This document discusses required returns and the cost of capital. It covers key topics such as: - The overall cost of capital of a firm is a weighted average of the costs of the individual sources of financing like debt and equity. - There are several methods to calculate the cost of equity including the dividend discount model, capital asset pricing model, and cost of debt plus risk premium approach. - The weighted average cost of capital (WACC) represents the firm's overall required rate of return and is calculated by weighting the cost of each component of the firm's capital structure. - Adjusted present value (APV) and net present value (NPV) methods are introduced to evaluate projects and determine

1. 5-1
Chapter 15Chapter 15
Required ReturnsRequired Returns
and the Cost ofand the Cost of
CapitalCapital
Instructor: Ajab Khan Burki

2. 5-2
Required Returns andRequired Returns and
the Cost of Capitalthe Cost of Capital
Creation of Value
Overall Cost of Capital of the Firm
Project-Specific Required Rates
Group-Specific Required Rates
Total Risk Evaluation

3. 5-3
Key Sources ofKey Sources of
Value CreationValue Creation
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

4. 5-4
Overall Cost ofOverall Cost of
Capital of the FirmCapital 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).

5. 5-5
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

6. 5-6
Cost of DebtCost of Debt is the required rate
of return on investment of the
lenders of a company.
ki = kd ( 1 - T )
Cost of DebtCost of Debt
P0 =
Ij + Pj
(1 + kd)jΣ
n
j =1

7. 5-7
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%.
Determination ofDetermination of
the Cost of Debtthe Cost of Debt
$385.54 =
$0 + $1,000
(1 + kd)10

8. 5-8
(1 + kd)10
= $1,000 / $385.54
= 2.5938
(1 + kd) = (2.5938) (1/10)
= 1.1
kd = .1 or 10%
ki = 10% ( 1 - .40 )
kkii = 6%6%
Determination ofDetermination of
the Cost of Debtthe Cost of Debt

9. 5-9
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

10. 5-10
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

11. 5-11
Dividend Discount ModelDividend Discount Model
Capital-Asset PricingCapital-Asset Pricing
ModelModel
Before-Tax Cost of DebtBefore-Tax Cost of Debt
plus Risk Premiumplus Risk Premium
Cost of EquityCost of Equity
ApproachesApproaches

12. 5-12
Dividend Discount ModelDividend Discount Model
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 =
∞
∞

13. 5-13
Constant Growth ModelConstant Growth 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.

14. 5-14
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) + .08
kkee = .05 + .08 = .13.13 or 13%13%
Determination of theDetermination of the
Cost of Equity CapitalCost of Equity Capital

15. 5-15
Growth Phases ModelGrowth Phases Model
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
(1+ke)t
+
Σ

16. 5-16
Capital AssetCapital Asset
Pricing ModelPricing 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)βj

17. 5-17
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)βj
= 4% + (11.2% - 4%)1.25
kkee = 4% + 9% = 13%13%
Determination of theDetermination of the
Cost of Equity (CAPM)Cost of Equity (CAPM)

18. 5-18
Before-Tax Cost of DebtBefore-Tax Cost of Debt
Plus Risk PremiumPlus 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

19. 5-19
Assume that Basket Wonders (BW)
typically adds a 3% premium to the
before-tax cost of debt.
ke = kd + Risk Premium
= 10% + 3%
kkee = 13%13%
Determination of theDetermination of the
Cost of Equity (kCost of Equity (kdd + R.P.)+ R.P.)

20. 5-20
Constant Growth Model 13%13%
Capital Asset Pricing Model 13%13%
Cost of Debt + Risk Premium 13%13%
Generally, the three methods
will not agree.
Comparison of theComparison of the
Cost of Equity MethodsCost of Equity Methods

21. 5-21
Cost of Capital = kx(Wx)
WACC = .35(6%) + .15(9%) +
.50(13%)
WACC = .021 + .0135 + .065
= .0995 or 9.95%
Weighted AverageWeighted Average
Cost of Capital (WACC)Cost of Capital (WACC)
Σ
n
x=1

22. 5-22
1.1. Weighting SystemWeighting System
Marginal Capital Costs
Capital Raised in Different
Proportions than WACC
Limitations of the WACCLimitations of the WACC

23. 5-23
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

24. 5-24
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 AddedEconomic Value Added

25. 5-25
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.
Economic Value AddedEconomic Value Added

26. 5-26
Add Flotation Costs (FC) to the
Initial Cash Outlay (ICO).
Impact: ReducesReduces the NPV
Adjustment toAdjustment to
Initial Outlay (AIO)Initial Outlay (AIO)
NPV = Σ
n
t=1
CFt
(1 + k)t
- ( ICO + FC )

27. 5-27
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)

28. 5-28
Initially assume all-equity financing.
Determine project beta.
Calculate the expected return.
Adjust for capital structure of firm.
Compare cost to IRR of project.
Determining Project-SpecificDetermining Project-Specific
Required Rates of ReturnRequired Rates of Return
Use of CAPM in Project Selection:

29. 5-29
Difficulty in DeterminingDifficulty in Determining
the Expected Returnthe Expected 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:

30. 5-30
Project AcceptanceProject Acceptance
and/or Rejectionand/or Rejection
SML
X
X
X
X
X
X
X
O O
O
O
O
O
O
SYSTEMATIC RISK (Beta)
EXPECTEDRATE
OFRETURN
Rf
Accept
Reject

31. 5-31
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

32. 5-32
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

33. 5-33
ke = Rf + (Rm - Rf)βj
= 4% + (11.2% - 4%)1.5
kkee = 4% + 10.8% = 14.8%14.8%
WACCWACC = .30(6%) + .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?

34. 5-34
Determining Group-SpecificDetermining Group-Specific
Required Rates of ReturnRequired Rates of Return
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:

35. 5-35
Comparing Group-SpecificComparing Group-Specific
Required Rates of ReturnRequired Rates of Return
Group-Specific
Required Returns
Company Cost
of Capital
Systematic Risk (Beta)
ExpectedRateofReturn

36. 5-36
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).
Qualifications to UsingQualifications to Using
Group-Specific RatesGroup-Specific Rates

37. 5-37
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

38. 5-38
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

39. 5-39
Firm-Portfolio ApproachFirm-Portfolio Approach
B
C
A
Indifference
Curves
STANDARD DEVIATION
EXPECTEDVALUEOFNPV
Curves show
“HIGH”
Risk Aversion

40. 5-40
Firm-Portfolio ApproachFirm-Portfolio Approach
B
C
A
Indifference
Curves
STANDARD DEVIATION
EXPECTEDVALUEOFNPV
Curves show
“MODERATE”
Risk Aversion

41. 5-41
Firm-Portfolio ApproachFirm-Portfolio Approach
B
C
A
Indifference
Curves
STANDARD DEVIATION
EXPECTEDVALUEOFNPV
Curves show
“LOW”
Risk Aversion

42. 5-42
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

43. 5-43
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.
Adjusted Present ValueAdjusted Present Value
APV =
Unlevered
Project Value
+
Value of
Project Financing

44. 5-44
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

45. 5-45
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

46. 5-46
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
Basket WondersBasket Wonders
APV SolutionAPV Solution

47. 5-47
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
Basket WondersBasket Wonders
APV SolutionAPV Solution

48. 5-48
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
Basket WondersBasket Wonders
APV SolutionAPV Solution

49. 5-49
What is the APVAPV?
APV = NPV + PV of TS - Flotation Cost
APV = -$1,946 + $13,513 - $10,000
APVAPV = $1,567$1,567
Basket WondersBasket Wonders
NPV SolutionNPV Solution