Banking Chapter 18 Homework Capital Budgeting And Valuation With Leverage Explain Whether Each The Following

Chapter 18

18–1. 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.

18–2. 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?

18–3. 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?

18-4. 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.

18-5. 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 debt-equity 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?

0.059 0.026

−

18-6. 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

18-7. 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?

L

wacc

58.58

V 490.94 r

==

and so

wacc 58.58

r 11.93%.

490.94

==

b. Using

wacc E D c

ED

r r r (1 )

E D D E

= + − 

++

,

E

360 130.94

11.93% r 6%(1 0.42)

490.94 490.94

= + −

solving for rE:

E490.94 130.94

r 11.93% 6%(1 0.42) 15%.

360 490.94



= − − =





18-8. 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.

1 2.4 1 2.4

++

b. Because Goodyear maintains a target leverage ratio, we can use Eq. 18.6:

U1 2.4

r 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.

18-9. 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 debt-equity 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?

18–10. 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.

–

2 3

1.09025 1.09025 1.09025

c. Using the results from problem 6(c):

Year 0 1 2 3

FCF –100 50 100 70

VL 185.86 151.64 64.52 0

D = d*VL 46.47 37.91 16.13 0.00

Interest 2.83 2.31 0.98

Tax Shield 0.99 0.81 0.34

The present value of the interest tax shield is

23

0.99 0.81 0.34

PV(ITS) 1.85

1.09025 1.09025 1.09025

= + + =

d. VL = APV = 184.01 + 1.85 = 185.86

This matches the answer in problem 6.

18–11. Consider Alcatel-Lucent’s project in Problem 6.

a. What is the free cash flow to equity for this project?

b. What is its NPV computed using the FTE method? How does it compare with the NPV based

on the WACC method?

Year 0 1 2 3

D46.47 37.91 16.13 0.00

FCF -$100.00 $50.00 $100.00 $70.00

After-tax Interest Exp. $0.00 -$1.84 -$1.50 -$0.64

Inc. in Debt $46.47 -$8.55 -$21.78 -$16.13

FCFE -$53.53 $39.60 $76.72 $53.23

2 3

39.60 76.72 53.23

1.10 1.10 1.10

248 Berk/DeMarzo, Corporate Finance, Fourth Edition, Global Edition

V(AMC) = $14,068 + $1,146 = $15,214.

The market value of the equity is therefore V – D = $15,214 – $5250 = $9,964.

e. Next year’s FCF is $2,100  0.58 = $1,218. It is expected to grow at 2.7%, so the WACC must

satisfy:

V(AMC)

wacc

$1,218 $15,214.

r 0.027

==

−

Solving for the WACC, we get WACC = 10.70%.

f. By definition,

( )

wacc E D c

ED

r r r 1

VV

=  +   − 

.

The return on the debt is 4.5%; the value of the debt is $5,250, the value of the firm is $15,214 and

therefore the value of the equity is $15,214 – $5,250 = $9,964. Plugging into the above expression,

we get:

( )

E

$9,964 $5,250

10.70% r 4.5% 1 0.42

$15,214 $15,214

=  +   −



E

r

= 14.965%.

g. From the CAPM,

E



must satisfy

( )

E

% 4.5% 9.9% 4.5%14.965 = + −

, so we conclude

E1.94=

.

The relationship holds since ($9,964/$15,214) × 1.94 = 1.27, and the beta of the debt equals 0.

h. The debt is expected to increase to $5,250  (1 + 0.027) = $5,391.75 so the equity holders will get

$141.75 due to the increase in debt. These proceeds will increase by 2.7% annually. (The second–

year debt will be $5,250  (1 + 0.027)² = $5,537.33, with an increase in debt of $145.58, 2.7%

higher than the $141.75 proceeds of year 1.) The expected FCF to equity at the end of the first

year is therefore EBIT – Interest – Taxes + Debt proceeds, or FCFE = (2,100 – 236.25)



(1 –

0.42) + 141.75 = $1,222.

This cash flow is expected to grow at 2.7% per year. Thus, another way to compute the value of

equity is to discount these cash flows directly at the MCR for the equity of 14.98% (from (f)):

E

FCFE 1,222

E 9,964.

r g 14.965% 2.7%

= = =

−−

This is the same value we computed in (d), using the APV.

