Calculating Cost of Capital Components

10 - 1
Copyright © 2001 by Harcourt, Inc. All rights reserved.
 Capital components: debt, preferred stock,
and common stock.
 Any increase in total assets must be financed
by an increase in one or more of these capital
components
 Kd: the interest rate on the firm’s new debt
Kps: the cost of preferred stock
Ks: the cost of retained earnings
Ke:the cost of common equity (equity obtained
by issuing new common stock as apposed to
retaining eanings

10 - 2
1. The cost of debt
Kd(1-T) is the after tax cost of debt. The
relevant cost of new debt, taking into
account the tax deductibility of interest.
In effect, the government pays part of the
cost of debt because interest is
deductible.
Note that the cost of debt is the interest
rate on new debt, not the interest rate
paid on existing or old debt.

10 - 3
A 15-year, 12% semiannual bond sells
for $1,153.72. What’s kd?
60 60 + 1,000
60
0 1 2 30
i = ?
30 -1153.72 60 1000
5.0% x 2 = kd = 10%
N I/YR PV FV
PMT
-1,153.72
...
INPUTS
OUTPUT

10 - 4
Component Cost of Debt
Interest is tax deductible, so
kd AT = kd BT(1 – T)
= 10%(1 – 0.40) = 6%.

10 - 5
2. The cost of preferred stock (Kp)
The rate of return investors require on the
firm’s preferred stock.
Preferred stock is a perpetuity that pays a
fixed dividend (Dp) forever.
Kp = Preferred dividend / the current price
of the preferred stock

10 - 6
What’s the cost of preferred stock?
Pp = $111.10; $10 dividend/share
Use this formula:
%.
0
.
9
090
.
0
10
.
111
$
10
$
P
D
k
p
p
p 




10 - 7
Note:
Preferred dividends are not tax
deductible, so no tax adjustment.
Just kp.
Nominal kp is used.
Our calculation ignores flotation
costs.

10 - 8
Why is there a cost for retained
earnings?
Earnings can be reinvested or paid
out as dividends.
Investors could buy other securities,
earn a return.
Thus, there is an opportunity cost if
earnings are retained.

10 - 9
Opportunity cost: The return
stockholders could earn on
alternative investments of equal risk.
They could buy similar stocks and
earn ks. So, ks is the cost of retained
earnings. The rate of return required by
stockholders on a firm’s common stock

10 - 10
Three ways to determine cost of
common equity, ks:
1. CAPM: ks = kRF + (kM – kRF)b.
2. The bond-yield plus risk-premium approach:
Ks= bond yield + firm’s risk premium
firms with risky, low-rated, and consequently
high-interest-rate debt will also have risky, high-
cost equity. The risk premium over a firm’s own
bond yield has generally ranged from 3 to 5
percentage.

10 - 11
3. Discount Cash Flow model
(Constant dividend growth model)
Ks = (D1/Po) + g
How to estimate g?
g = (1- dividend pay out ratio)*ROE

10 - 12
What’s the cost of common equity
based on the CAPM?
kRF = 7%, RPM = 6%, b = 1.2.
ks = kRF + (kM – kRF )b.
= 7.0% + (6.0%)1.2 = 14.2%.

10 - 13
What’s the DCF cost of common
equity, ks? Given: D0 = $4.19;
P0 = $50; g = 5%.
D1
P0
D0(1 + g)
P0
$4.19(1.05)
$50
ks = + g = + g
= + 0.05
= 0.088 + 0.05
= 13.8%.

10 - 14
Suppose the company has been
earning 15% on equity (ROE = 15%)
and retaining 35% (dividend payout =
65%), and this situation is expected to
continue.
What’s the expected future g?

10 - 15
Retention growth rate:
g = (1 – Payout)(ROE) = 0.35(15%)
= 5.25%.
Here (1 – Payout) = Fraction retained.

10 - 16
Find ks using the own-bond-yield-plus-
risk-premium method.
(kd = 10%, RP = 4%.)
This RP  CAPM RP.
Produces ballpark estimate of ks.
ks = kd + RP
= 10.0% + 4.0% = 14.0%

10 - 17
What’s a reasonable final estimate of ks?
Method Estimate
CAPM 14.2%
DCF 13.8%
kd + RP 14.0%
Average 14.0%

10 - 18
1. When a company issues new common
stock they also have to pay flotation costs
to the underwriter.
2. Issuing new common stock may send a
negative signal to the capital markets,
which may depress stock price.
Why is the cost of retained earnings
(ks) cheaper than the cost of issuing
new common stock (ke)?

10 - 19
Two approaches that can be used to
account for flotation costs:
Include the flotation costs as part of the
project’s up-front cost. This reduces the
project’s estimated return.
Adjust the cost of capital to include
flotation costs. This is most commonly
done by incorporating flotation costs in
the DCF model.

