Problem Set
PROBLEM SET: Valuation
Exercise 1.
Amarindo [15]
Amarindo, Inc. (AMR), is a newly public rm with 10 million shares outstanding. You are doing a valuation
analysis of AMR. You estimate its free cash ow in the coming year to be $15 million, and you expect the rm's
free cash ows to grow by 4% per year in subsequent years. Because the rm has only been listed on the stock
exchange for a short time, you do not have an accurate assessment of AMR's equity beta. However, you do have
beta data for UAL, another rm in the same industry:
Equity Beta Debt Beta Debt/Equity Ratio
UAL
1.5
0.30
1
AMR has a much lower debt-equity ratio of 0.30, which is expected to remain stable, and its debt is risk free.
AMR's corporate tax rate is 40%, the risk-free rate is 5%, and the expected return on the market portfolio is
11%.
1. Estimate AMR's equity cost of capital.
2. Estimate AMR's share price.
Exercise 2.
PG [10]
Prokter and Gramble (PG) has historically maintained a debt-equity ratio of approximately 0.20. Its current stock
price is $50 per share, with 2.5 billion shares outstanding. The rm enjoys very stable demand for its products,
and consequently it has a low equity beta of 0.50 and can borrow at 4.20%, just 20 basis points over the risk free
rate of 4%. The expected return on the market is 10%, and PG's tax rate is 35%.
(a) This year, PG is expected to have free cash ows of $6.0 billion. What constant expected growth rate of
free cash ow is consistent with its current stock price?
Exercise 3.
Markum
You are a consultant who was hired to evaluate a new product line for Markum Enterprises. The upfront investment
required to launch the product line is $10 million. The product will generate free cash ow of $750,000 the rst
year, and this free cash ow is expected to grow at a rate of 4% per year. Markum has an equity cost of capital
of 11.3%, a debt cost of capital of 5%, and a tax rate of 35%. Markum maintains a debt-equity ratio of 0.40.
1. What is the NPV of the new product line (including any tax shields from leverage)?
2. How much debt will Markum initially take on as a result of launching this product line?
3. How much of the product line's value is attributable to the present value of interest tax shields?
Exercise 4.
Which of the following methods are used in capital budgeting decisions?
A) Weighted average cost of capital (WACC) method
B) Adjusted present value (APV) method
C) Flow-to-equity (FTE) method
D) All of the above are used in capital budgeting decisions.
1
Exercise 5.
Section: 18.2 The Weighted Average Cost of Capital Method
Skill: Conceptual
2) Which of the following statements is FALSE?
A) The WACC can be used throughout the rm as the company wide cost of capital for new investments that
are of comparable risk to the rest of the rm and that will not alter the rm's debt-equity ratio.
B) A disadvantage of the WACC method is that you need to know how the rm's leverage policy is implemented
to make the capital budgeting decision.
C) The intuition for the WACC method is that the rm's weighted average cost of capital represents the average
return the rm must pay to its investors (both debt and equity holders) on an after-tax basis.
D) To be protable, a project should generate an expected return of at least the rm's weighted average cost of
capital.
Exercise 6.
Consider the following equation:
W ACC =
D
E
rD (1 − τ ) +
rE
D+E
D+E
the term rE in this equation is:
A the after-tax required rate of return on debt.
B the required rate of return on debt.
C the required rate of return on equity.
D the dollar amount of equity.
Exercise 7.
Consider the information for the following four rms:
Firm
Eenie
Meenie
Minie
Moe
Cash
$0
$0
$25
$50
Debt
$150
$250
$175
$350
Equity
$150
$750
$325
$150
rD
5%
6%
6%
7.50%
rE
10%
12%
11%
15%
τc
21%
21%
21%
21%
13) The weighted average cost of capital for "Moe" is closest to:
A) 10.00%.
B) 7.75%.
C) 8.25%.
D) 9.00%.
Exercise 8.
Section: 18.2 The Weighted Average Cost of Capital Method
Skill: Analytical
24) Suppose Luther Industries is considering divesting one of its product lines. The product line is expected to
generate free cash ows of $2 million per year, growing at a rate of 3% per year. Luther has an equity cost of
2
capital of 10%, a debt cost of capital of 7%, a corporate tax rate of 21%, and a debt-equity ratio of 2. If this
product line is of average risk and Luther plans to maintain a constant debt-equity ratio, what after-tax amount
must it receive for the product line in order for the divestiture to be protable?
Exercise 9.
The Aardvark Corporation is considering launching a new product and is trying to determine an appropriate
discount rate for evaluating this new product. Aardvark has identied the following information for three single
division rms that oer products similar to the one Aardvark is interested in launching:
Comparable Firm
Anteater Enterprises
Armadillo Industries
Antelope Inc.
Equity Cost of Capital
Debt Cost of Capital
12.50%
13%
14%
6.50%
6.10%
7.10%
Debt-to-Value Ratio
50%
40%
60%
The unlevered cost of capital for Antelope Incorporated is closest to:
A) 10.3%.
B) 9.9%.
C) 10.1%.
D) 9.5%.
Exercise 10.
UA [4]
UtilityAnalysis is examining a major new venture. The rm has provided you with the following estimates: the
risk free rate is 7.5%, which is also the costs of debt for Utility; the tax rate is 40%; the beta of the rm's equity
is 1, the expected return on the market portfolio is 16%, and the proportion of debt in the capital structure is
10%. The new venture requires an outlay of $1,800, and will produce after-tax operating cash inows of $550 for
each of 5 years.
