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# ch11 The Cost of Capital (solutions_nss_nc_10)

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ch11 The Cost of Capital (solutions_nss_nc_10)

Chapter 10

The Cost of Capital

Learning Objectives

After reading this chapter, students should be able to:

; Explain what is meant by a firm’s weighted average cost of capital.

; Define and calculate the component costs of debt and preferred stock. Explain why the cost of debt is

tax adjusted and the cost of preferred is not.

; Explain why retained earnings are not free and use three approaches to estimate the component cost

of retained earnings.

; Briefly explain the two alternative approaches that can be used to account for flotation costs. ; Briefly explain why the cost of new common equity is higher than the cost of retained earnings,

calculate the cost of new common equity, and calculate the retained earnings breakpointwhich is the

point where new common equity would have to be issued.

; Calculate the firm’s composite, or weighted average, cost of capital.

; Identify some of the factors that affect the WACCdividing them into factors the firm cannot control

and those they can.

; Briefly explain how firms should evaluate projects with different risks, and the problems encountered

when divisions within the same firm all use the firm’s composite WACC when considering capital

budgeting projects.

; List some problems with cost of capital estimates.

Chapter 10: The Cost of Capital Learning Objectives 243

Lecture Suggestions

Chapter 10 uses the rate of return concepts covered in previous chapters, along with the concept of the weighted average cost of capital (WACC), to develop a corporate cost of capital for use in capital budgeting.

We begin by describing the logic of the WACC, and why it should be used in capital budgeting. We next explain how to estimate the cost of each component of capital, and how to put the components together to determine the WACC. We go on to discuss factors that affect the WACC and how to adjust the cost of capital for risk. We conclude the chapter with a discussion on some problems with cost of capital estimates.

What we cover, and the way we cover it, can be seen by scanning the slides and Integrated Case solution for Chapter 10, which appears at the end of this chapter solution. For other suggestions about the lecture, please see the ―Lecture Suggestions‖ in Chapter 2, where we describe how we conduct our classes.

DAYS ON CHAPTER: 3 OF 58 DAYS (50-minute periods)

244 Lecture Suggestions Chapter 10: The Cost of Capital

10-1 Probable Effect on

r(1 T) r WACC ds

a. The corporate tax rate is lowered. + 0 +

b. The Federal Reserve tightens credit. + + +

c. The firm uses more debt; that is, it increases

its debt/assets ratio. + + 0

d. The dividend payout ratio is increased. 0 0 0

e. The firm doubles the amount of capital it raises

during the year. 0 or + 0 or + 0 or +

f. The firm expands into a risky new area. + + +

g. The firm merges with another firm whose earnings

are counter-cyclical both to those of the first firm and

to the stock market.

h. The stock market falls drastically, and the firm’s stock

falls along with the rest. 0 + +

i. Investors become more risk averse. + + +

j. The firm is an electric utility with a large investment in

nuclear plants. Several states propose a ban on

nuclear power generation. + + +

10-2 An increase in the risk-free rate will increase the cost of debt. Remember from Chapter 6, r = r RF

+ DRP + LP + MRP. Thus, if r increases so does r (the cost of debt). Similarly, if the risk-free RF

rate increases so does the cost of equity. From the CAPM equation, r = r + (r r)b. sRFMRF

Consequently, if r increases r will increase too. RFs

10-3 Each firm has an optimal capital structure, defined as that mix of debt, preferred, and common

equity that causes its stock price to be maximized. A value-maximizing firm will determine its

optimal capital structure, use it as a target, and then raise new capital in a manner designed to

keep the actual capital structure on target over time. The target proportions of debt, preferred

stock, and common equity, along with the costs of those components, are used to calculate the

firm’s weighted average cost of capital, WACC.

The weights could be based either on the accounting values shown on the firm’s balance

sheet (book values) or on the market values of the different securities. Theoretically, the weights

should be based on market values, but if a firm’s book value weights are reasonably close to its

market value weights, book value weights can be used as a proxy for market value weights.

Consequently, target market value weights should be used in the WACC equation.

10-4 In general, failing to adjust for differences in risk would lead the firm to accept too many risky

Chapter 10: The Cost of Capital Integrated Case 245

projects and reject too many safe ones. Over time, the firm would become more risky, its WACC would increase, and its shareholder value would suffer.

The cost of capital for average-risk projects would be the firm’s cost of capital, 10%. A

somewhat higher cost would be used for more risky projects, and a lower cost would be used for less risky ones. For example, we might use 12% for more risky projects and 9% for less risky projects. These choices are arbitrary.

10-5 The cost of retained earnings is lower than the cost of new common equity; therefore, if new common stock had to be issued then the firm’s WACC would increase.

The calculated WACC does depend on the size of the capital budget. A firm calculates its retained earnings breakpoint (and any other capital breakpoints for additional debt and preferred). This R/E breakpoint represents the amount of capital raised beyond which new common stock must be issued. Thus, a capital budget smaller than this breakpoint would use the lower cost retained earnings and thus a lower WACC. A capital budget greater than this breakpoint would use the higher cost of new equity and thus a higher WACC.

