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 
700 



Price per 
$12 



Market value 
$8400 




Outcomes 

Operating 
$500 
$1,000 
$1,500 
$2,000 
Earnings per 

Return on equity 
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 riskfree 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 
500 



Price per 
$12 



Market value 
$6000 




Outcomes 

Operating 
$500 
$1,000 
$1,500 
$2,000 
Interest Net Income Earnings per 
$240 $260 $0.52 
$240 $760 $1.52 
$240 $1260 $2.52 
$240 $1760 $3.52 
Return on 
4.33% 
12.66% 
21% 
29.33% 
c.
If the beta of Macbeth’s unlevered assets is 0.8 and its debt is
riskfree, what would be the beta of the equity after the debt issue?
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 riskfree
interest rate.
d. How
does this affect return on assets and return on equity? Calculate these values.Shown
In Table Below
Data 

Number of 
500 



Price per 
$12 



Market value 
$6000 




Outcomes 

Operating 
$500 
$1,000 
$1,500 
$2,000 
Return on 
5.95% 
11.9% 
17.86% 
23.81% 
Return on 
3.33% 
11.67% 
20% 
28.33% 
e.
Suppose that the ? of unlevered equity was 0.6. What will ?_{A}, ?_{E}, and ?_{D}
be after the change to the capital structure?
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?
b.
What is the firm’s WACC?
3. Consider
the case of Henrietta Ketchup, a budding entrepreneur with two possible
investment projects that offer the following payoffs:

Investment 
Payoff 
Probability 
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?
b. Is
this the same project that the bank would want Ms. Ketchup to undertake? Explain why or why not.
c.
What is the maximum amount the bank could lend that would induce Ms.
Ketchup to take the bank’s preferred project?
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?
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%
Riskfree interest rate: 5%
Corporate marginal tax rate: 0
a.
If Ledd is financed entirely by
equity,
i.
What is the value of the firm?
ii.
What is the return required by
stockholders?
iii.
What is the company’s WACC?
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
riskfree.
i.
What is the value of Ledd with
the new capital structure?
ii.
What is the return required by
stockholders of the leveraged firm?
iii.
What is the WACC?
iv.
What is the tax shield of debt?
c. The government implements a marginal
corporate tax rate of 36%.
i.
Recalculate
your answers to a) and b) in a world with taxes.