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CHAPTER 11The Cost of Capital

Sources of capital Component costs WACC

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Cost of Capital

The cost of capital represents the overall cost of financing to the firm

The overall cost of capital is a weighted average of the various sources, including debt, preferred stock, and common equity (retained earnings):

WACC = Weighted Average Cost of CapitalWACC = After-tax cost x weights

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What sources of long-term capital do firms use?

Long-Term Capital

Long-Term Debt Preferred Stock Common Stock

Retained Earnings New Common Stock

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Calculating the weighted average cost of capital

WACC = wdrd(1-T) + wpsrps + wers

The w’s refer to the firm’s capital structure weights.

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

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Should our analysis focus on before-tax or after-tax capital costs? Stockholders focus on After-Tax

CFs. Therefore, we should focus on A-Tax capital costs.

Only cost of debt needs adjustment, because interest is tax deductible.

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Should our analysis 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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How are the weights determined?

WACC = wdrd(1-T) + wprp + wers

As a percentage of total financing

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Weighting exampleBonds 40Pref. Stock 100Common 100Ret. Earn. 160Total L & E 400What is weight of each component?

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Weighting exampleBonds 40Pref. Stock 100Common 100Ret. Earn. 160Total L & E 400

Bonds = 40/400 = 10%Pref. Stock = 100/400 = 25%

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Component cost of debt WACC = wdrd(1-T) + wprp + wers

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

L-T debt is often used as a measure of rd.

Why tax-adjust, i.e. why rd(1-T)?

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Sales

1,000

1,000

Interest 100* 0

EBT 900

1,000

Tax 40% 360 400

EAT 540 600

*10% coupon rate for one bond

10% before tax = 6% after tax

60 difference

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Component cost of debt Interest is tax deductible, so

A-T rd = B-T rd (1-T) = 10% (1 - 0.40) = 6%

T = tax rate = 40%

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Component cost of preferred stock

WACC = wdrd(1-T) + wprp + wers

rp is the marginal cost of preferred stock.

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

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What is the cost of preferred stock? The cost of preferred stock can be

solved by using this formula:

rp = Dp / Pp

= $10 / $111.10 = 9%

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Component cost of preferred stock Preferred dividends are not tax-

deductible, so no tax adjustments necessary. Just use rp.

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Component cost of equity WACC = wdrd(1-T) + wprp + wers

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

Issuing new stock would cost a little more due to flotation (selling) costs.

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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.

If earnings are retained, there is an opportunity cost (the return that stockholders could earn on alternative investments of equal risk). Investors could buy similar stocks and earn rs. Firm could repurchase its own stock and earn rs. Therefore, rs is the cost of retained earnings.

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Two ways to determine the cost of common equity, ks

CAPM: rs = rRF + β(rM – rRF)

DCF: rs = (D1 / P0)+ g

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If the rRF = 7%, rM = 13% and the firm’s beta is 1.2, what’s the cost of common equity based upon the CAPM?

rs = rRF + (rM – rRF) β = 7.0% + (6.0%)1.2 = 14.2%

(rm- rRF) = market risk premium

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If D0 = $4.19, P0 = $50, and g = 5%, what’s the cost of common equity based upon the DCF approach? D1 = D0 (1+g) D1 = $4.19 (1 + .05) D1 = $4.4

rs = (D1 / P0)+ g = ($4.4 / $50) + 0.05= 13.8%

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What is a reasonable final estimate of rs?

Method EstimateCAPM 14.2%DCF 13.8%

Average 14.0%

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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.

To adjust rs = (D1/(P0 – F)) + g

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Calculate WACC If 40% of your financing is from

debt at an after tax cost of 8% and 60% is from pref. stock at 10%, what is the WACC?

It will be between what two numbers?

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40% (.08) + 60% (.10) .032 + .06 = .092 9.2%

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Balance Sheet

Cash 5,000 LT Debt 3,000

Equipment 5,000 Pref. Stock 1,000

Stock 6,000

Tot. Assets 10,000 Tot. Debt & Eq. 10,000

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Ignoring floatation costs, what is the firm’s WACC?

WACC = wdrd(1-T) + wprp + wers = 0.3(10%)(0.6) + 0.1(9%) +

0.6(14%)= 1.8% + 0.9% + 8.4%= 11.1%

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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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Optimum Capital Structure

The optimal (best) situation is associated with the minimum overall cost of capital: Optimum capital structure means the lowest

WACC Usually occurs with 30-50% debt in a

firm’s capital structure WACC is also referred to as the required

rate of return or the discount rate

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Optimal Capital Structure Cost (After-tax) Weights Weighted

CostFinancial Plan A:Debt………………………… 6.5% 20% 1.3%Equity………………………. 12.0 80 9.6 10.9%Financial Plan B:Debt………………………… 7.0% 40% 2.8%Equity………………………. 12.5 60 7.5

10.3%Financial Plan C:Debt………………………… 9.0% 60% 5.4%Equity………………………. 15.0 40 6.0 11.4%

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Draw a graph representing the cost of debt and equity

0 40% 80% Debt to Asset Mix

Cost of Capital

5%

10%

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Cost of capital curve