11
Cost of Capital
Chapter
McGraw-Hill/Irwin
Copyright © 2008 by The McGraw-Hill Companies,
Inc. All rights reserved.
Chapter 11 - Outline
•
•
•
•
PPT 11-2
Cost of Capital
Cost of Debt
Cost of Preferred Stock
Cost of Common Equity:
– Common Stock
– Retained Earnings
•
•
•
•
Optimum Capital Structure
Marginal Cost of Capital
The Security of Market Line
Summary and Conclusions
1-2
PPT 11-3
Cost of Capital
• The cost of capital represents the overall cost of future
financing to the firm
• The cost of capital is normally the relevant discount
rate to use in analyzing an investment
– It represents the minimal acceptable return from the investment
– If your cost of funds is 10%, you must earn at least 10% on your investments
to break even!
• The cost of capital is a weighted average of the
various sources of funds in the form of debt and equity
WACC = Weighted Average Cost of Capital
1-3
Steps in measuring a firm’s cost of
capital
1.
Compute the cost of each source of capital.
2.
Assign weights to each source.
Conversion of historical
cost of capital structure to market values may be required.
3.
Compute the weighted average of the component costs.
1-4
Cost of Capital – Baker Corporation
1-5
Cost of Debt
• Measured by interest rate, or yield, paid to
bondholders
– Example: $1,000 bond paying $100 annual
interest – 10% yield
– Calculation is complex discount rate or premium
from par value bonds
• To determine the cost of a new debt in the
marketplace:
– The firm will compute the yield on its currently
outstanding debt
1-6
Approximate Yield to Maturity (Y')
Annual interest payment + Principal payment – Price of the bond
Number of years to maturity
0.6 (Price of the bond) + 0.4 (Principal payment)
• Assuming:
Y' = $101. 50 +
$1,000 - $940
20
.6 ($940) + .4 ($1,000)
= $101.50 + 60
20
$564 + $400
Y’ = $101.50 + 3 = $104.50 = 10.84%
$964
$964
1-7
Tax and flotation cost consideration
•
Market-determined yields on various
financial instruments will equal the cost of
those instruments to the firm with adjustment
tax and flotation cost consideration
1-8
Adjusting Yield
for Tax Considerations
• Yield to maturity indicates how much the firm
has to pay on a before-tax basis
• Interest payment on a debt is a taxdeductible expense
– Due to this, the true cost is less than the stated
cost
1-9
Adjusting Yield
for Tax Considerations (cont’d)
• The after-tax cost of debt is calculated as shown
below:
• Assuming:
1-10
PPT 11-6
Yield of Preferred Stock
Preferred stock:
– has a fixed dividend (similar to debt)
– has no maturity date
– dividends are not tax deductible and are expected to be perpetual or
infinite
Yield of preferred stock
Yield of new preferred stock
=
annual dividend
price of stock
=
annual dividend
price-flotation costs
Flotation costs: selling and distribution costs (such as sales commissions) for
the new securities
1-11
Cost of Preferred Stock (cont’d)
• The cost of preferred stock is as follows:
• Where,
= Cost of preferred stock;
= Annual dividend on
preferred stock;
= Price of preferred stock; F =
Floatation, or selling cost
• Assuming annual dividend as $10.50, preferred stock is
$100, and flotation, or selling cost is $4. Effective cost is:
=
$10.50 = $10.50 = 10.94%
$100 - $4
$96
1-12
Cost of Common Equity –
Valuation Approach
• In determining the cost of common stock, the firm must be sensitive to
pricing and performance demands of current and future stockholders
• Dividend valuation model:
• Where,
= Price of the stock today; = Dividend at the end of the year (or
period);
= Required rate of return; g = Constant growth rate in
dividends
• Assuming = $2;
= $40 and g = 7%,
equals 12 percent
=
$2 + 7% = 5% + 7% = 12%
$40
1-13
Alternate Calculation of the
Required Return on Common Stock