1. Determine whether the rm should make the investment.
3
Solutions
PROBLEM SET: Valuation
Solution to Exercise 1.
Amarindo [15]
1. UAL Asset beta = (1/2) 1.5 + (1/2) 0.3 = 0.90
We can use this for AMR's asset beta.
To derive the equity beta, since AMR's debt is risk free we have
Equity Beta = Asset Beta
(1 + D/E) = 0.9 × 1.30 = 1.17.
From the SML
re = 5% + 1.17(11% − 5%) = 12.02%.
Alternatively, given an asset or unlevered beta of 0.90 for AMR, we have (from SML):
ru = 5% + 0.90(11% − 5%) = 10.4%.
Then we can solve for r e
re = 10.4% + 0.30(10.4% − 5%) = 12.02%.
b. Since D / E ratio is stable, we can value AMR using the WACC approach.
W ACC = (1/1.3)12.02% + (.3/1.3)5%(1 − 40%) = 9.94%
Levered value of AMR (as a constant growth perpetuity):
D+E =VL =
15
F CF
=
= $252.52million
(rwacc − g)
(9.94% − 4%)
E = (E/(D + E))V L = 252.52/1.3 = $194.25million
Share price = 194.25 / 10 = $19.43
Solution to Exercise 2.
PG [10]
The growth rate
g
is calculated from
V = Firm
where
F CF F1
are the freee cash ows to the rm,
Current value of equity:
E = 50 × 2.5
billion
=
r
Value
=
the WACC
F CF F1
r−g
and g the
growth rate.
125 billion.
Given a debt/equity ratio of 0.2
D
D
= 0.2 =
= 0.2
E
125
D = 0.2 × 125 = 25
V = 25 + 125 = 150
rE = 0.04 + 0.5(0.10 − 0.04) = 7%
rD = 0.042
25
125
W ACC =
0.042 · (1 − 0.35) +
0.07 ≈ 0.0629
25 + 125
150
There is an ambiguity in the way the FCF this year is specied. Since it is expected, most reasonable to set 6 as
150 =
6
0.0629 − g
4
F CF1
6
= 0.0629 − g
150
g = 0.0629 − 0.0375 = 0.0258 = 2.58%
Alternatively, one can assume that 6 is the current year's FCF (F CF0 ), in which case you would calculate
F CF1 =
F CF0 (1 + g).
6(1 + g)
0.0629 − g
150 × W ACC − 6
g=
= 2.2%
150 + 6
150 =
Either of those are possible answers.
Solution to Exercise 3.
Markum
1. Find NPV
W ACC = (1/1.4)(11.3%) + (.4/1.4)(5%)(1 − 0.35) = 9%
VL
= 0.75 / ( 9 % - 4 %) = $15 million
NPV = 10 + 15 = $5 million
2. Debt b. Debt-to-Value ratio is (0.4) / (1.4) = 28.57%.
Therefore Debt is 28.57%
Ö $15 million = $4.29 million.
3. Tax Shields:
u
u
Discounting at r gives unlevered value. r = ( 1 / 1.4 ) 11.3 % + ( .4 / 1.4 ) 5 % = 9.5 %
u
V = 0.75 / ( 9.5 % - 4 %) = $13.64 million
Tax shield value is therefore 15 13.64 = 1.36 million.
Alternatively, initial debt is $4.29 million, for a tax shield in the rst year of 4.29
Ö 5% Ö 0.35 = 0.075 million.
Then PV(ITS) = 0.075 / (9.5% 4%) = 1.36 million.
Solution to Exercise 4.
Answer: D
Di: 1
Solution to Exercise 5.
Answer: B
Explanation:
An advantage of the WACC method is that you do not need to know how the rm's leverage policy is
implemented to make the capital budgeting decision.
Di: 1
Solution to Exercise 6.
Answer: C
Di: 1
Solution to Exercise 7.
Answer: D
Explanation:
rwacc = rE + rD (1 - τ c ), where D = Net Debt = Debt - Cash
Firm
Cash
Debt
Equity
rD
rE
τc
Eenie
$0
$150
$150
5%
10%
21%
6.98%
Meenie
$0
$250
$750
6%
12%
21%
10.19%
Minie
$25
$175
$325
6%
11%
21%
9.02%
Moe
$50
$350
$150
7.50%
15%
21%
8.95%
5
Wacc
Di: 2
Solution to Exercise 8.
Answer:
rwacc = (.10) + (.07)(1 - .21) = .07020
=
= $49.751 million
Di: 2
Solution to Exercise 9.
Answer: B
Explanation:
rU = rE + rD
rU
Comparable Firm
Equity Cost of Capital
Debt Cost of Capital
Debt-to-Value Ratio
Anteater Enterprises
12.50%
6.50%
50%
9.50%
Armadillo Industries
13%
6.10%
40%
10.24%
Antelope Inc.
14%
7.10%
60%
9.86%
Di: 1
Solution to Exercise 10.
UA [4]
Need to calculate WACC:
W ACC =
D
E
(1 − τ )rD +
rE
D+E
E+D
Here
rD = 0.075
rE = 0.075 + 1(0.16 − 0.075) = 0.16
90
10
(1 − 0.4)0.075 +
0.16 = 0.1485
W ACC =
100
100
t
0
1
2
3
4
5
N P V = −1800 +
Ct
−1800
550
550
550
550
550
550
550
550
550
550
+
+
+
+
= 50.2522
(1 + 0.1485)1
(1 + 0.1485)2
(1 + 0.1485)3
(1 + 0.1485)4
(1 + 0.1485)5
6