Answers and Solutions: 21 – 1
Chapter 21
Dynamic Capital Structures and Corporate Valuation
21-1 a. An interest tax shield is the amount of cash flow that is sheltered from taxation due to
the tax deductibility of interest. It is equal to rd(D)(T).
If growth is constant, then the value of the tax shield is rdTD(1+gL)/(rTS − gL).
where rd is the interest rate on the debt and rTS is the discount rate for the tax shield.
cost of equity to determine the value of operations. It is called the compressed APV
because the FCF and tax shields are discounted at the same rate.
21-2 The value of a growing tax shield is greater than the value of a constant tax shield.
This means that for a given initial level of debt a growing firm will have more value
Answers and Solutions: 21 – 2
SOLUTIONS TO END-OF-CHAPTER PROBLEMS
21-3 VL = VU +
)g
sU
r(
)
c
T)(D(
d
r
= $800 +
)03.011.0(
)35.0)(60(05.0
21-4 a. bL = bU[1 + (1 − T)(D/S)].
bU =
)S/D)(T1(1
bL
=
)5.0/5.0)(4.01(1
8.1
=
6.1
8.1
= 1.125.
Answers and Solutions: 21 – 3
c. $2 Million Debt: VL = VU + TD = $10 + 0.25($2) = $10.5 million.
rsL = rsU + (rsU − rRF)(1 − T)(D/S)
= 15.625% + (15.625% − 10%)(0.75)($2/$8.5)
= 15.625 + 5.625% (0.75)($2/$8.5) = 16.62%.
The mathematics of MM result in the required return, and, thus, the same financial
risk premium. However, the market value debt ratio has increased from $6/$11.5 =
52% to $6/$10.4 = 58% at the higher tax rate. Hence, a higher tax rate reduces the
financial risk premium at a given market value debt/equity ratio. This is because a
)T1(EBIT
rsL = rsU + (rsU – rd)(1 – T)(D/S)
c. SL =
sL
d
r
)T1)(DrEBIT(
=
15.0
6.0)]10($05.02[$
= $6 million.
VL = SL + D = $6 + $10 = $16 million.
WACCL = (D/V)rd(1 – T) + (S/V)rs = ($10/$16)5%(0.6) + ($6/$16)15%
= 7.50%.
21-6 a. VU = $500,000/(rsU – g) = $500,000/(0.13 – 0.09) = 12,500,000.
million 5x 0.40x 0.07
)07.1( 40$
522.10 753.33
$563.29
c. TS = (Interest expense)(T)
07.013.0
$57.86
e. Total valuet=0 = $563.29 + $57.86 = $621.15.
website, in whole or in part.
SOLUTION TO SPREADSHEET PROBLEM
21-8 The detailed solution for the problem is available in the file Ch21 P08 Build a Model
Solution.xlsx on the textbook’s Web site.
Mini Case: 21 – 7
MINI CASE
David Lyons, CEO of Lyons Solar Technologies, is concerned about his firm’s level of debt
financing. The company uses short-term debt to finance its temporary working capital
needs, but it does not use any permanent (long-term) debt. Other solar technology
companies average about 30 percent debt, and Mr. Lyons wonders why they use so much
more debt, and what its effects are on stock prices. To gain some insights into the matter,
he poses the following questions to you, his recently hired assistant:
a. Who were Modigliani and Miller (MM), and what assumptions are embedded in
the MM and Miller models?
Answer: Modigliani and Miller (MM) published their first paper on capital structure (which
assumed zero taxes) in 1958, and they added corporate taxes in their 1963 paper.
Mini Case: 21 – 8
b. Assume that firms U and L are in the same risk class, and that both have EBIT =
$500,000. Firm U uses no debt financing, and its cost of equity is rsU = 14%.
Firm L has $1 million of debt outstanding at a cost of rd = 8%. There are no
taxes. Assume that the MM assumptions hold, and then:
1. Find v, s, rs, and WACC for firms U and L.
Answer: First, we find Vu and VL:
VU =
sU
r
EBIT
=
14.0
000,500$
= $3,571,429.
VL = VU = $3,571,429.
To find rsL, it is necessary first to find the market values of firm L’s debt and equity.
The value of its debt is stated to be $1,000,000. Therefore, we can find s as follows:
D + SL = VL
SL = VL – D = $3,571,429 – $1,000,000 = $2,571,429.
Now we can find L’s cost of equity, rsL:
rsL = rsU + (rsU – rd)(D/S)
= 14.0% + (14.0% – 8.0%)($1,000,000/$2,571,429)
= 14.0% + 2.33% = 16.33%.
We know from Proposition I that the WACC must be WACC = rsU = 14.0% for all
firms in this risk class, regardless of leverage, but this can be verified using the
WACC formula:
WACC = wdrd + wcers = (D/V)rd + (S/V)rs
= ($1,000/$3,571)(8.0%) + ($2,571/$3,571)(16.33%)
= 2.24% + 11.76% = 14.0%.