• Capital asset pricing model (CAPM)
• Where:
= Required return on common stock;
= Risk-free rate of return,
usually the current rate on Treasury bill securities; = Beta coefficient
(measures the historical volatility of an individual stock’s return relative
to a stock market index;
= return in the market as measured by an
approximate index
• Assuming = 5.5%,
= 12%, = 1.0,
would be:
= 5.5% + 1.0 (12% - 5.5%) = 5.5% + 1.0 (6.5%)
= 5.5% + 6.5% = 12%
1-14
Cost of Retained Earnings
• Sources of capital for common stock equity:
– Purchaser of the new shares – external source
– Retained earnings – internal source
• Represent the present and past earnings of the firm
minus previously distributed dividends
• Belong to the current stockholders – may be paid in
the form of dividends or reinvested in the firm
• Reinvestments represent a source of equity capital
supplied by the current stockholders
• An opportunity cost is involved
1-15
Cost of Retained Earnings (cont’d)
• The cost of retained earnings is equivalent to the rate of return on the
firm’s common cost representing the opportunity cost
•
represents both the required rate of return on common stock, and
the cost of equity in the form of retained earnings
• For ease of reference,
= Cost of common equity in the form of retained earnings
= Dividend at the end of the first year, $2
= Price of stock today, $40
g = Constant growth rate in dividends, 7%
= $2 + 7% = 5% + 7% = 12%
$40
1-16
Cost of New Common Stock
• A slightly higher return than , representing
the required rate of return of present
stockholders, is expected
– Needed to cover the distribution costs of the
new securities
Common stock
New common stock
1-17
Cost of New Common Stock (cont’d)
• Assuming
= $2,
$4 and g = 7%;
= $40, F (Flotation or selling costs) =
=
$2
+ 7%
$40 - $4
= $2 + 7%
$36
= 5.6% + 7% = 12.6%
1-18
Overview of Common Stock Costs
1-19
Optimum Capital Structure
PPT 11-8
The optimum (best) situation is associated
with the minimum overall cost of capital:
– Optimum capital structure means the lowest
WACC
– Usually occurs with 40-70% debt in a firm’s
capital structure
– WACC is also referred to as the required rate of
return or the discount rate
– Based upon the market value rather than the
book value of the firm’s debt and equity
1-20
Optimal Capital Structure –
Weighting Costs (cont’d)
• Assessment of different plans (next slide):
– Firm is able to initially reduce weighted average
cost of capital with debt financing
– Beyond Plan B, continued use of debt becomes
unattractive and greatly increases costs of
sources of financing
1-21
Optimal Capital Structure –
Weighting Costs (cont’d)
Cost (After-tax)
Weights
Weighted Cost
Financial Plan A:
Debt…………………………
Equity……………………….
6.5%
12.0
20%
80
1.3%
9.6
10.9%
Financial Plan B:
Debt…………………………
Equity……………………….
7.0%
12.5
40%
60
2.8%
7.5
10.3%
Financial Plan C:
Debt…………………………
Equity……………………….
9.0%
15.0
60%
40
5.4%
6.0
11.4%
1-22
Cost of Capital Curve
1-23
Debt as a Percentage of Total Assets
(2006)
1-24
Capital acquisition and investment
decision making
• The discount rate used in evaluating capital projects should
be the weighted average cost of capital.
• If the cost of capital is earned on all projects, the residual
claimants of the earnings stream, the owners, will receive
their required rate of return. If the overall return of the firm is
less than the cost of capital, the owners will receive less
than their desired rate of return because providers of debt
capital must be paid.
• For most firms, the cost of capital is fairly constant within a
reasonable range of debt-equity mixes. Changes in money
and capital market conditions (supply and demand for
money), however, cause the cost of capital for all firms to
vary upward and downward over time.
