Returns on cash of capital

15.1 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited 2009. Created by Gregory Kuhlemeyer.
Chapter 15Chapter 15
Required ReturnsRequired Returns
and the Cost ofand the Cost of
CapitalCapital

1. Explain how a firm creates value and identify the key sources of
value creation.
2. Define the overall “cost of capital” of the firm.
3. Calculate the costs of the individual components of a firm’s cost of
capital - cost of debt, cost of preferred stock, and cost of equity.
4. Explain and use alternative models to determine the cost of equity,
including the dividend discount approach, the capital-asset pricing
model (CAPM) approach, and the before-tax cost of debt plus risk
premium approach.
5. Calculate the firm’s weighted average cost of capital (WACC) and
understand its rationale, use, and limitations.
6. Explain how the concept of economic Value added (EVA) is related
to value creation and the firm’s cost of capital.
7. Understand the capital-asset pricing model's role in computing
project-specific and group-specific required rates of return.
After Studying Chapter 15,After Studying Chapter 15,
you should be able to:you should be able to:

• Creation of Value
• Overall Cost of Capital of the Firm
• Project-Specific Required Rates
• Group-Specific Required Rates
• Total Risk Evaluation
Required Returns andRequired Returns and
the Cost of Capitalthe Cost of Capital

Growth
phase of
product
cycle
Barriers to
competitive
entry
Other --
e.g., patents,
temporary
monopoly
power,
oligopoly
pricing
Cost
Marketing
and
price
Perceived
quality
Superior
organizational
capability
Industry AttractivenessIndustry Attractiveness
Competitive AdvantageCompetitive Advantage
Key Sources ofKey Sources of
Value CreationValue Creation

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).
Overall Cost ofOverall Cost of
Capital of the FirmCapital of the Firm

Type of Financing Mkt Val Weight
Long-Term Debt $ 35M 35%
Preferred Stock $ 15M 15%
Common Stock Equity $ 50M 50%
$ 100M 100%
Market Value ofMarket Value of
Long-Term FinancingLong-Term Financing

Cost of DebtCost of Debt is the required rate
of return on investment of the
lenders of a company.
ki = kd ( 1 – T )
P0 =
Ij + Pj
(1 + kd)jΣ
n
j=1
Cost of DebtCost 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 =
$0 + $1,000
(1 + kd)10
Determination ofDetermination of
the Cost of Debtthe Cost of Debt

(1 + kd)10
= $1,000 / $385.54
= 2.5938
(1 + kd) = (2.5938) (1/10)
= 1.1
kd = 0.1 or 10%
ki = 10% ( 1 – .40 )
kkii = 6%6%
Determination ofDetermination of
the Cost of Debtthe Cost of Debt

Cost of Preferred StockCost of Preferred Stock is the
required rate of return on
investment of the preferred
shareholders of the company.
kP = DP / P0
Cost of Preferred StockCost 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
kkPP = 9%9%
Determination of theDetermination of the
Cost of Preferred StockCost of Preferred Stock

• Dividend Discount ModelDividend Discount Model
• Capital-Asset Pricing ModelCapital-Asset Pricing Model
• Before-Tax Cost of Debt plusBefore-Tax Cost of Debt plus
Risk PremiumRisk Premium
Cost of EquityCost of Equity
ApproachesApproaches

The cost of equity capitalcost 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
(1 + ke)1
(1 + ke)2
(1 + ke)
+ . . . ++P0 =
∞
∞
Dividend Discount ModelDividend Discount Model

The constant dividend growthconstant dividend growth
assumptionassumption reduces the model to:
ke = ( D1 / P0 ) + g
Assumes that dividends will grow
at the constant rate “g” forever.
Constant Growth ModelConstant Growth Model

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.
ke = ( D1 / P0 ) + g
ke = ($3(1.08) / $64.80) + 0.08
kkee = 0.05 + 0.08 = 0.130.13 or 13%13%
Cost of Equity CapitalCost of Equity Capital

D0(1 + g1)t
Da(1 + g2)t–a
(1 + ke)t
(1 + ke)t
P0 =
The growth phases assumptiongrowth phases assumption
leads to the following formulaleads to the following formula
(assume 3 growth phases):(assume 3 growth phases):
Σ + Σ
t=1
a
t=a+1
b
t=b+1
∞ Db(1 + g3)t–b
+
Σ
Growth Phases ModelGrowth Phases Model
(1 + ke)t

