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Project Appraisal
Swagat Kishore MishraDepartment of Economics and FinanceWILP:
Project Appraisal
Lecture 10
Email: [email protected]
Tel. 0832-2580207 (O) 08879506995 (M)
Course No. ETZC414Project Appraisal
September 16, 2014
mailto:[email protected]:[email protected]:[email protected]:[email protected]
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Cost of Capital
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The Cost of Capital
To value a company using enterprise DCF, we discount free cash
flow by the weightedaverage cost of capital (WACC). The WACC
represents the opportunity cost that
investors face for investing their funds in one particular
business instead of others with
similar risk.
In its simplest form, the weighted average cost of capital is
the market-based weightedaverage of the after-tax cost of debt and
cost of equity:
To determine the weighted average cost of capital, we must
calculate its three
components: (1) the cost of equity, (2) the after-tax cost of
debt, and (3) the
companys target capital structure.
emd kV
E)T(1k
V
DWACC
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Successful Implementation Requires Consistency
The most important principle underlying successful
implementation of the cost ofcapital is consistency between the
components of WACC and free cash flow. To
assure consistency,
It must include the opportunity costs from all sources of
capital debt, equity,and so onsince free cash flow is available to
all investors.
It must weight each securitys required return by its
market-based target weight,not by its historical book value.
It must be computed after corporate taxes (since free cash flow
is calculated inafter-tax terms). Any financing-related tax shields
not included in free cash flow
must be incorporated into the cost of capital or valued
separately.
It must be denominated in the same currency as free cash
flow
It must be denominated in nominal terms when cash flows are
stated in nominalterms
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The Cost of Capital: An Example
Source ofcapital
Debt
Equity
WACC
Proportionof totalcapital
8.3%
91.7%
100.0%
Cost ofcapital
4.7%
9.9%
Marginaltax rate
38.2%
After-taxopportunitycost
2.9%
9.9%
Contribution toweightedaverage
0.2%
9.1%
9.3%
The Cost of Capital: Home Depot
The weighted average cost of capital at Home Depot equals 9.3%.
The majority of
enterprise value is held by equity holders (91.7%), whose
CAPM-based required
return equals 9.9%. The remaining capital is provided by debt
holders at 2.9% of
an after-tax basis.
Lets examine the components of WACC one-
by-one, starting with the cost of equity
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The Cost of Equity
To estimate the cost of equity, we must determine the expected
rate of return of the
companys stock. Since expected rates of return are unobservable,
we rely on asset-
pricing models that translate risk into expected return.
The three most common asset-pricing models differ primarily in
how they define risk.
The capital assets pric ing model (CAPM)states that a stocks
expected return
is driven by how sensitive its returns are to the market
portfolio. This sensitivity is
measured using a term known as beta.
The Fama-French three-factor modeldefines risk as a stocks
sensitivity to
three portfolios: the stock market, a portfolio based on firm
size, and a portfolio
based on book-to-market ratios.
The Arb itrage Pric ing Theory (APT)is a generalized
multi-factor model, butunfortunately provides no guidance on the
appropriate factors that drive returns.
The CAPM is the most common method for estimating expected
returns, so we begin
our analysis with that model.
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The Capital Assets Pricing Model
Expected returnPercent
Beta (systematic risk)
The CAPM postulates that the
expected rate of return on acompanys stock equals the risk-
free rate plus the securitys beta
times the market risk premium:
E[Ri] = rf+ Bi(E[Rm]rf)
To estimate a stocks expected
return, you need to measure
three inputs:
1. The risk-free rate
2. The market risk premium
3. The stocks beta
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Component 1 of the CAPM: The Risk Free Rate
Percent
Source:Bloomberg Years to maturity
To estimate the risk-free rate, we look to government
default-free bonds. For
simplicity, most valuation analysts choose a single yield to
maturity from one
government bond that best matches the entire cash flow stream
being valued.
For U.S.-based corporate valuation, the most common proxy is the
10-year
government bond rate. This rate can be found in any daily
financial publication.
Yield to Maturity on Government Bonds
Ideally, each cash
flow should be
discounted using a
government bond witha similar maturity.
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Component 2 of the CAPM: The Market Risk Premium
Sizing the market risk premiumthe difference between the markets
expected return
and the risk-free rateis arguably the most debated issue in
finance.
Methods to estimate the market risk premium fall in three
general categories:
1. Ex trapo late h is to r ical excess re tu rns. If the risk
premium is constant, we can
use a historical average to estimate the future risk
premium.
2. Regress ion analysi s. Using regression, we can link current
market variables,such as the aggregate dividend-to-price ratio, to
expected market returns.