18–13. Prokter and Gramble (PKGR) has historically maintained a debt-equity ratio of approximately

0.16. Its current stock price is $48 per share, with 2.6 billion shares outstanding. The firm enjoys

very stable demand for its products, and consequently it has a low equity beta of 0.4 and can

borrow at 4.7%, just 20 basis points over the risk-free rate of 4.5%. The expected return of the

market is 10.2%, and PKGR’s tax rate is 32%.

a. This year, PKGR is expected to have free cash flows of $5.8 billion. What constant expected

growth rate of free cash flow is consistent with its current stock price?

b. PKGR believes it can increase debt without any serious risk of distress or other costs. With a

higher debt-equity ratio of 0.4, it believes its borrowing costs will rise only slightly to 5%. If

PKGR announces that it will raise its debt-equity ratio to 0.4 through a leveraged recap,

determine the increase in the stock price that would result from the anticipated tax savings.

Chapter 18/Capital Budgeting and Valuation with Leverage 249

From CAPM: Equity Cost of Capital = 4.5% + 0.4(10% – 4.5%) = 6.7%

WACC = (124.8 / 144.77)6.7% + (19.67 / 144.77)4.7% (1 – 32%) = 6.21%

VL = FCF/(rwacc – g)  g = rwacc – FCF/V = 6.21% – 5.8/144.77 = 2.20%

b. Initial Unlevered cost of capital (Eq. 18.6) = (124.8 / 144.77)6.7% + (19.97 / 144.77)4.7% =

6.42%

New Equity cost of capital (Eq. 18.10) = 6.42% + (0.4)(6.42% – 5%) = 6.99%

New WACC = (1 / 1.4)6.99% + (0.4 / 1.4)5% (1 – 32%) = 5.96%

VL = FCF / (rwacc – g) = 5.8 / (5.96% – 2.20%) = $154.26

This is a gain of 154.26 – 144.77 = $9.49 billion or 9.49/2.6 = $3.65 per share.

Thus, share price rises to $51.65/share.

18–14. Amarindo, Inc. (AMR), is a newly public firm with 10.5 million shares outstanding. You are

doing a valuation analysis of AMR. You estimate its free cash flow in the coming year to be

$15.37 million, and you expect the firm’s free cash flows to grow by 4.4% per year in subsequent

years. Because the firm 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 firm in the same industry:

AMR has a much lower debt-equity ratio of 0.36, which is expected to remain stable, and its debt

is risk free. AMR’s corporate tax rate is 25%, the risk-free rate is 5.5%, and the expected return

on the market portfolio is 11.3%.

a. Estimate AMR’s equity cost of capital.

b. Estimate AMR’s share price.

Chapter 18/Capital Budgeting and Valuation with Leverage 251

a. Calculate the NPV of this investment opportunity using the APV method.

b. Using your answer to part a, calculate the WACC of the project.

c. Verify that you get the same answer using the WACC method to calculate NPV.

d. Finally, show that flow-to-equity also correctly gives the NPV of this investment opportunity.

18–17. Tybo Corporation adjusts its debt so that its interest expenses are 21% of its free cash flow. Tybo

is considering an expansion that will generate free cash flows of $2.16 million this year and is

expected to grow at a rate of 3.8% per year from then on. Suppose Tybo’s marginal corporate

tax rate is 40%.

a. If the unlevered cost of capital for this expansion is 10.6%, what is its unlevered value?

b. What is the levered value of the expansion?

c. If Tybo pays 5.5% interest on its debt, what amount of debt will it take on initially for the

expansion?

d. What is the debt-to-value ratio for this expansion? What is its WACC?

e. What is the levered value of the expansion using the WACC method?

254 Berk/DeMarzo, Corporate Finance, Fourth Edition, Global Edition

b. Suppose that you can finance $478 million of the cost of the plant using 10-year, 9.3%

coupon bonds sold at par. This amount is incremental new debt associated specifically with

this project and will not alter other aspects of the firm’s capital structure. What is the value

of the project, including the tax shield of the debt?

a. First we compute the FCF:

Using Eq. 7.6:

b. Because the debt level is predetermined, we can use the APV approach. Because the bonds

18-20. Parnassus Corporation plans to invest $150 million in a new generator that will produce free

cash flows of $20 million per year in perpetuity. The firm is all equity financed, with an equity

cost of capital of 10%.

a. What is the NPV of the project ignoring any costs of raising funds?

b. Suppose the firm will issue new equity to raise the $150 million, and has after-tax issuance

costs equal to 8% of the proceeds. What is the NPV of the project including these issuance

costs, assuming all future free cash flows generated by it will be paid out?

c. Suppose that instead of paying out the project’s future free cash flows, a substantial portion

of these free cash flows will be retained and invested in other projects, reducing Parnassus’

required fundraising in the future. Specifically, suppose the firm will reinvest all free cash

flows for the next 10 years, and then pay out the cash flows after that. If its issuance costs

remain constant at 8%, what is the NPV of the project including issuance costs in this case?

