Cost of Capital in Valuation and
Corporate Models
Valuation
1
July 17
Cost of Capital Contents
• Actual Cost of Capital Process
• WACC Computation and Theory
• Alternative Models
• Capital Asset Pricing Model
Beta Measurement
Market Premium
Asset Beta
Cost of Capital
2
July 17
Financial Management and Finance Theory
• A crucial issue in financial analysis is establishing the discount
rate and risk measurement using capital asset pricing models.
• Financial principles of efficient markets, market expectations and
event studies lie behind a number of modeling and financial
management concepts.
• The general opinion is that cost of capital is over-estimated and
compensated for with optimistic assumptions.
• Recent work on cost of capital
 Lower equity risk premium
 CAPM discredited
 Analyst growth rates are too high
Cost of Capital
3
July 17
Example of Discount Rates in Merger Analysis
• In order to determine the value of Pennzoil-Quaker State's common stock, Morgan
Stanley performed a 5-year discounted cash flow analysis that included the use of
two different scenarios, or case assumptions. The Management Case reflects
Pennzoil-Quaker State management's estimates of the company's future financial
performance, excluding any future acquisitions.
• The Market Case reflects publicly available estimates of Pennzoil-Quaker State's
future performance of certain securities research analysts. These cases were used
to project future cash flows which were discounted back to a present value using
a range of discount rates of 8% to 10%.
• The range was determined based upon a calculation of Pennzoil-Quaker State's
weighted average cost of capital (WACC), which was calculated based upon the
WACC for comparable companies in three industry segments: Mid-Cap Consumer
Products, Auto Aftermarket and Auto OEM.
• Morgan Stanley also applied a terminal EBITDA multiple of 7.0x to 9.0x to the
projected 2006 EBITDA, for purposes of calculating a terminal value of PennzoilQuaker State at the end of 2006. This terminal value together with the projected
annual un-levered free cash flows from 2002 through 2006 was then discounted to
the present, assuming cash flows occurred mid-year, using discount rates of 8% to
10%.
Cost of Capital
4
July 17
Cost of Capital Example
• The estimated after-tax free cash flows for BellSouth’s Wireline segment
for calendar years 2006 through 2008 and the terminal values calculated
for BellSouth’s Wireline segment were then discounted to the present
value using discount rates of 7.0% to 8.0%.
• The estimated after-tax free cash flows for Cingular for calendar years
2006 through 2008 and the terminal values calculated for Cingular were
then discounted to the present value using discount rates of 8.5% to 9.5%
and multiplied by 40%. The estimated after-tax free cash flows for
BellSouth’s Directories segment for calendar years 2006 through 2008
and the terminal values calculated for BellSouth’s Directories segment
were then discounted to the present value using discount rates of 7.0% to
8.0%.
• Lehman Brothers and Evercore discounted the unlevered free cash flow
streams and the estimated terminal value to a present value at a range of
discount rates from 7.5% to 8.5%. The discount rates utilized in this
analysis were chosen by Lehman Brothers and Evercore based on their
expertise and experience with the telecommunications industry and also
on an analysis of the weighted average cost of capital of BellSouth and
other comparable companies.
Cost of Capital
5
July 17
Surveys of Managers
•
Late Fifties
Payback period
•
Sixties
Present Value
•
Seventies (Fremgen)
Internal rate of return
Net Present Value
•
•
•
Eighties
•
27 Highly Regarded Corporations and 10
Leading Investment Banks
DCF with WACC is dominant valuation
technique
WACC uses market rather than book
weights
Debt cost from marginal cost and
statutory tax rates
CAPM is predominant model for cost
of equity
Mean Cost of Capital 14.2%
Most use treasury as long-term
treasury rate
Gordon model and CAPM
Equity premium
Nineties
 Majority less than 6%
CAPM Most popular
 11% use lower than 4.5%
Risk premium of 6%
 10% use 5%
Current
Equity premium of 5% or less
Cost of Capital
 50% use 7.0% to 7.4%
Current Equity Premium 5% or Less
6
July 17
Use Correct Discount Rate for Correct Cash Flow
OPFCF
FCFE
WACC
Cost of equity
Enterprise value
Equity value
The key is to match the right cash flow with the right discount rate
And to the thing being valued
Cost of Capital
7
July 17
Common Problems in Applying Cost of Capital to Cash
Flow
•
Given difficulties in estimating cost of capital, present a range in cost of
capital in valuations.
•
Discount rate should reflect project characteristics
 Contracts
 Risks
•
Generally companies over-estimate the cost of capital (McKinsey)
 2001 Survey – managers use 12.2%
 Actual market premium is much less
•
Optimistic assumptions to compensate for high required return
•
Over-payment for acquisitions
•
Mis-timing of investments in commodity price businesses
Cost of Capital
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July 17
Weighted Average Cost of Capital
Valuation
9
July 17
WACC Points
• Use target capital structure
• Use nominal cost of capital in currency consistent with the free cash flow
• Should be market weights and incremental cost of capital
• Tricky Items
Convertible Bonds
 Lower rate is due to equity value
 Bond value
 Equity Option
Term of Debt
Credit Spread on Debt
Callable and No callable debt (effect on cash flow)
Cost of Capital
10
July 17
WACC Computation
• In the WACC formula, we know
Debt percent
Equity percent
Cost of new debt
Income tax rate
• The hard part is the cost of equity
• If the capital structure changes, the cost of equity should change
• In theory, if the capital structure changes, the cost of equity should
change to maintain the same overall WACC
• Therefore, if the capital structure changes in the model, careful with
assumption about how the WACC changes.
