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
Concept of the Cost of Capital
 When a firm invests money in a
project, it should earn at least as
much as it cost the firm to acquire
the funds. Therefore, the cost of
capital may be defined as the
minimum acceptable rate of return.
 The term “cost of capital” has also
been referred to as the firm’s
required rate of return, the hurdle
rate, and the opportunity cost.
Computing a Firm’s Cost of Capital
 Weighted Cost of Capital:

For a given amount of investment capital to
be raised, the cost of capital is a weighted
average of the after-tax costs of the individual
sources of financing.
 Example: Assume a firm wishes to raise $10
million using 40% debt, 10% preferred stock, and
50% common equity financing. Given the
following, calculate the firm’s cost of capital.
Source of Financing After-Tax Cost Weight
Debt
8%
.4
Preferred Stock
10%
.1
Common Equity
14%
.5
Weighted Average Cost of Capital:
.4(8%) + .1(10%) + .5(14%) = 11.2%
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 the
cost of capital and the amount of
investment capital to be raised?
Cost of Individual Sources of Capital
 Cost of Debt (kd)
k d  Y(1  T)
where : k d  after - tax cost of debt
Y  before - tax cost of debt
(i.e., interest rate on new debt,
or yield to maturity on a bond)
T = marginal tax rate
Note: Flotation costs on new debt (if any) have been ignored
since the majority of debt is privately placed and has no
flotation cost. If, however, bonds are publicly placed and
involve flotation costs, an adjustment could be made to the
before-tax cost of debt.
Cost of Individual Sources (Continued)
 Cost of Preferred Stock (kp):
kp 
Dp
Pp  F
where : Dp  annual dividend
Pp  price of preferred stock
F  flotation costs
No adjustment for taxes is required, since
preferred dividends are not tax deductible .
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 cost
concept (i.e., what rate of return could the
stockholders earn if they invested the funds in
other alternatives of comparable risk.) An
extremely difficult number to estimate.
 Cost of Retained Earnings (ke):
D1
ke   g
P0
 Cost of New Common Stock (kn):
(Using the constant growth in dividends model)
D1
kn 
g
P0  F)
where :
F  the flotation costs
Note: If it were not for flotation costs, the cost
of newly issued common stock would be
equal to the cost of retained earnings.
(They are both sources of common equity).
Using the Capital Asset Pricing Model
(CAPM) to Estimate the Cost of
Common Equity
k e  R f  (k m  R f )β
 where:
 Rf = risk-free rate of return
 Km = required return on the market
 b = beta coefficient
Beta Coefficient
(Measure of Market Risk)

The extent to which the returns on a given asset
move with the overall market
Change in the Asset's Returns
β
Change in the Market's Returns
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.
The CAPM
ke
18
16
14
12
10
8
Rf 6
4
2
0
The Market
0
0.5
1
1.5
2
b
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?
Cost of Capital
30
ke
25
20
ka
15
kd
10
5
0
0
0.2
0.4
0.6
Debt/Asset Ratio
0.8
Stock Price
35
30
25
20
15
10
5
0
0
0.2
0.4
0.6
Debt/Asset Ratio
0.8
Expected EPS
2.5
2
1.5
1
0.5
0
0
0.2
0.4
0.6
Debt/Asset Ratio
0.8
Marginal Cost of Capital (MCC)
 MCC is the cost of obtaining an
additional dollar of new capital. If,
during a given period of time, a firm
tries to raise more and more
capital, a higher cost of capital may
result. Whenever any of the costs
of the individual sources increase,
the weighted average cost of
capital (ka) must be recalculated to
reflect the cost of obtaining
additional capital (MCC).
Marginal Cost of Capital (MCC)
(Continued)
 To develop a MCC schedule, all break points must
be determined, and at each point ka must be
recalculated.
 A break point is a level of financing at which ka
increases because one of the individual costs
increased.
 In the example that follows only retained earnings
break points will be illustrated. In practice,
however, changes in the costs of all components
(e.g., debt, preferred stock) must be taken into
account.
MCC Schedule
Addition to Retained Earnings
Break Point 
Weight of Common Equity
MCC
Break Point
15
10
ka 2
ka 1
5
0
0
10
20
Amount of New Capital
($ millions)
30
Combining the MCC and Investment
Opportunities Schedule (IOS)
 A firm should continue to invest funds as
long as the rates of return received on the
investments exceed the firm’s cost of
acquiring the investment capital. In the
following graph the firm should accept
projects A and B, and reject project C. The
point of intersection determines the firm’s
optimal capital budget, and the firm’s cost
of capital for its average risk projects.
MCC and IOS Schedules
Percent
A
20
18
16
14
12
10
8
6
4
2
0
B
MCC
C
0
10
20
IOS
30
Amount of New Capital ($ millions)