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8/2/2019 FIN3004 2011-2012s2 Lecture04 Cost of Capital
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Lecture 4
Cost of Capital
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Learning Outcome
Know how to determine a firm’scost of equity capital
Understand the impact of beta indetermining the firm’s cost of equity capital
Know how to determine the firm’s
overall cost of capital Understand the impact of flotation
costs on capital budgeting
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Lecture Outline
The Cost of Equity Capital
Estimating the Cost of Equity Capital with theCAPM
Estimation of Beta
Beta, Covariance and Correlation
Determinants of Beta
Dividend Discount Model
Cost of Capital for Divisions and Projects
Cost of Fixed Income Securities
The Weighted Average Cost of Capital
Estimating Eastman Chemical’s Cost of Capital
Flotation Costs and the Weighted Average Cost of Capital
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Where Do We Stand?
Earlier discussions on capitalbudgeting focused on the
appropriate size and timing of cash flows.
This lecture discusses the
appropriate discount rate whencash flows are risky.
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Invest in project
The Cost of Equity Capital
Firm with
excess cash
Shareholder’sTerminal
Value
Pay cash dividend
Shareholder
invests in
financial
asset
Because stockholders can reinvest the dividend in risky financial assets,
the expected return on a capital-budgeting project should be at least asgreat as the expected return on a financial asset of comparable risk.
A firm with excess cash can either pay adividend or make a capital investment
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The Cost of Equity Capital
From the firm’s perspective, theexpected return is the Cost of EquityCapital:
)( F M iF i R R β R R • To estimate a firm’s cost of equity capital, we need
to know three things:
1. The risk-free rate, RF
F M R R 2. The market risk premium,
2
,
)(
),(
M
M i
M
M ii
σ
σ
RVar
R RCov β 3. The company beta,
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Example
Suppose Quantram has a beta of 1.3,and the firm is 100% equity financed.
Assume a risk-free rate of 5% and a
market risk premium of 8.4%.
What is the appropriate discount rate foran expansion of this firm?
)( F M iF R R β R R
%92.15
%,4.83.1%5
R
R
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Example
Suppose the stock of StansfieldEnterprises, a publisher of PowerPointpresentations, has a beta of 2.5. The
firm is 100% equity financed. Assume a risk-free rate of 5% and a
market risk premium of 10%.
What is the appropriate discount rate for
an expansion of this firm?
)( F M iF R R β R R
%105.2%5 R
%30 R
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Example
Suppose Stansfield Enterprises is evaluating
the following independent projects. Each costs$100 and lasts one year.
Project Project b Project’sEstimated Cash
Flows Next
Year
IRR NPV at30%
A 2.5 $150 50% $15.38
B 2.5 $130 30% $0
C 2.5 $110 10% -$15.38
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Using the SML
An all-equity firm should accept projects whose
IRRs exceed the cost of equity capital and reject
projects whose IRRs fall short of the cost of capital.
P r o j e c t
I R R
Firm’s risk (beta)
SML
5%
Good
project
Bad project
30%
2.5
A
B
C
Reject Region
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The Risk-free Rate
Treasury securities are close proxies forthe risk-free rate.
The CAPM is a period model. However,projects are long-lived. So, averageperiod (short-term) rates need to be used.
The historic premium of long-term (20-year) rates over short-term rates forgovernment securities is 2%.
So, the risk-free rate to be used in theCAPM could be estimated as 2% belowthe prevailing rate on 20-year treasurysecurities.
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The Market Risk Premium
Method 1: Use historical data
Method 2: Use the Dividend
Discount Model:
Market data and analyst forecasts
can be used to implement the DDMapproach on a market-wide basis
gP D R
0
1
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Estimation of Beta
Market Portfolio - Portfolio of allassets in the economy. In practice,
a broad stock market index, such asthe S&P 500 or the Hang SengIndex, is used to represent themarket.
Beta - Sensitivity of a stock’s returnto the return on the market
portfolio.
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Estimation of Beta
)(
),(
M
M i
RVar
R RCov β
• Problems
1. Betas may vary over time.
2. The sample size may be inadequate.
3. Betas are influenced by changing financial leverage and business risk.
• Solutions
– Problems 1 and 2 can be moderated by more sophisticated statisticaltechniques.
– Problem 3 can be lessened by adjusting for changes in business andfinancial risk.
– Look at average beta estimates of comparable firms in the industry.
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Stability of Beta
Most analysts argue that betas aregenerally stable for firms remainingin the same industry.
That is not to say that a firm’s betacannot change.