Cost of Capital
11
July 17
Weighted Average Cost of Capital
• Step 1:
 Equity Cost from Asset Cost
Ke = Be x Rm + Rf
Ke = (Ba x (V/E)) x Rm + Rf
• Step 2
 Debt Cost from Rf plus Credit Spread
Kd = Rf + CS
After tax Kd
• Step 3
 WACC = (D/V) * Kd x (1-t) + (E/V) * Ke
Cost of Capital
12
July 17
Alternative Approaches to Computing the Cost of Capital
• Dividend growth model (analogous to P/E ratio)
Works if there are stable dividends
A variant is P/E = (1-g/r)/(k-g)
• Debt capacity model (project finance)
• Risk premium method (analogous to the CAPM)
K = Rf + Risk Premium
• Implied cost of capital in EBITDA ratios
• Arbitrage Pricing Model (extension of CAPM and related to risk neutral
valuation)
• Implied cost of capital from reverse engineering financial models
(described in the M&A discussion)
Cost of Capital
13
July 17
Classic MM
Cost of Capital
14
July 17
MM without Tax and WACC – Increasing Interest Cost
40%
WACC and Cost of Equity with MM
• .
35%
30%
Int Rate
Equity Cost
25%
WACC
20%
15%
10%
5%
0%
0%
9.0%
18.0%
27.0%
36.0%
45.0%
54.0%
63.0%
72.0%
81.0%
90.0%
Debt to Capital
Cost of Capital
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July 17
MM with increasing Debt Cost – Equity Cost Decreases
because of Option in Equity Cost
Higher Interest Rate with Higher
Probability of Default
Cost of Capital
16
July 17
CAPM: k = rf + β x rm
Valuation
17
July 17
CAPM Inputs
• Rf,i is the risk free rate for the current period (i) and it is the only variable
directly affected by movements in the overall cost of capital in the
economy.
• βi is the covariance between returns on the security and the market
returns divided by the overall variance of market returns. This parameter
is the only input affected by the risk of the security in question and the βi
parameter is not expected to vary over time unless there is a change in
business and/or the financial risk of the company.
• EMRP is the expected return on a fully diversified portfolio of equity
securities over and above the rate of return on risk free securities. This
variable is a function only of aggregate preferences by people in the
economy for risky investments versus risk free investments. It is not
affected by current interest rates, the risk of the security, or movements in
the overall stock market.
Cost of Capital
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July 17
CAPM and Real and Risk Free Rate
Geared Equity
Be
Asset/Ungeared
equity – Ba x Market
Market Premium
Average
Debt
Inflation
Plus Real
Rate - Rf
Real
Cost of Capital
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July 17
CAPM Theory
• CAPM has many problems, but the basic theory upon which the
CAPM is built is a foundation of finance.
• The foundation of the CAPM is:
Risk is measured by variation and standard deviation in
returns
Standard deviation is reduced from diversification
Variance (a + b) where the portfolio if a and b are have a
weight of .5 is:
.25 variance (a) + .25 variance (b) + .5 covariance(a,b)
If the covariance is zero, the variance of the portfolio is much
lower than the variance without diversification
Cost of Capital
20
July 17
CAPM Problems
• Problems with the CAPM theory are recounted by Ravi Jagannathan and
Iwan Meier in their 2001 article “Do We Need CAPM for Capital
Budgeting:”
• The CAPM as a model has been seriously challenged in the academic
literature…. [S]ince the critique by Fama and French (1992) there is
consensus in the academic literature that the CAPM as taught in MBA
classes is not a good model – it provides a very imprecise estimate of the
cost of capital…. [T]here is overwhelming evidence in the academic
literature that for over two decades business schools have been teaching
the wrong model – or at least recommending the use of the wrong inputs
– for calculating the cost of capital.[1]
•
[1] Jagannathan, R. and Meier, I. 2001, “Do We Need CAPM For Capital
Budgeting?”, Kellogg School of Management, Finance Department, pp 13.
Cost of Capital
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July 17
CAPM Problems
• “Not only has the CAPM proved wrong, but we do not even know that the
market premium is.”
Ravi Jagannathan and Iwan Meyer, “Do We Need CAPM for Capital
Budgeting” Kellog School of Management
• Fama and French:
Statistical analysis showing no relation between returns and beta
Statistical modeling: Time series to compute the Beta and then cross
section to compute the significance
Statistical problems: errors in variables and all variables should be
based on expectations rather than actual
CAPM may be un-testable
Cost of Capital
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July 17
Cost of Capital and the CAPM
• Use of CAPM to compute equity cost of capital and cost of capital
to apply to free cash flow
Risk free rate to apply in the CAPM
Alternative methods to evaluate the risk premium for the
overall market
Data sources and computation of Beta
Adjustments to Beta to compute Beta for application to free
cash flow
Adjustments to CAPM for interest tax shield
Theoretical problems with the CAPM
Alternative approaches to the CAPM
Cost of Capital
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July 17
Discussion of CAPM Components
• The CAPM requires estimation of three components (Rf, Rm and Beta).
Each of these has some controversy.
