Fin 3322
Capital Structure Homework
1.
If a firm permanently borrows $50 million at an interest rate of 8%, how much is
firm value increased over an un-levered firm? Assume a 35% tax rate..
50,000,000 * 0.35 = $17,500,000
2.
Firm U and firm L are identical except for their capital structure. U is all equityfinanced and its equity is worth $1,000, while firm L has a D/E ratio of 1.5.
Assume all debts is risk-free. Investor Bob owns $100 of firm L’s stock. Ignore
taxes.
a) What is the alternative investment strategy in U’s stock and risk-free bonds that
generate identical cash flows for Bob? (Specify exactly what strategy you use)
D/E=1.5  D=(1.5/2.5)*1,000 = 600, E=(1/2.5)*1000 = 400
So Bob owns 25% of El
 Need to buy 25% of Eu ($250) and borrow 25% of D ($150)
(b) Show that the cash flows from both strategies are the same.
Investment in Vl
Alternative Investment
Cost Today
$100
$100
Payoff
25% * (Profit – (rf * Dl))
25% * Profit – 25% * (rf * Dl)
25% * (Profit - (rf * Dl))
Own $100 of L’s stock: cost $100, payoff: 25% (Profit – Interest)
Interest = rf * Dl
Investment in Unlevered and risk free
Cost $250-$150 = $100, payoff: 25% profit – 25% *( rf * Dl)
3.
Sparky’s Inc. currently has an equity beta of 2.84, is financed with 10% debt and
has a total firm value of $10 million. Sparky’s CEO thinks that they should
increase the firm’s leverage by issuing $2 million of debt and buying back $2
million of equity. This debt will be perpetual and have a yield of 7%. Sparky’s
has a 35% tax rate. What is the value of Sparky’s after the swap, and how much
of that value will be equity?
Old Capital Structure
Vl = Vu + Tc * D
10,000,000 = Vu + 0.35 * (0.1*10,000,000)
10,000,000 = Vu + 0.35 * 1,000,000
10,000,000 = Vu + 350,000
New Capital Structure
Vl = Vu + Tc * D
Vl =9,650,000+0.35*3,000,000
Vl = 9,650,000 + 1,050,000
Vl = 10,700,000
Vu = 9,650,000
Vl = D + E
E = Vl - D
E = 10,700,000 - 3,000,000 = 7,700,000
E/V = 7,700,000/10,700,000 = 0.719626682 = 72%
OR
Vnew = Vold + PV( Additional Tax Shield)
Vnew = 10m + 2m * 0.35
Vnew = 10.7m
Enew = 10.7m – 3m = 7.7m or 72%
4. Skim and Cream are identical firms except that Skim is more leveraged than
Cream. The probability of a recession is equal to the probability of an expansion.
If an expansion occurs, each firm will have EBIT of $2 million next year. If a
recession occurs, each firm will have EBIT of $ 1 million next year. Cream’s
debt obligation requires the firm to make $1 million in payments. Because Skim
carries more debt, its debt payment obligations are $1.5 million. Assume that all
of the firm’s cash flows are discounted at 15%, the firm exists for one period and
there are no taxes. Use the provided data to calculate:
a. The value of equity for each firm
Skim’s Equity expects $0.25 million next year
0.5(2-1.5) + 0.5(0) = 0.25 million
Discounted back to today, the market value of Skim’s Equity = $0.22 million
0.25/1.15=0.2173913043
Cream’s Equity expects $0.5 million next year
0.5(2-1) + 0.5(0) = 0. 5 million
Discounted back to today, the market value of Cream’s Equity = $0.43
million
0.5/1.15=0.4347826087
b. The value of debt for each firm
Skim’s Debt expects $1.25 million next year
0.5(1.5) + 0.5(1) = 1.25 million
Discounted back to today, the market value of Skim’s Equity = $1.09 million
1.25/1.15=1.086956522
Cream’s Equity expects $1 million next year
0.5(1) + 0.5(1) = 1 million
Discounted back to today, the market value of Cream’s Equity = $0.870
million
1/1.15=0.8695652174
c. The total value of the firms. Do they have the same value? Briefly explain.
