chapter 12 im 10th ed

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CHAPTER 12

Cost of Capital

CHAPTER ORIENTATION

In Chapters 7 and 8 we considered the valuation of debt and equity instruments. Theconcepts advanced there serve as a foundation for determining the required rate of return for the firm and for specific investment projects. The objective in this chapter is to determine therequired rate of return to be used in evaluating investment projects.

CHAPTER OUTLINE

I. The concept of the cost of capital

A. Defining the cost of capital:

1. The rate that must be earned in order to satisfy the required rate of return

2. The rate of return on investments at which the price of a firm'scommon stock will remain unchanged.

B. Investor’s required rate of return is not the same as the firm’s cost of capitaldue to

1. Taxes: Interest payments on debt are tax deductible to the firm.

2. Flotation costs: Firms incur expenses when issuing securities thatreduce the proceeds to the firm.

C. Financial Policy

1. Each type of capital used by the firm (debt, preferred stock, andcommon stock) should be incorporated into the cost of capital, withthe relative importance of a particular source being based on the percentage of the financing provided by each source of capital.

2. Using the cost of a single source of capital as the hurdle rate istempting to management, particularly when an investment is financedentirely by debt. However, doing so is a mistake in logic and cancause problems.

II. Computing the weighted cost of capital. A firm's weighted cost of capital is a functionof (l) the individual costs of capital, (2) the capital structure mix, and (3) the level of financing necessary to make the investment.

A. Determining individual costs of capital.

50



1. The before-tax cost of debt is found by trial-and-error by solving for k d in

NPd = td

tn

1t )k (1

$I

+∑=

+ nd )k (1

$M

+

where NPd = the market price of the debt, less flotation

costs,

$It = the dollar interest paid to the investor each

period,

$M = the maturity value of the debt

k d = before-tax cost of the debt (before-taxrequired rate of return on debt)

n = the number of periods to maturity.

The after-tax cost of debt equals: k d (1 - T)

where T = corporate tax rate2. Cost of preferred stock (required rate of return on preferred stock),

k ps, equals the dividend yield based upon the net price (market price

less flotation costs), or

k ps = pricenet

dividend =

ps NP

D

3. Cost of Common Stock. There are two measurement techniques toobtain the required rate of return on common stock.

a. dividend-growth model

b. capital asset pricing model

4. Dividend growth model

a. Cost of internally generated common equity, k cs

k cs = pricemarket

year1individend+

dividendsin

growthannual

k cs =cs

1

P

D+ g

51



b. Cost of new common stock, k ncs

k ncs =cs

1

NP

D+ g

where NPcs = the market price of the common stock less

flotation costs incurred in issuing new shares.5. Capital asset pricing model

k c = k rf + β(k m - k rf )

where k c = the cost of common stock

k rf = the risk-free rate

β = beta, measure of the stock's systematic risk

k m = the expected rate of return on the market

6. It is important to notice that the major difference between theequations presented here and the equations from Chapters 7 and 8 isthat the firm must recognize the flotation costs incurred in issuing thesecurity.

B. Selection of weights. The individual costs of capital will be different for eachsource of capital in the firm's capital structure. To use the cost of capital ininvestment analyses, we must compute a weighted, or overall, cost of capital.

1. It will be assumed that the company's current financial mix resultingfrom the financing of previous investments is relatively stable and thatthese weights will closely approximate future financing patterns.

2. In computing weights, we could use either the current market valuesof the firm's securities or the book values as shown in the balancesheet. Since we will be issuing new securities at their current marketvalue, and not at book (historical) values, we should use the marketvalue of the securities in calculating our weights.

III. PepsiCo approach to weighted average cost of capital

A. PepsiCo calculates the divisional cost of capital for its snack, beverage andrestaurant organizations by first finding peer-group firms for each division andusing their average betas, after adjusting for differences in financial leverage,to compute the division's cost of equity. They also use accounting betas inestimating the cost of equity. They then compute the cost of debt for each

division. Finally, they calculate a weighted cost of capital for each division.