Changes in product line
Changes in technology
Deregulation
Changes in financial leverage
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Using an Industry Beta
It is frequently argued that one can betterestimate a firm’s beta by involving the
whole industry.
If you believe that the operations of thefirm are similar to the operations of therest of the industry, you should use theindustry beta.
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Using an Industry Beta
If you believe that the operations of thefirm are fundamentally different from theoperations of the rest of the industry, you
should use the firm’s beta. Do not forget about adjustments for
financial leverage.
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Example
Microsoft 0.86
Apple 2.43
ADP 0.76
EDS
1.13
Oracle 1.54
Computer Sciences 1.19
CA 2.03
Fiserv 1.24 Accenture 1.18
Symantec 0.64
Paychex 0.96
Equally Weighted Portfolio 1.27
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Example
Given Rf = 1.2%, Rm – Rf = 7%
Cost of capital of Symantec =
1.2% + 0.64 * 7% = 5.68% Or, Symantec wants to use
industry beta, so
Cost of capital will be
1.2 % + 1.27 * 7% = 10.09%
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Beta, Covariance and Correlation
Beta is qualitatively similar to the covariance since thedenominator (market variance) is a constant.
Beta and correlation are related, but different. It ispossible that a stock could be highly correlated to themarket, but it could have a low beta if its deviation wererelatively small.
)(
)(
)(
)(
2
,
M
i
M
M i
i R
R
R
R RCov
b
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Determinants of Beta
Business Risk
Cyclicality of Revenues
Operating Leverage Financial Risk
Financial Leverage
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Cyclicality of Revenues
Highly cyclical stocks have higher betas.
Empirical evidence suggests that retailers andautomotive firms fluctuate with the business cycle.
Transportation firms and utilities are less dependent
on the business cycle.
Note that cyclicality is not the same asvariability — stocks with high standard
deviations need not have high betas.
Movie studios have revenues that are variable,depending upon whether they produce ―hits‖ or―flops,‖ but their revenues may not be especiallydependent upon the business cycle.
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Operating Leverage
The degree of operating leveragemeasures how sensitive a firm (orproject) is to its fixed costs.
Operating leverage increases as fixedcosts rise and variable costs fall.
Operating leverage magnifies the
effect of cyclicality on beta. The degree of operating leverage is
given by: DOL =
EBIT D Sales
SalesD EBIT×
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Operating Leverage
Sales
$
Fixed costs
Total
costs
D EBIT
D Sales
Operating leverage increases as fixed costs rise
and variable costs fall.
Fixed costs
Total
costs
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Financial Leverage and Beta
Operating leverage refers to the sensitivity tothe firm’s fixed costs of production.
Financial leverage is the sensitivity to a firm’s
fixed costs of financing. The relationship between the betas of the
firm’s debt, equity, and assets is given by:
• Financial leverage always increases the equity beta relative
to the asset beta.
b Asset =Debt + Equity
Debt× b Debt +
Debt + Equity
Equity× b Equity
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Financial Leverage and Beta
The beta of debt is low in practice, sosometimes it is convenient to assumebeta of debt = 0 and a simplified version
of the above formula will be:
)1(,S
Band
S B
S
Asset Equity
Equity Asset
b b
b b
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ExampleConsider Grand Sport, Inc., which is
currently all-equity financed and has abeta of 0.90.
The firm has decided to lever up to a capital
structure of 1 part debt to 1 part equity.
Since the firm will remain in the sameindustry, its asset beta should remain0.90.
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ExampleHowever, assuming a zero beta for its debt,
its equity beta would become twice aslarge:
b Asset = 0.90 =
1 + 1
1× b Equity
b Equity
= 2 × 0.90 = 1.80
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Example
Rapid is currently all equity and hasa beta of 0.8. The firm desires tohave 1 part of debt and 2 parts of equity.
Because the firm stays in the sameindustry, its asset beta remain the
same. Assuming a beta of 0 for debt,we have:
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Example
If 1 part of debt to 1 part of equity, equitybeta will be:
2.1,2
118.0
),1(
Equity Equity
Asset EquityS
B
b b
b b
6.11
118.0
Equity b
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Dividend Discount Model
The DDM is an alternative to the CAPM forcalculating a firm’s cost of equity.
The DDM and CAPM are internally consistent,
but academics generally favor the CAPM andcompanies seem to use the CAPM moreconsistently.
This may be due to the measurement error associated
with estimating company growth.
gP
RD
1
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Capital Budgeting & Project Risk
A firm that uses one discount rate for all projects may over
time increase the risk of the firm while decreasing its value.
