest rate is 5%.
a. Suppose the rm has no debt and pays out its net income as a dividend each year. What is the value of the
rm's equity?
b. Suppose instead the rm makes interest payments of $500 per year. What is the value of equity? What is the value of debt?
c. What is the dierence between the total value of the rm with leverage and without leverage?
d. The dierence in part (c) is equal to what percentage of the value of the debt?
Exercise 17.
Grommit [3]
Grommit Engineering expects to have net income next year of $20.75 million and free cash ow of $22.15 million.
Grommit's marginal corporate tax rate is 35%.
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 ow change?
Exercise 18.
Pelamed Pharmaceuticals [2]
Pelamed Pharmaceuticals has EBIT of $325 million in 2006. In addition, Pelamed has interest expenses of $125 million and a corporate tax rate of 40%.
a. What is Pelamed's 2006 net income?
b. What is the total of Pelamed's 2006 net income and interest payments?
c. If Pelamed had no interest expenses, what would its 2006 net income be? How does it compare to your answer in part b?
d. What is the amount of Pelamed's interest tax shield in 2006?
Problem Set Solutions
PROBLEM SET: Capital Structure
Solution to Exercise 1.
[4]
Some points to consider are: Taxestax shield to debt if TC> TB
Type of Assetstangible assets based rms have lower costs of nancial distress Uncertainty of operating income rms in higher risk classes have greater probability of experiencing nancial distress
Pecking order and Financial slack
External nancing is more expensive Financial slack allows for shortfall coverage Solution to Exercise 2.
Utility [4]
Share Price = 1.25
0.12 − 0.03 = 13.89 Value of Equity = 46 mill × 13.89 = 638.94 mill.
Value of Firm = Value of Equity + Value of Debt = 638.94 + 350 = 988.94mill Solution to Exercise 3.
Caterpillar [2]
E = 665 million ×$74.77 = $49.7 billion, D = $25 billion, D/E = 25/49.722 = 0.503.
E = 700 million ×$83.00 = $58.1 billion. Constant D/E implies D = 58.1 × 0.503 = $29.2 billion.
Solution to Exercise 4.
Caterpillar [5]
On the rst date, Equity has a market value of 74.77 × 665 mill shares = 49722.05, or 49.7 billion, with 25 billion in debt.
Here equity is
wE= E
E + D = 49.72
49.72 + 25 = 0.66 wD= 1 − wE = 1 − 0.66 = 0.34 Three years later, value of equity is 83 × 700 million = 58 billion.
If the D/E ratio is constant, solve for D in
E
D + E = 0.66 58
D + 58= 0.66 58
0.66= D + 58 D = 58
0.66− 58 ≈ 29.88 or, carrying more decimals D = 29.1633.
Solution to Exercise 5.
[Medium]
New Firm Value: $500,000 + (.34) ($200,000) = $568,000 New Price Per Share = $568,000/200,000 = $2.84
Number of shares repurchased = $200,000/$2.84 = $70,422.5 Solution to Exercise 6.
[1]
D
Solution to Exercise 7.
[3]
C Rationale:
rs=.10 +.60/.40(.10-.08) =.10 +.03 =.013 = 13%
Solution to Exercise 8.
[2]
Answer: C
Explanation: Value of equity = Total value - value of debt = $400M - $150M = $250M Solution to Exercise 9.
[2]
Answer: C
Explanation: The NPV created by the project represents the value to the existing shareholders of the rm.
Solution to Exercise 10.
[1]
Answer: A
Solution to Exercise 11.
Answer: A
Explanation: Modigliani and Miller's conclusion went against the common view that even with perfect capital markets, leverage would aect a rm's value.
Solution to Exercise 12.
[2]
Answer: A
Solution to Exercise 13.
[2]
Answer: A
Explanation: EBIT = NI + Taxes + Interest expense (EBIT - Interest Expense)(1 - .21) = NI
(EBIT - $3 million)(.79) = $24 million EBIT = $24 million/.79 + $3 million = $33.38 Solution to Exercise 14.
[2]
Answer: B
Explanation: (EBIT - Interest Expense - chg IE)(1 - .21) = NI + chg NI (-1)(chg IE)(.79) = chg NI
-$1,000,000(.79) = -$790,000 Or, -$1 million(1 - .21) = -$790,000 Solution to Exercise 15.
[2]
Answer: A
Explanation: EBIT does not change with a change in interest expense.
Solution to Exercise 16.
equity value
a. Net income. Thus, equity holders receive dividends of $600 per year with no risk.
b. Net income. Debt holders receive interest of $500 per year D = $10,000
c. With leverage = 6,000 + 10,000 = $16,000 Without leverage = $12,000
Dierence = 16,000 12,000 = $4000 d. corporate tax rate
Solution to Exercise 17.
Grommit [3]
a. Net income will fall by the after-tax interest expense to $20.750 − 1 × (1 − 0.35) = $20.10 million.
b. Free cash ow is not aected by interest expenses.
Solution to Exercise 18.
Pelamed Pharmaceuticals [2]
a. Net Income = EBIT - Interest - Taxes = (325 − 125) × (1 − 0.4) = 120 million.
b. Net income + Interest = 120 + 125 = $245 million
c. Net income = EBIT + Taxes = $ 195 million. This is 50 million lower than part (b).
d. Interest tax shield 50 million
