CHAPTER 7 The Cost of Capital

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Copyright © 1999 by Harcourt Brace & Company All rights reserved.

CHAPTER 7The Cost of Capital

Cost of capital componentsAccounting for flotation costsWACCAdjusting cost of capital for riskEstimating project risk

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What’s the firm’s cost of capital ?

• Opportunity cost of capital• Capital components• Target capital structure• Weighted average cost of

capital :marginal cost

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What types of long-term capital do firms use?

Long-term debtPreferred stockCommon equity:

Retained earnings New common stock

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Should we focus on before-tax or after-tax capital costs?

Stockholders focus on A-T CFs.Thus, focus on A-T capital costs,i.e., use A-T costs in WACC. Onlykd needs adjustment.

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Should we focus on historical (embedded) costs or new (marginal)

costs?

The cost of capital is used primarily to make decisions which involve raising new capital. So, focus on today’s marginal costs (for WACC).

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A 15-year, 12% semiannual bond sells for $1,153.72. What’s kd?

60 60 + 1,00060

0 1 2 30i = ?

30 -1153.72 60 1000

5.0% x 2 = kd = 10%

N I/YR PV FVPMT

-1,153.72

...

INPUTS

OUTPUT

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Component Cost of Debt

Interest is tax deductible, so

kd AT = Interest rate - Tax saving

= kd BT - kd BT *T

= kd BT(1 - T)

= 10%(1 - 0.40) = 6%. Use nominal rate,new debt cost,marginal cost Kd:outstanding debt cost (YTM,YTC)

no publicly traded debt=>similar co.’s YTM Flotation costs small. Ignore.

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What’s the cost of preferred stock? Pp = $111.10; 10%Q; Par = $100.

Use this formula:

%.0.9090.010.111$

10$

p

pp P

Dk

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Picture of Preferred

%.94%25.2 %;25.210.111$

50.2$ NompPer kk

2.50 2.50

0 1 2kp = ?

-111.1

¥...

2.50

.50.2$

10.111$PerPer

Q

kk

D

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Note:

Preferred dividends are not tax deductible, so no tax adjustment. Just kp.

Nominal kp is used.

Our calculation ignores flotation costs.

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Is preferred stock more or less risky to investors than debt?

More risky; company not required to pay preferred dividend.

However, firms try to pay preferred dividend. Otherwise, (1) cannot pay common dividend, (2) difficult to raise additional funds, (3) preferred stockholders may gain control of firm.

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Why is yield on preferred lower than kd?

Corporations own most preferred stock, because 70% of preferred dividends are nontaxable to corporations.

Therefore, preferred often has a lower B-T yield than the B-T yield on debt.

The A-T yield to an investor, and the A-T cost to the issuer, are higher on preferred than on debt. Consistent with higher risk of preferred.

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Example:

kp = 9% kd = 10% T = 40%

kp, AT = kp - kp (1 - 0.7)(T)

= 9% - 9%(0.3)(0.4) = 7.92%.

kd, AT = 10% - 10%(0.4) = 6.00%

A-T Risk Premium on Preferred = 1.92%

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Why is there a cost for retained earnings?

Earnings can be reinvested or paid out as dividends.

Investors could buy other securities, earn a return.

Thus, there is an opportunity cost if earnings are retained.

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Opportunity cost: The return stockholders could earn on alternative investments of equal risk.

They could buy similar stocks and earn ks, or company could repurchase its own stock and earn ks. So, ks is the cost of common stock.

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Three ways to determine cost of common stock, ks:

1.CAPM: ks = kRF + (kM - kRF)b.

2.DCF: ks = D1/P0 + g.

3.Own-Bond-Yield-Plus-Risk

Premium: ks = kd + RP.

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What’s the cost of common stock based on the CAPM?

kRF = 7%, MRP = 6%, b = 1.2.

ks = kRF + (kM - kRF )b.

= 7.0% + (6.0%)1.2 = 4.2%.

