Cashman
Capital Structure
1.MacroHard has 10 million shares outstanding each selling at $22.50 per share. The
market value of debt represents 30% of the firm’s capital structure and the yield to
maturity on debt is 12%. The corporate tax rate is 30%.
a) What is the market value of equity, the market value of debt, and the market value of
the whole firm?
MV(E) = 225 million
MV(D) = .3(V) → MV(E) = .7(V)
225 = .7(V) → V = 225/0.7
V = 321.43
So MV(D) =.3(321.43)
MV(D) = 96.43
b) Assume the firm’s levered cost of equity is 16%. What is the firm’s weighted average
cost of capital (WACC)?
D
E
rD 1  Tc  
rE
DE
DE
96.43
225

0.121  .3 
0.16
321.43
321.4
 0.0252  0.112
rW ACC 
rW ACC
rW ACC
rW ACC  13.72%
c) Assume the firm’s levered cost of equity is 16%. What would the firm’s weighted
average cost of capital (WACC) be if it were all-equity financed? Explain why the allequity cost of capital is the same, higher, or lower than the levered firm’s weighted
average cost of capital.
D
rE  rA  (rA  rD )(1  TC )
E
96.43
(rA  0.12)(1  0.3)
225
0.16  rA  0.4285778(rA  0.12)(0.7) Lower as we are decreasing the risk to
shareholders
0.16  rA  0.30000444(rA  0.12)
0.16  rA 
0.16  1.30000444rA  0.036
0.196  1.30000444rA
rA  15.10%
2. Slo Co. currently has an equity beta of 2.84, is financed with 10% debt (and 90%
equity) and has a total firm value of $10 billion. Slo’s CFO thinks that they should
increase the firm’s leverage by issuing $2 billion of debt and buying back $2 billion of
equity. This debt will be perpetual and have yield of 7%. The expected return on the
market is 13% and the risk free rate is 3%. Slo has a 35% tax rate. What is Slo’s value
after the swap, and how much of that value will be equity?
Increase value = PV(Tax Shields)
= 0.35*(2 billion)
= .7 billion (or 700 million)
So, the balance sheet is
Before swap
D= 1
E= 9
V=10
Therefore, E must equal V-D = 7.7.
After swap:
D=3
E=?
V=10.7 (Old value of 10 + .7 PV of tax shields)
3. Pages.com is a publishing company, with an equity beta of 1 and a debt-to-equity
ratio of 1. The firm is considering a new line of business, making movies of its books.
They have found a company – Films, Inc. – that only makes movies, has a debt-to-equity
ratio of 2 and an equity beta of 1.8. Films, Inc. has zero-coupon bonds outstanding, which
trade at 400 (face value of 1,000) and have 10 years remaining to maturity. Pages.com
believes it can borrow at a similar cost to that of Films, Inc. The risk free rate is 6%, and
the market risk premium is 6%, what discount rate should Pages.com use on its movie
projects (assuming they maintain their current capital structure)? The tax rate is 40%.
