Chapter 15
Required Returns
and the Cost of
Capital
15-1
© 2001 Prentice-Hall, Inc.
Fundamentals of Financial Management, 11/e
Created by: Gregory A. Kuhlemeyer, Ph.D.
Carroll College, Waukesha, WI
Required Returns and
the Cost of Capital
15-2

Creation of Value

Overall Cost of Capital of the Firm

Project-Specific Required Rates

Group-Specific Required Rates

Total Risk Evaluation
Key Sources of
Value Creation
Industry Attractiveness
Growth
phase of
product
cycle
Cost
15-3
Marketing
and
price
Barriers to
competitive
entry
Other -e.g., patents,
temporary
monopoly
power,
oligopoly
pricing
Perceived
quality
Competitive Advantage
Superior
organizational
capability
Overall Cost of
Capital of the Firm
Cost of Capital is the required
rate of return on the various
types of financing. The overall
cost of capital is a weighted
average of the individual
required rates of return (costs).
15-4
Market Value of
Long-Term Financing
15-5
Type of Financing
Mkt Val
Weight
Long-Term Debt
$ 35M
35%
Preferred Stock
$ 15M
15%
Common Stock Equity $ 50M
50%
$ 100M
100%
Cost of Debt
Cost of Debt is the required rate
of return on investment of the
lenders of a company.
n
P0 = S
j =1
Ij + Pj
(1 + kd)j
ki = kd ( 1 - T )
15-6
Determination of
the Cost of Debt
Assume that Basket Wonders (BW) has
$1,000 par value zero-coupon bonds
outstanding. BW bonds are currently
trading at $385.54 with 10 years to
maturity. BW tax bracket is 40%.
$385.54 =
15-7
$0 + $1,000
(1 + kd)10
Determination of
the Cost of Debt
(1 + kd)10 = $1,000 / $385.54
= 2.5938
(1 + kd) = (2.5938) (1/10)
= 1.1
kd = .1 or 10%
15-8
ki
= 10% ( 1 - .40 )
ki
= 6%
Cost of Preferred Stock
Cost of Preferred Stock is the
required rate of return on
investment of the preferred
shareholders of the company.
kP = DP / P0
15-9
Determination of the
Cost of Preferred Stock
Assume that Basket Wonders (BW)
has preferred stock outstanding with
par value of $100, dividend per share
of $6.30, and a current market value of
$70 per share.
kP = $6.30 / $70
kP = 9%
15-10
Cost of Equity
Approaches
 Dividend
Discount Model
 Capital-Asset
Pricing
Model
 Before-Tax
Cost of Debt
plus Risk Premium
15-11
Dividend Discount Model
The cost of equity capital, ke, is
the discount rate that equates the
present value of all expected
future dividends with the current
market price of the stock.
D1
D2
D
+
+...+
P0 =
1
2
(1+ke) (1+ke)
(1+ke)
15-12
Constant Growth Model
The constant dividend growth
assumption reduces the model to:
ke = ( D1 / P0 ) + g
Assumes that dividends will grow
at the constant rate “g” forever.
15-13
Determination of the
Cost of Equity Capital
Assume that Basket Wonders (BW) has
common stock outstanding with a current
market value of $64.80 per share, current
dividend of $3 per share, and a dividend
growth rate of 8% forever.
15-14
ke
= ( D 1 / P0 ) + g
ke
= ($3(1.08) / $64.80) + .08
ke
= .05 + .08 = .13 or 13%
Growth Phases Model
The growth phases assumption
leads to the following formula
(assume 3 growth phases):
a
P0 = S
t=1