10 - 20
Ke = [D1/Po(1-F) ] + g
F is the percentage flotation cost incurred in
selling the new stock.
So, Po (1-F) is the net price per share
received by the company.

10 - 21
New common, F = 15%:
g
)
F
1
(
P
)
g
1
(
D
k
0
0
e




 
 
%.
4
.
15
%
0
.
5
50
.
42
$
40
.
4
$
%
0
.
5
15
.
0
1
50
$
05
.
1
19
.
4
$







10 - 22
 Because of flotation costs, dollars raised by
selling new stock must “work harder” than
dollars raised by retaining earnings.
Moreover, since no flotation costs are
involved, retained earnings have a lower cost
than new stock.
 Therefore, the firms should utilize retained
earnings to the extent possible to avoid the
costs of new common stock.
 However, if a firm has more good investment
opportunities, issuing new common stock is
necessary.

10 - 23
The retained earnings breakpoint represents
the total amount of financing that can be
raised before the firm is forced to sell new
common stock.
Retained earnings breakpoint
= addition to retained earnings/equity fraction

10 - 24
E.g) Suppose a firm estimates its
earnings to be $100M next year and
has a payout ratio of 40%. Its capital
structure consists of 45% debt, 2%
preferred, and 53% equity.
The break point will be $60M/0.53 =
$113.2M; After the firm has raised
total capital of $113.2M, the firm will
be forced to issue new common
stock.

10 - 25
Comments about flotation costs:
Flotation costs depend on the risk of
the firm and the type of capital being
raised.
The flotation costs are highest for
common equity. However, since
most firms issue equity infrequently,
the per-project cost is fairly small.
We will frequently ignore flotation
costs when calculating the WACC.

10 - 26
5. Weighted Average Cost of Capital (WACC)
If all new equity will come from retained earnings:
WACC = Wd [Kd(1-t)] + Wp(Kps) + Wc(Ks)
Wd, Ws, Wc are the weights used for debt, preferred
stock, and common equity.
Assume that the firm has established such a target
and will finance all new investments so as to
maintain a constant target capital structure.
Weights should be based on the market value.

10 - 27
What’s the firm’s WACC (ignoring
flotation costs)?
WACC = wdkd(1 – T) + wpkp + wcks
= 0.3(10%)(0.6) + 0.1(9%) + 0.6(14%)
= 1.8% + 0.9% + 8.4% = 11.1%.

10 - 28
The company has a target capital
structure of 40 percent debt and 60
percent equity
Bonds pay 10% coupon (semiannual),
mature in 20 years and sell for $849.54
the company stock beta is 1.2
rf = 10%, market risk premium = 5%
the company is a constant growth firm
that just paid a dividend of $2, sells for
$27 per share, and a growth rate of 8%
marginal tax rate is 40%.

10 - 29
What factors influence a company’s
composite WACC?
Market conditions. (the level of interest
rates, tax rates…)
The firm’s capital structure and dividend
policy.
The firm’s investment policy. Firms with
riskier projects generally have a higher
WACC.

10 - 30
WACC Estimates for Some Large
U. S. Corporations, Nov. 1999
Company WACC
Intel 12.9%
General Electric 11.9
Motorola 11.3
Coca-Cola 11.2
Walt Disney 10.0
AT&T 9.8
Wal-Mart 9.8
Exxon 8.8
H. J. Heinz 8.5
BellSouth 8.2

10 - 31
Should the company use the
composite WACC as the hurdle rate for
each of its projects?
NO! The composite WACC reflects the
risk of an average project undertaken
by the firm. Therefore, the WACC only
represents the “hurdle rate” for a
typical project with average risk.
Different projects have different risks.
The project’s WACC should be adjusted
to reflect the project’s risk.

10 - 32
Subjective adjustments to the
firm’s composite WACC.
Attempt to estimate what the cost
of capital would be if the
project/division were a stand-alone
firm. This requires estimating the
project’s beta.
What procedures are used to determine
the risk-adjusted cost of capital for a
particular project or division?

10 - 33
Find the division’s market risk and cost
of capital based on the CAPM, given
these inputs:
Target debt ratio = 40%.
kd = 12%.
kRF = 7%.
Tax rate = 40%.
betaDivision = 1.7.
Market risk premium = 6%.

10 - 34
Beta = 1.7, so division has more market
risk than average.
Division’s required return on equity:
ks = kRF + (kM – kRF)bDiv.
= 7% + (6%)1.7 = 17.2%.
WACCDiv. = wdkd(1 – T) + wcks
= 0.4(12%)(0.6) + 0.6(17.2%)
= 13.2%.

10 - 35
How does the division’s market risk
compare with the firm’s overall market
risk?
Division WACC = 13.2% versus
company WACC = 11.1%.
Indicates that the division’s market risk
is greater than firm’s average project.
“Typical” projects within this division
would be accepted if their returns are
above 13.2%.

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