Rf
 Should the long-term treasury rate be used
 Country premiums
Rm
 Method of estimation expected returns
 Actual use in practice
Beta
 Estimation
 Accuracy
Cost of Capital
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July 17
Risk Free Rate in CAPM
Valuation
25
July 17
Risk Free Rate Discussion
• There are debates concerning implementation of the risk free rate in the
CAPM.
Some suggest using long-term Treasury bond yields, some
advocate short-term Treasury Bills and still others argue for use of
the yield on inflation indexed bonds plus the expected rate of
inflation.
The primary argument against using long-term Treasury Bond yields
as a proxy for the risk free rate is that holders of long-term bonds
accept inflation risk and those yields are therefore not risk-free.
Further, during times at which an inverted yield curve exists, the
long-term treasury yield will produce a lower risk free parameter than
the Treasury Bill rate.
Those opposed to use of a short-term rate contend that the duration
of cash flows from short-term investments does not match the
duration of cash flows received from an investment in a stock.
Cost of Capital
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July 17
CAPM - Risk Free Rate
•
The primary issue in estimating the risk free rate is what risk free
security should be used:
 Common equity pays cash flow to investors over a long
period
 In theory the duration of dividends could be computed
 Use t-bill yield to maturity of 10 years
 Example
 Treasury Bond Yield -- 2016 -- 5.53%
 Treasury Bond Yield -- 2011 -- 4.98%
Cost of Capital
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July 17
Sources of Risk Free Rate
CH
HK
ID
MA
TH
KO
IN
PH
SI
TW
10 Year RMB Govt bond
HKMA Hong Kong Exchange Fund Notes 10 Years
Indonesia SBI 1 Month Auction Average Yield
Malaysia Government Bonds 10 Year Government
Thailand Government Bonds 10 Year Note
South Korea 10 Year Government Generic
India Government Bonds 10 Year
Philippines Generic 10-Year Fix Treasury Note T-Bond
Monetary Authority of Singapore - Government Benchmark : 10 Year Yield
Taiwan Government Bonds 10 Year Note Generic Bid Yield
Cost of Capital
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July 17
Country Adjustments to Risk Free Rate
Cost of Capital
29
July 17
Equity Market Risk Premium
Valuation
30
July 17
General Points on EMRP
•
The EMRP is expressed in real terms and is not a nominal number. This means the EMRP does
not increase or decrease when interest rates change or when the expected rate of inflation
changes. It would be wrong, for example, to update this number in the midst of a case because of
changes in the interest rate.
•
The EMRP comes from the general risk preferences of agents in an economy for equities relative
to risk free securities. If people did not have risk aversion for equities relative to risk free bonds,
the EMRP would be zero. This means changes in the EMRP are driven by changes in general
preferences for equities relative to risk free securities. Because the EMRP comes from risk
preferences, it should be stable over long time periods as risk preferences do not swing from
month to month or year to year.
•
Third, the EMRP is an expected number rather than a number that can be directly measured from
actual realized returns. The fact that the EMRP is an expected number means that it does not
change when the stock market goes up or down because realized earnings change or because
general economic activity is robust or depressed.
•
Fourth, the EMRP is an economy wide number not unique to ComEd. Unlike Beta which measures
the risk associated with a specific company, the EMRP is the same whether it is used in valuing a
paper company, gauging the rate of return for an oil project or assessing the share price of an
airline company.
•
Fifth, the EMRP has been the subject of a very large body of research. This research has been
performed by people who are not funded by parties who have a vested interest in producing a
particularly high or a particularly low risk premium number. Since the EMRP is not unique to
ComEd, since it is an expected number difficult to calculate, and since it is not expected to change
over short time periods, the EMRP research is directly relevant to this and other regulatory
proceedings.
Cost of Capital
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July 17
Current Opinions with Respect to EMRP
• Enrique Arzac recaps a wide body of research by stating “We show that
both the historic record, financial theory, and prospective estimates based
on stock prices and growth expectations, all indicate that the future equity
premium in developed capital markets is likely between 3 and 5%...”
• Seth Artimage summarizes many different studies by noting: “Consensus
is lacking at present on the best way of estimating the equity premium,
and reasonable estimates lie in the rage of 1% or 5%...”
• Koller et al. describe the general biases in EMRP: “Historical estimates
found in most textbooks (and locked in the mind of many), which often
report numbers near 8% are too high for valuation purposes because they
compare the market risk premium versus short-term bonds, use only 75
years of data, and are biased by the historical strength of the U.S. market.
Cost of Capital
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July 17
Historic EMRP
• Enrique Arzac refers to research by Blanchard who “developed a
dynamic model of the expectations of real returns on stocks and
bonds. He found that the risk premium during the 1930’s and
1940’s was unusually high ranging from 3 to 5% in the early
1930’s to more than 10% in the 1940’s. Afterwards, it started a
gradual decline with some relatively minor fluctuations and
reached between 2 and 3% in the early 1990’s.”
• Claus and Thomas emphasize the notion that historic returns
exceed the expected amounts: “Despite substantial variation in
the underlying fundamentals across markets and over time,
observing that every one of our 69 country-year estimates lies
well below eight percent suggests that the Ibbotson estimate is
too high for our sample period.”
