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Chapter 7
COST OF CAPITAL
Chapter Outline

The Cost of Capital: Introduction

The Cost of Equity (CAPM and DDM)

The Costs of Debt and Preferred Stock

The Weighted Average Cost of Capital

Divisional and Project Costs of Capital
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Why Cost of Capital is Important

Return earned on assets depends on the risk of
those assets

The return to an investor is the same as the
cost to the company

Cost of capital provides with an indication of
how the market views the risk of assets

Knowing cost of capital can also help determine
required return for capital budgeting projects
2
Required Return

The required return is the same as the
appropriate discount rate and is based on the
risk of the cash flows

The required rate of return is used to calculate
NPV

We need to earn at least the required return to
compensate investors for the financing they
have provided
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Cost of Equity

The cost of equity is the return required
by equity investors given the risk of the
cash flows from the firm

There are two major methods for
determining the cost of equity
◦ Dividend growth model (Gordon growth
model)
◦ SML or CAPM
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The Dividend Growth Model
Approach

Can be rearranged to solve for RE
D1
P0 
RE  g
RE
D1

g
P0
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Example
Suppose that a company is expected to
pay a dividend of $1.50 per share next
year. There has been a steady growth in
dividends of 5.1% per year and the
market expects that to continue. The
current price is $25. What is the cost of
equity?
Solution: RE = 11.1%

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Example: Estimating the Dividend
Growth Rate

One method for estimating the growth
rate is to use the historical average
◦
◦
◦
◦
◦
◦

Year
1995
1996
1997
1998
1999
Dividend
1.23
1.30
1.36
1.43
1.50
Percent Change
5.7%
4.6% Geom. = 5.0864
5.1%
4.9% Ar. Av = 5.0872
Analysts’ forecast can be used
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Alternative Approach to Estimating
Growth

If the company has a stable ROE, a stable dividend
policy and is not planning on raising new external
capital, then the following relationship can be
used:
g = Retention ratio x ROE
A company has a ROE of 15% and payout ratio is
35%. If management is not planning on raising
additional external capital, what is its growth rate?
Solution: g= 9.75%

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Advantages and Disadvantages of Dividend
Growth Model
 – easy to understand and use
:
◦ Only applicable to companies currently paying
dividends
◦ Not applicable if dividends aren’t growing at a
reasonably constant rate
◦ Extremely sensitive to the estimated growth
rate – an increase in g of 1% increases the
cost of equity by 1%
◦ Does not explicitly consider risk
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The SML Approach (CAPM)

Use the following information to compute
our cost of equity
◦ Risk-free rate, Rf
◦ Market risk premium, E(RM) – Rf
◦ Systematic risk of asset, 
E(RA) = Rf + A(E(RM) – Rf)
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SML example
Suppose the company has an equity beta
of .58 and the current risk-free rate is
6.1%. If the expected market risk
premium is 8.6%, what is the cost of
equity capital?
Solution: RE = 11.08%

Do
both approaches have the same
result?
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Advantages and Disadvantages of
SML
:
◦ Explicitly adjusts for systematic risk
◦ Applicable to all companies, as long as beta can be
computed
:
◦ Have to estimate the expected market risk premium,
which does vary over time
◦ Have to estimate beta, which also varies over time
◦ We are relying on the past to predict the future,
which is not always reliable
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Cost of Equity

Suppose the company has a beta of 1.5. The
market risk premium is expected to be 9% and
the current risk-free rate is 6%. Dividends will
grow at 6% per year and last dividend was $2.
The stock is currently selling for $15.65. What is
our cost of equity?
◦ Using SML: RE = 19.5%
◦ Using DGM: RE = 19.55%
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Cost of Debt

The cost of debt is the required return on a
company’s debt

Usually the cost of long-term debt or bonds only is
taken into account

The required return is best estimated by computing
the yield-to-maturity on the existing debt