1-25
Cost of capital over time
Cost of capital (Ka)
Ka t
Ka t + 1
Ka t + 2
y
x
Debt-equity mix (percent)
1-26
Investment Projects Available
to the Baker Corporation
1-27
Cost of capital and investment projects for
the Baker Corporation
Percent
16.0
14.0
12.0
10.0
8.0
-
A
B
C
10.41%
D
E
F
4.0 2.0 0.0 -
G
H
6.0
10 15 19
39
50
70
Amount of capital ($ millions)
85
Ka Weighted
average
cost of
capital
95
1-28
The Marginal Cost of Capital
• The market may demand a higher cost of
capital for each amount of fund required if a
large amount of financing is required
– Equity (ownership) capital is represented by
retained earnings
• Retained earnings cannot grow indefinitely as the
firm’s capital needs to expand
• Retained earnings is limited to the amount of past
and present earnings that can be redeployed into
investments
1-29
The Marginal Cost of Capital (cont’d)
• Assumptions:
– 60% is the amount of equity capital a firm must maintain to keep a
balance between fixed income securities and ownership interest
– Baker Corporation has $23.40 million of retained earning available
for investment
• There is adequate retained earning to support the capital structure as
shown below:
• Assuming: X =
Retained earnings
;
Percent of retained earnings in the capital structure
• Where X represents the size of the capital structure that retained
earnings will support
X = $23.40 million = $39 million
.60
1-30
Costs of Capital for
Different Amounts of Financing
1-31
Increasing Marginal Cost of Capital
• Both
and
represent the cost of capital
– The mc subscript after K indicates the increase
in cost of capital
• Increase is because common equity is now
in the form of new common stock rather than
retained earnings
• The aftertax cost of the new common stock
is more expensive than retained earnings
because of flotation costs
1-32
Increasing Marginal Cost of Capital
(cont’d)
• Equation for the cost of new common stock:
=
$2
+ 7% = $2 + 7% = 5.6% + 7% = 12.6%
$40 - $4
$36
• The $50 million figure can be derived thus:
Z =
Amount of lower-cost debt
;
Percent of debt in the capital structure
Z = $15 million = $50 million
.30
• Where Z represents the size of the capital structure in which lower-cost
debt can be used
1-33
Cost of Capital for
Increasing Amounts of Financing
1-34
Changes in the
Marginal Costs of Capital
1-35
PPT 11-16
Marginal cost of capital and Baker
Corporation investment alternatives
Percent
16.0
14.0
12.0
10.0
8.0
-
A
B
10.77%
C
11.23%
Kmc Marginal
cost of
capital
10.41%
D
E
F
4.0 2.0 0.0 -
G
H
6.0
10 15 19
39
50
70
Amount of capital ($ millions)
85
95
1-36
Cost of Components
in the Capital Structure
1-37
Basic form of the CAPM
The basic form of the CAPM is a linear relationship between
returns on individual stocks and the market over time.
Using least squares regression analysis, the return
Kj = α + βRm + e
Where:
Kj = return on individual common stock of company
α = Alpha, the intercept on the y-axis
β = Beta, the coefficient
Rm = Return on the stock market
e = Error term of the regression equation
1-38
PPT 11-18
Table 11A-1
Performance of PAI and the market
Rate of Return on Stock
Year
PAI
Market
1 . . . . . . . . . . . .
12.0%
2 . . . . . . . . . . . .
16.0
18.0
3. . . . . . . . . . . .
20.0
16.0
4 . . . . . . . . . . . .
16.0
10.0
5 . . . . . . . . . . . .
6.0
8.0
Mean return
Standard deviation
14.0%
4.73%
10.0%
12.4%
3.87%
1-39
Linear regression of returns between PAI and
the market
Return on PAI
common stock Kj
Percent (y)
21.0
Kj =  j Rm + ej
(3)
= 2.8 + .9 (Rm ) + ej
(4)
(1)
15.0
(2)
.9
9.0
Beta =  j = Slope of the line
(5)
3.0
2.8

3.0
9.0
15.0
21.0
Return on the market Rm
(x)
Rm
1-40
PPT 11-20
Linear regression of returns between
PAI and the market
Year
1. . . . .
2. . . . .
3. . . . .
4. . . . .
5. . . . .