The value of the two firms will be the same (MM prop1), same cash flows and
no taxes → capital structure does not matter.
V = D+E
Skim = 0.21 + 1.09 = 1.3
Cream = 0.43 + 0.87 = 1.3
d. Is investing in Skim’s equity more or less risky than investing in Cream’s
equity? Briefly explain.
More Risky as Skim is exposed to the same business risk, but has more
financial risk.
5.
Anderson’s Furniture Outlet has an un-levered cost of capital of 10%, a tax rate of
34%, and expected earnings before interest and taxes of $1,600. The company has
$3,000 in bonds outstanding that have an 8% coupon and pay interest annually.
The bonds are selling at par value. What is the cost of equity?
VU = [EBIT  (1  Tc)]  RU = [$1,600  (1 0.34)]  0.10 = $10,560
VL = VU + (Tc  D) = $10,560 + (0.34  $3,000) = $11,580
VL  VD = VE = $11,580  $3,000 = $8,580
RE = RU + (RU  RD)  D/E  (1  TC) =
0.10 + [(0.10  0.08)  ($3,000  $8,580)  (1  0.34)] = 0.10 + .00462 =
0.10462 = 10.46%
6.
A firm has a debt-to-equity ratio of 1. Its cost of equity is 16%, and its cost of
debt is 8%. If the corporate tax rate is 25%, what would its cost of equity be if the
debt-to-equity ratio were 0?
RE
0.16
0.16
0.22
Ra
=
=
=
=
=
Ra + (D/E) * (1  Tc)*(Ra  Rd )
Ra + (1) (1 - .25) (Ra - 0.08)
Ra + 0.75 Ra – 0.06
1.75 Ra
12.57%
With no debt in the capital structure the WACC = RE
Use the following to answer questions 7 & 8
Earn and Learn Company is financed entirely by common stock, which is priced
to offer a 20% expected rate of return. The stock price is $60 and the earnings per
share are $12.
7.
If the company repurchases 50% of the stock and substitutes an equal value of
debt yielding 8%, what is the expected earnings per share value after refinancing?
Because we don’t have the total number of shares we do everything on a per
share bases.
Half of each share is converted to debt with an interest rate of 8%.
Interest per share will be = 60*0.5*0.08 = $2.40
Now the new EPS will be the old EPS minus the interest per share, as debt
holders are paid before equity holders.
However, there are now only half of the original shares outstanding. So:
EPS = [12-2.4]/0.5 = $19.20
Aside, think of it like this is, if the company simply removed half their shares
outstanding (reverse stock split) then what would happen to the EPS? It would
double, because earnings are unaffected, but they are being spread over half as
many shares.
Because the company issued debt to buy back the equity, this is only half the
story, because the debt holders want to be paid, and get paid first. So we have to
take off what we pay the debt holders from the EPS.
8.
Suppose that before refinancing, an investor owned 100 shares of Earn and Learn
common stock. What should he do if he wishes to ensure that risk and expected
return on his investment are unaffected by refinancing? Assume that share price
doesn’t change.
Before equity offered a 20% return, now it’s offering a higher return.
19.2/60 = 0.32 = 32%
However, our investor wants to keep his 20% return, and the only
investment opportunities are equity with a 32% return and debt with an 8%.
Therefore we need to create a portfolio of the two assets.
0.2 = We * 0.32 + Wd * 0.08
We know that We + Wd = 1 so can sub in for Wd
0.2 = We * 0.32 + (1 - We) * 0.08
0.2 = 0.32W + 0.08 – 0.08W
0.12 = 0.24W
W= 0.5
So half of our portfolio is in equity, the other is in debt. The total size of the
portfolio is 60*100 = 6,000 → 3,000 in equity and 3,000 in debt
So we sell off 50 shares and buy 3,000 worth of debt.
9.
Given the following information, leverage will add how much value to the
unlevered firm per dollar of debt?
Corporate tax rate: 34%
Personal tax rate on income from bonds: 40%
Personal tax rate on income from stocks: 40%
[1-((1-TC)(1-TpE)/(1-Tp))]D =
[1-((0.66)(0.6)/0.6]D =
0.34D
$0.34