cost of capital estimation. methods for benchmarking the cost of equity capital 1. capital asset...
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Cost of Capital Estimation
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Methods for Benchmarking the Cost of Equity Capital1. Capital Asset Pricing Model using beta from a
regression analysis (top-down method)2. Capital Asset Pricing Model weighting beta
estimates for individual divisions using industry betas (bottom-up method)
3. Implied Cost of Equity using stock valuation model, given stock price and expected growth rates
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Only Systematic Risk is Priced in the Capital Asset Pricing Model The key result of the CAPM is that the relevant risk of
any asset is the risk that it adds to the market portfolio—the systematic risk Systematic risk is exposure to market factors that affect all
securities to a greater or lesser degree (e.g. inflation, GDP growth, interest rates, political events, etc.)
In well diversified portfolios exposure to firm-specific (unsystematic) events is diversified away (e.g. management changes, product announcements, litigation, etc.)
The systematic risk is measured by the security’s co-movement with a broadly diversified portfolio
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Risk measures
Standard deviation (stdev)
Covariance (covar.s)
Correlation
Coefficient (correl)
.1n
rrn
1i
2^
i
2n
rrrr
)AB(Cov
n
1i
B
^
BiA
^
Ai
BAAB
)AB(Cov
The standardization confines the ρ to values between –1 and +1
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Portfolio standard deviation for a two-security portfolio:
ABBA2B
2B
2A
2Ap COVww2ww
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Two-Security PortfolioVariance-Covariance Matrix The two-security portfolio contains two
covariance (market risk) terms and two variance (stand-alone risk) terms
2A CovA.B
CovB.A 2B
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Three-Security PortfolioVariance-Covariance Matrix
2A CovA.B CovA.C
CovB.A 2B CovB,C
CovC,A CovC.B 2C
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Standard deviation and risk
The standard deviation of a single security includes both systematic and unsystematic risk
For well diversified portfolios, the standard deviation includes systematic risk only
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Efficient Portfolios
Combining assets with less than perfect correlation improves portfolio efficiency by reducing unsystematic risk
An efficient portfolio is one that offers: the most return for a given amount of risk, or the least risk for a give amount of return.
The collection of efficient portfolios is called the efficient frontier
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ExpectedPortfolio Return, E(Rp)
Risk, p
Efficient Frontier
See two-security example
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Capital Asset Pricing Model
The CAPM is an equilibrium model that specifies a linear relationship between risk and required rate of return for assets held in well-diversified portfolios.
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When a risk-free security with return rRF is added, investors can create portfolios that combine this security with a portfolio of risky securities.
Since the risk-free asset has zero variance, its covariance is also zero Thus the standard deviation of a 2-security
portfolio of the risk-free asset and the market portfolio, M, is: wmσm
Adding a risk-free security
mmw mmw
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What impact does rRF have onthe efficient frontier?
Both the standard deviation and expected return are linear functions of the weights wrf and wm
The straight line connecting rRF with M (market), the tangency point between the line and the old efficient frontier, becomes the new efficient frontier.
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M
rRF
M Risk, p
Efficient Frontier with a Risk-Free Asset
The Capital MarketLine (CML):
New Efficient Frontier
.rM^
ExpectedReturn, rp
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rp = rRF +^ p.rM - rRF^
M
p is determined by selecting weights on:the risk-free security (wrf)the market portfolio (wm)
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The equation for the Security Market Line, the principal result of the Capital Asset Pricing Model, gives the risk/return relationship for individual securities.
Substitute the contribution of an individual security’s risk to the market portfolio standard deviation, ρi,mσi , for σp:
The Security Market Line (SML)
m
im,irfm
^
rfi
^
]rr[rr
irfm
^
rfi
^
beta]rr[rr
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Beta
2,
2,
,m
mi
m
mimi
m
imii
Covbeta
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Beta intuition
Beta is simply a measure of relative systematic risk, or relative exposure to the economic variables that drive market returns.
For example, a security with a beta of 1.20 exhibits 20 percent more variability in response to market returns as compared with a typical security.