Kj
Rm
12%
16%
20%
16%
6%
70%
10%
18%
16%
10%
8%
62%
Kj Rm
936
Kj  Rm
4,340
 Rm2
844
(  Rm )2
3,844
n Kj Rm – Kj Rm
5(936) - 4,340
j 


n  Rm2 – (  Rm )2
5(844) - 3,844

Kj –  Rm
70 - 0.9 (62)


n
5
1-41
PPT 11-21
Linear regression of returns between PAI and
the market
Calculator
Mode: Stat
Input 10 (x,y) 12 Data
18 (x,y) 16 Data
16 (x,y) 20 Data
10 (x,y) 16 Data
8 (x,y) 6 Data
2ndF a gives 2.79
Note that the values for the x axis(Rm)
are input first
2ndF b gives .90
This is the beta coefficient
2ndF r gives .74
This is the correlation coefficient, a
measure of how well the formula
describes the relationship. The
closer to 1.00, the better the fit
This is the alpha coefficient
1-42
Improved CAPM (risk premium model)
Investors expect higher returns if higher risks are taken
Kj = Rf + β(Rm-Rf)
Where:
Kj= Required return on Common Stock
Rf = Risk-free rate of return
β= Beta coefficient. The beta measures
the historical
volatility of an individual stock's return relative to a stock
market index. A beta greater than 1 indicates greater
volatility (price movements) than the market, while the
reverse would be true for a beta less than 1.
Rm-Rf _= Premium or excess return of the market versus the risk-free rate.
β(Rm-Rf) = Expect return above the risk-free rate for the stock of
company j, given the level of risk.
1-43
The security market line (SML)
Required rates
of return
Percent
20.0
K2
18.0
SML = Rf +  (Rm – Rf)
16.0
14.0
K1 12.0
K.5
Rf
6.5 % market risk premium
10.0
8.0
5.5
0.5
1.0
1.5
2.0
Beta (risk)
1-44
The security market line and
changing interest rates
SML1
Required rates
of return (percent)
20.0
SML0
18.0
16.0
14.0
Rf increased 2%
12.0
10.0
Rf1 7.5
Rf0 5.5
0.5
1.0
1.5
2.0
Beta (risk)
1-45
PPT 11-24
The security market line and changing
investor expectations
Required rates
of return (percent)
SML1
22.0
More risk aversion
20.0
18.0
SML0
16.0
14.0
12.0
10.0
8.0
5.5
Rf
0.5
1.0
1.5
2.0
Beta (risk)
1-46
Net income (NI) approach
Value of the firm ($)
Cost of capital (percent)
Ke
Ka
Kd
100
0
Debt/value ratio (percent)
0
Debt/value ratio (percent)
100
Ke = Cost of Equity: Kd = Cost of debt; Ka = Cost of capital
Value is the market value of the firm
1-47
Net operating income (NOI)
approach
Value of the firm ($)
Cost of capital (percent)
Ke
Ka
Kd
100
0
Debt/value ratio (percent)
0
100
Debt/value ratio (percent)
1-48
Traditional approach as described by Durand
Cost of capital (percent)
Value of the firm ($)
Ke
Ka
Kd
0
100
Debt/value ratio (percent)
0
100
Debt/value ratio (percent)
1-49
Modigliani and Miller with corporate taxes
Value of the firm ($)
Cost of capital (percent)
Ke
VL
VU
Ka
Cost of
debt
Kd
adjusted
for the tax 0
100
Debt/value ratio (percent)
effect of
interest
0
100
Debt/value ratio (percent)
1-50
Combined impact of the corporate tax effect and
bankruptcy effect on valuation and cost of capital
A. Cost of capital (percent)
Ka (M +M with tax effect and bankruptcy effect)
Ka (original M + M)
Ka (M + M with tax effect)
0
Debt/value ratio (percent)
100
1-51
Combined impact of the corporate tax effect and
bankruptcy effect on valuation and cost of capital
B. Value of the firm ($)
VL (M + M with tax effect)
VU (original M +M)
(M + M with tax effect and bankruptcy effect)
100
0
Debt/value ratio (percent)
1-52