P.V. VISWANATH
2
 Since financial resources are finite, there is a hurdle
that projects have to cross before being deemed
acceptable.
 This hurdle will be higher for riskier projects than for
safer projects.
 A simple representation of the hurdle rate is as follows:
Hurdle rate = Return for postponing consumption +
Return for bearing risk
Hurdle rate = Riskless Rate + Risk Premium
 The two basic questions that every risk and return
model in finance tries to answer are:


How do you measure risk?
How do you translate this risk measure into a risk premium?
P.V. Viswanath
3
 Most finance valuation models use the mean-variance
framework – investors prefer higher mean returns and
lower variance of portfolio returns.
 The variance on any investment measures the disparity
between actual and expected returns.
Low Variance Investment
High Variance Investment
Expected Return
P.V. Viswanath
4
 The risk (variance) on any individual investment can be
broken down into two sources: firm-specific risk and
market-wide risk, which affects all investments.
 The risk faced by a firm can be fall into the following
categories:





(1) Project-specific; an individual project may have higher or lower
cash flows than expected.
(2) Competitive Risk: the earnings and cash flows on a project can be
affected by the actions of competitors.
(3) Industry-specific Risk: covers factors that primarily impact the
earnings and cash flows of a specific industry.
(4) International Risk: arising from having some cash flows in
currencies other than the one in which the earnings are measured
and stock is priced
(5) Market risk: reflects the effect on earnings and cash flows of
macro economic factors that essentially affect all companies
P.V. Viswanath
5
 Firm-specific risk (project specific, competitive and
industry-specific) can be reduced, if not eliminated, by
increasing the number of investments in your portfolio.
 International risk can be reduced by holding a globally
diversified portfolio.
 Market-wide risk cannot be avoided.
 Diversifying and holding a larger portfolio eliminates
firm-specific risk for two reasons

(a) Each investment is a much smaller percentage of the portfolio,
muting the effect (positive or negative) on the overall portfolio.
(b) Firm-specific actions can be either positive or negative. In a
large portfolio, it is argued, these effects will average out to zero.
(For every firm, where something bad happens, there will be some
other firm, where something good happens.)
P.V. Viswanath
6
 The marginal investor in a firm is the investor who is most
likely to be the buyer or seller on the next trade. Hence this
person determines the market value of an asset.
 Since trading is required, the largest investor may not be the
marginal investor, especially if he or she is a
founder/manager of the firm (Michael Dell at Dell Computers
or Bill Gates at Microsoft)
 The marginal investor is likely to be well diversified. This
makes sense since diversified investors will, all else being the
same, be willing to pay a higher price for a given asset, and
will drive non-diversified investors out of the market.
 Hence in valuing a firm, we ignore diversifiable risk.
P.V. Viswanath
7
 Assuming diversification costs nothing (in terms of
transactions costs), and that all assets can be traded, the
limit of diversification is to hold a portfolio of every single
asset in the economy (in proportion to market value). This
portfolio is called the market portfolio.
 Hence the CAPM assumes that the marginal investor holds
the market portfolio as the risky part of his/her portfolio.
 (The overall risk of an investor’s portfolio can be modified
by investing a portion of the total investment in the riskless
asset. This does not affect diversification.)
P.V. Viswanath
8
 We already know that the pricing of an asset is determined
by the marginal investor
 Hence the risk premium required for a particular asset is
the risk premium demanded by the marginal investor for
that asset.
 And since the marginal investor holds the market portfolio,
the risk premium for an average asset, i.e. one that mimics
the market, is the required risk premium on the market –
the excess of the expected return on the market over the
risk-free rate (E(Rm) – Rf).
 The risk premium for any other asset is proportional to the
risk that it adds to the market portfolio, that is, to the
variance of the market portfolio.
P.V. Viswanath
9
 This asset risk can be measured by how much an asset moves




