Chapter 8

The Cost of Capital

© 2005 Thomson/South-Western

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Cost of Capital

Firm’s average cost of funds, which is the average return required by firm’s investors

What must be paid to attract funds

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Required Rate of Return(Opportunity Cost Rate)

The return that must be raised on invested funds to cover the cost of financing such investments

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The Logic of the Weighted Average Cost of Capital = WACC

The use of debt impacts the ability to use equity, and vice versa.

The weighted average cost must be used to evaluate projects, regardless of the specific financing used to fund a particular project.

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Basic Definitions Capital Component

Types of capital used by firms to raise moneykd = before tax interest costkdT = kd(1-T) = after tax cost of debtkps = cost of preferred stockks = cost of retained earningske = cost of external equity (new

stock)

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Basic Definitions

WACC Weighted Average Cost of Capital

Capital StructureA combination of different types of capital (debt and equity) used by a firm

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After-Tax Cost of DebtThe relevant cost of new debtTakes into account the tax deductibility of interestUsed to calculate the WACC

kdT = bondholders’ required rate of return minus tax savings

kdT = kd - (kd x T) = kd(1-T)

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Cost of Preferred Stock Rate of return investors require on

the firm’s preferred stock The preferred dividend divided by

the net issuing price

)F1(P

D

costs FlotationP

D

NP

Dk

0

ps

0

pspsps

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sk̂ g

0P

1D̂

RP RF

ks

k

Cost of Retained Earnings

Rate of return investors require on the firm’s common stock

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The CAPM Approach

sRFk- MkRFksk ( )

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The Discounted Cash Flow Approach

Price and expected rate of return on a share of common stock depend on the dividends expected on the stock.

Can use when growth (g) is constant

g0

P1

D̂

sk̂

sk

1214% 4% 10%

premium Risk yield Bond s

k

The Bond-Yield-Plus-Premium Approach

Estimating a risk premium above the bond interest rate

Judgmental estimate for premium“Ballpark” figure only

13 g

F10P1D̂

gNP

1D̂ek

Cost of Newly Issued Common Stock

External equity, keBased on the cost of retained

earningsAdjusted for flotation costs (the

expenses of selling new issues)

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Target Capital Structure

Optimal Capital StructurePercentage of debt, preferred stock,

and common equity in the capital structure that will maximize the price of the firm’s stock

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sspspsdTd k

w

k

w

k

w

equitycommon

of Cost

equitycommon of

Proportion

stockpreferred

of Cost

stockpreferred of

Proportion

debt of cost

tax-After

debtof

Proportion

Weighted Average Cost of Capital, WACC

A weighted average of the component costs of debt, preferred stock, and common equity

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Marginal Cost of Capital

MCCCost of obtaining another dollar of

new capitalWeighted average cost of the last

dollar of new capital raised

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Marginal Cost of Capital

Marginal Cost of Capital ScheduleA graph that relates the firm’s

weighted average of each dollar of capital to the total amount of new capital raised

Reflects changing costs, depending on amounts of capital raised

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Marginal Cost of Capital (MCC) Schedule

Weighted Average Cost of Capital (WACC) (%)

100 150

New Capital Raised (millions of dollars)

11.5 -

11.0 -

10.5 -WACC1=10.5%

WACC2=11.0%

WACC3=11.5%

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Point structure capital in the capital of type thisof Proportiongiven type a of capitalcost lower ofamount TotalBreak

Break PointBP

The dollar value of new capital that can be raised before an increase in the firm’s weighted average cost of capital occurs

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Point structure capital in the capital of type thisof Proportiongiven type a of capitalcost lower ofamount TotalBreak

Break Point Formulas

BPdebt = debt/% debt BPret earn = retained earnings/% equity If the capital budget $ > breakpoint $,

the cost of capital will be at the next higher interest rate

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MCC ScheduleWeighted Average Cost of Capital (WACC) (%)

New Capital Raised (millions of dollars)

100 150

11.5 -

11.0 -

10.5 -WACC1=10.5%

WACC2=11.0%

WACC3=11.5%

BPRE BPDebt

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MCC Schedule

Schedule and break points depend on capital structure used.

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Combining the MCC and Investment Opportunity Schedules

Use the MCC schedule to find the cost of capital for determining projects’ net present values.

Investment Opportunity Schedule (IOS)Graph of the firm’s investment

opportunities ranked in order of the projects’ internal rate of return

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Optimal Capital Budget - $115

Combining the MCC and Investment Opportunity Schedules

New Capital Raised and invested (millions of dollars)

IRRC = 12.1%

IRRB = 11.7%IRRD = 11.5%

IRRE = 11.3%

IRRA = 10.2%

Percent

20 40 60 80 100 120 140 160

12.0 -

11.0 -

10.0 -

MCC

IOSWACC1=10.0%

WACC3=11.0%

WACC2=10.5%

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Before Next Class:

1.Review Chapter 82.Do chapter 8 homework3.Prepare for Chapter 8 quiz4.Read chapter 9