52



B. PepsiCo's WACC basic computation

k wacc = k cs

+ED

E+ k d[1-T]

+ED

D

where:

k wacc = the weighted average cost of capitalk cs = the cost of equity capital

k d = the before-tax cost of debt capital

T = the marginal tax rate

E/(D+E)= percentage of financing from equity

D/(D+E)= percentage of financing from debt

C. Calculating the Cost of Equity

Based on capital asset pricing model:

k cs = k rf + β(k m - k rf )

where:

k cs = the cost of common stock

k rf = the risk-free rate

β = beta, measure of the stock's systematic risk

k m = the expected rate of return on the market

Betas for each division are estimated by calculating an average unlevered betafrom a group of divisional peers.

The average beta for each division's peer group is unlevered and then re-levered using that division's target debt-to-equity ratio.

D. Calculating the Cost of Debt

The after-tax cost of debt is equal to:

k d (1 - T)

where:

k d = before-tax cost of debt

T = marginal tax rate

53



IV. Required rate of return for individual projects

A. Using the weighted cost of capital. Investments with an internal rate of returnexceeding the weighted cost of capital should be accepted. Doing so, wemust assume that the project has similar business risk as existing assets.Otherwise, the weighted cost of capital does not apply.

B. The weighted cost of capital, k wacc does not allow for varying levels of projectrisk. We need to specify the appropriate required rates of return for investments having different amounts of risk.

C. Risk also results from the decisions made within the company. This risk isgenerally divided into two classes:

1. Business risk is the variability in returns on assets and is affected bythe company’s investment decisions.

2. Financial risk is the increased variability in returns to the commonstockholder as a result of using debt and preferred stock.

ANSWERS TOEND-OF-CHAPTER QUESTIONS

12-1. The cost of capital is the rate that must be earned on investments in order to satisfythe required rate of return of the firm's investors. This rate is a function of theinvestors' required rate of return, the corporation's tax rate, and the flotation costsincurred in issuing new securities. Therefore, the cost of capital determines the rateof return that must be achieved on the company's investments, so as to earn the targetreturn of the firm's investors. Stated differently, the cost of capital is the rate of return that will leave the price of the common stock unchanged.

12-2. Two objectives may be given for determining a company's weighted average cost of capital:

(1) The weighted average cost of capital is used as the minimum acceptable rateof return for capital investments. The value of the firm should be maximized by accepting all projects where the net present value is positive whendiscounted at the firm's weighted average cost of capital.

(2) The weighted average cost of capital is also used in evaluating a firm’shistorical performance. That is, to create shareholder value a firm must notonly earn a profit in the traditional accounting sense, but it must earn a returnon its invested capital that is acceptable to the investors who provide thefirm’s financing. This “acceptable return” is the firm’s weighted average costof capital.

12-3. All types of capital, including debt, preferred stock, and common stock, should beincorporated into the cost of capital computation, with the relative importance of a particular source being based upon the percentage of financing to be provided.

12-4. The effect of taxes on the firm's cost of capital is observed in computing the cost of debt. Since interest is a tax deductible expense, the use of debt indirectly decreasesthe firm's taxes. Therefore, since we have computed the internal rate of return on an

54



after-tax basis, we also compute the cost of debt on an after-tax basis. In completinga security offering, investment bankers and other involved individuals receive acommission for their services. As a result, the amount of capital net of these flotationcosts is less than the funds invested by the individual purchasing the security.Consequently, the firm must earn more than the investors' required rate of return tocompensate for this leakage of capital.

12-5. a. Equity capital can be raised by either retaining profits within the firm or byissuing new common stock. Either route represents funds invested by thecommon stockholder. The first avenue simply indicates that the commonstockholder permits management to retain capital that could be remitted tothese investors.

b. Even though a new stock issue does not result from retaining internal commonequity, these funds should not be reinvested unless management canreasonably expect to satisfy the investors' required rate of return. In essence,even though no explicit out-of-pocket cost results from retaining the capital,the cost in measuring a firm's cost of capital is actually the opportunity costassociated with these funds for the investor.

c. The two popular methods for computing the cost of equity capital include (1)the dividend-growth model, and (2) the capital asset pricing model. The firstapproach finds the rate of return that equates the present value of futuredividends, assuming a constant growth rate, with the current market price of the security. The CAPM finds the appropriate required rate of return, giventhe firm's systematic risk.

