What is the maximum amount the bank could lend that would induce Ms. Ketchup to take the bank’s preferred project?
PROBLEM SET 4
1. Consider Macbeth Spot Removers, a publically traded company with an infinite life span, which faces a range of annual operating incomes as depicted in the table below. The rate of return on Treasury bonds is 10%.
Data | ||||
Number of shares | 700 | |||
Price per share | $12 | |||
Market value of equity | $8400 | |||
Outcomes | ||||
Operating income | $500 | $1,000 | $1,500 | $2,000 |
Earnings per share | $0.71 | $1.43 | $2.14 | $2.86 |
Return on equity | 5.95% | 11.90% | 17.86% | 23.81% |
a. Calculate the earnings per share and return on equity in the table above.
i. Shown In Table Above
Macbeth Spot Removers issues $2,400 of risk-free debt and uses the proceeds to repurchase 200 shares.
b. Rework the table above to show how earning per share and equity returns now vary with operating income. Shown In Table Below
Data | ||||
Number of shares | 500 | |||
Price per share | $12 | |||
Market value of equity | $6000 | |||
Outcomes | ||||
Operating income | $500 | $1,000 | $1,500 | $2,000 |
Interest
Net Income Earnings per share |
$240
$260 $0.52 |
$240
$760 $1.52 |
$240
$1260 $2.52 |
$240
$1760 $3.52 |
Return on equity | 4.33% | 12.66% | 21% | 29.33% |
c. If the beta of Macbeth’s unlevered assets is 0.8 and its debt is risk-free, what would be the beta of the equity after the debt issue?
i. 0.966 or 1.12
Ms. Macbeth’s investment bankers have just informed her that the new issue of debt is risky. Debtholders will demand a return of 12.5%, which is 2.5% above the risk-free interest rate.
d. How does this affect return on assets and return on equity? Calculate these values. Shown In Table Below
Data | ||||
Number of shares | 500 | |||
Price per share | $12 | |||
Market value of equity | $6000 | |||
Outcomes | ||||
Operating income | $500 | $1,000 | $1,500 | $2,000 |
Return on Assets | 5.95% | 11.9% | 17.86% | 23.81% |
Return on equity | 3.33% | 11.67% | 20% | 28.33% |
e. Suppose that the β of unlevered equity was 0.6. What will β_{A}, β_{E}, and β_{D} be after the change to the capital structure?
i. β_{A} = 0.6 or 0.84 β_{E} = 0.74 and β_{D}_{ }= 0.25
2. Happy Valet, Inc. has a 14.5% cost of unlevered equity and can issue debt at a rate of 8%. It faces marginal corporate income tax rate of 40% and has debt and equity assets of 30% and 70%, respectively (calculated using market values).
a. What rate of return do stockholders require on Happy Valet’s levered equity assets?
i. 10.15% or 16.17%
b. What is the firm’s WACC?
i. 11.59% or 12.76%
3. Consider the case of Henrietta Ketchup, a budding entrepreneur with two possible investment projects that offer the following payoffs:
Investment | Payoff | Probability of Payoff | |
Project 1 | 20.4 | 25.5 | 1.0 |
Project 2 | 20.4 | 40.8 | 0.6 |
0 | 0.4 |
Ms. Ketchup approaches her bank and asks to borrow the present value of $10 (she will fund the rest out of internal funds).
a. Calculate the expected payoffs to the bank and to Ms. Ketchup if the bank lends the present value of $10. Which project would Ms. Ketchup undertake?
a. Project 1 – 5.1 or 15.5 ; Project 2 – 4 or 18.48 .(Ms. Ketchup); Project 1 – 10 ; Project 2 – 6.(Bank) ; Ms. Ketchup would take Project 2 because there is a probability for a higher payoff.
b. Is this the same project that the bank would want Ms. Ketchup to undertake? Explain why or why not.
a. No the bank would choose project 1 because there is less risk involved and more probability that they can get their money back.
c. What is the maximum amount the bank could lend that would induce Ms. Ketchup to take the bank’s preferred project?
a. $15.30 or $2.54
d. If the bank was to lend the $10, but was acting strategically in its own interest, what interest rate would the bank require on its loan?
a. 1.96% or 25.4%
4. You have the following information about Ledd—a publicly traded (and therefore infinitely lived) company:
Operating income: $20 million
Cost of unlevered equity: 10%
Risk-free interest rate: 5%
Corporate marginal tax rate: 0
a. If Ledd is financed entirely by equity,
i. What is the value of the firm?
1. 200 million (w/o tax) ; 200 million(with tax)
ii. What is the return required by stockholders?
1. 10% (w/o tax) ;10% (with tax)
iii. What is the company’s WACC?
1. 10% (w/o tax) ; 10% (with tax)
b. Ledd decides to issue bonds with the market value of 40% of total assets, using the proceeds to repurchase equity. The bonds are considered to be risk-free.
i. What is the value of Ledd with the new capital structure?
1. 200 million (w/o tax);228.8 million (with tax)
ii. What is the return required by stockholders of the leveraged firm?
1. 6% or 13.33% (w/o tax); 13.21%(with tax)
iii. What is the WACC?
1. 8% or 10% (w/o tax); 9.21%(with tax)
iv. What is the tax shield of debt?
1. 0 (w/o tax) ; 28.8 million (with tax)
c. The government implements a marginal corporate tax rate of 36%.
i. Recalculate your answers to a) and b) in a world with taxes.
1. Shown Above (2^{nd} Answer)