3. Use DCF to reverse engineer the r isk premium. Using DCF,
along with
estimates of return on investment and growth, we can reverse
engineer the
markets cost of capital and subsequently the market risk
premium.
None of the methods precisely estimate the market risk premium.
Still, based onevidence from each of these models, we believe the
market risk premium as of year-
end 2003 was approximately 5 percent.
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Method 1: Use Historical Excess Returns
Investors, being risk-averse,demand a premium for holding
stocks rather than bonds.
If the level of risk aversion hasntchanged over the last 100
years,
then historical excess returns are a
reasonable proxy for future
premiums. But many econometricissues quickly arise. For
instance,
Which risk free rate should beused to compute the excess
return?
Which method of averaging isbetter, arithmetic or geometric?
Is a prediction based on U.S.data too high?
Arithmetic Geometric Standard
Percent over bonds mean mean deviation
Japan 9.5 5.4 33.3
Germany 8.7 4.9 29.7
Australia 7.6 6.0 19.0
Italy 7.6 4.1 30.2
Sweden 7.2 4.8 22.5
South Africa 6.8 5.2 19.4
United States 6.4 4.4 20.3
The Netherlands 5.9 3.8 21.9
Median 5.9 4.0 20.3
France 5.8 3.6 22.1
Canada 5.5 4.0 18.2
United Kingdom 5.1 3.8 17.0
Ireland 4.8 3.2 18.5
Spain 3.8 1.9 20.3Switzerland 2.9 1.4 17.5
Denmark 2.7 1.5 16.0
Source: Ibbotson Associates: Dimson-Marsh-Staunton (DMS),
2003
Historical Annual Market Risk Premium, 1900-2002
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Using Historical Excess Returns: Best Practices
To best measure the risk premium using historical data, you
should:
Calculate the premium over long-term government bonds
Use long-term government bonds, because they match the duration
of a
companys cash flows better than do short-term rates.
Use the longest period possible
If the market risk premium is stable, a longer history will
reduce estimation
error. Since, no statistically significant trend is observable,
we recommend thelongest period possible.
Use an arithmetic average of longer-dated intervals (such as
five years)
Although the arithmetic average of annual returns is the best
predictor of future
one year returns, compounded averages will be upward biased (too
high).Therefore, use longer-dated intervals to build discount
rates.
Adjust the result for econometric issues, such as survivorship
bias.
Predictions based on U.S. data (a successful economy) are
probably too high.
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Method 2: Regression Analysis
Source: Lewellen (2004); Goyal and Welch (2003); McKinsey
analysis
-5
-3
-1
1
3
5
7
9
1955 1960 1965 1970 1975 1980 1985 1990 1995 2000
Percent
Predicted Market Risk Premiumbased on the dividend to price
ratio
Using advanced regression
techniques unavailable to earlierauthors, Jonathan Lewellen
of
Dartmouth found that observable
variables, such as dividend
yields, do predict future market
returns.
Plotting the models predictions
reveals one major drawback: the
risk premium prediction can be
negative!
Other authors question the idea
of using financial ratios, arguingunconditional historical
averages
predict better than more
sophisticated regression
techniques.
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Method 3: Reverse Engineer Discounted Cash Flow
Using the principles of discounted cash flow, along with
estimates of growth, various
authors have attempted to reverse engineer the market risk
premium.
We use the key value driver formula to reverse engineer the
market risk premium.
After stripping out inflation, the expected market return (not
excess return) is
remarkably constant, averaging 7.0%.
0
5
10
15
20
1962 1972 1982 1992 2002
Percent
Predicted Market Risk Premium
By reverse engineering market DCF
Subtracting the real
interest rate of 2.1%
from our estimate of
7.0% leads to a riskpremium just under 5%.
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Component 3 of the CAPM: Measuring Beta
S&P 500 monthly returns
HomeDepotmon
thly
stockreturns
Percent
According to the CAPM, a stocks
expected return is driven by beta,
which measures how much the
stock and market move together.
Since beta cannot be observed
directly, we must est imateits
value.
The most common regression
used to estimate a companys raw
beta is the market model:
The Beta for Home Depot
mi RR
Based on data from 1998-2003,
Home Depots beta is estimated
at 1.37
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Estimating Beta: Best Practices
As can be seen on the previous slide, estimating beta is a noisy
process. Based oncertain market characteristics and a variety of
empirical tests, we reach several
conclusions about the regression process:
Raw regressions should use at least 60 data points (e.g., five
years of monthlyreturns). Rolling betas should be graphed to
examine any systematic changes in a
stocks risk.