Dividend policy has a significant impact on the WACC. The R/E breakpoint is calculated as the addition to retained earnings divided by the equity fraction. The higher the firm’s dividend payout, the smaller the addition to retained earnings and the lower the R/E breakpoint. (That is, the firm’s WACC will increase at a smaller capital budget.)

246 Integrated Case Chapter 10: The Cost of Capital

Solutions to End-Of-Chapter Problems

11-1 r(1 T) = 0.12(0.65) = 7.80%. d

11-2 P = \$47.50; D = \$3.80; r = ? ppp

D\$3.80pr = = = 8%. p\$47.50Pp

11-3 40% Debt; 60% Common equity; r = 9%; T = 40%; WACC = 9.96%; r = ? ds

WACC = (w)(r)(1 T) + (w)(r) ddcs

0.0996 = (0.4)(0.09)(1 0.4) + (0.6)r s

0.0996 = 0.0216 + 0.6r s

0.078 = 0.6r s

r = 13%. s

11-4 P = \$30; D = \$3.00; g = 5%; r = ? 01s

D\$3.001a. r = + g = + 0.05 = 15%. sP\$30.000

b. F = 10%; r = ? e

D\$3.001r = + g = + 0.05 eP(1F)\$30(10.10)0

\$3.00 = + 0.05 = 16.11%. \$27.00

11-5 Projects A, B, C, D, and E would be accepted since each project’s return is greater than the firm’s

WACC.

D\$2.14111-6 a. r = + g = + 7% = 9.3% + 7% = 16.3%. sP\$230

b. r = r + (r r)b sRFMRF

= 9% + (13% 9%)1.6 = 9% + (4%)1.6 = 9% + 6.4% = 15.4%.

c. r = Bond rate + Risk premium = 12% + 4% = 16%. s

d. Since you have equal confidence in the inputs used for the three approaches, an average of

the three methodologies probably would be warranted.

Chapter 10: The Cost of Capital Integrated Case 247

16.3%;15.4%;16% = = 15.9%. rs3

D111-7 a. r = + g sP0

\$3.18 = + 0.06 \$36

= 14.83%.

b. F = (\$36.00 \$32.40)/\$36.00 = \$3.60/\$36.00 = 10%.

c. r = D/[P(1 F)] + g = \$3.18/\$32.40 + 6% = 9.81% + 6% = 15.81%. e10

11-8 Debt = 40%, Common equity = 60%.

P = \$22.50, D = \$2.00, D = \$2.00(1.07) = \$2.14, g = 7%. 001

D\$2.141r = + g = + 7% = 16.51%. sP\$22.500

WACC = (0.4)(0.12)(1 0.4) + (0.6)(0.1651)

= 0.0288 + 0.0991 = 12.79%.

11-9 Capital Sources Amount Capital Structure Weight

Long-term debt \$1,152 40.0%

Common Equity 1,728 60.0

\$2,880 100.0%

WACC = wr(1 T) + wr = 0.4(0.13)(0.6) + 0.6(0.16) ddcs

= 0.0312 + 0.0960 = 12.72%.

11-10 If the investment requires \$5.9 million, that means that it requires \$3.54 million (60%) of common

equity and \$2.36 million (40%) of debt. In this scenario, the firm would exhaust its \$2 million of

retained earnings and be forced to raise new stock at a cost of 15%. Needing \$2.36 million in

debt, the firm could get by raising debt at only 10%. Therefore, its weighted average cost of

capital is: WACC = 0.4(10%)(1 0.4) + 0.6(15%) = 11.4%.

11-11 r = D/P + g = \$2(1.07)/\$24.75 + 7% s10

= 8.65% + 7% = 15.65%.

WACC = w(r)(1 T) + w(r); w = 1 w. ddcscd

13.95% = w(11%)(1 0.35) + (1 w)(15.65%) dd

0.1395 = 0.0715w + 0.1565 0.1565w dd

-0.017 = -0.085w d

w = 0.20 = 20%. d

248 Integrated Case Chapter 10: The Cost of Capital

11-12 a. r = 10%, r(1 T) = 10%(0.6) = 6%. dd

D/A = 45%; D = \$2; g = 4%; P = \$20; T = 40%. 00

Project A: Rate of return = 13%.

Project B: Rate of return = 10%.

r = \$2(1.04)/\$20 + 4% = 14.40%. s

b. WACC = 0.45(6%) + 0.55(14.40%) = 10.62%.

c. Since the firm’s WACC is 10.62% and each of the projects is equally risky and as risky as the

firm’s other assets, MEC should accept Project A. Its rate of return is greater than the firm’s

WACC. Project B should not be accepted, since its rate of return is less than MEC’s WACC.

11-13 If the firm's dividend yield is 5% and its stock price is \$46.75, the next expected annual dividend can be calculated.

Dividend yield = D/P 10

5% = D/\$46.75 1

D = \$2.3375. 1

Next, the firm's cost of new common stock can be determined from the DCF approach for the cost of equity.

r = D/[P(1 F)] + g e10

= \$2.3375/[\$46.75(1 0.05)] + 0.12

= 17.26%.

