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```Tutorial 7: Capital Budgeting and Valuation with Leverage
Discussion:
Summary of the WACC Method
1. Determine the free cash flow of the investment.
2. Compute the weighted average cost of capital.
3. Compute the value of the investment, including the tax benefit of leverage, by
discounting the free cash flow of the investment using the WACC.
•
The WACC can be used throughout the firm as the companywide cost of capital for
new investments that are of comparable risk to the rest of the firm and that will not
alter the firm’s debt-equity ratio.
Summary of the APV Method
1. Determine the investment’s value
without leverage.
2. Determine the present value of the interest tax shield.
a. Determine the expected interest tax shield.
b. Discount the interest tax shield.
3. Add the unlevered value to the present value of the interest tax shield to determine the
value of the investment with leverage.
•
The APV method has some advantages.
– It can be easier to apply than the WACC method when the firm does not
maintain a constant debt-equity ratio.
– The APV approach also explicitly values market imperfections and therefore
allows managers to measure their contribution to value.
Summary of the Flow-to-Equity Method
1. Determine the free cash flow to equity of
the investment.
2. Determine the equity cost of capital.
3. Compute the equity value by discounting the free cash flow to equity using the equity
cost of capital.
•
The FTE method offers some advantages.
– It may be simpler to use when calculating the value of equity for the entire
firm if the firm’s capital structure is complex and the market values of other
securities in the firm’s capital structure are not known.
– It may be viewed as a more transparent method for discussing a project’s
benefit to shareholders by emphasizing a project’s implication for equity.
•
The FTE method has a disadvantage.
– One must compute the project’s debt capacity to determine the interest and net
borrowing before capital budgeting decisions can be made.
1. Explain whether each of the following projects is likely to have risk similar to the
average risk of the firm.
a. The Clorox Company considers launching a new version of Armor All designed to
clean and protect notebook computers.
b. Google, Inc., plans to purchase real estate to expand its headquarters.
c. Target Corporation decides to expand the number of stores it has in the southeastern
United States.
d. GE decides to open a new Universal Studios theme park in China.
a. While there may be some differences, the market risk of the cash flows from this
new product is likely to be similar to Clorox’s other household products. Therefore,
it is reasonable to assume it has the same risk as the average risk of the firm.
b. A real estate investment likely has very different market risk than Google’s other
investments in Internet search technology and advertising. It would not be
appropriate to assume this investment has risk equal to the average risk of the firm.
c. An expansion in the same line of business is likely to have risk equal to the average
d. The theme park will likely be sensitive to the growth of the Chinese economy. Its
market risk may be very different from GE’s other divisions, and from the company
as a whole. It would not be appropriate to assume this investment has risk equal to
the average risk of the firm.
2. Suppose Caterpillar, Inc., has 666 million shares outstanding with a share price of
\$73.09 and \$24.41 billion in debt. If in three years, Caterpillar has 709 million shares
outstanding trading for \$86.62 per share, how much debt will Caterpillar have if it
maintains a constant debt-equity ratio?
E = 666 million × \$73.09 = \$48.678 billion, D = \$24.41 billion, D/E = 24.41/48.678 =
0.501.
E = 709 million × \$86.62 = \$61.41 billion. Constant D/E implies D = 61.41 × 0.501 =
\$30.766 billion.
3. In 2015, Intel Corporation had a market capitalization of \$134 billion, debt of \$13.2
billion, cash of \$13.8 billion, and EBIT of nearly \$16 billion. If Intel were to increase
its debt by \$1 billion and use the cash for a share repurchase, which market
imperfections would be most relevant for understanding the consequence for Intel’s
value? Why?
Intel’s debt is a tiny fraction of its total value. Indeed, Intel has more cash than debt, so
its net debt is negative. Intel is also very profitable; at an interest rate of 6%, interest on
Intel’s debt is only \$792 million per year, which is around 4.95% of its EBIT. Thus, the
risk that Intel will default on its debt is extremely small. This risk will remain extremely
small even if Intel borrows an additional \$1 billion. Thus, adding debt will not really
change the likelihood of financial distress for Intel (which is nearly zero), and thus will
also not lead to agency conflicts. As a result, the most important financial friction for
such a debt increase is the tax savings Intel would receive from the interest tax shield.
A secondary issue may be the signaling impact of the transaction—borrowing to do a
share repurchase is usually interpreted as a positive signal that management may view
the shares to be underpriced.
4. Backcountry Adventures is a Colorado-based outdoor travel agent that operates a series
of winter backcountry huts. Currently, the value of the firm (debt + equity) is \$3.5
million. But profits will depend on the amount of snowfall: If it is a good year, the firm
will be worth \$5 million, and if it is a bad year it will be worth \$2.5 million. Suppose
managers always keep the debt to equity ratio of the firm at 25%, and the debt is
riskless.
a. What is the initial amount of debt?
b. Calculate the percentage change in the value of the firm, its equity and its debt once
the level of snowfall is revealed, but before the firm adjusts the debt level to achieve
its target debt to equity ratio.
c. Calculate the percentage change in the value of outstanding debt once the firm
adjusts to its target debt-equity ratio.
d. What does this imply about the riskiness of the firm’s tax shields? Explain.
a. Initially the firm’s debt is \$0.7 million, and the equity is \$2.8 million.
b. Before recapitalization, the value of debt remains constant so
% change in Firm
value
Good state (5 – 3.5)/3.5=42.86%
(2.5 – 3.5)/3.5= –
28.57%
% change in
Equity value
(4.3 –
2.8)/2.8=53.57%
(1.8 – 2.8)/2.8= –
35.71%
% change in
Debt value
0%
0%
c. After the recapitalization, the debt-equity ratio is reset to 25% implying
% change in Firm
value
% change in
Equity value
% change in Debt
value
Good
state
(5 – 3.5)/3.5=42.86%
(4 – 2.8)/2.8=42.86%
(1 – 0.7)/0.7=42.86%
(2.5 – 3.5)/3.5= –
28.57%
(2 – 2.8)/2.8= –
28.57%
(0.5 – 0.7)/0.7= –
28.57%
d. Because the debt is riskless, the only risk to the tax shields is the amount of
outstanding debt. This risk is identical to the risk of the firm as a whole, so the
riskiness of the tax shields are identical to the riskiness the firm as a whole.
5. Suppose Goodyear Tire and Rubber Company is considering divesting one of its
manufacturing plants. The plant is expected to generate free cash flows of \$1.69 million
per year, growing at a rate of 2.6% per year. Goodyear has an equity cost of capital of
8.5%, a debt cost of capital of 7.1%, a marginal corporate tax rate of 33%, and a debtequity ratio of 2.4. If the plant has average risk and Goodyear plans to maintain a
constant debt-equity ratio, what after-tax amount must it receive for the plant for the
divestiture to be profitable?
We can compute the levered value of the plant using the WACC method. Goodyear’s
WACC is
rwacc 
1
2.4
8.5% 
7.1%(1  0.33)  0.025  0.034  0.059  5.9%.
1  2.4
1  2.4
Therefore, V L 
1.69
 \$51.21 million
0.059  0.026
A divestiture would be profitable if Goodyear received more than \$51.21 million after
tax.
6. Suppose Alcatel-Lucent has an equity cost of capital of 9.4%, market capitalization of
\$9.49 billion, and an enterprise value of \$13 billion. Suppose Alcatel-Lucent’s debt cost
of capital is 7.1% and its marginal tax rate is 35%.
a. What is Alcatel-Lucent’s WACC?
b. If Alcatel-Lucent maintains a constant debt-equity ratio, what is the value of a
project with average risk and the following expected free cash flows?
c. If Alcatel-Lucent maintains its debt-equity ratio, what is the debt capacity of the
project in part b?
a. rwacc 
9.49
13  9.49
9.4% 
7.1%(1  0.35)  0.0686  0.0125  0.0811  8.11%
13
13
b. Using the WACC method, the levered value of the project at date 0 is
VL 
52
100
65