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Result of the CAPM
Expected return for stocks includes a risk-free component a risky component as determined by a risk premium
for the average stock, known as the ‘market risk premium’, (rm - rrf)
and the beta of the individual stock, which measures the degree of market risk exposure for the individual security
The expected (required) return on the stock is the issuing company’s cost of Equity
irfm
^
rfi
^
beta]rr[rr SML:
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Security Markey Line
0%
5%
10%
15%
20%
25%
0 0.5 1 1.5 2 2.5 3
Beta
Exp
ecte
d R
etur
n
Risk-free rate
Expected return on market
= Rm - Rrf
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Std. Deviation BetaSecurity A 20% 1.25Security B 30% 0.95
Which security has more unsystematic risk?
Which security has more systematic risk? Which security should have the higher
required return?
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Estimating the CAPM Inputs
The beta of the security The expected market risk premium The current risk-free rate
irfm
^
rfi
^
beta]rr[rr
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Estimating Beta (top-down approach) Standard approach is to regress stock returns
against those of a broad market index, where the slope of the regression line is the beta coefficient: most services use either 5 years (monthly returns) or
2-3 years (weekly) regressed on the S&P 500 A 5-year interval insures against possible aberrant
shocks to the beta due to unusual short-term events A shorter interval may better reflect the company’s
current risk profile if its business or operating environment have changed
Many services adjust beta toward 1.0 Example: Adj. Beta = 0.67*beta + 0.33*1.0
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26
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Bottom-up Betas The beta of a portfolio is a market-value weighted
average of the betas of the assets comprising the portfolio the beta of a firm is a weighted average of the
individual divisions or projects in which the firm invests
A bottom-up beta estimates beta for each of the divisions using industry betas, and uses a weighted average of these division betas to estimate the corporate beta
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Advantages of Bottom-up Betas
Since the procedure involves averaging across several regression betas, the estimation error is lower, and the estimates are more stable
The bottom-up beta may provide a better estimate of the true beta when the firm has reorganized or restructured itself substantially during the period of the regression Weight the division betas based on the current mix
Division betas are required to make investment decisions
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Division Cost of Capital
Rate of Return (%)
WACC
Project H
Division H’s WACC
Risk
Project L Composite WACC for Firm A
13.0
7.0
10.0
11.0
9.0
Division L’s WACC
0 RiskL RiskAverage RiskH
The firm’s overall cost of capital cannot be applied to individual divisions or projects when there are differences in risk: 1) operating (business) risk; 2) financial risk
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Operating Risk
Variability in Earnings Before Interest and Taxes Two sources:
1) Industry Effects on sales Cyclical companies have higher business risk than non-cyclical
firms Firms which sell more high-cost and discretionary products will
have higher business risk
2) Operating leverage effects: Operating leverage refers to the proportion of the total costs of the firm that are fixed.
Other things equal, higher operating leverage results in greater earnings variability
Operating leverage measure = % Change in EBIT / % Change in Revenues
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Operating Leverage
Revenue 100 200 300
Variable costs (20%) (20) (40) (60)
Fixed costs (100) (100) (100)
EBIT (20) 60 140
Revenue 100 200 300
Variable costs (50%) (50) (100) (150)
Fixed costs (40) (40) (40)
EBIT 10 60 110
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Financial Risk
As firms borrow, they create fixed costs (interest payments) that make their earnings to equity investors more volatile
This increased earnings volatility increases the equity Beta
As more variance is added, and some fraction of this variance is correlated with markets, beta increases
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The Pure-Play approach to Beta estimation The typical approach is to find publicly traded
‘pure play’ companies operating primarily in division’s business Can expand to customers and suppliers if difficult to
find companies They should have levels of operating risk (EBIT
variance) that are comparable to that of the division since they are in the same industry
Their levels of financial risk, however, will vary due to differences in financing choice
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The Pure-Play approach to Beta estimation Process for dealing with financial leverage
differences: Unlever the betas of the pure-play firms
removes the effects of their debt-equity mix on beta Take an average of these unlevered betas Relever the betas at the division’s target debt-to-stock
ratio
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The Cost of Equity at Different Levels of Debt: Hamada’s Equation bL = bU [1 + (1 - t)(D/S)] bU is the beta of a firm when it has no debt (the unlevered beta) Use this equation to unlever the observed pure play betas
(bL’s), then average the resulting bU’s Use the debt-stock mix (D/S) and marginal tax rates (t) of these companies
to unlever
Divide bL by term in brackets
Relever average unlevered beta at the division’s target capital structure (D/S) and marginal tax rate (t) Multiply resulting average bU by term in brackets
Plug relevered beta into CAPM to yield rs
See AOL example
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Levered Beta Calculation
Division's target capital structure (D/S) = 0.6Tax Rate = 40%
Pure Play Actual
Market
ValueMarket
Value Unlevered
Company Beta (bL) Debt Equity D/S Beta (bu)
A 0.8 1000 1000 1.00 0.50
B 1.2 800 500 1.60 0.61
C 0.6 1500 2000 0.75 0.41
Average 0.51
Levered beta =
.51[1+(1-.4)*.6]
Result 0.69
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Second CAPM Input:The Market Risk Premium The equity market risk premium is the
premium that investors demand for investing in an average risk investment, above the risk-free rate, (rm – rrf)
The expected rate of return on the average stock minus the risk-free rate at any point in time.
