133 Chapter 112002

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Chapter 11 - Cost of Capital

Concept of the Cost of Capital

Computing a Firm’s Cost of Capital

Cost of Individual Sources of Capital

Optimal Capital Structure Marginal Cost of Capital

Combining the MCC and IOS

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Concept of the Cost of Capital

When a firm invests money in aproject, it should earn at least asmuch as it cost the firm to acquirethe funds. Therefore, the cost of

capital may be defined as theminimum acceptable rate of return.

The term “cost of capital” has alsobeen referred to as the firm’srequired rate of return, the hurdlerate, and the opportunity cost.

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Weighted Cost of Capital:

For a given amount of investment capital tobe raised, the cost of capital is a weightedaverage of the after-tax costs of the individualsources of financing.

Example: Assume a firm wishes to raise $10million using 40% debt, 10% preferred stock, and50% common equity financing. Given thefollowing, calculate the firm’s cost of capital.

Source of Financing After-Tax Cost Weight

Debt 8% .4Preferred Stock 10% .1

Common Equity 14% .5

Weighted Average Cost of Capital:

.4(8%) + .1(10%) + .5(14%) = 11.2%

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(Continued)

Questions to be Addressed:

1. What are the costs of the individual

sources of capital? 2. What set of weights (i.e., the capital

structure) is appropriate?

3. What is the relationship between thecost of capital and the amount of investment capital to be raised?

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Cost of Individual Sources of Capital

Cost of Debt (kd)

Note: Flotation costs on new debt (if any) have been ignored

since the majority of debt is privately placed and has noflotation cost. If, however, bonds are publicly placed andinvolve flotation costs, an adjustment could be made to the

before-tax cost of debt.

ratetaxmarginal=T

bond)aonmaturitytoyieldor

debt,newonrateinterest(i.e., debtof costtax-beforeY

debtof costtax-afterk :where

T)Y(1k

d

d

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Cost of Individual Sources (Continued)

Cost of Preferred Stock (kp):

.deductibletaxnotaredividendspreferred

sincerequired,istaxesforadjustmentNo

costsflotationF

stock preferredof priceP

dividendannualD :where

FP

Dk

p

p

p

p

p

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Using the Constant Growth in Dividends Model to

Estimate the Cost of Common Equity

Cost of Common Equity: The rate of return required by the firm’s

common stockholders. An opportunity costconcept (i.e., what rate of return could the

stockholders earn if they invested the funds inother alternatives of comparable risk.) Anextremely difficult number to estimate.

Cost of Retained Earnings (ke):

gP

Dk

0

1e

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Cost of New Common Stock (kn):

(Using the constant growth in dividends model)

Note: If it were not for flotation costs, the costof newly issued common stock would be

equal to the cost of retained earnings.

(They are both sources of common equity).

costsflotationtheF

:where

gF)P

Dk

0

1n

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Using the Capital Asset Pricing Model(CAPM) to Estimate the Cost of

Common Equity

)βR (k R k f mf e

where:

Rf = risk-free rate of return

Km = required return on the market

b = beta coefficient

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Beta Coefficient(Measure of Market Risk)

The extent to which the returns on a given asset

move with the overall market

ReturnssMarket'theinChange

ReturnssAsset'theinChangeβ

Higher betas mean greater risk. For example, a beta of 2.0 indicates that an asset’s return should increase 2%

for every 1% increase in the market. Conversely, the

asset’s return should decrease 2% for every 1%

decrease in the market.

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The CAPM

0

24

6

8

10

12

14

16

18

0 0.5 1 1.5 2

k e

b

The MarketR f

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Optimal Capital Structure

What is the appropriate combination of debt and

equity? If a firm were 100% equity financed (debt

ratio = 0), financial risk would be zero (only business

risk would exist), and the weighted average cost of

capital (ka) would be equal to the cost of equity (ke).Initially, the use of debt may reduce (ka) as a lower

cost of debt is combined with a higher cost of equity.

Beyond some point, however, as added financial risk

drives up both the cost of debt and the cost of equity,(ka) will increase.

Problem: At what level of financial leverage will (ka)

be minimized?

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0

5

10

15

20

25

30

0 0.2 0.4 0.6 0.8

Cost of Capital

ke

ka

kd

Debt/Asset Ratio

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0

5

10

15

20

25

30

35

0 0.2 0.4 0.6 0.8

Stock Price

Debt/Asset Ratio

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0

0.5

1

1.5

2

2.5

0 0.2 0.4 0.6 0.8

Expected EPS

Debt/Asset Ratio

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Marginal Cost of Capital (MCC)

MCC is the cost of obtaining anadditional dollar of new capital. If,during a given period of time, a firmtries to raise more and more

capital, a higher cost of capital mayresult. Whenever any of the costsof the individual sources increase,

the weighted average cost of capital (ka) must be recalculated toreflect the cost of obtaining

additional capital (MCC).

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Marginal Cost of Capital (MCC)(Continued)

To develop a MCC schedule, all break pointsmust be determined, and at each point ka must berecalculated.

A break point is a level of financing at which ka increases because one of the individual costsincreased.

In the example that follows only retained earningsbreak points will be illustrated. In practice,however, changes in the costs of all components(e.g., debt, preferred stock) must be taken intoaccount.

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MCC Schedule

0

5

10

15

0 10 20 30

ka 1ka 2

Break PointMCC

Amount of New Capital($ millions)

EquityCommonof Weight

EarningsRetainedoAddition t

PointBreak

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Combining the MCC and InvestmentOpportunities Schedule (IOS)

A firm should continue to invest funds aslong as the rates of return received on the

investments exceed the firm’s cost of acquiring the investment capital. In thefollowing graph the firm should acceptprojects A and B, and reject project C. The

point of intersection determines the firm’soptimal capital budget, and the firm’s cost

of capital for its average risk projects.

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MCC and IOS Schedules

0

2

4

6

8

10

12

14

16

18

20

0 10 20 30

Percent

MCC

IOS

AB

C

Amount of New Capital ($ millions)

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