CHAPTER 10 The Cost of Capital

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Copyright © 2002 by Harcourt, Inc. All rights reserved.

CHAPTER 10The Cost of Capital

Sources of capitalComponent costsWACCAdjusting for flotation costsAdjusting for risk

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What sources of long-term capital do firms use?

Long-Term Long-Term CapitalCapital

Preferred StockPreferred Stock Common StockCommon StockLong-Term Long-Term DebtDebt

New Common New Common StockStock

RetainedEarnings

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WACC = wdkd(1 – T) + wpkp + wsks

WACC = wdkd(1 – T) + wpkp + weke

How do you calculate the weighted average cost of capital?

The w’s refer to the capital structure weights.

The k’s refer to the cost of each component.

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Stockholders focus on A-T CFs.Therefore, we should focus on A-T capital costs, i.e., use A-T costs in WACC. Only kd needs adjustment, because interest is deductible.

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

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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 that involve raising new capital. So, focus on today’s marginal costs (for WACC).

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WACC = wdkd(1 – T) + wpkp + wsks.WACC = wdkd(1 – T) + wpkp + weke.

How do you determine the weights?

Use market value Use optimal capital structure So if a company has $300 million in debt outstanding, $100

million in preferred stock, & $600 million of common stock, and this is considered optimal for the company:

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How do you determine the weights?

300/1000 = 30% debt wd = .3100/1000 = 10% p.s. wps = .1600/1000 = 60% c.s. wcs = .6Since this is considered optimal, then these weights will stay constant

throughout the problem.

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Component Cost of Debt

kd is the marginal cost of debt capital.The yield to maturity on outstanding LT

debt is often used as a measure of kd.Why tax-adjust, i.e., why kd(1 - T)?

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

60 60 + 1,00060

0 1 2 30i = ?

30 -1153.72 60 1000

10% P/Y set to 2N I/YR PV FVPMT

-1,153.72

...

INPUTS

OUTPUT

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Interest is tax deductible, sokd AT = kd BT(1 – T)

= 10%(1 – 0.40) = 6%.Flotation costs small. Ignore.

Component Cost of Debt

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Component Cost of Preferred Stock

kp is the marginal cost of preferred stock.

The rate of return investors require on the firm’s preferred stock.

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0.090 9.0%.

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

Use this formula:

10.111$10$

PD

kp

pp= = = =

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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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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.

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

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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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Component Cost of Equity

ks is the marginal cost of common equity using retained earnings.

The rate of return investors require on the firm’s common equity using new equity is ke.

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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.

Why is there a cost for retained earnings?

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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 retained earnings.

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Three ways to determine cost of common equity, 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 equity based on the CAPM?

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

ks = kRF + (kM – kRF )b.

= 7.0% + (6.0%)1.2 = 14.2%.

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

P0 = $50; g = 5%.

D1

P0

D0(1 + g)P0

$4.19(1.05)$50

ks = + g = + g

= + 0.05

= 0.088 + 0.05= 13.8%.

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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 check.

ks = kd + RP

= 10.0% + 4.0% = 14.0%

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What’s a reasonable final estimateof ks?

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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Suppose new common stock had a flotation cost of 15%. What is ke?

ke = + gD0(1 + g)P0(1 – F)

= + 5.0%

= + 5.0% = 15.4%.

$4.19(1.05)$50(1 – 0.15)$4.40

$42.50The final realized profit from issuing new common stockwill be given, you will not have to compute P0(1-F).

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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.

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What are the firm’s WACC’s?

WACC = wdkd(1 – T) + wpkp + wsks

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

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

WACC = wdkd(1 – T) + wpkp + weke

= 0.3(10%)(0.6) + 0.1(9%) + 0.6(15.4%)

= 1.8% + 0.9% + 9.24% = 11.94%.

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How to distinguish which WACC is applicable.

Must find the break point, or turning point, for retained earnings: ks

Find NI $50,000,000

Find Dividends paid out 50%

($50,000,000) * (.5) = $25,000,000

Find R/E available $25,000,000

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R/E available $25,000,000

Break point = Addition to Retained Earnings /Equity fraction (weight) used in financing

BP = $25,000,000/.6

BP = $41,666,667 Level of Capital Spending that would have to be reached to use up all the ks.

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So if the company has acceptable capital projects amounting to less than $41,666,667, their weighted average cost of capital will be 11.1%, because they would use their internally generated funds to finance the projects, together with debt and preferred stock.

If acceptable capital projects are greater than $41,666,667, their weighted average cost of capital will be 11.94%, and they would be issuing new common stock to finance the common equity portion of the projects, together with debt and preferred stock.

CHAPTER 10 The Cost of Capital

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