Raw regressions should be based on monthly returns. Using
shorter return periods,such as daily and weekly returns, leads to
systematic biases.
Company stock returns should be regressed against a
value-weighted, well-diversified portfolio, such as the S&P 500
or MSCI World Index.
Next, recalling that raw regressions provide only estimates of a
companys true beta,
we improve estimates of a companys beta by deriving an unlevered
industry beta
and then relevering the industry beta to the companys target
capital structure.
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An Alternative Model: Fama & French
In 1992, Eugene Fama and Kenneth French published a paper in the
Journal of
Financethat received a great deal of attention because they
concluded,
In short, our tests do not support the most basic prediction of
the
SLB [Sharpe-Lintner-Black] Capital Asset Pricing Model that
average
stock returns are positively related to market betas.
Based on prior research and their own comprehensive regressions,
Fama and French
concluded that:
Equity returns are inversely related to the size of a company
(as measured by
market capitalization).
Equity returns are positively related to the ratio of the book
value to market value
of the companys equity.
With this model, a stocks excess returns are regressed on excess
market returns, the
excess returns of small stocks over big stocks (SMB), and the
excess returns of high
book-to-market stocks over low book-to-market stocks (HML).
Th C t f D bt
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The Cost of Debt
The weighted average cost of capital represents the blended rate
of return for acompanys investors, both debtholders and equity
holders:
emd kV
E)T(1k
V
DWACC
To compute the WACC, we must estimate the cost of debt (kd). To
do this we look to theyield to maturity (YTM). Although YTM
represents a promised yield, it is a good
approximation for expected return for investment grade
companies.
To compute yield-to-maturity, you have two options:
1. Compute the yield-to-maturity on long-term bonds by reverse
engineering thediscount rate needed to set DCF equal to the
price.
2. Compute the yield-to-maturity indirectly by adding a default
premium (based on thecompanys rating) to the risk free rate.
Lets examine the indirect method
T i l M k t W i ht A I d t i
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Typical Market Weights Across Industries
Note: Market value of debt proxied by book value. Enterprise
value proxiedby book value of debt plus market value of equity
22
26
30
33
47
19
15
13
12
4
0Information technology
Healthcare
Aerospace and defence
Industrial machinery
Consumer discretionary
Consumer staples
Oil and gas
Chemicals, paper, metals
Telecommunications
Airlines
Utilities
Median Debt-to-Value, 2003
In percent To place the companyscurrent capital structure in
the proper context, compare
its capital structure with
those of similar companies.
Industries with heavy fixedinvestment in tangible assets
tend to have higher debt
levels.
High-growth industries,
especially those withintangible investments, tend
to use very little debt.
The Purpose of the
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The Purpose of theCost of Capital
The cost of capital is the average rate paid for the use ofthe
firms capital funds
Capital refers to money acquired for use over long
periodsGenerally used to start businesses and acquire long-lived
assets
The cost of capital provides a benchmark against which
toevaluate investment returns
Projects should not be undertaken unless they return more than
the costof the funds invested in them => the cost of
capital.
Rule is equivalent toProject IRR exceeds the cost of
capitalProject NPV > 0 when calculated at the cost of
capital
Capital Components
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Capital Components
A firms Capital ComponentsareDebtBorrowed money, either loans or
bondsCommon equityOwnership interest
Preferred stockA hybrid security, a cross between debt and
equity
Capital structureis the mix of the three capitalcomponents -
generally expressed in percentages
Returns on Investments and the
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Returns on Investments and theCosts of Capital Components
Investors provide capital by purchasing securitiesReturns paid
to investors adjusted for taxes and administrative
expenses are the firms costs
The risk levels of Capital Component securities differLeads to
different investor returns for each componentAnd different costs to
the issuing firm for each componentEquity is the riskiest
investment, earns the highest return, and has the
highest costDebt is the safest investment, earns the lowest
return, and costs the
firm leastPreferred Stock offers investors intermediate risk and
return levels andhas a cost between that of equity and debt
The Weighted Average CalculationThe WACC
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g g
A firms cost of capital is a weighted average ofthe costs of the
three capital componentswhere the weights reflect the $ amounts
ofeach component in use
Referred to in two waysk, the cost of capital
WACC, for weighted average cost of capital
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The Weighted Average Calculation
Q: Calculate the WACC for the Zodiac Company given the following
information about itscapital structure.