\$11\$100(0.11)11-14 r = = = 11.94%. p\$92.15\$92.15

11-15 a. Examining the DCF approach to the cost of retained earnings, the expected growth rate can

be determined from the cost of common equity, price, and expected dividend. However, first,

this problem requires that the formula for WACC be used to determine the cost of common

equity.

WACC = w(r)(1 T) + w(r) ddcs

13.0% = 0.4(10%)(1 0.4) + 0.6(r) s

10.6% = 0.6r s

r = 0.17667 or 17.67%. s

From the cost of common equity, the expected growth rate can now be determined.

r = D/P + g s10

0.17667 = \$3/\$35 + g

g = 0.090952 or 9.10%.

Chapter 10: The Cost of Capital Integrated Case 249

b. From the formula for the long-run growth rate:

g = (1 Div. payout ratio) ROE = (1 Div. payout ratio) (NI/Equity)

0.090952 = (1 Div. payout ratio) (\$1,100 million/\$6,000 million)

0.090952 = (1 Div. payout ratio) 0.1833333

0.496104 = (1 Div. payout ratio)

Div. payout ratio = 0.503896 or 50.39%.

11-16 a. With a financial calculator, input N = 5, PV = -4.42, PMT = 0, FV = 6.50, and then solve for

I/YR = g = 8.02% 8%.

b. D = D(1 + g) = \$2.60(1.08) = \$2.81. 10

c. r = D/P + g = \$2.81/\$36.00 + 8% = 15.81%. s10

D111-17 a. r = + g sP0

\$3.600.09 = + g \$60.00

0.09 = 0.06 + g

g = 3%.

b. Current EPS \$5.400

Less: Dividends per share 3.600

Retained earnings per share \$1.800

Rate of return 0.090

Increase in EPS \$0.162

Plus: Current EPS 5.400

Next year’s EPS \$5.562

Alternatively, EPS = EPS(1 + g) = \$5.40(1.03) = \$5.562. 10

11-18 a. r(1 T) = 0.10(1 0.3) = 7%. d

r = \$5/\$49 = 10.2%. p

r = \$3.50/\$36 + 6% = 15.72%. s

b. WACC:

After-tax Weighted

Component Weight Cost = Cost

Debt [0.10(1 T)] 0.15 7.00% 1.05%

Preferred stock 0.10 10.20 1.02

Common stock 0.75 15.72 11.79

WACC = 13.86%

c. Projects 1 and 2 will be accepted since their rates of return exceed the WACC.

250 Integrated Case Chapter 10: The Cost of Capital

Chapter 10: The Cost of Capital Integrated Case 251

10-19 a. If all project decisions are independent, the firm should accept all projects whose returns

exceed their risk-adjusted costs of capital. The appropriate costs of capital are summarized

below:

Required Rate of Cost of

Project Investment Return Capital

A \$4 million 14.0% 12%

B 5 million 11.5 12

C 3 million 9.5 8

D 2 million 9.0 10

E 6 million 12.5 12

F 5 million 12.5 10

G 6 million 7.0 8

H 3 million 11.5 8

Therefore, Ziege should accept projects A, C, E, F, and H.

b. With only \$13 million to invest in its capital budget, Ziege must choose the best combination of

Projects A, C, E, F, and H. Collectively, the projects would account for an investment of \$21

million, so naturally not all these projects may be accepted. Looking at the excess return

created by the projects (rate of return minus the cost of capital), we see that the excess

returns for Projects A, C, E, F, and H are 2%, 1.5%, 0.5%, 2.5%, and 3.5%. The firm should

accept the projects which provide the greatest excess returns. By that rationale, the first

project to be eliminated from consideration is Project E. This brings the total investment

required down to \$15 million, therefore one more project must be eliminated. The next lowest

excess return is Project C. Therefore, Ziege's optimal capital budget consists of Projects A, F,

and H, and it amounts to \$12 million.

c. Since Projects A, F, and H are already accepted projects, we must adjust the costs of capital

for the other two value producing projects (C and E).

Required Rate of Cost of

Project Investment Return Capital

C \$3 million 9.5% 8% + 1% = 9%

E 6 million 12.5 12% + 1% = 13%

If new capital must be issued, Project E ceases to be an acceptable project. On the other

hand, Project C's expected rate of return still exceeds the risk-adjusted cost of capital even

after raising additional capital. Hence, Ziege's new capital budget should consist of Projects A,

C, F, and H and requires \$15 million of capital, so \$3 million of additional capital must be

raised.

(1 T) = 0.09(1 0.4) = 5.4%. 11-20 a. After-tax cost of new debt: rd

Cost of common equity: Calculate g as follows:

With a financial calculator, input N = 9, PV = -3.90, PMT = 0, FV = 7.80, and then solve for

I/YR = g = 8.01% 8%.

D(0.55)(\$7.80)\$4.291r = + g = + 0.08 = + 0.08 = 0.146 = 14.6%. sP\$65.00\$65.000

252 Integrated Case Chapter 10: The Cost of Capital

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