Cost of Capital
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July 17
Use of DCF to Estimate EMRP
• Seth Armitage describes the DCF studies as follows: “The arithmetic mean real
premium between 1900 and 2000 was … 7.0% for the United States, measured
against the yield on long-term bonds. But a simple forward looking estimate based
on applying the dividend discount model to the market suggests a risk premium of
3% to 4%. This is why many people do not expect the premium in the future to be as
large as it has been in the past, especially in the second half of the twentieth century.
They place more faith in reasonable expectations about the future than in outcomes
observed in recent decades. Furthermore, several researchers have argued recently
that investors did not expect premiums as large as they got in the twentieth century.
Armitage concludes that Most of the studies indicate a range for historic ex ante
premiums … of between 1.5% and 4.5% -- considerably below the actual arithmetic
mean premium since 1920…”
• Enrique Arzac uses a DCF model to estimate the equity market premium of between
3.08% and 3.32%.
• In their widely cited 2002 article, Fama and French state that “the equity premium
estimates from the dividend and earnings growth models, 2.55 percent and 4.32
percent, are far below the estimate from the average return, 7.43 percent….The
expected return estimates from the dividend and earnings growth models are more
precise than the average return. The standard error of the dividend growth estimate
of the expected return for 1951 to 2000 is 0.74 percent, versus 2.43 percent for the
average stock return….The earnings growth model is not, however, clearly superior
to the dividend growth model.”
Cost of Capital
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July 17
Surveys of Investors
• “In the US, Merrill Lynch publishes ‘bottom up’ expected returns on the Standard and
Poor’s 500, derived by averaging expected return estimates for stocks in the
Standard & Poor’s 500….In recent years, the Merrill Lynch expected return estimates
have indicated an EMRP in the region of 4% to 5%.
• “The Value Line projected market risk premia are somewhat more volatile than those
from the Merrill Lynch DDM model. In recent years they have generally ranged from
2% to 6%....”
• Greenwich Associates had published the results of an annual survey of pension plan
officers regarding expected returns on the Standard and Poor’s 500 for a five-year
holding period. The Greenwich Associates survey has generally indicated and
EMRP in a 2%-3% range.”
• Claus and Thomas also cite investor expectations. They summarize the information
as follows: “Surveys of institutional investors also suggest an equity premium
substantially below eight percent (e.g., Burr (1998)), and there are indications that
this belief has been held for many years (e.g., Benore (1983)) . Also, the weighted
average cost of capital used in discounted cash flow valuations provided in analysts’
research reports usually implies an equity premium below five percent.”
Cost of Capital
35
July 17
Risk Premium
• There is a wide range in premiums used in theory and practice. The following
shows results from one study.
Cost of Capital
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July 17
Equity Market Risk Premium
• A well known study by Fama and French, published in 2002, finds that
“estimates [of the equity market risk premium] for 1951 to 2000, 2.55
percent and 4.32 percent, are much lower than the equity premium
produced by the average stock return, 7.43 percent.”
• In another oft cited paper published in 2001 by Claus and Thomas titled
“Equity Premia as Low as Three Percent? Evidence from Analysts’
Earnings Forecasts for Domestic and International Stock Markets,” the
authors conclude that “for each year between 1985 and 1998, we find that
the equity premium is around three percent (or less) in the United States
and five other markets.”
• “The Cost of Capital: Intermediate Theory” which was published in 2005
summarizes the current research as follows: “Almost all researchers on
this question agree that the premium in the twentieth century in the United
States … has turned out to be larger than investors expected it to be.”
Cost of Capital
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July 17
Estimated Risk Premiums from Actual Returns
• The market premium is unobservable
• Studies have attempted to measure the expected market premium using the PE
method
• Actual Market Risk Premiums
1926-1998
 Arithmetic 7.8%
 Geometric 5.9%
1974 – 1998
 Arithmetic 5.5%
 Geometric 4.9%
1964 – 1998
 Arithmetic 4.7%
 Geometric 3.6%
Cost of Capital
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July 17
CAPM - Market Premium
•
McKinsey -- 4.50%
•
Investment Bank Low -- 3.5%
•
Investment Bank High -- 5.5%
•
Brealy and Meyers – 6% to 8.5%
•
Gordon’s model – 2.9%
•
Exelon Rate Case -- 9.98%
•
Issue: Sample Bias from Bankruptcy
Cost of Capital
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July 17
Equity Risk Premium in Hong Kong
Hong Kong equity premium calculation
The median estimate of ERP is in the 4-5% range for mature markets
Cost of Capital
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July 17
Problems with historic data in estimating market
premium
•
The problem with market premium estimates is that the market
premium should be an expected return rather than the historical
actual returns that may or may not have been expected:
 Real time now matters more than historic periods.
 Samples drawn from the past have little relevance to what
investors expect now.
 What was 75% probable yesterday has an unknown
probability tomorrow.
Cost of Capital
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July 17
Beta
Valuation
42
July 17
Sources of Beta and Differences in Measurement
• The table below shows that beta measurement can be
dramatically different for the same companies.
