CORPORATE FINANCE
Meeting XI
Cost of Capital
Chapter Outline
•
•
•
•
•
Cost of Capital
Cost of Debt
Cost of Preferred Stock
Cost of Common Equity:
– Retained Earnings
– New Common Stock
Optimum Capital Structure
Cost of Capital



The cost of capital represents the overall cost of
financing to the firm
The cost of capital is normally the relevant discount
rate to use in analyzing an investment
The overall cost of capital is a weighted average of
the various sources:
–
WACC = Weighted Average Cost of
Capital
–
WACC = After-tax cost x weights
Table
Eg. Cost of capital–Baker Corporation
(1)
Cost
(2)
(3)
(aftertax)
Weights
Cost
30%
2.12%
10
1.09
Weighted
Debt . . . . . . . . . .
Kd
7.05%
Preferred stock . . . .
Kp
10.94
Common equity
(retained earnings) . . .
Ke
12.00
Weighted average
cost of capital . . . . .
Ka
60
7.20
10.41%
Cost of Debt


The cost of debt to the firm is the effective
yield to maturity (or interest rate) paid to its
bondholders
Since interest is tax deductible to the firm, the
actual cost of debt is less than the yield to
maturity:
– After-tax cost of debt = yield x (1 - tax
rate)
Cost of New 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
Cost of preferred stock = dividend
price - flotation cost
Cost of Preferred—an Example
Baker Corporation has preferred stock that sells for $100 per share and pays an annual
dividend of $10.50. If the flotation costs are $4 per share, what is the cost of new
preferred stock?
KP 
$10.50
 .1094  10.94%
$100 - 4
Cost of Common Equity:
Retained Earnings


Common stock equity is available through
retained earnings (R/E) or by issuing new
common stock:
– Common equity = R/E + New common
stock
The cost of common equity in the form of
retained earnings is equal to the required rate
of return on the firm’s common stock (this is
the opportunity cost)
Cost of Common Equity:
New Common Stock

The cost of new common stock is higher than
the cost of retained earnings because of
flotation costs