12-6 In general, the relative costs of various sources of capital reflect the riskness of thesource to the investor. For example, for a given firm, we would expect debtsecurities to be less risky than preferred stock which is less risky than common stock.Consequently, debt would demand a lower required return than the firm’s preferredstock, which is lower than the required rate of return for common stock.

55



SOLUTIONS TOEND-OF-CHAPTER PROBLEMS

The following notations are used in this group of problems:

k ps = the cost of preferred stock.

k cs = the cost of internally generated common funds

k ncs = the cost of new common stock.

g = the growth rate.

k d = the before-tax cost of debt.

T = the marginal tax rate.

Dt = dollar dividend per share, where Do is the most recently paid dividend

and D1 is the forthcoming dividend.

P = the value (present value) of a security. NP = the value of a security less any flotation costs incurred in issuing the

security

12-1A.

a. Net price after flotation costs = $1,125 (1 - .05)

= $1068.75

$1068.75 = t

d

10

1t )k (1

$110

+∑=

+ 10d )k (1

$1,000

+

k d = 9.89%

= k d(1-T)

= 6.53%

b. k ncs =cs

1

NP

D+ g

= )05.1(50.27$

)07.1(80.1$

−+

+ .07

= .1437 = 14.37%

c. k cs =cs

1

P

D+ g

56



=43$

50.3$+ .07

= .1514 = 15.14%

d. k ps = ps NP

D=

)12.1(175$

150$09.

− x

=154$

50.13$

= .0877 = 8.77%

e. debtof costAfter tax

= k d (1 - T)

= 12% (1 - .34)

= 7.92%

12-2A.

a. debtof costAfter tax

= k d(1 - T)

= 8%(1 - 0.34)

= 5.28%

b. k ncs =cs

1

NP

D+ g

k ncs =)09.01(25$

)05.01(05.1$

−+

+ 0.05 = 9.85%

c. $1,150(.90) = $1,035 = net price after flotation costs

$1,035 = td

20

1t )k (1

$120

+∑=

+ 20d )k (1

$1,000

+

Rate Value Value

57



For: 11% $1,079.56 $1,079.56

k d% 1,035.00

12% 1,000 .00

$ 44 .56 $ 79 .56

k d = 0.11 +

56.79$

56.44$ × 0.01 = .1156 = 11.56%

debtof costAfter tax

= k d (1 - T)


= 11.56% (1 - 0.34) = 7.63%

d. k ps = ps NPD

k ps =85$

7$= 8.24%

e. k cs =cs

1

P

D+ g

k cs =38$

3$+ 0.04 = 11.90%

12-3A. k ncs =cs

1

NP

D+ g

k ncs =)06.01(27$

)06.01(45.1$

−+

+ 0.06 = .1206 = 12.06%

58



12-4A. $958 (1 - 0.11) = $852.62 = the net price (value less flotation costs).

$852.62 = td

15

1t )k (1

$70

+∑=

+ 15d )k (1

$1,000

+

Rate Value ValueFor: 8% $914.20 $914.13

k d% 852.62

9% ______ 839 .27

$61 .58 $74 .86

k d = 0.08 +

86.74$

58.61$ × 0.01 = .0882 = 8.82%

= 8.82% (1 - 0.18) = 7.23%

12-5A. k ps = ps NP

D=

50.32$

50.2$= 7.69%

12-6A. NPd = td

tn

1t )k (1

$I

+∑=

+ nd )k (1

$M

+

$945 = td

15

1t )k (1

$120

+∑=

+ 15d )k (1

$1,000

+

Since the net price on the bonds, $945, is less than the $1,000 par value, the before-tax cost of the debt must be greater than the 12 percent coupon interest rate ($120 ÷$1,000).