We need to find the assets beta of Films, so first we need to find Film’s debt beta
N = 10; I/Y = ? ; PV = 400; PMT = 0; FV = 1,000
I/Y = 9.596%
0.09596 = 0.06 + Beta Debt * 0.06
0.03596 = Beta Debt * 0.06
Beta Debt = 0.59933
Now we need to find Film’s asset beta
Beta equity
= Beta Assets + (D/E*)(Beta Assets – Beta Debt)*(1-Tc)
1.8
= Beta Assets + (2) (Beta Asset – 0.59933) (1-0.4)
1.8
= Beta Assets + 1.2*(Beta Assets -0.59933)
1.8
= Beta Assets + 1.2*Beta Assets – 0.7192
2.5192 = 2.2*Beta Assets
Beta Assets = 1.145
This 1.145 represents the systematic risk of the making movies, however if Pages
expands into this area it will have to account for its own level of financial risk so
Beta equity
= Beta Assets + (D/E*)(Beta Assets – Beta Debt)*(1-Tc)
Beta Equity
Beta Equity
Beta Equity
Beta Equity
= 1.145 + (1) (1.145 – 0.59933) (1-0.4)
= 1.145 + 0.6*(0.54567)
= 1.145 + 0.3274
= 1.4724
Cost of equity
E(R)
=0.06 + 1.4724(0.06)
E(R)
= 14.834%
Cost of debt is the same as Films: 9.596%
After tax this is 9.6(1-0.4) = 5.76
WACC = 0.5(0.0576) + 0.5(0.14834) = 10.297%
4. Suppose the risk free rate is 3%, and the expected return on the market is 8%. GM’s
market value of equity is 19.4 billion, they have 0.566 billion shares outstanding, and the
market value of debt is 219 billion. Suppose GM were to replace $25 billion of debt by
issuing $25 billion of equity (and that this swap would be in perpetuity). Assume that GM
has an equity beta of 1.3, a tax rate of 20%, and a cost of debt equal to 8%. What would
the total value of GM be after the swap?
Debt would go from 219 to 194 =219-25
The equity holders would lose the tax shield → TcD = .2(25 Bill) = 5 Billion.
So the existing equity would fall to 14.4 = 19.4 – 5.
At the same time, we’re adding $25 billion in equity, → 14.4 + 25 = 39.4
The total value of the firm would be 39.4 + 194 = 233.4.
V new = V old – PV (lost tax shields)
= 238.4 – 5 = 233.4
5. The Mandem Co., has a debt to equity ratio of .45. The firm’s required return on
unlevered equity is 17%, and the pre-tax cost of debt is 9%. Sales revenues are expected
to be $23.5 million in perpetuity and variable costs are expected to be 60% of sales. The
tax rate is 40%, and the company pays out all earnings as dividends at the end of each
year. If the company were financed only by equity, what would it be worth?
Revenues
VC @ .6
Tx @ .4
23.5
14.1
9.4
3.76
5.64 Cash flow to the unlevered firm.
Value = C/r = 5.64/.17 = 33.176
6. Your friend Toni, is interning in the CFO’s office at Frys. Shares of Frys are currently
trading at $22, and the firm has 800 million shares outstanding. Toni estimates that Frys
beta is 0.04; the current yield-to-maturity on T-Bills is 1.7%, and the market risk
premium is 9.5%. Using this information, according to the CAPM, the cost of equity for
Frys is: 1.7% + 0.04 (9.5%) = 2.08%.
Further, based on their latest balance sheet,
Frys’ long-term debt is $10 billion, and the book value of equity is $3.2 billion. The
firm’s debt is currently selling at 95% of par ($1,000) and has a yield-to-maturity of 7%.
Fry’s marginal tax rate is 35%. Toni calculates Frys’ after-tax weighted average cost of
capital as 3.95% based on the following:
E
rS   D rB 1  TC 
rW ACC 
ED
ED
3.2
0.0208  10 0.07 1  0.35
0.0395 
13.2
13.2
a)
Carefully assess Toni’s analysis leading to the WACC and identify any potential
problems with the analysis. If those problems involve a calculation, show what
calculation you would use as an alternative. (5 points)
The problem is that Toni is using book values not market values. Calculation
should be:
E = 22 * 800m = 17,600m
D = 10,000m * 0.95 = 9,500m
V = 1,760m + 9,500m = 27,100m
WACC = (17,600/27,100)*(0.0208) + (9,500/27,100)*(0.07)*(1-0.35) =
2.9459%
b)
If Fry’s were to increase their debt level, would the shareholders’ required return
change? Explain. (5 points)
The shareholders would require a higher return on their investment as the risk of
their claim on the company has increased. This makes sense as shareholders are
residuals claimants, as we increase the level of debt we are exposing them to more
risk, and thus their required return increases.