Beta from
Googlefinance
Website
AGL Resources Inc. (ATG)
Energy East Corp. (EAS)
IdaCorp, Inc. (IDA)
Nisource Inc. (NI)
Peoples Energy Corp. (PGL)
Pepco Holdings Inc. (POM)
SCANA Corp. (SCG)
Southern Co. (SO)
WGL Holdings Inc. (WGL)
Wisconsin Energy Corp. (WEC)
Xcel Energy Inc. (XEL)
Beta from
Yahoo
Website
Value
Line Beta
0.49
0.50
0.80
0.61
0.37
0.45
0.53
(0.12)
0.25
0.14
1.13
0.13
0.34
0.49
0.18
0.66
0.57
0.36
0.23
0.71
0.46
0.52
0.95
0.90
1.00
0.90
0.90
0.90
0.80
0.65
0.80
0.80
0.90
Median
0.49
0.46
0.90
Average
0.47
0.42
0.86
Cost of Capital
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July 17
Betas
Sector risk adjustment factors or asset betas
Market
Cyclical Services
Distributors
General retailers
Rests, pub, brews
Support services
Transport
Defensives
Electricity
Gas dist
Water
Food producers
Beverages
Tobacco
Food retail
Aerospace and defence
Financials
Banks
Insurance
Life assurance
Investment companies
Real estate
Speciality finance
Cost of Capital
1.0
1.0
0.7
1.0
1.1
0.7
0.5
0.5
0.5
0.7
0.7
0.5
0.7
1.0
1.3
1.3
1.0
0.7
1.3
1.3
Mature Cyclicals
Chemicals
Construction and building
Paper
Steel
Engineering
Diversified industrials
Autos
Packaging
New growth
Fixed telecom
Mobile telecom
Computer hardware
Semiconductors
Telecom equipment
Computer services
Internet
Software
Media
Resources
Mining
Oil
Traditional growth
Pharmaceuticals
Personal care/h'hold products
Leisure
Health
Household gds & textiles
Electrical equip
1.0
1.0
0.7
1.3
1.0
0.7
1.3
1.0
1.1
1.1
1.3
1.4
1.3
1.0
1.6
1.0
1.0
0.7
0.5
0.7
1.0
1.0
1.0
1.0
1.3
44
July 17
Beta Measurement
•
Beta is measured from historic returns
•
Beta is cov(Rm,Rt)/variance(Rm)
Cost of Capital
45
July 17
Beta Adjustments
• Value Line computes its beta from a regression equation that
measures an unadjusted beta. Then, Value Line adds an
adjustment to move the beta toward 1.0 using the following
equation[1]:
• Adjusted beta = 2/3 x Unadjusted beta + 1/3 x 1.0
• or
• Unadjusted beta = Adjusted beta x 3/2 – 1/2
•
[1] Patterson, C.S., 1995, The Cost of Capital: Theory and
Estimation, Westport CT: Quorum Books, p. 130.
Cost of Capital
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July 17
Beta Adjustments for Mean Reversion
• The adjustment for betas is generally accepted in cost of capital
literature for companies with betas above 1.0 because of a
tendency of betas to revert to the mean. Statistical studies have
demonstrated that “there appeared to be greater measurement
error associated with the betas of extreme values.”[1] The mean
reversion adjustment is accepted for companies with observed
high betas. The risk of these high beta companies often moves
towards 1.0 over time due to statistical measurement problems
and due to the tendency of high business risk companies to
eventually moderate. However, the mean reversion is far less
accepted for utility companies with betas of below 1.0.
[1] Ogier, T, Rugman, J., Spicer, L., 2004, The Real Cost of
Capital A Business Field Guide to Better Financial Decisions,
Great Britain: FT Prentice Hall, page 54.
Cost of Capital
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July 17
Example of Beta Adjustments
• The case of NICOR demonstrates that using a mean reversion adjustment wherein
betas are pushed towards 1.0 to correct statistical irregularity is inappropriate for
utility companies. Instead, the statistical anomalies should push the beta back to the
industry average beta for utility companies. The 1.10 beta obviously does not
measure prospective risk and making a correction by moving the beta towards 1.0
would not help. The NICOR example effectively demonstrates that mean reversion
adjustments of utility betas are not appropriate. These adjustments do not improve
the measurement of beta but instead simply result in increased cost of equity
numbers.
NICOR and S&P Indicies: Beta from 02/00 to 12/05 -- 0.50
Beta from 07/02 to 12/05 -- 1.18 Beta from 02/00 to 07/03 -- 0.53
Beta from 08/03 to 12/05 -- 0.32
1.60
Index
1.40
NICOR
1.20
S&P 500
1.00
0.80
Cost of Capital
9/3/2005
5/3/2005
1/3/2005
9/3/2004
5/3/2004
1/3/2004
9/3/2003
5/3/2003
1/3/2003
9/3/2002
5/3/2002
1/3/2002
9/3/2001
5/3/2001
1/3/2001
9/3/2000
5/3/2000
• .
1/3/2000
0.60
48
July 17
Asset Beta versus Equity Beta
• Without Taxes
Ba = (D/V)*Bd + (E/V)*Be
Be measured with stock prices
D,V,E are debt, enterprise value and equity value measured at
market value.
Often assume Bd = 0
Or, Be = (Ba – (D/V)*Bd) * V/E
• With taxes
Ba = (D x (1-t))/(E+D*(1-t)) * Bd + (E/(D*(1-t) + E *(1-t))*Be
Assumes that all cash flows from debt are tax deductible
Cost of Capital
49
July 17
Example of Asset and Equity Beta
• Cathay Pacific has an observed beta of 1.3 and a debt to equity
ratio of 50%. Singapore Airlines has a debt equity ratio of 25%.