Rate Value Value

12% $1,000.00 $1,000.00

k d% 945.00

13% _______ 935.44

$ 55.00 $ 64.56

k d = .12 +

56.64$

00.55$ × .01 = .1285 = 12.85%


= k d(1 - T) = 12.85%(1 - .34) = 8.48%

12-7A. Cost of preferred stock (k ps)

59



k ps =Price Net

Dividend=

ps NP

D

=$98

$100x14%=

98$

14$

= 14.29%

12-8A. k cs =cs

1

P

D+ g

=50.21$

)15.01(70.0$ ++ 0.15

= .1874 = 18.74%

12-9A.If the firm pays out 50 percent of its earnings in dividends, its recent earnings musthave been $8 ($4 dividend divided by .5).

Thus, earnings increased from $5 to $8 in five years. Using Appendix C and lookingfor a table value of .625 ($5/$8), the annual growth rate is approximately ten percent.

a. Cost of internal common stock (k cs):

k cs =

cs

1

P

D+ g

=58$

)10.1(4$ ++ .10 =

58$

40.4$+ .10

= .1759 = 17.59%

b. Cost of external common (new common) stock, k ncs

k ncs =

cs

1

NP

D+ g

=)08.01(58$

40.4$

− + .10

=36.53$

40.4$+ .10

= .1825 = 18.25%

12-10A.

a. Price (Pd) = t

10

1t 0.09)(1

$140

+∑=

+ 10)09.01(

000,1$

+

60



= $140(6.418) + $1000(.422)

= $1,320.52

b. NPd = $1,320.52(1 - 0.105)

= $1,181.87

c. Number of Bonds =87.181,1$

000,500$= 423.06 ≈ 424 Bonds

d. Cost of debt:

$1,181.87 = td

10

1t )k (1

$140

+∑=

+ 10d )k (1

$1,000

+

Rate Value Value

For 10% $1,246.30 $1,246.30

k d% 1,181.87

11% ________ 1,176 .46

$ 64 .43 $ 69 .84

k d = 0.10 + )01.0(

84.69$

43.64$ ×

= .1092 = 10.92%


= 10.92%(1 - 0.34) = 7.21%

12-11A.

a. 1. Price (Pd) = t

10

1t 0.09)(1

$100

+∑=

+ 10)09.01(

000,1$

+

= $100 (6.418) + $1,000 (.422)

= $1,063.80

61



2. NPd = $1,063.80 (1 - 0.105)

= $952.10

3. Number of Bonds =10.952$

000,500$

= 525.15 ≈ 526 Bonds

4. Cost of debt:

$952.10 = td

10

1t )k (1

$100

+∑=

+ 10d )k (1

$1,000

+

Rate Value Value

For: 10% $1,000.00 $1,000.00kd% 952.10

11% ________ 940 .90$ 47 .90 $ 59 .10

k d = 0.10 + )01.0( 10.59$

90.47$×

= .1081 = 10.81%


= 10.81%(1 - 0.34) = 7.13%

b. There is a very slight decrease in the cost of debt because the flotation costsassociated with the higher coupon bond are higher ($138.65 in flotation costs

for the 14 percent coupon bond versus $111.70 for the 10 percent coupon bond).

12-12A.

Source Capital Structure After-tax cost of capital Weighted costCommon Stock 40% 18% 7.2%Preferred Stock 10% 10% 1.0%Debt 50% 8% x (1-.35) 2.6%

k wacc = 10.8%

62



12-13A.