Chapter 18/Capital Budgeting and Valuation with Leverage 255

Thus, the NPV is now $38 + 9.8 = $47.8 million.

Note that once we adjust for the savings of future issuance costs, the net cost is only 50 – 47.8 =

$2.2 million, or 2.2/150 = 1.47% of the initial investment.

18–21. DFS Corporation is currently an all-equity firm, with assets with a market value of $155 million

and 4 million shares outstanding. DFS is considering a leveraged recapitalization to boost its

share price. The firm plans to raise a fixed amount of permanent debt (i.e., the outstanding

principal will remain constant) and use the proceeds to repurchase shares. DFS pays a 25%

corporate tax rate, so one motivation for taking on the debt is to reduce the firm’s tax liability.

However, the upfront investment banking fees associated with the recapitalization will be 1% of

the amount of debt raised. Adding leverage will also create the possibility of future financial

distress or agency costs; shown below are DFS’s estimates for different levels of debt:

a. Based on this information, which level of debt shown above is the best choice for DFS?

b. Estimate the stock price once this transaction is announced.

Debt amount ($ million)

0.00

10,00

20,00

30,00

40,00

50,00

PV of expected distress

and agency costs

0.00

−0.16

−1.81

−3.52

−7.41

−11,46

Firm value

155.00

Investment banking fees

0.00

−0.10

−0.20

−0.30

−0.40

−0,50

Debt tax shield

0.00

2.50

5.00

7.50

10.00

12,50

Net benefit:

0.00

2.24

2.99

3.68

2.19

0,54

Based on this information, the greatest net benefit occurs for debt = $30 million.

b. Value of assets goes up from $155M to $158.68.7M. Thus, the share price should rise to $39.67.

18–22. Your firm is considering a $120 million investment to launch a new product line. The project is

expected to generate a free cash flow of $20 million per year, and its unlevered cost of capital is

8%. To fund the investment, your firm will take on $72 million in permanent debt.

a. Suppose the marginal corporate tax rate is 35%. Ignoring issuance costs, what is the NPV of

the investment?

b. Suppose your firm will pay a 4% underwriting fee when issuing the debt. It will raise the

remaining $48 million by issuing equity. In addition to the 7% underwriting fee for the

equity issue, you believe that your firm’s current share price of $39 is $4 per share less than

its true value. What is the NPV of the investment including any tax benefits of leverage?

(Assume all fees are on an after-tax basis.)

18–23. Consider Avco’s RFX project from Section 18.3. Suppose that Avco is receiving government loan

guarantees that allow it to borrow at the 6% rate. Without these guarantees, Avco would pay

6.5% on its debt.

a. What is Avco’s unlevered cost of capital given its true debt cost of capital of 6.5%?

b. What is the unlevered value of the RFX project in this case? What is the present value of the

interest tax shield?

c. What is the NPV of the loan guarantees? (Hint: Because the actual loan amounts will

fluctuate with the value of the project, discount the expected interest savings at the

unlevered cost of capital.)

d. What is the levered value of the RFX project, including the interest tax shield and the NPV

of the loan guarantees?

2 3 4

1.0825 1.0825 1.0825 1.0825

c. The loan guarantee reduces the interest paid from 6.5% to 6% each year. Thus, the savings in year

0.50 0.50

8.5% (0.37) 4.8% (8.5% 4.8%) 7.76%

1.50 1.50



= − + − =





wacc u c D u D

Alternatively, from Eq. 18.17:

1

0.50 1.085

8.5% (0.37)4.8% 7.90%

1.50 1.048



+

=− +



= − =





u

wacc u c D

D

r

r r d r r

c. In case (a),

10.2 $100.88 million.

0.0791 0.022

==

+

L

V

In case (b),

10.2 $101 million.