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Note: estimating Ks based on CAPM Krf:T-Bond rate. Beta: 專業投顧公司 Km=T-Bill rate + inflation + economic growth rate+ stock risk premiu

m.• Several problems with the CAPM 1. 若股東未能達到最佳風險分散的狀態 , 則尚有

個別股票的風險存在 , 則公司真正的風險無法由beta 反映出 ;

2.even if the CAPM is valid,it’s hard to estiamte Beta : Krf, Beta ,marktet premium.

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What’s the DCF cost of commonstock, ks? Given: D0 = $4.19;

P0 = $50; g = 5%.

g

P

gDg

P

Dks

0

0

0

1 1

%.8.13

05.0088.0

05.050$

05.119.4$

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Note: g 難以估計 , g 的估計1. 證券分析師之預測2. 保留成長分析法 : (the retention growth rate method.Suppose the company has been earning 15% on equity (ROE = 15%) and retaining 35% (dividend payout = 65%), and this situation is expected to continue.

What’s the expected future g?

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Retention growth rate:

g = b(ROE) = 0.35(15%) = 5.25%.

Here b = Fraction retained.

Close to g = 5% given earlier. Think of bank account paying 10% with b = 0, b = 1.0, and b = 0.5. What’s g?

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Could DCF methodology be applied if g is not constant?

YES, nonconstant g stocks are expected to have constant g at some point, generally in 5 to 10 years.

But calculations get complicated.

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Find ks using the own-bond-yield-plus-risk-premium method. (kd = 10%, RP = 4%.)

This RP ¹ CAPM RP. Produces ballpark estimate of ks. Useful ch

eck. RP=CS-LR Bonds (judgmental RP) Empirical evidence:RP are between 4 to 7% Too subjective

ks = kd + RP = 10.0% + 4.0% = 14.0%

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What’s a reasonable final estimate of k

s?

Method Estimate

CAPM 14.2%

DCF 13.8%

kd + RP 14.0%

Average 14.0%

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1. When a company issues new common stock they also have to pay flotation costs to the underwriter.

2. Issuing new common stock may send a negative signal to the capital markets, which may depress stock price.

Why is the cost of retained earnings cheaper than the cost of issuing new

common stock?

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Two approaches that can be used to account for flotation costs:

Include the flotation costs as part of the project’s up-front cost. This reduces the project’s estimated return.

Adjust the cost of capital to include flotation costs. This is most commonly done by incorporating flotation costs in the DCF model.

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New common, F = 15%:

%.4.15%0.550.42$

40.4$

%0.515.0150$

05.119.4$

gFP

gDke

)1(

)1(

0

0

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Comments about flotation costs:

Flotation costs depend on the risk of the firm and the type of capital being raised.

The flotation costs are highest for common equity. However, since most firms issue equity infrequently, the per-project cost is fairly small.

We will frequently ignore flotation costs when calculating the WACC.

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What’s the firm’s WACC (ignoring flotation costs)?

WACC = wdkd(1 - T) + wpkp + wcks

= 0.3(10%)(0.6) + 0.1(9%) + 0.6(14%)

= 1.8% + 0.9% + 8.4% = 11.1%.

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What factors influence a company’s composite WACC?

Market conditions: interest rate and tax.The firm’s capital structure and dividend policy.The firm’s investment policy. Firms with riskier

projects generally have a higher WACC.

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WACC Estimates for Some Large U.S. Corporations

Company WACC

Intel 13.6%General Electric 12.7Walt Disney 12.6Motorola 11.5AT&T 10.7Exxon 10.4Wal-Mart 9.9Coca-Cola 9.7H. J. Heinz 9.5BellSouth 8.9

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Should the company use the composite WACC as the hurdle rate for

each of its projects?

NO! The composite WACC reflects the risk of an average project undertaken by the firm. Therefore, the WACC only represents the “hurdle rate” for a typical project with average risk.

Different projects have different risks. The project’s WACC should be adjusted to reflect the project’s risk.

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CHAPTER 7 The Cost of Capital