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)βj
Capital AssetCapital Asset
Pricing ModelPricing Model

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 11.4%
ke = Rf + (Rm – Rf)βj
= 4% + (11.4% – 4%)1.25
kkee = 4% + 9.25% = 13.25%13.25%
Cost of Equity (CAPM)Cost of Equity (CAPM)

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
Before-Tax Cost of DebtBefore-Tax Cost of Debt
Plus Risk PremiumPlus Risk Premium

Assume that Basket Wonders (BW)
typically adds a 2.75% premium to the
before-tax cost of debt.
ke = kd + Risk Premium
= 10% + 2.75%
kkee = 12.75%12.75%
Cost of Equity (kCost of Equity (kdd + R.P.)+ R.P.)

Constant Growth Model 13.00%13.00%
Capital Asset Pricing Model 13.25%13.25%
Cost of Debt + Risk Premium 12.75%12.75%
Comparison of theComparison of the
Cost of Equity MethodsCost of Equity Methods
Generally, the three methods will not agree.
We must decide how to weight –
we will use an average of these three.

Cost of Capital = kx(Wx)
WACC = 0.35(6%) + 0.15(9%) +
0.50(13%)
WACC = 0.021 + 0.0135 + 0.065
= 0.0995 or 9.95%
Σ
n
x=1
Weighted AverageWeighted Average
Cost of Capital (WACC)Cost of Capital (WACC)

1.1. Weighting SystemWeighting System
• Marginal Capital Costs
• Capital Raised in Different
Proportions than WACC
Limitations of the WACCLimitations of the WACC

2.2. Flotation CostsFlotation Costs are the costs
associated with issuing securities
such as underwriting, legal, listing,
and printing fees.
a. Adjustment to Initial Outlay
b. Adjustment to Discount Rate
Limitations of the WACCLimitations of the WACC

• 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 AddedEconomic Value Added

EVA = NOPAT – [Cost of
Capital x Capital Employed]
• 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.
• NOPAT – net operating profit after tax is a
company’s potential after-tax profit if it was all-
equity-financed or “unlevered.”
Economic Value AddedEconomic Value Added

Add Flotation Costs (FC) to the
Initial Cash Outlay (ICO).
Impact: ReducesReduces the NPV
NPV = Σ
n
t=1
CFt
(1 + k)t
– ( ICO + FC )
Adjustment toAdjustment to
Initial Outlay (AIO)Initial Outlay (AIO)

Subtract Flotation Costs from the
proceeds (price) of the security and
recalculate yield figures.
Impact: IncreasesIncreases the cost for any
capital component with flotation costs.
Result: Increases the WACC, which
decreasesdecreases the NPV.
Adjustment toAdjustment to
Discount Rate (ADR)Discount Rate (ADR)

• Initially assume all-equity financing.
• Determine project beta.
• Calculate the expected return.
• Adjust for capital structure of firm.
• Compare cost to IRR of project.
Use of CAPM in Project Selection:
Determining Project-SpecificDetermining Project-Specific
Required Rates of ReturnRequired Rates of Return

• 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 beta and create the SML.
Determining the SML:
Difficulty in DeterminingDifficulty in Determining
the Expected Returnthe Expected Return

SML
X
X
X
X
X
X
X
O O
O
O
O
O
O
SYSTEMATIC RISK (Beta)
EXPECTEDRATE
OFRETURN
Rf
Accept
Reject
Project AcceptanceProject Acceptance
and/or Rejectionand/or Rejection

1. Calculate the required return
for Project k (all-equity financed).
Rk = Rf + (Rm – Rf)βk
2. Adjust for capital structure of the
firm (financing weights).
Weighted Average Required Return = [ki]
[% of Debt] + [Rk][% of Equity]
Determining Project-SpecificDetermining Project-Specific
Required Rate of ReturnRequired Rate of Return

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%.
Project-Specific RequiredProject-Specific Required
Rate of ReturnRate of Return ExampleExample

ke = Rf + (Rm – Rf)βj
= 4% + (11.2% – 4%)1.5
kkee = 4% + 10.8% = 14.8%14.8%
WACCWACC = 0.30(6%) + 0.70(14.8%)
= 1.8% + 10.36% = 12.16%12.16%
IRRIRR = 19%19% > WACCWACC = 12.16%12.16%
Do You Accept the Project?Do You Accept the Project?