Flotation costs:
– selling and distribution costs (such as sales
commissions) for the new securities
Finding the Required Return on Common Stock
using the Capital Asset Pricing Model
The Capital Asset Pricing Model (CAPM) is a formula that we can use to estimate the
required return on individual stocks. Here is the formula:
K j  R f   j K m  R f  (11 - 5)
where
Kj
=
Required return on stock j
Rf
j
=
=
Risk-free rate of return (usually current rate on Treasury Bill).
Beta coefficient for stock j—represents risk of the stock
Km
=
Return in market as measured by some proxy portfolio (index)
Suppose that Baker has the following values:
R
=
5.5%
j f
=
1.0
Km
=
12%
Then,
using
the
would get a required return for Baker of
12CAPM
K j  5.5
 1.0
- 5.5  we
12%
.
Cost of Retained Earnings
The cost of Retained Earnings can be estimated using equations from the prior chapter.
Suppose that Baker Corporation will pay an annual dividend at the end of the year of $2
per share. The price of the stock today is $40 and dividends are expected to grow at 7%
per year. Then:
Ke 
D1
$2
g
 7%  12% .
P0
$40
Cost of NEW common stock
The cost of NEW common stock can be estimated using equations from the prior chapter.
Suppose that Baker Corporation will pay an annual dividend at the end of the year of $2
per share. The price of the stock today is $40 and dividends are expected to grow at 7%
per year. New flotation costs will be $4 per share. Then:
Ke 
D1
$2
g
 7%  12.6% .
P0  F
$40 - $4
Optimum Capital
Structure
The optimal (best)
situation is associated
with the minimum
overall cost of capital:
Optimum capital
structure means
the lowest
WACC
Optimal Capital Structure
usually occurs with 3050% debt in a firm’s
capital structure—but this
can vary widely among
firms and industries
WACC is also referred
to as the required rate of
return or the discount
rate
Debt is usually
cheaper than equity,
but its costs rise as
we add increasing
amounts of debt.
As we begin to add debt, the
cost of equity may initially
drop (reflecting the
advantages of lower-cost debt
to shareholders), but will
eventually rise as debt adds
more risk for shareholders.
Figure (next slide)
shows how we find an
optimal WACC.
Figure
Cost of capital curve
Cost of equity
Cost of capital
(percent)
Weighted
average cost
of captial
U-shaped
Cost of debt
Minimum point for
cost of capital
0
40
Debt-assets mix (percent)
80
Capital
Acquisition and
Investment
Decision Making
Figure (next slide)
shows a theoretical costof-capital curve at three
different points in time.
As we move from time period t to
time period t+2, falling interest rates
and rising stock prices cause a
downward shift.
 The
graph illustrates two basic
points:
(1)The firm wants to keep
its debt-to-equity ratio
between x and y along the
bottom axis at all times
because this is the lowest
area on each of the three
curves.
(2)The firm would like to
finance its long-term needs at
time period t+2 rather than
the other two time periods
because overall costs are
lowest during this time frame.
Cost of Capital in the Capital
Budgeting Decision
 Assume
that Baker Corporation is
considering making an investment
in eight projects and the returns
and costs are shown in Table (next
slide)
Table
Investment projects available to the Baker
Corporation
Projects
A . . . .
B. . . .
C. . . .
D. . . .
E. . . .
F. . . .
G. . . .
H. . . .
Expected
Returns
16.00%
14.00
13.50
11.80
10.65
9.50
8.60
7.00
Cost
($ millions)
$10
5
4
20
11
20
15
10
$95 million
Figure
Cost of capital and investment projects for the Baker
Corporation
Percent
14.0 12.0 10.0 8.0 16.0
A
B
C
10.41%
D
E
F
4.0 2.0 0.0 -
G
H
6.0
10 15 19
39
50
70
Amount of capital ($ millions)
85
Ka Weighted
average
cost of
capital
95
The Marginal
Cost of Capital
Let us make the following
assumptions about Baker
The weights will remain constant at their
current level of 60% equity and 30% debt.
2. Once current retained earnings ($23.4
million) are exhausted, equity must be sold
at a cost of 12.6% (due to flotation costs).
3. The firm can raise up to $15 million of debt at
7.05%. Above that amount, debt will cost
7.56%.
1.
Baker will have the following
break points:
 Point
where equity cost rises:
$23.4 million / .6 = $39 million
 Point where debt cost rises:
$15 million / .3 = $50 million
Baker faces these conditions:
•
•
•
First $39 million
– Cost of debt = 7.05%
– Cost of preferred = 10.94%
– Cost of equity = 12%
From $39 million to $50 million
– Cost of debt = 7.05%
– Cost of preferred = 10.94%
– Cost of equity = 12.6%
Above $50 million
– Cost of debt = 8.60%
– Cost of preferred = 10.94%
– Cost of equity = 12.6%
Table
Cost of capital for different amounts of financing
First $39 Million
A/T
Cost
Debt . . . .
Preferred. .
Common
equity *. .
Kd 7.05%
Kp 10.94
Ke 12.00
Next $11 Million
Weighted
Wts.
Cost
.30
.10
.60
A/T
Cost
Wts.
2.12%
1.09
Debt . . . Kd 7.05% .30
Preferred .
Kp 10.94
.10
2.12%
1.09
7.20
Common
equity † . . Kn 12.60
7.56
Ka = 10.41%
*Retained earnings.
Weighted
Cost
.60
Kmc =
†New
common stock.
10.77%
Table Cost of capital for increasing amounts of
financing
Over $50 Million
Cost
(aftertax)
Debt (higher cost)
Kd
Preferred stock
Kp
Common equity
(new common stock)
Kn
8.60%
Weights
Weighted
Cost
.30
2.58%
10.94
.10
1.09
12.60
.60
7.56
11.23%
Kmc =
Table
Marginal cost of capital and Baker Corporation
projects
Percent
14.0 12.0 10.0 8.0 16.0
A
B
10.77%
C
11.23%
Kmc Marginal
cost of
capital
10.41%
D
E
F
4.0 2.0 0.0 -
G
H
6.0
10 15 19
39
50
70
Amount of capital ($ millions)
85
95
Capital Asset Pricing Model
 We
begin with observations
about how a company, Parts
Associates, Inc. (PAI) has
performed, compared to the
market, over a period of time.
Table
Performance of PAI and the market
Rate of Return
on Stock
Year
1 . . . . . . . . . . . .
PAI
Market
12.0%
10.0%
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%
12.4%
3.87%
The Security Market Line
 By
making some assumptions
about markets and investor risk
preferences, we can move from
the regression results to the
Security Market Line (SML)
 The equation for the SML is the
CAPM.
Figure
The security market line (SML)
Required rates
of return
Percent
20.0
K2
18.0
SML = Rf +  (Km – 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)
We can observe how the relation
between risk and return changes when
basic parameters of the CAPM change
 The
line shifts up as the risk-free rate
increases.
 The line becomes steeper as beta
rises (as investors become more risk
averse)
Figure
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)
Figure
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)
CORPORATE FINANCE
End of Slides