Calculate the equity beta of Singapore Airlines. The tax rates in
Hong Kong and Singapore are 15 and 20% respectively.
Cost of Capital
Equity beta
Debt/ Equity
Asset beta
CPA
1.3
50%
0.91
SIA
1.09
25%
0.91
50
July 17
WACC Illustration Using Unlevered Beta
• The WACC
Slide shows
the relation
between the
WACC and
the Asset
Beta
Cost of Capital
51
July 17
Asset Beta
Cost of Capital
52
July 17
Adjustments to Cost of Equity
• Additional Premiums for
Size
Liquidity
Three Factor Model: Size,
Beta, Market to Book
• Arbitrage Pricing Model
• Liquidity Dimensions
Size
Time
Quantity
Cost of Capital
53
July 17
Gordon’s Model and Implicit Discount Rates
k = D1/P + g
Valuation
54
July 17
DCF Issues
• How should one select an appropriate sample of comparable
companies with similar risk to ComEd to derive the implied cost of
equity capital;
• What method should be used to compute the constant expected
growth rate of marginal investors for each company in the
comparable sample;
• Whether a valuation model for using earnings is a better way to
derive the implicit cost of equity capital than dividend growth
model; and,
• Should adjustments for quarterly compounding be made in
deriving implicit discount rates.
Cost of Capital
55
July 17
Growth Rate Issues
• In their text titled “Valuation: Measuring and Managing the Value of Companies”
published in 2005, Tim Koller, Marc Goedhart and David Wessels state that “analyst
forecasts focus on the short term and are severely upward biased.”
• Enrique Arzac comments on the difficulty of predicting growth rates and the potential
for the DCF model to over-estimate the cost of equity as follows: “The problem with
[the DCF] approach is that long-term dividend growth rate of an individual company
cannot be estimated with any degree of precision. Hence, the dividend growth
model is not likely to produce reliable estimates of the cost of equity capital of
individual companies….A number of empirical studies have documented optimistic
bias in analysts’ opinions….Thus, it seems reasonable to conclude that [the DCF
equation] yields an upper bound to the equity premium.”
• Claus and Thomas conclude that earnings and dividend growth rates used for the
DCF model “exhibit substantial optimism bias and need to be adjusted downward.”
• Louis Chan and his coauthors conclude that “over the period 1982 to 1998, the
median of the distribution of IBES growth forecasts is about 14.5 percent, a far cry
from the median realized five year growth rate of about 9 percent for income before
extraordinary items.”
• Fama and French state that “In short, we find no evidence to support a forecast of
strong future dividend or earnings growth at the end of our sample period.”
Cost of Capital
56
July 17
Use of ROE x (1-Payout) to Estimate Growth
• If the dividend payout ratio is 100% then even when a utility is currently
earning more than its cost of capital (such as Exelon and NICOR) the
earnings and book value do not grow (unless equity is issued at a market
to book value above 1.0). Since the equity base does not increase
because no earnings are retained, a constant future return on equity
applied to a constant amount of equity means that the income also
remains constant. With no earnings growth, the EPS growth is zero.
• At the other extreme, if the dividend payout ratio is zero, then earnings
increase book value of equity on a one for one basis. In this case without
dividend payments (again assuming a constant return on equity) the book
value of equity increases by the return on equity multiplied by the initial
amount of equity on the balance sheet. Assuming a constant return is
multiplied by the book value that increases at a growth rate defined by the
return on equity, the earnings also growth at the return on equity. This is
the growth rate implied by the formula above.
• For intermediate cases where the dividend payout is between zero and
one, the growth rate in earnings is the return on equity multiplied by one
minus the dividend payout ratio under the assumption of a constant return
on equity.
Cost of Capital
57
July 17
Importance of Cost of Capital in Decision Making
•
Investment decisions and cost of capital
•
Cost of capital and valuation
•
Cost of capital applied to free cash flow
•
Residual value
•
Relative valuation
•
DCF Compared to payback rule and accounting earnings criteria
Cost of Capital
58
July 17
Example of Discounted Dividends
•
Morgan Stanley calculated terminal values by applying a range
of multiples to the estimated EPS in fiscal year 2009 and the
dividend streams and terminal values were then discounted to the
present using a range of discount rates representing an estimated
range of the cost of equity for each of PSEG and Exelon. Based
on this analysis, Morgan Stanley calculated per share values for
PSEG ranging from $42.75 to $47.10. Morgan Stanley noted that
the implied consideration to be paid for each share of PSEG
common stock was $53.14 as of December 15, 2004, which was
greater than the range implied by this analysis. In addition, based
on this analysis, Morgan Stanley calculated per share values for
Exelon ranging from $38.15 to $42.01 and noted that the closing
price of Exelon common stock on December 15, 2004 was
$43.38, which was greater than the range implied by this analysis.