 48.10  85.56  51.44  185.1.
2
1.0811 1.0811 1.08113
Given a cost of 100 to initiate, the project’s NPV is 185.1 – 100 = 85.1.
c. Alcatel-Lucent’s debt-to-value ratio is d = (13 – 9.49) / 13 = 0.27. The project’s
debt capacity is equal to d times the levered value of its remaining cash flows at
each date.
Year
FCF
VL
D = d*VL
0
–100
185.11
49.98
1
52
148.12
39.99
2
100
60.13
16.23
3
65
0
0.00
7. Acort Industries has 10 million shares outstanding and a current share price of \$36 per
share. It also has long-term debt outstanding. This debt is risk free, is four years away
from maturity, has annual coupons with a coupon rate of 10%, and has a \$115 million
face value. The first of the remaining coupon payments will be due in exactly one year.
The riskless interest rates for all maturities are constant at 6%. Acort has EBIT of \$101
million, which is expected to remain constant each year. New capital expenditures are
expected to equal depreciation and equal \$18 million per year, while no changes to net
working capital are expected in the future. The corporate tax rate is 42%, and Acort is
expected to keep its debt-equity ratio constant in the future (by either issuing additional
new debt or buying back some debt as time goes on).
a. Based on this information, estimate Acort’s WACC.
b. What is Acort’s equity cost of capital?
a. We don’t know Acort’s equity cost of capital, so we cannot calculate WACC
directly. However, we can compute it indirectly by estimating the discount rate that
is consistent with Acort’s market value. First, E = 10 × 36 = \$360 million. The
market value of Acort’s debt is
D  11.5 
1 
1  115
 39.85  91.09  \$130.94 million.
1 