irfmrfi betarrrr ][^^
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Approaches to Estimating the Market Risk Premium Assume that the actual premium delivered over
long time periods is equal to the expected premium - i.e., use historical data
Estimate the implied premium using today’s security prices and expected growth in earnings
Forecasts future stock returns based on fundamentals: payouts, multiples and growth
Survey data
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The Historical Risk Premium Approach Defines a time period for the estimation Calculates the difference between average
returns on a stock index and average returns on a riskless security during the period
Uses the difference as a premium looking forward
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The Historical Risk Premium Approach The limitations of this approach are:
Assumes that the risk aversion of investors has not changed in a systematic way across time. (The risk aversion may change from year to year, but it reverts back to historical averages)
Assumes that the riskiness of the “risky” portfolio (stock index) has not changed in a systematic way across time.
Strange results, since after periods of high returns, you conclude that investors have become risk averse, when the opposite is probably true.
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Risk Premium Based on Forecasted Fundamentals R = PAYOUT * E/P + G≈ 7.5% ≈ 50% 7% ≈ 4% (a P/E of 14) (2 real +
2 inflation)
Use P/E ratio to determine earnings yield, multiply by payout which includes dividends and repurchases
Add an expected LT growth rate for earnings to arrive at 7.5% forecast yield for large stocks (S&P 500)
Subtracting long-term Treasury yield of 1.8% yields an estimated risk premium of 5.7%
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Implied Market Risk Premiums
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43
2011 survey data on the Market Risk Premium
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Third CAPM Input:The Risk-free Rate U.S. Treasuries are used as the risk-free rate While open to debate, most favor using a long-term
Treasury rate for the following reasons: The LT rate reflects an average of future expected short-term
rates over the life of the investment The LT rate is much more stable than ST rates The cash flows underlying stocks are long-lived
The 10-year Treasury is commonly used The Treasury rates can be found on:
http://www.bloomberg.com/markets/rates/index.html
irfmrfi betarrrr ][^^
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Implied Cost of Equity as another benchmark As an alternative to the CAPM approach, bottom-up
or top-down, for corporate finance purposes the cost of Equity can be estimated using the stock price and expected growth in Free Cash Flow to Equity
)/(10 FCFEgrFCFEP
Since stock price and consensus analyst growth forecasts are known, the company can back into an implied cost of Equity by solving for ‘r’ using a stock valuation model.
Constant growth version:
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Advantages of Implied Cost
Market-based measure Do not have to estimate beta Do not have to estimate market risk
premium These assumptions are implicit in the
market’s valuation
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Weighted Average Cost of Capital
The overall required rate of return % onInvested Capital (Debt + Stock)
WACC = (D/V)rd(1-T) + (S/V)rs
rd = % weighted average yield-to-maturity on debtrs = % required return on stock (cost of Equity)
D = $Debt market valueS = $Stock market valueT = % tax rateV = $Enterprise value = D + S
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Key Terms
Capital Asset Pricing Model Systematic risk Beta (unlevered and levered) Market risk premium Operating risk Financial risk
48