S
t=b+1
15-15
D0(1+g1)t
(1+ke)t
Db(1+g3)t-b
(1+ke)t
b
+
S
t=a+1
Da(1+g2)t-a
(1+ke)t
+
Capital Asset
Pricing Model
The cost of equity capital, ke, is
equated to the required rate of
return in market equilibrium. The
risk-return relationship is described
by the Security Market Line (SML).
ke = Rj = Rf + (Rm - Rf)bj
15-16
Determination of the
Cost of Equity (CAPM)
Assume that Basket Wonders (BW) has
a company beta of 1.25. Research by
Julie Miller suggests that the risk-free
rate is 4% and the expected return on
the market is 11.2%
ke = Rf + (Rm - Rf)bj
= 4% + (11.2% - 4%)1.25
15-17
ke = 4% + 9% = 13%
Before-Tax Cost of Debt
Plus Risk Premium
The cost of equity capital, ke, is the
sum of the before-tax cost of debt
and a risk premium in expected
return for common stock over debt.
ke = kd + Risk Premium*
* Risk premium is not the same as CAPM risk
premium
15-18
Determination of the
Cost of Equity (kd + R.P.)
Assume that Basket Wonders (BW)
typically adds a 3% premium to the
before-tax cost of debt.
ke = kd + Risk Premium
= 10% + 3%
ke = 13%
15-19
Comparison of the
Cost of Equity Methods
Constant Growth Model
13%
Capital Asset Pricing Model 13%
Cost of Debt + Risk Premium 13%
Generally, the three methods
will not agree.
15-20
Weighted Average
Cost of Capital (WACC)
n
Cost of Capital =
S
x=1
15-21
kx(Wx)
WACC
= .35(6%) + .15(9%) +
.50(13%)
WACC
= .021 + .0135 + .065
= .0995 or 9.95%
Limitations of the WACC
1. Weighting System
15-22

Marginal Capital Costs

Capital Raised in Different
Proportions than WACC
Limitations of the WACC
2. Flotation Costs are the costs
associated with issuing securities
such as underwriting, legal, listing,
and printing fees.
15-23
a.
Adjustment to Initial Outlay
b.
Adjustment to Discount Rate
Economic Value Added
15-24

A measure of business performance.

It is another way of measuring that
firms are earning returns on their
invested capital that exceed their
cost of capital.

Specific measure developed by
Stern Stewart and Company in late
1980s.
Economic Value Added
EVA = NOPAT – [ Cost of
Capital x Capital Employed ]
15-25

Since a cost is charged for equity capital
also, a positive EVA generally indicates
shareholder value is being created.

Based on Economic NOT Accounting
Profit.
Adjustment to
Initial Outlay (AIO)
Add Flotation Costs (FC) to the
Initial Cash Outlay (ICO).
n
CFt
- ( ICO + FC )
NPV = S
t
(1
+
k)
t=1
Impact: Reduces the NPV
15-26
Adjustment to
Discount Rate (ADR)
Subtract Flotation Costs from the
proceeds (price) of the security and
recalculate yield figures.
Impact: Increases the cost for any
capital component with flotation costs.
Result: Increases the WACC, which
decreases the NPV.
15-27
Determining Project-Specific
Required Rates of Return
Use of CAPM in Project Selection:
15-28

Initially assume all-equity financing.

Determine project beta.

Calculate the expected return.

Adjust for capital structure of firm.

Compare cost to IRR of project.
Difficulty in Determining
the Expected Return
Determining the SML:
 Locate
a proxy for the project (much
easier if asset is traded).
 Plot
the Characteristic Line
relationship between the market
portfolio and the proxy asset excess
returns.
 Estimate
15-29
beta and create the SML.
Project Acceptance
and/or Rejection
EXPECTED RATE
OF RETURN
Accept
X
X
X
X
O
Rf
X
O
X
O
O
SML
X
O
Reject
O
SYSTEMATIC RISK (Beta)
15-30
O
Determining Project-Specific
Required Rate of Return
1. Calculate the required return
for Project k (all-equity financed).
Rk = Rf + (Rm - Rf)bk
2. Adjust for capital structure of the
firm (financing weights).
15-31
Weighted Average Required Return =
[ki][% of Debt] + [Rk][% of Equity]
Project-Specific Required
Rate of Return Example
Assume a computer networking project is
being considered with an IRR of 19%.
Examination of firms in the networking
industry allows us to estimate an all-equity
beta of 1.5. Our firm is financed with 70%
Equity and 30% Debt at ki=6%.
The expected return on the market is 11.2%
and the risk-free rate is 4%.
15-32
Do You Accept the Project?
ke = Rf + (Rm - Rf)bj
= 4% + (11.2% - 4%)1.5
ke = 4% + 10.8% = 14.8%
WACC = .30(6%) + .70(14.8%)
= 1.8% + 10.36% = 12.16%
IRR = 19% > WACC = 12.16%
15-33
Determining Group-Specific
Required Rates of Return
Use of CAPM in Project Selection:
 Initially
assume all-equity financing.
 Determine
 Calculate
 Adjust
the expected return.
for capital structure of group.
 Compare
project.
15-34
group beta.
cost to IRR of group
Expected Rate of Return
Comparing Group-Specific
Required Rates of Return
Company Cost
of Capital
Group-Specific
Required Returns
Systematic Risk (Beta)
15-35
Qualifications to Using
Group-Specific Rates
15-36

Amount of non-equity financing
relative to the proxy firm.
Adjust project beta if necessary.