0.06  1.064  1.064
Therefore, Acort’s enterprise value is E + D = 360 + 130.94 = 490.94.
Acort’s
FCF = EBIT × (1 –  C ) + Dep – Capex – Inc in NWC
FCF = 101 × (1 – 0.42) = 58.58
Because Acort is not expected to grow,
V L  490.94 
b. Using rwacc 
58.58
58.58
 11.93%.
and so rwacc 
490.94
rwacc
E
D
rE 
rD (1  c ) ,
ED
DE
11.93% 
360
130.94
rE 
6%(1  0.42)
490.94
490.94
solving for rE:
rE 
490.94 
130.94

11.93% 
6%(1  0.42)   15%.
360 
490.94

8. Suppose Goodyear Tire and Rubber Company has an equity cost of capital of 8.5%, a
debt cost of capital of 7.1%, a marginal corporate tax rate of 33%, and a debt-equity
ratio of 2.4. Assume that Goodyear maintains a constant debt-equity ratio.
a. What is Goodyear’s WACC?
b. What is Goodyear’s unlevered cost of capital?
c. Explain, intuitively, why Goodyear’s unlevered cost of capital is less than its equity
cost of capital and higher than its WACC.
a. rwacc 
1
2.4
8.5% 
7.1%(1  0.33)  0.025  0.034  0.059  5.9%
1  2.4
1  2.4
b. Because Goodyear maintains a target leverage ratio, we can use Eq. 18.6:
rU 
1
2.4
8.5% 
7.1%  7.51%.
1  2.4
1  2.4
c. Goodyear’s equity cost of capital exceeds its unlevered cost of capital because
leverage makes equity riskier than the overall firm. Goodyear’s WACC is less than
its unlevered cost of capital because the WACC includes the benefit of the interest
tax shield.
9. You are a consultant who has been hired to evaluate a new product line for Markum
Enterprises. The upfront investment required to launch the product is \$6 million. The
product will generate free cash flow of \$700,000 the first year, and this free cash flow
is expected to grow at a rate of 6% per year. Markum has an equity cost of capital of
11.3%, a debt cost of capital of 6.28%, and a tax rate of 32%. Markum maintains a debtequity ratio of 0.70.
a. What is the NPV of the new product line (including any tax shields from leverage)?
b. How much debt will Markum initially take on as a result of launching this product
line?
c. How much of the product line’s value is attributable to the present value of interest
tax shields?
a. WACC = (1 / 1.7)(11.3%) + (0.7 / 1.7)(6.28%)(1 – .32) = 8.41%
VL  0.700 8.41  6 \$29.05 million
NPV = –6 + 29.05 = \$23.05 million
b. Debt-to-Value ratio is (0.7) / (1.7) = 41.18%.
Therefore Debt is 41.18% × \$29.05 million = \$11.96 million.
c. Discounting at ru gives unlevered value. ru  1 1.711.3  .7 1.76.28 
9.233
Vu  0.700 9.233  6  \$21.65 million
Tax shield value is therefore 29.05 – 21.65 = 7.4 million.
Alternatively, initial debt is \$11.96 million, for a tax shield in the first year of 11.96
× 6.28% × 0.32 = 0.2403 million. Then PV(ITS) = 0.2403 / (9.233% – 6%) = 7.4
million.
10. Consider Alcatel-Lucent’s project in Problem 6.
a. What is Alcatel-Lucent’s unlevered cost of capital?
b. What is the unlevered value of the project?
c. What are the interest tax shields from the project? What is their present value?
d. Show that the APV of Alcatel-Lucent’s project matches the value computed using
the WACC method.
a. rU 
9.49
13  9.49
9.4% 
7.1%  8.78%
13
13
b. V U 
52
100
65


 182.81
1.0878 1.08782 1.08783
c. Using the results from problem 6(c):
Year
FCF
VL
D = d*VL
Interest
Tax Shield
0
–100
182.81
49.36
1
52
146.86
39.65
3.50
1.23
2
100
59.75
16.13
2.82
0.99
The present value of the interest tax shield is
PV(ITS) 
1.23
0.99
0.40


 2.28
2
1.0878 1.0878 1.08783
d. VL  APV  182.81  2.28  185.10
This matches the answer in problem 6.
11. Consider Alcatel-Lucent’s project in Problem 6.
a. What is the free cash flow to equity for this project?
3
65
0
0.00
1.15
0.40
b. What is its NPV computed using the FTE method? How does it compare with the
NPV based on the WACC method?
a. Using the debt capacity calculated in problem 6, we can compute FCFE by adjusting
FCF for after-tax interest expense (D  rD  (1 – tc)) and net increases in debt (Dt –
Dt – 1).
Year
D
FCF
After-tax Interest Exp.
Inc. in Debt
FCFE
b. NPV  50.64 
0
49.36
1
39.65
2
16.13
3
0.00
-\$100.00
\$0.00
\$49.36
-\$50.64
\$52.00
-\$2.28
-\$9.71
\$40.02
\$100.00
-\$1.83
-\$23.52
\$74.65
\$65.00
-\$0.74
-\$16.13
\$48.12
40.02 74.65 48.12


 \$85.10
1.094 1.0942 1.0943
```
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