Cost of Capital
59
July 17
Company Profiles
Cost of Capital
60
July 17
Impact of the Cost of Capital on Value
• Compute free cash flow from calculations sheet in the corporate
model
• Apply different discount rates to the free cash flow
• Assume the final year cash flow occurs into perpetuity
• Compute enterprise value, equity value and equity value per
share
Cost of Capital
61
July 17
Deriving Implicit Discount Rate with Corporate Models
•
Using the same discount rate is a very lose form of risk neutral
valuation
•
Using the this process illustrates how your stock is the currency
of the transaction
•
Step by Step Approach
 Value your company using a set of base case assumptions
 Back into the discount rate that makes the value in the
model equal to the current market value
 Use same discount rate and same set of assumptions to
value the target
Cost of Capital
62
July 17
Adjusted Net Present Value
Valuation
63
July 17
Objectives of APV
• NPV assumes
Capital structure remains the same
Leveraged Buyout
Constant Tax Rates
NOL
• APV corrects for some assumptions
Changing WACC
Distortions in WACC for capital structure
Changing tax rates
Cost of Capital
64
July 17
Adjusted Net Present Value
• Value the Company as if it were entirely financed by equity using
the statutory income rates
• Add the tax shields due to interest expense separately and use
the debt discount rate to value this shield
• Compute the present value of net operating losses using the
equity discount rate
Cost of Capital
65
July 17
Adjusted Net Present Value
• Steps
Present Value of Free Cash Flow at discount rate using Ba
without tax adjustments
Present value of tax shield from interest at the debt rate
Present Value of net operating loss
• Interest Tax Shield
PV of interest x tax rate
Plus: terminal value of debt
Cost of Capital
66
July 17
Comparison between AVP and DCF with WACC
• WACC
Tax shield in the discount rate
Different accounting for NOL (WACC must use changing
effective tax rates)
Changing value of debt
Timing of debt repayments
• Example
Same operating cash flows
Alternative debt payoff assumptions
Cost of Capital
67
July 17
APV and WACC
• APV (No taxes)
K = Ba x (Rm) + Rf
Since Ba = (E/V) x Be + 0
WACC = (E/V) x Be x Rm + Rf
• Normal WACC assuming Rf = Kd
WACC = (E/V) x (Be x Rm + Rf) + (D/V) x Kd
 WACC = (E/V) x (Be x Rm + Rf) + (D/V) x Rf
WACC = (E/V) x (Be x Rm ) + Rf
• Since Kd = Rf + Credit Spread
WACC = (E/V) x (Be x Rm) + (E/V) * Rf + (D/V) * (Rf + Credit Spred)
Cost of Capital
68
July 17
APV Case
Cost of Capital
69
July 17
Growth Rate and Discount Rate
• A stable growth rate is a growth rate that can be sustained
forever. Since no firm, in the long term, can grow faster than
the economy which it operates it - a stable growth rate
cannot be greater than the growth rate of the economy.
• It is important that the growth rate be defined in the same
currency as the cash flows and that be in the same term (real
or nominal) as the cash flows.
• In theory, this stable growth rate cannot be greater than the
discount rate because the risk-free rate that is embedded in
the discount rate will also build on these same factors - real
growth in the economy and the expected inflation rate.
Cost of Capital
70
July 17
Common errors in dividend discount model valuation
• The most common errors in dividend discount model
valuation are in the assumptions about the payout ratio as
the growth rate changes.
• Many high growth firms either pay low dividends or no
dividends. As the growth rate changes, the dividend payout
ratio should rise. If it does not, these firms will not be worth
much using these models.
Cost of Capital
71
July 17
Asset and Equity Beta with Taxes
• The asset beta can be computed using the formula:
• B(asset) = B(equity) x (Equity/EV) + B(debt) x (Debt/EV)
• The weights must be at market value

 geared  ungeared  1  


Vd(1- Tax rate)  


Ve
thus
ungeared 
Cost of Capital
 geared

 Vd(1- Tax rate)  
1






Ve

72
July 17
What Term of Treasury Bond Should be Used
• One of the slides says we should use 10-year treasury as
risk-free rate. It would be helpful to give more depth, such as,
do you use a 10-year US government bond or local currency
bond and why not 30-years bond rather than 10-year bond.
• In theory, the duration of the risk free rate should be the same as
the duration of the equity cash flows to eliminate interest rate risk.
To see this, consider the venture capital example when the cash
flows all occurred in 7 years. Pretend that somehow the cash
flow could be hedged in futures markets in year 7 and there is no
risk. In this example, a risk free zero coupon rate bond that
matures in 7 years would clearly match the cash flow of the
equity. A bond with a seven year duration would accomplish this.
Cost of Capital
73
July 17
What Term of Treasury Bond Should be Used
• One of the slides says we should use 10-year treasury as
risk-free rate. It would be helpful to give more depth, such as,
do you use a 10-year US government bond or local currency
bond and why not 30-years bond rather than 10-year bond.
• In practice of course, the duration of equity cash flows is not
known. The duration is computed using the formula:
• Duration = ∑ (t x PV of Cash Flow)/Present Value
• The duration can be computed for a 10 year bond and for equity
as illustrated in the following slides.