Standard problems in the use of
CAPM. Potential insolvency is a
total-risk problem rather than
just systematic risk (CAPM).
Project Evaluation
Based on Total Risk
Risk-Adjusted Discount Rate
Approach (RADR)
The required return is increased
(decreased) relative to the firm’s
overall cost of capital for projects
or groups showing greater
(smaller) than “average” risk.
15-37
Project Evaluation
Based on Total Risk
Probability Distribution
Approach
Acceptance of a single project
with a positive NPV depends on
the dispersion of NPVs and the
utility preferences of
management.
15-38
EXPECTED VALUE OF NPV
Firm-Portfolio Approach
C
B
A
Curves show
“HIGH”
Risk Aversion
STANDARD DEVIATION
15-39
Indifference
Curves
EXPECTED VALUE OF NPV
Firm-Portfolio Approach
C
B
A
Curves show
“MODERATE”
Risk Aversion
STANDARD DEVIATION
15-40
Indifference
Curves
EXPECTED VALUE OF NPV
Firm-Portfolio Approach
C
B
A
Curves show
“LOW”
Risk Aversion
STANDARD DEVIATION
15-41
Indifference
Curves
Adjusting Beta for
Financial Leverage
bj = bju [ 1 + (B/S)(1-TC) ]
bj: Beta of a levered firm.
bju: Beta of an unlevered firm
(an all-equity financed firm).
B/S: Debt-to-Equity ratio in
Market Value terms.
TC : The corporate tax rate.
15-42
Adjusted Present Value
Adjusted Present Value (APV) is the
sum of the discounted value of a
project’s operating cash flows plus the
value of any tax-shield benefits of
interest associated with the project’s
financing minus any flotation costs.
APV =
15-43
Unlevered
Project Value
+
Value of
Project Financing
NPV and APV Example
Assume Basket Wonders is considering a
new $425,000 automated basket weaving
machine that will save $100,000 per year
for the next 6 years. The required rate on
unlevered equity is 11%.
BW can borrow $180,000 at 7% with
$10,000 after-tax flotation costs. Principal
is repaid at $30,000 per year (+ interest).
The firm is in the 40% tax bracket.
15-44
Basket Wonders
NPV Solution
What is the NPV to an all-equityfinanced firm?
NPV = $100,000[PVIFA11%,6] - $425,000
NPV = $423,054 - $425,000
NPV = -$1,946
15-45
Basket Wonders
APV Solution
What is the APV?
First, determine the interest expense.
Int Yr 1
Int Yr 2
Int Yr 3
Int Yr 4
Int Yr 5
Int Yr 6
15-46
($180,000)(7%)
( 150,000)(7%)
( 120,000)(7%)
( 90,000)(7%)
( 60,000)(7%)
( 30,000)(7%)
= $12,600
= 10,500
= 8,400
= 6,300
= 4,200
= 2,100
Basket Wonders
APV Solution
Second, calculate the tax-shield benefits.
TSB Yr 1
TSB Yr 2
TSB Yr 3
TSB Yr 4
TSB Yr 5
TSB Yr 6
15-47
($12,600)(40%)
( 10,500)(40%)
( 8,400)(40%)
( 6,300)(40%)
( 4,200)(40%)
( 2,100)(40%)
= $5,040
= 4,200
= 3,360
= 2,520
= 1,680
=
840
Basket Wonders
APV Solution
Third, find the PV of the tax-shield benefits.
TSB Yr 1
TSB Yr 2
TSB Yr 3
TSB Yr 4
TSB Yr 5
TSB Yr 6
15-48
($5,040)(.901)
( 4,200)(.812)
( 3,360)(.731)
( 2,520)(.659)
( 1,680)(.593)
( 840)(.535)
= $4,541
= 3,410
= 2,456
= 1,661
=
996
=
449
PV = $13,513
Basket Wonders
NPV Solution
What is the APV?
APV = NPV + PV of TS - Flotation Cost
APV = -$1,946 + $13,513 - $10,000
APV = $1,567
15-49