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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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Computing a Firm’s Cost of Capital
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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Computing a Firm’s Cost of Capital
(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)