Cost of Capital
74
July 17
Duration of 10 Year Bond
Duration of 10 year Bond at 5%
Coupon
Term
Par
YTM
Credit Spread
Date
5%
10
1000
5%
0%
Cash
Flow
Period
1/1/2005
7/1/2005
1/1/2006
7/1/2006
1/1/2007
7/1/2007
1/1/2008
7/1/2008
1/1/2009
7/1/2009
1/1/2010
7/1/2010
1/1/2011
7/1/2011
1/1/2012
7/1/2012
1/1/2013
7/1/2013
1/1/2014
7/1/2014
Cost of Capital
Value
Sum PV x t
Duration
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
Discout
Rate
25
25
25
25
25
25
25
25
25
25
25
25
25
25
25
25
25
25
25
1025
Duration of 10 year Bond at 5%
1000
15,979
7.99
PV x t
0.98
0.95
0.93
0.91
0.88
0.86
0.84
0.82
0.80
0.78
0.76
0.74
0.73
0.71
0.69
0.67
0.66
0.64
0.63
0.61
24.39
47.59
69.64
90.60
110.48
129.34
147.22
164.15
180.16
195.30
209.59
223.07
235.76
247.70
258.92
269.45
279.31
288.52
297.13
12,510.55
Coupon
Term
Par
YTM
Credit Spread
Date
0%
10
1000
5%
0%
Cash
Flow
Period
1/1/2005
7/1/2005
1/1/2006
7/1/2006
1/1/2007
7/1/2007
1/1/2008
7/1/2008
1/1/2009
7/1/2009
1/1/2010
7/1/2010
1/1/2011
7/1/2011
1/1/2012
7/1/2012
1/1/2013
7/1/2013
1/1/2014
7/1/2014
Value
Sum PV x t
Duration
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
Discout
Rate
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1000
610.27094
12,205
10.00
PV x t
0.98
0.95
0.93
0.91
0.88
0.86
0.84
0.82
0.80
0.78
0.76
0.74
0.73
0.71
0.69
0.67
0.66
0.64
0.63
0.61
12,205.42
75
July 17
What Term of Treasury Bond Should be Used
• One of the slides says we should use 10-year treasury as
risk-free rate. It would be helpful to give more depth, such as,
do you use a 10-year US government bond or local currency
bond and why not 30-years bond rather than 10-year bond.
• Practical – “The 10-year rate is less susceptible to two problems
involved in using a longer rate, such as a 30 year Treasury Bond
rate. Its price is less sensitive to unexpected changes in inflation
and so has a smaller beta that the thirty year rate. Also, the
liquidity built into 10 year rates may be lower than that of 30 year
bonds.
Cost of Capital
76
July 17
WACC and Cost of Capital Estimation in Practice
• Rather than just providing the formula of WACC, it would be
useful to give instructions on where to find the market
premium data, betas and what is the best method vs the
most practical method.
Should we include country risk, exchange rate risks etc and
how to get them.
Copeland says: “the most common errors in setting the
WACC are:
Making ad hoc adjustments for risk, and
 Using the WACC to discount foreign currency cash flow
Cost of Capital
77
July 17
WACC and Cost of Capital Estimation in Practice
• Rather than just providing the formula of WACC, it would be useful
to give instructions on where to find the market premium data, betas
and what is the best method vs the most practical method.
Example: Assume that you are valuing Dragon Air and there is no
Beta available for this company.
Assume you use US Airlines with and that the average Beta is 1.0.
The Beta is Cov(Rm,Ri)/Var(Rm)
In this case Rm is US Market
Cost of Capital in US is Rf+Rm
Cost of capital in HK should by Rf(HK) + Rm (US),
 not Rf(HK) + Rm (HK), because the Beta was computed from the US Rm
Use US Rm, otherwise, the Beta would not be consistent with the
Rm
Cost of Capital
78
July 17
Practical Estimation of WACC and Cost of Capital
• Try some very simple steps:
• Divide the market into three beta groups
Above average 1.2
Below average
Average
.8
1.0
• Find out what investors expect in local markets in terms of the premium
above the risk free rate.
E.g. 5% in London and 7% in China
• Add the local risk free rate to the market premium adjusted for the three
categories of beta.
• Make adjustments for country risk with political risk insurance rates
Cost of Capital
79
July 17
Example of Beta and Risk Premium Computation
• Assume that Rm in Hong Kong is 7% and the Rm is the US is
5%.
• If Beta is used for a comparable 1.0 and is measured in the US,
the expected return is 5% plus the Rf. This reflects the return
investors require to be compensated for risk. If it is applied to a
company with similar risks in Hong Kong, the
• If this Beta is applied to the Hong Kong Rm, the cost of capital
implied is 7% plus the Rf.
Cost of Capital
80
July 17
WACC and Cost of Capital Estimation in Practice
• Rather than just providing the formula of WACC, it would be
useful to give instructions on where to find the market
premium data, betas and what is the best method vs the
most practical method.
In computing WACC in a merger, should you use the
incremental cost of debt for the target or the acquirer
Often the debt is retired, in which case it is clear that the
cost of debt of the acquirer should be used
Future debt will be financed by the acquirer not the target, so
the acquirer cost of debt should be used
The value of debt in the valuation should also be at the
acquirer cost of debt as in the example we developed in
class
Cost of Capital
81
July 17
WACC and Cost of Capital Estimation in Practice
• Rather than just providing the formula of WACC, it would be
useful to give instructions on where to find the market
premium data, betas and what is the best method vs the
most practical method.
To compute premiums for country risk, I suggest using risk
insurance premiums that are offered by institutions such as
the ADB.
The ADB provides insurance for nationalization, non
conversion of currency and contract abrogation. After these
risks are removed, the risk should be similar to places where
these risks are not present.
The ADB provides percentages to add to debt which can be
added to the Rf
Cost of Capital
82
July 17
Contacts
• Ed Bodmer
• [email protected]
• www.edbodmer.com
• 1-630-886-2745
Cost of Capital
83
July 17