Net price after flotation costs = $975 - $15

= $960.00

Cost of debt:

$960.00 = t

d

15

1t )k (1

$60

+∑=

+ 15d )k (1

$1,000

+

Rate Value Value

For: 6% $1,000.00 $1,000.00k d% 960.007% ________ 908 .48

$ 40 .00 $ 91 .52

k d = 0.06 + )01.0( 52.91$

00.40$×

= .064 = 6.4%


= 6.4%(1 - 0.30) = 4.48%

Cost of common stock, k ncs

k ncs =

cs

1

NP

D+ g

=)05.01(30$

25.2$

− + .05

= .129 = 12.9%

Source Capital Structure After-tax cost of capital Weighted cost

Debt 60% 4.48% 2.69%

Common Stock 40% 12.9% 5.16%

k wacc = 7.85%

63



12-14A. Net price after flotation costs = $1,050 (1-.04)

= $1,008.00

Cost of debt:

$1,008.00 = t

d

10

1t )k (1

$70

+∑=

+ 10

d )k (1

$1,000

+Rate Value Value

For: 6% $1,096.84 $1,096.84k d% 1,008.007% ________ 1,000 .00

$ 88 .84 $ 96 .84

k d = 0.06 + )01.0( 84.96$

84.88$×

= .069 = 6.9%

debtof cost

After tax= 6.9 %(1 - 0.30) = 4.8%

Cost of preferred stock (k ps)

k ps =Price Net

Dividend=

ps NP

D

=3$25$

00.2$

−=

22$

2$

= .091 = 9.1%


k ncs =

cs

1

NP

D+ g

=5$55$

)10.1(3$

−+

+ .10

= .166 = 16.6%

Source Market Value Weight After-tax cost of capital Weighted Cost

Bonds $4,000,000 .33 4.8% 1.6%

Preferred Stock 2,000,000 .17 9.1% 1.5%

Common Stock 6,000,000 .50 16.6% 8.3%

12,000,000 1.00 k wacc = 11.4%

64



SOLUTION TO INTEGRATIVE PROBLEM

Nealon, Inc. - Weighted Cost of Capital

Cost of Debt:

$1,035 (1 - .15) = $879.75 = NPd

$879.75 =t

d

16

1t )k (1

$80

+∑=

+16

d )k (1

$1,000

+

Rate Value Value

For: 9% $917.04 $917.04k d% 879.75

10% 843 .92$ 37 .29 $ 73 .12

k d = 0.09 + )01.0(x12.73$

29.37$

= .0951 = 9.51%


= 9.51%(1 - .34) = 6.28%

Cost of Preferred Stock:

k ps = ps NP

D=

)01.2$19($

50.1$

−= 8.83%

Cost of Internal Common Equity:

k cs =cs

1

P

D+ g

=35$

)06.01(50.2$ ++ 0.06

= .1357 = 13.57%

Weighted Cost of Capital (k wacc) is calculated as follows:

Weights Costs Weighted CostsBonds .38 6.28% 2.39%Preferred Stock .15 8.83% 1.32%Common Stock .47 13.57% 6 .38%

1.00 k wacc = 10.09%

Solutions for Problem Set B

65



The following notations are used in this group of problems:

k ps = the cost of preferred stock.

k cs = the cost of internally generated common funds

k ncs = the cost of new common stock.

g = the growth rate.

k d = the before-tax cost of debt.

T = the marginal tax rate.

Dt = dollar dividend per share, where Do is the most recently paid dividend

and D1 is the forthcoming dividend.

P = the value (present value) of a security.

NP = the value of a security less any flotation costs incurred in issuing the

security

12-1B.

a. Net price after flotation costs = $1,125 (1 - .06)

= $1,057.50

$1,057.50 = td

10

1t )k (1

$120

+∑=

+ 10d )k (1

$1,000

+

Rate Value ValueFor: 11% $1,058.68 $1,058.68

k d% 1,057.50

12% 1,000 .00$ 1 .18 $ 58 .68

k d = .11 +

68.58$

18.1$× .01 = .1102 = 11.02%


= k d(1 - T)


= 11.02%(1 - .34) = 7.27%

66



b. k ncs =cs

1

NP

D+ g

=)05.1(00.28$

)08.1(75.1$

−+

+ .08

= .1511 = 15.11%

c. k cs =cs

1

P

D+ g

=50.43$

25.3$+ .07

= .1447 = 14.47%

d. k ps = ps NPD =

)12.1(150$)125$(10.