0.0790 0.022

==

+

L

V

Note the minor difference in the two cases. Case (b) is higher because the tax shields are less risky

when debt is fixed over the year.

18–25. XL Sports is expected to generate free cash flows of $11.2 million per year. XL has permanent

debt of $35 million, a tax rate of 37%, and an unlevered cost of capital of 10.4%.

a. What is the value of XL’s equity using the APV method?

b. What is XL’s WACC? What is XL’s equity value using the WACC method?

c. If XL’s debt cost of capital is 4.6%, what is XL’s equity cost of capital?

d. What is XL’s equity value using the FTE method?

18–26. Propel Corporation plans to make a $50.2 million investment, initially funded completely with

debt. The free cash flows of the investment and Propel’s incremental debt from the project

follow:

258 Berk/DeMarzo, Corporate Finance, Fourth Edition, Global Edition

Propel’s incremental debt for the project will be paid off according to the predetermined

schedule shown. Propel’s debt cost of capital is 7.7%, and its tax rate is 35%. Propel also

estimates an unlevered cost of capital for the project of 12.2%.

a. Use the APV method to determine the levered value of the project at each date and its initial

NPV.

b. Calculate the WACC for this project at each date. How does the WACC change over time?

Why?

c. Compute the project’s NPV using the WACC method.

d. Compute the equity cost of capital for this project at each date. How does the equity cost of

capital change over time? Why?

e. Compute the project’s equity value using the FTE method. How does the initial equity value

compare with the NPV calculated in parts (a) and (c)?

Then we compute the value of the future interest tax shields at each date by discounting at rate

rD = 7.7%:

Year 0 1 2 3

D50.2 29.3 15.1 0

interest at 7.7% 3.8654 2.2561 1.1627

tax shield at 35% 1.35289 0.789635 0.406945

PV(ITS) $2.26 $1.08 $0.38

Finally, we compute VL = APV = VU + PV(ITS):

V

$68.44

$37.03

$22.21

2. The WACC fluctuates because the leverage ratio of the project changes over time (as does the

persistence of the debt).

d = D/V

L

73%

79%

68%

T

s

$2.26

$1.08

$0.38

f = T

s

/t

c

D

12.9%

10.6%

7.1%

r

wacc

10.07%

9.94%

10.29%

L

Chapter 18/Capital Budgeting and Valuation with Leverage 259

c. We can compute the levered value of the project by discounting the FCF using the WACC at each

date:

3

2

24.5 $22.21

1 (2) 1.1029

= = =

+

L

wacc

FCF

Vr

22

1

18.5 22.21 $37.03

1 (1) 1.0994

++

= = =

+

L

wacc

FCF V

Vr

11

0

38.3 37.03 $68.44.

1 (0) 1.1007

++

= = =

+

L

wacc

FCF V

Vr

Note that these results coincide with part (a).

d. We can compute the project’s equity cost of capital using Eq. 18.20. Note that Ds = D − Ts = D

− PV(ITS):

Debt net of predetermined tax

shield (Ds)

$47.94

$28.22

$14.72

Equity (E)

$18.24

$7.73

$7.11

Ds/E

2.63

3.65

2.07

Equity cost of capital (rE)

24.03%

28.62%

21.51%

Note the equity cost of capital rises and then falls with the project’s effective debt-equity ratio,

DsE.

e. We first compute FCFE at each date by deducting the after-tax interest expenses (equivalently,

deducting interest and adding back the tax shield) and adding net increases in debt:

Year

0

1

2

3

Free cash flows

50.20

38.30

18.50

24.50

Debt

50.20

29.30

15.10

0

Debt tax shield

1.35

0.79

0.41

FCFE

14.88749

2.833535

8.644245

Then, we compute the equity value of the project by discounting FCFE using rE at each date:

3

2

8.644 $7.11

1 (2) 1.2151

= = =

+E

FCFE

Er

22

1

2.8335 7.11 $7.73

1 (1) 1.2862

++

= = =

+E

FCFE E

Er

11

0

14.887 7.73 $18.24

1 (0) 1.2403

++

= = =

+E

FCFE E

Er

These values for equity match those computed earlier, and match the project’s initial NPV.

Note that to use the WACC or FTE methods here, we relied on VL computed in the APV method.

We could also solve for the value using the WACC or FTE methods directly using the techniques

in appendix 18A.3.