with the market (called the covariance)
Beta is a standardized measure of this covariance.
An asset’s beta can be measured by the covariance of its
returns with returns on a market index, normalized by the
variance of returns on the market portfolio:
b = Cov(Rasset, Rm)/Var(Rm).
The risk premium for an asset with a given asset risk of b is
equal to b times the risk premium for a stock of average risk.
That is, the required rate of return on an asset will be:
Required ROR = Rf + b (E(Rm) - Rf)
P.V. Viswanath
10
 A portion of portfolio variance can be diversified away, and





only the non-diversifiable portion that is rewarded.
The non-diversifiable risk is measured by beta, which is
standardized around one.
The beta is the sensitivity of asset returns to changes in the
return on the portfolio held by investors who determine
asset prices in the market.
The CAPM relates beta to the required rate of return:
Reqd. ROR = risk-free rate + b (Risk Premium)
The CAPM works as well as the next best alternative in
most cases.
We now proceed to actual methods of estimation of the
cost of capital.
P.V. Viswanath
11
 According to the CAPM, the required rate of return on an
asset will be:
Required ROR = Rf + b (E(Rm) - Rf)
 The inputs required to estimate the required ROR are:
(a) the current risk-free rate
(b) the expected market risk premium (the premium
expected for investing in risky assets over the riskless
asset)
(c) the beta of the asset being analyzed.
P.V. Viswanath
12
 The risk-free rate is the rate on a zero coupon government




bond matching the time horizon of the cash flow being
analyzed.
Theoretically, this means using different risk-free rates for
each cash flow - the 1 year zero coupon rate for the cash flow
in year 1, the 2-year zero coupon rate for the cash flow in
year 2 ...
Practically, if there is substantial uncertainty about expected
cash flows, it is enough to use a single risk-free rate for all
flows.
Using a long term government rate (even on a coupon bond)
as the risk-free rate on all of the cash flows in a long term
analysis will yield a close approximation of the true value.
For short term analysis, it is appropriate to use a short term
government security rate as the risk-free rate.
P.V. Viswanath
13
 The risk premium is the premium that investors
demand for investing in an average risk
investment, relative to the risk-free rate.
 As a general proposition, this premium should be



greater than zero
increase with the risk aversion of the investors in that
market
increase with the riskiness of the “average” risk
investment
P.V. Viswanath
14
 This is the default approach used by most to arrive at the
premium to use in the model
 In most cases, this approach does the following
it defines a time period for the estimation (1926-Present, 1962Present....)
 it calculates average returns on a stock index during the period
 it calculates average returns on a riskless security over the period
 it calculates the difference between the two
 and uses it as a premium looking forward

 The limitations of this approach are:
 it 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)
 it assumes that the riskiness of the “risky” portfolio (stock index)
has not changed in a systematic way across time.
P.V. Viswanath
15
Historical period Stocks - T.Bills
Stocks - T.Bonds
Arith
Geom
Arith
Geom
1926-1999
9.41%
8.14%
7.64%
6.60%
1962-1999
7.07%
6.46%
5.96%
5.74%
1981-1999
13.24%
11.62%
16.08%
14.17%
In practice, a risk premium of about 5.5% is used. However,
depending upon perceptions of investor risk preferences at a given
time, this number can be moved upwards or downwards.
P.V. Viswanath
16
 The standard procedure for estimating betas is to
regress stock returns (Rj) against market returns (Rm) Rj = a + b Rm