• Initially assume all-equity financing.
• Determine group beta.
• Calculate the expected return.
• Adjust for capital structure of group.
• Compare cost to IRR of group
project.
Use of CAPM in Project Selection:
Determining Group-SpecificDetermining Group-Specific

Group-Specific
Required Returns
Company Cost
of Capital
Systematic Risk (Beta)
ExpectedRateofReturn
Comparing Group-SpecificComparing Group-Specific

• 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).
Qualifications to UsingQualifications to Using
Group-Specific RatesGroup-Specific Rates

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.
Project EvaluationProject Evaluation
Based on Total RiskBased on Total Risk

Discount Rate (%)
0 3 6 9 12 15
RADR – “high”
risk at 15%
(Reject!)
RADR – “low”
risk at 10%
(Accept!)
Adjusting for risk correctly
may influence the ultimate
Project decision.
NetPresentValue
$000s
15
10
5
0
–4
RADR and NPVRADR and NPV

Probability Distribution
Approach
Acceptance of a single project
with a positive NPV depends on
the dispersion of NPVs and the
utility preferences of
management.
Project EvaluationProject Evaluation
Based on Total RiskBased on Total Risk

B
C
A
Indifference
Curves
STANDARD DEVIATION
EXPECTEDVALUEOFNPV
Curves show
“HIGH”
Risk Aversion
Firm-Portfolio ApproachFirm-Portfolio Approach

B
C
A
Indifference
Curves
STANDARD DEVIATION
EXPECTEDVALUEOFNPV
Curves show
“MODERATE”
Risk Aversion

B
C
A
Indifference
Curves
STANDARD DEVIATION
EXPECTEDVALUEOFNPV
Curves show
“LOW”
Risk Aversion

ββjj == ββjuju [ 1 + ([ 1 + (B/SB/S)(1 –)(1 – TTCC) ]) ]
ββj: Beta of a levered firm.
ββju: 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.
Adjusting Beta forAdjusting Beta for
Financial LeverageFinancial Leverage

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 =
Unlevered
Project Value
+
Value of
Project Financing
Adjusted Present ValueAdjusted Present Value

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.
NPV and APV ExampleNPV and APV Example

What is the NPVNPV to an all-equity-to an all-equity-
financed firmfinanced firm?
NPV = $100,000[PVIFA11%,6] – $425,000
NPV = $423,054 – $425,000
NPVNPV = – $1,946– $1,946
Basket WondersBasket Wonders
NPV SolutionNPV Solution

What is the APVAPV?
First, determine the interest expense.
Int Yr 1 ($180,000)(7%) = $12,600
Int Yr 2 ( 150,000)(7%) = 10,500
Int Yr 3 ( 120,000)(7%) = 8,400
Int Yr 4 ( 90,000)(7%) = 6,300
Int Yr 5 ( 60,000)(7%) = 4,200
Int Yr 6 ( 30,000)(7%) = 2,100
APV SolutionAPV Solution

Second, calculate the tax-shield benefits.
TSB Yr 1 ($12,600)(40%) = $5,040
TSB Yr 2 ( 10,500)(40%) = 4,200
TSB Yr 3 ( 8,400)(40%) = 3,360
TSB Yr 4 ( 6,300)(40%) = 2,520
TSB Yr 5 ( 4,200)(40%) = 1,680
TSB Yr 6 ( 2,100)(40%) = 840

Third, find the PV of the tax-shield benefits.
TSB Yr 1 ($5,040)(.901) = $4,541
TSB Yr 2 ( 4,200)(.812) = 3,410
TSB Yr 3 ( 3,360)(.731) = 2,456
TSB Yr 4 ( 2,520)(.659) = 1,661
TSB Yr 5 ( 1,680)(.593) = 996
TSB Yr 6 ( 840)(.535) = 449
PV = $13,513PV = $13,513

What is the APVAPV?
APV = NPV + PV of TS – Flotation Cost
APV = –$1,946 + $13,513 – $10,000
APVAPV = $1,567$1,567
NPV SolutionNPV Solution

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