−

=132$

5.12$

= .0947 = 9.47%

e. debtof costAfter tax

= k d (1 - T)

= 13% (1 - .34)

= 8.58%

12-2B.

a. debtof costAfter tax

= k d(1 - T)


= 9%(1 - 0.34)


= 5.94%

67



b. k ncs =cs

1

NP

D+ g

k ncs =)09.01(30$

)06.01(25.1$

−+

+ 0.06 = 10.85%

c. $1,125(.90) = $1,012.50 = net price after flotation costs

$1,012.50 =t

d

20

1t )k (1

$130

+∑=

+ 20

d )k (1

$1,000

+

Rate Value ValueFor: 12% $1,074.97 $1,074.97

k d% 1,012.5013% 1,000 .00

$ 62 .47 $ 74 .97

k d = 0.12 +

97.74$

47.62$0.01 = .1283 = 12.83%


= k d (1 - T)


= 12.83% (1 - 0.34) = 8.47%

d. k ps = ps NPD

k ps =90$

75.8$= 9.72%

e. k cs =cs

1

P

D+ g

k cs = + 0.05 = 15.52%

68



12-3B. k ncs =cs

1

NP

D+ g

k ncs =)06.01(28$

)07.01(30.1$

−+

+ 0.07 = .1229 = 12.29%

12-4B. $950 (1 - 0.11) = $845.50 = the net price (value less flotation costs).

$845.50 = td

15

1t )k (1

$80

+∑=

+ 15d )k (1

$1,000

+

Rate Value ValueFor: 10% $847.48 $847.48

k d% 845.5011% 784 .28

$1 .98 $63 .20

k d = 0.10 +

20.63$

98.1$ × 0.01 = .1004 = 10.04%


= 10.04% (1 - 0.19) = 8.13%

12-5B. k ps = ps NP

D=

50.32$

75.2$= 8.46%

12-6B. NPd = td

tn

1t )k (1

$I

+∑=

+ nd )k (1

$M

+

$950 = td

15

1t )k (1$130 +∑=

+ 15d )k (1

$1,000+

Since the net price on the bonds, $950, is less than the $1,000 par value, the before-tax cost of the debt must be greater than the 13 percent coupon interest rate ($130 ÷$1,000).

Rate Value Value13% $1,000.00 $1,000.00k d% 950.00

14% 938 .46$ 50 .00 $ 61 .54

k d = .13 +

54.61$

00.50$ × .01 = .1381 = 13.81%


= k d(1 - T) = 13.81%(1 - .34) = 9.11%

69



12-7B. Cost of preferred stock (k ps)

=Price Net

Dividend=

ps NP

D

=97$

100$%13 x

=97$

13$

= 13.40%

12-8B. k cs =cs

1

P

D+ g

=50.22$

)16.01(80.0$ ++ 0.16

= .2012 = 20.12%

12-9B. If the firm pays out 50 percent of its earnings in dividends, its recent earnings musthave been $9 ($4.50 dividend divided by .5).

Thus, earnings increased from $5 to $9 in five years. Using Appendix C and lookingfor a table value of .556 ($5/$9), the annual growth rate is approximately twelve percent.

a. Cost of internal common stock (k cs):

k cs =

cs

1

P

D+ g

=60$

)12.1(50.4$ ++ .12

=60$

04.5$+ .12

= .204 = 20.4%

b. Cost of external common (new common) stock, k ncs

k ncs =

cs

1

NP

D+ g

=)09.01(60$

04.5$

−+ .12

=60.54$

04.5$+ .12

= .2123 = 21.23%

12-10B.