Estimates of current rates based on the bond rating
can be used
The
cost of debt is NOT the coupon rate
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Cost of Debt example
Suppose you have a bond issue currently
outstanding that has 25 years left to
maturity. The coupon rate is 9% and
coupons are paid semiannually. The bond
is currently selling for $908.72 per $1000
bond. What is the cost of debt?
Solution: RD = 10% (YTM)

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Cost of Preferred Stock

Preferred stock generally pays a constant
dividend every period

Dividends are expected to be paid every
period forever

Preferred stock is an annuity
RP = D / P0
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Cost of Preferred Stock example

A company has preferred stock that has
an annual dividend of $3. If the current
price is $25, what is the cost of preferred
stock?
Solution: RPE =
3
25
= 12%
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The Weighted Average Cost of
Capital (WACC)

Individual costs of capital are used to find
cost of capital for the firm

WACC is the required return assets,
based on the market’s perception of the
risk of those assets

The weights are determined by how
much of each type of financing that we
use – target D/E ratio
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Capital Structure Weights
V = market value of the firm’s D + E
 Weights

◦ wE = E/V = percent financed with equity
◦ wD = D/V = percent financed with debt
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Capital Structure Weights example

Suppose you have a market value of
equity equal to $500 million and a market
value of debt = $475 million.
◦ What are the capital structure weights?
Solution:
WE =
WD =
475
475+500
=.4872
500
= .5128
475+500
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Taxes and the WACC
We are concerned with after-tax cash
flows, so the effect of taxes on the various
costs of capital has to be considered
 Interest expense reduces tax liability

◦ Reduction in taxes reduces cost of debt
◦ After-tax cost of debt = RD(1-TC)

Dividends are not tax deductible, so there
is no tax impact on the cost of equity
WACC = wERE + wDRD(1-TC)
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WACC (1)

Equity Information

◦
◦
◦
◦
50 million shares
$80 per share
Beta = 1.15
Market risk premium =
9%
◦ Risk-free rate = 5%
Debt Information
◦ $1 billion in
outstanding debt (face
value)
◦ Current quote = 110
◦ Coupon rate = 9%,
semiannual coupons
◦ 15 years to maturity

Tax rate = 40%
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WACC (2)
What is the cost of equity?
RE =15.35% (by SML)
What is the cost of debt?
RD =7.85 (YTM)
What is the after-tax cost of debt?
7.85*(1-.4)=4.71
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WACC (3)
What are the capital structure weights?
 E=80*50mil= 4bln
 D=1.1bln (110% of face)
V= 5.1bln
 What is the WACC?
 WACC=4/5.1*15.35 + 1.1/5.1*4.71=
 = 12.0392% + 1.0159 = 13.0551

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Divisional and Project Costs of
Capital
Using
the WACC as discount rate is only
appropriate for projects that have the same
risk as the firm’s current operations
If
we are looking at a project that has NOT
the same risk as the firm, then the
appropriate discount rate for that project
has to be determined

Divisions also often require separate
discount rates because they have different
levels of risk
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Using WACC for All Projects
example

What would happen if we use the WACC
for all projects regardless of risk?

Assume the WACC = 15%
Project
A
B
C
Required Return
20%
15%
10%
IRR
17%
18%
12%
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The Pure Play Approach
The pure play approach = use of a WACC that
is unique to a particular project
Find one or more companies that specialize in
the product or service that we are considering
2. Compute the beta for each company
3. Take an average
4. Use that beta along with the CAPM to find the
appropriate return for a project of that risk
1.
Often
difficult to find pure play companies
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Subjective Approach
Consider the project’s risk relative to the firm
overall
 If the project is more risky than the firm, use a
discount rate greater than the WACC
 If the project is less risky than the firm, use a
discount rate less than the WACC
 You may still accept projects that you shouldn’t
and reject projects you should accept, but your
error rate should be lower than not considering
differential risk at all

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Subjective Approach example
Risk Level
Discount Rate
Very Low Risk
WACC – 8%
Low Risk
WACC – 3%
Same Risk as Firm
WACC
High Risk
WACC + 5%
Very High Risk
WACC + 10%
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