A: First calculate the capital structure weights based on the
values given. For example theweight of debt is $60,000 $200,000 =
30%. Next, each components cost is multiplied byits weight and the
results are summed as shown:E
xample $200,000
1490,000Common stock
1150,000Preferred Stock
9%$60,000Debt
CostValueCapital Component
WACC=
14
11
9%
Cost
100%
45%
25%
30%
Weight
11.75%$200,000
6.30%90,000Common stock
2.75%50,000Preferred Stock
2.70%$60,000Debt
ValueCapital Component
Capital Structure and CostBook Versus Market
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pValue
We can think of the WACC in terms of either book ormarket values
of capital components
For both structure and component costsWhich is the correct
focus?
WACC used to evaluate next years capital projectsMust be
supported by capital raised next yearBook values reflect capital
raised and spent years agoCurrent market values represent our best
estimate of next years
capital market conditions
Market values are the appropriate basis for WACCFor capital
structureFor component costs
Capital Structure Customary Approach
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y
Structure: Assume the firm will either Maintain present capital
structure based on the current market prices of its
securities Or strive to achieve some target structure also based
on current market prices. Costs: Always use market-based component
costs to develop the WACC.
Calculating the WACC
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Calculating the WACC
Step 1: Develop a market-based capital structure Step 2: Adjust
market returns on the underlying securities to reflect the costs of
the
three capital component Step 3: Combine in calculating the
WACC
De eloping Market Val e Based
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Developing Market-Value-BasedCapital Structures
Example 13.2
Q: The Wachusett Corporation has the following capital
situation.
Debt: Two thousand bonds were issued five years ago at a coupon
rateof 12%. They had 30-year terms and $1,000 face values. They are
now
selling to yield 10%.
Preferred stock: Four thousand shares of preferred are
outstanding,each of which pays an annual dividend of $7.50. They
originally sold toyield 15% of their $50 face value. They're now
selling to yield 13%.
Equity: Wachusett has 200,000 shares of common stock
outstanding,currently selling at $15 per share.
Develop Wachusett's market-value-based capital structure.
Example
Developing Market Value Based
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Developing Market-Value-BasedCapital Structures
A: The market value of each capital component is the current
price of eachsecurity multiplied by the number outstanding.
The price of Wachusett's bonds in the market must be determined.
We
know the bonds have 25 years remaining until maturity, pay
interest of$120 annually ($60 semi-annually) and are yielding 10%
annually (5%semi-annually). Thus, each bond is selling for
$1,182.55 in the market,calculated as shown below.
Because there are 2,000 bonds outstanding, the market value of
debt is$1,182.55 x 2,000 = $2,365,100
Example
Pb= PMT[PVFAk,n] + FV[PVFk,n]
= $60[PVFA5,50] + $1,000[PVF5,50]
= $60(18.2559) + $1,000(0.0872) = $1,182.55
Developing Market-Value-Based
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Developing Market-Value-BasedCapital Structures
The firm's preferred stock represents a perpetuity that pays
$7.50 annuallyand is yielding 13%. Thus, the value of each share of
preferred stock is
$7.50 / .13 = $57.69
And the total market value of Wachusett's preferred stock is
$57.69 x 4,000 = $230,760
Each share of Wachusett's common stock is trading at $15, thus
the totalmarket value of the firm's equity is
$15 x 200,000 shares = $3,000,000
Next summarize and calculate the component weights:
Example
100.0%$5,595,860
53.63,000,000Equity
4.1230,760Preferred
42.3%$2,365,100Debt
Calculating ComponentCosts of Capital
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Costs of Capital
Begin with the market return received by new investors ineach
capital component
kd, kp, and ke Make adjustments for the effects of taxes and
transaction
costs to arrive at cost to the issuing firm
Tax adjustment applies only to debt (Tax rate is T) Interest is
tax deductible to the paying firm Cost of debt = kd(1T) Debt, the
cheapest source, made even cheaper by tax adjustment Flotation
costs are a percentage of a securitys price (f) Apply to preferred
and new sales of common equity
Increases effective cost Cost of component = kp/ (1 f) or ke/
(1f)
Cost of Debt
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Example 13.3
Example
Q.Blackstone Inc. has 12% coupon rate bonds outstanding
thatyield 8% to investors buying them now. Blackstones marginaltax
rate including federal and state taxes is 37%. What isBlackstones
cost of debt?
A. First notice that kd is the current market yield of 8%, not
thecoupon rate. To calculate the cost of debt we simply
writeequation 13.1 and substitute from the information given.
cost of debt = kd(1 - T)= .08(1 - .37)
= 5.04%
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September 16, 2014
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THANKYOU
Course No. ETZC414Project Appraisal 25.07.13
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