where a is the intercept and b is the slope of the regression.
 Often five years of monthly data is used to estimate
these parameters.
 The slope of the regression corresponds to the beta of
the stock, and measures the riskiness of the stock.
P.V. Viswanath
17
 The intercept of the regression provides a simple measure of
performance during the period of the regression, relative to the
capital asset pricing model.
Rj
Rj
= Rf
+ bj (Rm - Rf)
= Rf (1-bj) + bj Rm
= aj
+ b j Rm
........... Capital Asset Pricing Model
........... Regression Equation
 If aj > Rf (1-bj) ..Stock did better than expected during reg period
aj = Rf (1-bj) ..Stock did as well as expected during regr period
aj < Rf (1-bj) ..Stock did worse than expected during reg period
 Jensen's alpha, a measure of stock performance, is measure as
aj - Rf (1-b)
P.V. Viswanath
18
 Boeing’s Beta was estimate on December 31, 1998
to be 0.96
 risk-free Rate = 5.00% (Long term Government
Bond rate)
 Risk Premium = 5.50% (Approximate historical
premium)
 Expected Return = 5.00% + 0.96 (5.50%) =
10.31%
P.V. Viswanath
19
 Managers at Boeing
 need to make at least 10.31% as a return for their equity
investors to break even.
 this is the hurdle rate for projects, when the investment is
analyzed from an equity standpoint
 In other words, Boeing’s cost of equity is 10.31%.
 What is the cost of not delivering this cost of
equity?
P.V. Viswanath
20
 Type of Business: Firms in more cyclical businesses
or that sell products that are more discretionary to their
customers will have higher betas than firms that are in
non-cyclical businesses or sell products that are
necessities or staples.
 Operating Leverage: Firms with greater fixed costs
(as a proportion of total costs) will have higher betas
than firms will lower fixed costs (as a proportion of
total costs)
 Financial Leverage: Firms that borrow more (higher
debt, relative to equity) will have higher equity betas
than firms that borrow less.
P.V. Viswanath
21
 If a firm is using leverage to shield income from




corporate taxes, then it will adjust its debt level so that its
interest expenses grow with earnings. In this case, it is
not too far off the mark to assume that the firm’s interest
payments stay constant as a proportion of the firm’s free
cashflow.
In this case, the riskiness of the tax benefit is the same as
the riskiness of the debt itself.
Consequently, we can write the tax benefit simply as tD.
If we now think of debt in terms of the net debt liability –
i.e. the total debt liability less the tax benefit, we can
write the total value of the firm as V=E+(1-t)D.
We can then write: bu = (E/V)beq + (D(1-t)/V) bdebt
If the debt is relatively risk-free, we can write bdebt =0.
22
 In this case, the beta of equity alone can be written as a
function of the unlevered beta and the debt-equity ratio
bL = bu (1+ (1-t)D/E)
where
bL = Levered or Equity Beta
bu = Unlevered Beta
t = Corporate marginal tax rate
D = Market Value of Debt
E = Market Value of Equity
 The unlevered beta measures the riskiness of the business
that a firm is in and is often called an asset beta.
P.V. Viswanath
23
 The regression beta for Boeing is 0.96. This beta is a
levered beta (because it is based on stock prices, which
reflect leverage) and the leverage implicit in the beta
estimate is the average market debt equity ratio during
the period of the regression (1993 to 1998)
 The average debt equity ratio during this period was
17.88%.
 The unlevered beta for Boeing can then be
estimated:(using a marginal tax rate of 35%)
= Current Beta / (1 + (1 - tax rate) (Average Debt/Equity))
= 0.96 / ( 1 + (1 - 0.35) (0.1788)) = 0.86
P.V. Viswanath
24
Debt to
Capital
0.00%
10.00%
20.00%
30.00%
40.00%
50.00%
60.00%
70.00%
80.00%
90.00%
Debt/Equity
Ratio
0.00%
11.11%
25.00%
42.86%
66.67%
100.00%
150.00%
233.33%
400.00%
900.00%
P.V. Viswanath
Beta
0.86
0.92
1.00
1.10
1.23
1.42
1.70
2.16
3.10
5.89
Effect
of Leverage
0.00
0.06
0.14
0.24
0.37
0.56
0.84
1.30
2.24
5.03
25
 The beta of a portfolio is always the market-value
weighted average of the betas of the individual
investments in that portfolio.
 Thus,


the beta of a mutual fund is the weighted average of the
betas of the stocks and other investment in that portfolio
the beta of a firm after a merger is the market-value
weighted average of the betas of the companies involved in
the merger.
P.V. Viswanath
26
 Firm Betas as weighted averages: The beta of a
firm is the weighted average of the betas of its
individual projects.
 At a broader level of aggregation, the beta of a
firm is the weighted average of the betas of its
individual division.
P.V. Viswanath
27
 The top-down beta for a firm comes from a regression
 The bottom up beta can be estimated by doing the
following:




Find out the businesses that a firm operates in
Find the unlevered betas of other firms in these businesses
Take a weighted (by sales or operating income) average of these
unlevered betas
Lever up using the firm’s debt/equity ratio
 The bottom up beta will give you a better estimate of the
true beta when



the standard error of the beta from the regression is high (and) the
beta for a firm is very different from the average for the business
the firm has reorganized or restructured itself substantially during
the period of the regression
when a firm is not traded
P.V. Viswanath
28
Compa ny Na me
Buil ding Materi als
Catal ina Ligh ting
Cont'l Material s Corp
Eagl e Hardware
Emco Li mite d
Fas tena l Co.
HomeBa se Inc.
Hughe s Sup ply
Lowe's Cos .
Waxma n In dustries
Wes tburn e In c.
Wol ohan Lum ber
Sum
Averag e
Market Cap $ (Mil)
Beta
$13 6
1.0 5
$16
1
$32
0.5 5
$61 2
0.9 5
$18 7
0.6 5
$1,157
1.2 5
$22 7
1.1
$61 0
1
$12 ,554
1.2
$18
1.2 5
$60 7
0.6 5
$76
0.5 5
$16 ,232
0.9 3
P.V. Viswanath
Deb t Due 1-Yr Ou t
$1
$7
$2
$6
$39
$16
$1
$11 1
$6
$9
$2
$20 0
Lon g-Term Deb t
$11 3
$19
$7
$14 6
$11 9
$
$11 6
$33 5
$1,046
$12 1
$34
$20
$2,076
29
 Average Beta of comparable firms = 0.93
 D/E ratio of comparable firms = (200+2076)/16,232 =
14.01%
 Unlevered Beta for comparable firms = 0.93/(1+(10.35)(.1401))
= 0.86
 If the Home Depot’s D/E ratio is 20%, our bottom-up
estimate of Home Depot’s beta is 0.86[1+(1-.35)(.2)] =
0.9718
P.V. Viswanath
30
 The cost of capital is a composite cost to the firm of raising




financing to fund its projects.
In addition to equity, firms can raise capital from debt.
If the firm has bonds outstanding, and the bonds are traded,
the yield to maturity on a long-term, straight (no special
features) bond can be used as the interest rate.
If the firm is rated, use the rating and a typical default
spread on bonds with that rating to estimate the cost of
debt.
If the firm is not rated,


and it has recently borrowed long term from a bank, use the interest
rate on the borrowing or
estimate a synthetic rating for the company, and use the synthetic
rating to arrive at a default spread and a cost of debt
P.V. Viswanath
31
 Market Value of Equity should include the following
 Market Value of Shares outstanding
 Market Value of Warrants outstanding
 Market Value of Conversion Option in Convertible Bonds
 Market Value of Debt is more difficult to estimate because
few firms have only publicly traded debt. There are two
solutions:


Assume book value of debt is equal to market value
Estimate the market value of debt from the book value; for Boeing, the
book value of debt is $6,972 million, the interest expense on the debt is
$ 453 million, the average maturity of the debt is 13.76 years and the
pre-tax cost of debt is 5.50%.
Estimated MV of Boeing Debt =
P.V. Viswanath
1


(1


6, 972
(1.055 )13.76 
453 

13.76  $7, 631
.055
(1.055)






32
 Equity
 Cost of Equity = 5% + 1.01 (5.5%) = 10.58%
 Market Value of Equity =
$32.60 Billion
 Equity/(Debt+Equity ) =
82%
 Debt
 After-tax Cost of debt =
 Market Value of Debt =
 Debt/(Debt +Equity) =
5.50% (1-.35) = 3.58%
$ 8.2 Billion
18%
 Cost of Capital = 10.58%(.80)+3.58%(.20) = 9.17%
P.V. Viswanath
33
 Either the cost of equity or the cost of capital
(WACC) can be used as a hurdle rate, depending
upon whether the returns measured are to equity
investors or to all claimholders on the firm
(capital)
 If returns are measured to equity investors, the
appropriate hurdle rate is the cost of equity.
 If returns are measured to capital (or the firm),
the appropriate hurdle rate is the cost of capital.
P.V. Viswanath