70



a. Price (Pd) = t

10

1t 0.10)(1

$150

+∑=

+ 10)10.01(

000,1$

+

= $150(6.145) + $1000(.386)

= $1,307.75

b. NPd = $1,307.75(1 - 0.115)

= $1,157.36

c. Number of Bonds =36.157,1$

000,600$

= 518.4 ≈ 519 bonds

d. Cost of debt:

$1,157.36 = t)dk (1

$15010

1t +∑= + 10d )k (1

$1,000

+

Rate Value Value

For 12% $1,169.50 $1,169.50

k d% 1,157.36

13% 1,108 .90

$ 12 .14 $ 60 .60

k d = 0.12 + )01.0(

60.60$

14.12$×

= 12.20%


= 12.20%(1 - 0.34) = 8.05%

12-11B.

a. 1. Price (Pd) = ∑= +

10

tt

1 )10.01(

100$ + 10)10.01(

000,1$

+

= $100 (6.145) + $1,000 (.386)

= $1,000.00

2. NPd = $1,000.00 (1 - 0.115)

= $885.00

71



3. Number of Bonds =00.885$

000,600$

= 678 Bonds

4. Cost of debt:

$885.00 = td

10

1t )k (1

$100

+∑=

+ 10d )k (1

$1,000

+

Value ValueFor: 12% $887.00 $887.00

k d% 885.0013% 837.60

$2.00 $49.40

k d = 0.12 + )01.0( 40.49$00.2$ ×

= .1204 = 12.04%


= 12.04%(1 - 0.34) = 7.95%

b,There is a very slight decrease in the cost of debt because the flotation costsassociated with the higher coupon bond are higher (flotation costs are$150.39 for the 15 percent coupon bond versus $115 for the 10 percentcoupon bond)

12-12B. Bias Corporation - Weighted Cost of Capital

Capital Individual WeightedStructure Weights Costs Costs

Bonds $1,100 0.2178 6.0% 1.31%Preferred Stock 250 0.0495 13.5% 0.67%Common Stock 3,700 0 .7327 19.0% 13 .92%

$5,050 1.0000 15.90%

12-13B.

Source Capital Structure After-tax cost of capital Weighted costCommon Stock 50% 20% 10.0%Preferred Stock 15% 12% 1.8%Debt 35% 10% (1-.34) 2.3%

100% k wacc = 14.1%

72



12-14B.

Net price after flotation costs = $1,100- $20

= $1,080.00

Cost of debt:

$1,080.00 = t

d

40

1t )k (1

$40 +∑= + 40

d )k (1

$1,000

+

Semi-annual Rate Value Value

For: 3% $1,231.60 $1,231.60

k d% 1,080.00

4% ________ 1,000 .00

$ 151 .60 $ 231 .60

semi-annual k d = 0.03 + )01.0(

60.231$

6.151$×

= .0365 = 3.65%

annual k d = 3.65% x 2 = 7.3%


= 7.3%(1 - 0.34) = 4.8%


k ncs =

cs

1

NP

D+ g

= )10.01(80$

00.2$

− + .08

= .108 = 10.8%

Source Capital Structure After-tax cost of capital Weighted cost

Common Stock 60% 10.8% 6.48%

Debt 40% 4.8% 1.92%

k wacc = 8.4%

73



12-15B. Net price after flotation costs = $950 (1-.06)

= $893.00

Cost of debt:

$893.00 = td

20

1t )k (1

$80

+∑= + 20d )k (1

$1,000

+

Rate Value Value

For: 9% $908.32 $908.32

k d% 893.00

10% ________ 830 .12

$ 15 .32 $ 78 .20

k d = 0.09 + )01.0( 20.78$

32.15$×

= .092 = 9.2%


=10.4 % x (1 - 0.34) = 6.07%

Cost of preferred stock (k ps)

k ps =Price Net

Dividend=

ps NP

D

=5$35$

50.2$

−=

30$

50.2$

= .083 = 8.3%


k ncs =

cs

1

NP

D+ g

=)10.1(50$

)08.1(2$

−+

+ .08

= .128 = 12.8%

Source Market Value Weight After-tax cost of capital Weighted Cost

Bonds $500,000 .50 6.07% 3.04%

Preferred Stock 100,000 .10 8.3% .83%

Common Stock 400,000 .40 12.8% 5.12%

$1,000,000 1.00 k wacc = 8.99%

chapter 12 im 10th ed

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