P r o j e c t I R R
Firm’s risk (beta)
SML
r f
b FIRM
Incorrectly rejected
positive NPV projects
Incorrectly accepted
negative NPV projects
Hurdle
rate)( F M FIRM F R R β R
The SML can tell us why:
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Suppose the Conglomerate Company has a cost of capital,based on the CAPM, of 17%. The risk-free rate is 4%, themarket risk premium is 10%, and the firm’s beta is 1.3.
17% = 4% + 1.3 × 10%
This is a breakdown of the company’s investment projects:
1/3 Automotive Retailer b = 2.0
1/3 Computer Hard Drive Manufacturer b = 1.3
1/3 Electric Utility b = 0.6
average b of assets = 1.3
When evaluating a new electrical generation investment,
which cost of capital should be used?
Capital Budgeting & Project Risk
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Capital Budgeting & Project Risk
P r o j e c t I R
R
Project’s risk (b)
17%
1.3 2.00.6
R = 4% + 0.6×(14% – 4% ) = 10%
10% reflects the opportunity cost of capital on an investmentin electrical generation, given the unique risk of the project.
10%
24%
Investments in harddrives or auto retailing
should have higher
discount rates.
SML
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Cost of Debt
Interest rate required on new debtissuance (i.e., yield to maturity onoutstanding debt)
Adjust for the tax deductibility of interest expense
Cost of debt (after corporate tax) =
RB x (1 – tC)
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Example
Borrowing Rate (RB)= 10%
Tax Rate (tC) = 40%
After tax cost of debt = RB x (1 – tC) = 10% x (1 – 0.4) = 6%
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Cost of Preferred Stock
Preferred stock is a perpetuity,so its price is equal to the
coupon paid divided by thecurrent required return.
Rearranging, the cost of
preferred stock is: RP = C / PV
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The Weighted Average Cost of Capital
The Weighted Average Cost of Capital is givenby:
• Because interest expense is tax-deductible, wemultiply the last term by (1 – T C ).
RWACC =Equity + Debt
Equity × R Equity +Equity + Debt Debt × R Debt × (1 – T C )
RWACC =S + B
S× RS +
S + B
B× R B × (1 – T C )
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Example: International Paper
First, we estimate the cost of equityand the cost of debt.
We estimate an equity beta toestimate the cost of equity.
We can often estimate the cost of debt by observing the YTM of the
firm’s debt.
Second, we determine the WACC byweighting these two costs
appropriately.
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Example: International Paper
The industry average beta is0.82, the risk free rate is 3%,
and the market risk premium is8.4%.
Thus, the cost of equity capital
is: RS = RF + bi × ( R M – RF )
= 3% + 0.82×8.4%= 9.89%
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Example: International Paper
The yield on the company’s debtis 8%, and the firm has a 37%marginal tax rate.
The debt to value ratio is 32%
8.34% is International’s cost of capital. It should be used to
discount any project where one believes that the project’s risk
is equal to the risk of the firm as a whole and the project has
the same leverage as the firm as a whole.
= 0.68 × 9.89% + 0.32 × 8% × (1 – 0.37)
= 8.34%
RWACC = S + B
S× RS +
S + B
B× R B × (1 – T C )
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Flotation Costs
Flotation costs represent theexpenses incurred upon the issue, orfloat, of new bonds or stocks.
These are incremental cash flows of the project, which typically reducethe NPV since they increase the initial
project cost (i.e., CF0).
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Flotation Costs
Amount Raised = NecessaryProceeds / (1-% flotation cost)
The % flotation cost is a weightedaverage based on the average cost of issuance for each funding source andthe firm’s target capital structure:
f A = (E/V)* f E + (D/V)* f D
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Example
If Spatt is an all equity firm andwants to raise $100M throughequity. If flotation cost of equity is
10%, how much equity should Spattsell?
$100 M = (1 – 0.1) X AmountRaised, so Amount Raised = $100 M
/ 0.9 = $111.11 M
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Example
Now if Spatt is financed by 60%equity and 40% debt, and f S =10%as before, and f B = 0.05
The weighted average flotation costwill be: f A = (E/V)* f E + (D/V)* f D = 0.6 * 0.1 +
0.4*0.05 = 0.08
Amount raised will be $100 M / (1-0.08) =$108.70 M
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Revision Topics and Checkpoints
How do we determine the cost of equity capital?
How can we estimate a firm or
project beta? How does leverage affect beta?
How do we determine the weighted
average cost of capital? How do flotation costs affect the
capital budgeting process?
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