The Cost of CapitalThe Cost of Capital

Chapter 12

Cost of CapitalCost of Capital

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

What must be paid to attract funds

The use of debt impacts a fim’s ability to use equity, and vice versa, so the weighted average cost must be used to evaluate projects, regardless of the specific financing used to fund a particular project

The Logic of the Weighted The Logic of the Weighted Average Cost of CapitalAverage Cost of Capital

Basic DefinitionsBasic Definitions

Capital component types of capital used by firms to raise

money

kd = before tax interest cost

kdT = kd(1-T) = after tax cost of debt

kps = cost of preferred stock

ks = cost of retained earnings

ke = cost of external equity (new stock)

Basic DefinitionsBasic Definitions

WACC = weighted average cost of capital

Capital structure combination of different types of capital

used by a firm

After-Tax Cost of DebtAfter-Tax Cost of Debt

The relevant cost of new debt—its yield to maturity (YTM)

Taking into account the tax deductibility of interest

Used to calculate the WACC kdT = bondholders’ required rate of

return minus tax savings kdT = kd - (kd T) = kd(1-T)

Cost of Preferred StockCost of Preferred Stock

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

the preferred dividend divided by the net issuing price

costs Flotation-P

D

NP

Dk

0

pspsps ==

s0

1RFs k̂

P

D̂RPkk =+=+= g

Cost of Retained EarningsCost of Retained Earnings

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

Three solutions:1. CAPM2. Bond yield plus risk premium3. Discounted cash flow (DCF)

The CAPM ApproachThe CAPM Approach

( ) sRFMRFs â k - kkk +=

The Bond-Yield-Plus-The Bond-Yield-Plus-Premium ApproachPremium Approach

Estimate a risk premium above the bond interest rate

Judgmental estimate for premium “Ballpark” figure only

14% 4% 10%

premium Risk yield Bond k s

=+=+=

The Discounted Cash Flow The Discounted Cash Flow (DCF) Approach(DCF) Approach

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

( ) ( ) ( )

( )∑∞

=

∞∞

+=

+++

++

+=

1tt

s

t

sss

k1

D̂

k1

D̂

k1

D̂

k1

D̂P L

22

11

0

DCF ApproachDCF Approach

Internal equity, ks

based on the fact that investors demand the firm use funds that are retained to earn an appropriate rate of return

gP

D̂k

0

1s +=

Cost of Newly Issued Cost of Newly Issued Common StockCommon Stock

External equity, ke

based on the cost of retained earnings adjusted for flotation costs (the expenses of

selling new issues)

( ) gFP

D̂g

NP

D̂k

0

11e +

−=+=

1

Optimal capital structure percentage of debt, preferred stock, and

common equity that will maximize the price of the firm’s stock

Target Capital StructureTarget Capital Structure

Weighted Average Cost of Weighted Average Cost of Capital, WACCCapital, WACC

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

k

W

k

W

k

W

equity

common

ofCost

equity

common of

Proportion

stock

preferred

ofCost

stock

preferred of

Proportion

debt

ofcost

tax-After

debt

of

Proportion

sspspsdTd ×+×+×=

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛×⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛+

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛×⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛+

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛×⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛=

Marginal Cost of CapitalMarginal Cost of Capital

MCC the cost of obtaining another dollar of new

capital the weighted average cost of the last dollar

of new capital raised

MCC ScheduleMCC Schedule

Marginal cost of capital schedule a 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

Weighted 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%

MCC ScheduleMCC Schedule

Break PointBreak Point

BP the dollar value of new capital that can be

raised before an increase in the firm’s weighted average cost of capital occurs

Point structure capital the in capital of type this of Proportion

type given a of capitalcost lower ofamount TotalBreak=

Weighted 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

MCC ScheduleMCC Schedule

MCC ScheduleMCC Schedule

Schedule and break points depend on capital structure used

Weighted Average Cost of Capital (WACC) (%)

Dollars of New Capital Raised0 -

WACC

Smooth, or Continuous, Marginal Cost of Capital Schedule

MCC ScheduleMCC Schedule

Combining the MCC and Combining the MCC and Investment Opportunity SchedulesInvestment Opportunity Schedules

Use the MCC schedule to find the cost of capital for determining whether a project should be purchased

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

opportunities ranked in order of the projects’ rates of return

Percent

New Capital Raised and invested (millions of dollars)20 40 60 80 100 120 140 160 180

12.0 -

11.5 -

11.0 -

10.5 -

MCC

IOS

WACC1=10.5%

WACC2=11.0%

WACC3=11.5%

ReturnC = 12.0%

ReturnB = 11.6%ReturnD = 11.5%

ReturnE = 11.3%

IRRA = 10.8%

Optimal Capital Budget - $139

Combining the MCC and Combining the MCC and Investment Opportunity SchedulesInvestment Opportunity Schedules

End of Chapter 12End of Chapter 12

The Cost of Capital