Cost of Capital Rev 1.0

7/29/2019 Cost of Capital Rev 1.0

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Chapter 11

The Costof Capital


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Copyright 2006 Pearson Addison-Wesley. All rights reserved. 11-2

The Firms Capital Structure


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Some Key Assumptions

Business Riskthe risk to the firm of being unable tocover operating costsis assumed to be unchanged.This means that the acceptance of a given project doesnot affect the firms ability to meet operating costs.

Financial Riskthe risk to the firm of being unable tocover required financial obligationsis assumed to beunchanged. This means that the projects are financedin such a way that the firms ability to meet financing

costs is unchanged. After-tax costs are considered relevantthe cost of

capital is measured on an after-tax basis.


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Specific Sources of Capital:The Cost of Long-Term Debt

The pretax cost of debt is equal to the the yield-to-maturity on the firms debt adjusted for flotation costs.

Recall that a bonds yield-to-maturity depends upon a

number of factors including the bonds coupon rate,maturity date, par value, current market conditions, andselling price.

After obtaining the bonds yield, a simple adjustment

must be made to account for the fact that interest is atax-deductible expense.

This will have the effect of reducing the cost of debt.


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Duchess Corporation, a major hardware manufacturer, iscontemplating selling $10 million worth of 20-year, 9% coupon

bonds with a par value of $1,000. Because current market

interest rates are greater than 9%, the firm must sell the bonds

at $980. Flotation costs are 2% or $20. The net proceeds to

the firm for each bond is therefore $960 ($980 - $20).

Net Proceeds

Specific Sources of Capital:The Cost of Long-Term Debt (cont.)


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Before-Tax Cost of Debt

Approximating the Cost



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Find the after-tax cost of debt for Duchessassuming it has a 40% tax rate:

ki = 9.4% (1-.40) = 5.6%

This suggests that the after-tax cost of raisingdebt capital for Duchess is 5.6%.



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Duchess Corporation is contemplating the issuance of a

10% preferred stock that is expected to sell for its $87-per

share value. The cost of issuing and selling the stock is

expected to be $5 per share

Specific Sources of Capital:The Cost of Preferred Stock


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Duchess Corporation is contemplating the issuance of a10% preferred stock that is expected to sell for its $87-per

share value. The cost of issuing and selling the stock is

expected to be $5 per share. The dividend is $8.70 (10%

x $87). The net proceeds price (Np) is $82 ($87 - $5).

KP = DP/Np = $8.70/$82 = 10.6%

Specific Sources of Capital:The Cost of Preferred Stock


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Specific Sources of Capital:The Cost of Common Stock

There are two forms of common stock financing:retained earnings and new issues of common stock.

In addition, there are two different ways to estimate the

cost of common equity: any form of the dividendvaluation model, and the capital asset pricingmodel (CAPM).

The dividend valuation models are based on thepremise that the value of a share of stock is based onthe present value of all future dividends.


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kS = (D1/P0) + g

kE = rF + b(kM - RF).

Using the constant growth model, we have:

We can also estimate the cost of commonequity using the CAPM:

Specific Sources of Capital:The Cost of Common Stock (cont.)


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ks = D1/P0 + g

For example, assume a firm has just paid a dividend of

$2.50 per share, expects dividends to grow at 10%

indefinitely, and is currently selling for $50.00 per share.

First, D1 = $2.50(1+.10) = $2.75, and

kS = ($2.75/$50.00) + .10 = 15.5%.


Cost of Retained Earnings (kE)

Constant Dividend Growth Model


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ks = rF + b(kM - RF).

For example, if the 3-month T-bill rate is currently 5.0%,

the market risk premium is 9%, and the firms beta is

1.20, the firms cost of retained earnings will be:

ks = 5.0% + 1.2 (9.0%) = 15.8%.

Cost of Retained Earnings (kE)

Security Market Line Approach



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kn = = D1/Nn - g

Continuing with the previous example, how much would it

cost the firm to raise new equity if flotation costs amountto $4.00 per share?

kn = [$2.75/($50.00 - $4.00)] + .10 = 15.97% or 16%.

Cost of New Equity (kn)

Constant Dividend Growth Model



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WACC = ka = wiki + wpkp + wskr or n

The weights in the above equation are intended to

represent a specific financing mix (where wi = % of

debt, wp = % of preferred, and ws= % of common).

Specifically, these weights are the target percentages

of debt and equity that will minimize the firms overall

cost of raising funds.

The Weighted Average Cost of Capital

Capital Structure Weights


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One method uses boo k valuesfrom the firms balance

sheet. For example, to estimate the weight for debt,

simply divide the book value of the firms long-term debt

by the book value of its total assets.

To estimate the weight for equity, simply divide the total

book value of equity by the book value of total assets.


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A second method uses the market valuesof the firms debtand equity. To find the market value proportion of debt,

simply multiply the price of the firms bonds by the number

outstanding. This is equal to the total market value of the

firms debt.

Next, perform the same computation for the firms equity

by multiplying the price per share by the total number of

shares outstanding.





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Finally, add together the total market value of the firms

equity to the total market value of the firms debt. This

yields the total market value of the firms assets.

To estimate the market value weights, simply dividend

the market value of either debt or equity by the market

value of the firms assets .


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For example, assume the market value of the firms debt is $40

million, the market value of the firms preferred stock is $10

million, and the market value of the firms equity is $50 million.

Dividing each component by the total of $100 million gives us

market value weights of 40% debt, 10% preferred, and 50%

common.


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Using the costs previously calculated along with the

market value weights, we may calculate the weighted

average cost of capital as follows:

WACC = .40(5.67%) + .10(9.62%) + .50(15.8%)

= 11.13%

This assumes the firm has sufficient retained earnings to

fund any anticipated investment projects.


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The Weighted Average Cost of Capital:Economic Value Added (EVA)

EVA is a popular measure used by firms todetermine whether an investment contributes toowners wealth.

EVA can be calculated as the differencebetween Net Operating Profits After Taxes(NOPAT) and the cost of funds used to financethe investment.

The cost of funds is found by multiplying thedollar amount of funds used to finance theinvestment by the firms WACC.


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For Example, the EVA of an investment of $3.75 million

by a firm with a WACC of 10% in a project expected to

generate NOPAT of $410,000 would be:

EVA = $410,000 (10% x $3,750,000) = $35,000

Because the EVA is positive, the proposed investment isexpected to increase owner wealth and is therefore

acceptable.

The Weighted Average Cost of Capital:Economic Value Added (EVA)

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Cost of Capital Rev 1.0