CHAPTER 13
The Cost of Capital

Sources of capitalComponent costsWACC

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Cost of Capital

The cost of capital represents the overall cost of financing to the firmThe cost of capital is normally the relevant discount rate to use in analyzing an investmentThe overall cost of capital is a weighted average of the various sources, including debt, preferred stock, and common equity:

WACC = Weighted Average Cost of Capital

WACC = After-tax costs 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 = xd(pretax kd)(1-Tax rate) + xpskps + xcskcs

The xs refer to the firms capital structure weights.The ks refer to the cost of each component.

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Should our analysis focus on before-tax or after-tax 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 costs or new (marginal) costs?

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

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How are the weights determined?

WACC = xd(pretax kd)(1-Tax rate) + xpkp + xcskcs

As a percentage of total financing

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Weighting example

Bonds 40

Pref. Stock 100

Common 100

Ret. Earn. 160

Total L & E 400

What is weight of each component?

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Weighting example

Bonds 40

Pref. Stock 100

Common 100

Ret. Earn. 160

Total L & E 400

Bonds = 40/400 = 10%

Pref. Stock = 100/400 = 25%

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Component cost of debt

WACC = xd(pretax kd)(1-T) + xpkp + xcskcs

kd is the marginal cost of debt capital.The yield to maturity on outstanding L-T debt is often used as a measure of kd.Why tax-adjust, i.e. why kd(1-Tax rate)?

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If tax rate is 40% then
10% before tax = 6% after tax

60 difference

Sales 1,000 1,000 Interest100*0EBT900 1,000 Tax 40%360400EAT540600

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Component cost of debt

Interest is tax deductible, so

aftertax kd = pretax kd (1-T)

= 10% (1 - 0.40) = 6%

T = tax rate = 40%

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Cost of debt

What is the current cost of debt for a firm that has a 9% coupon bond with 5 years to maturity and a current price of $962?What is the after tax cost if it is in the 40% tax bracket?

Component cost of
preferred stock

WACC = xdkd(1-T) + xpkp + xcskcs

kp is the marginal cost of preferred stock.The rate of return investors require on the firms 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:

kp = Dp / Pp

= $8 / $111

= 7.2%

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Component cost of
preferred stock

Preferred dividends are not tax-deductible, so no tax adjustments necessary.

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Component cost of equity

WACC = xd(pretax kd)(1-T) + xpkp + xcskcs

kcs is the marginal cost of common equity

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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 kcs.Firm could repurchase its own stock and earn kcs.Therefore, kcs is the cost of retained earnings.

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Two ways to determine the cost of common equity, kcs

1. CAPM: kcs = RRF + x (Mkt. risk premium [E(RM) RRF])

RRF = Risk Free Rate (now around 2.7%)RM = Return on the market = Beta - the relation of its returns with that of the stock market e.g. 0 not correlated 1 - moves with the market 2 twice as volatile

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Two ways to determine the cost of common equity, kcs

2. DCF: P0 = (D1 / r - g)

r = kcs

kcs = (D1 / P0)+ g

If the market premium is 6%, risk-free rate is 2.7% and the firms beta is 1.48, whats the cost of common equity based upon the CAPM?

kcs = RRF + (mkt premium)

= 2.7% + 1.48(6.0%) = 11.58%

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If D0 = $1.72, P0 = $43, and g = 5%, whats the cost of common equity based upon the DCF approach?

D1 = D0 (1+g)

D1 = $1.72 (1 + .05)

D1 = $1.81

kcs = (D1 / P0)+ g

= ($1.81 / $43) + 0.05

= 9.2%

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What is a reasonable final estimate of kcs?

MethodEstimate

CAPM 11.58%

DCF 9.2%

Average 10.4%

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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 = .0929.2%

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Balance Sheet
use costs that were just calculated

Market values

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 issuance costs, what is the firms WACC?

WACC = xd(pretax kd)(1-Tax) + xpkp + xcskcs

= .3(10%)(0.6) + .1(7.2%) + .6(10.4%)

= 1.8% + 0.72% + 6.2%

= 8.7%

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WACC

You are analyzing the cost of capital for a firm that is financed with 60 percent equity and 40 percent debt. The after-tax cost of debt capital is 10 percent, while the cost of equity capital is 20 percent for the firm. What is the overall cost of capital for the firm?(.6 x .2) + (.4 x .1) = 16%

Equity + Debt

Cardinal Health has bonds outstanding with 15 years to maturity and are currently priced at $800. If the bonds have a coupon rate of 8.5 percent, then what is the after-tax cost of debt for Beckham if its marginal tax rate is 30%? 7.9%

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 projects WACC should be adjusted to reflect the projects 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 WACCUsually occurs with 30-50% debt in a firms capital structureWACC 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 Cost

Financial 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%

Cost of capital curve

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