Picking the Right Investments
Choosing the Right Discount Rate
P.V. Viswanath
Based on Damodaran’s Corporate Finance
What is a investment or a project?
 Any decision that requires the use of resources (financial or
otherwise) is a project.
 Broad strategic decisions
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Entering new areas of business
Entering new markets
Acquiring other companies
 Tactical decisions
 Management decisions
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The product mix to carry
The level of inventory and credit terms
 Decisions on delivering a needed service
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Lease or buy a distribution system
Creating and delivering a management information system
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The notion of a benchmark
 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:
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How do you measure risk?
How do you translate this risk measure into a risk premium?
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The Capital Asset Pricing Model
 Uses variance as a measure of risk
 Specifies that a portion of variance can be diversified away,
and that is only the non-diversifiable portion that is
rewarded.
 Measures the non-diversifiable risk with beta, which is
standardized around one.
 Relates beta to hurdle rate or the required rate of return:
Reqd. ROR = Riskfree rate + b (Risk Premium)
 Works as well as the next best alternative in most cases.
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The Mean-Variance Framework
 The variance on any investment measures the
disparity between actual and expected returns.
Low Variance Investment
High Variance Investment
Expected Return
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The Importance of Diversification:
Risk Types
 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:
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(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
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The Effects of Diversification
 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 firmspecific risk for two reasons
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(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.)
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The Role of the Marginal Investor
 The marginal investor in a firm is the investor who is most
likely to be the buyer or seller on the next trade.
 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)
 We assume that the marginal investor is 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.
 The marginal investor determines the price of an asset since
s/he is the most likely trader of the asset.
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The Market Portfolio
 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.
 We assume 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.)
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The Risk and Risk Premium of an
Individual Asset
 We already know that the pricing of an asset is determined
with respect to 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,
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the risk premium for an average security, i.e. one that mimics the
market, is the required risk premium on the market, i.e., the excess of
the expected return on the market over the riskfree rate (E(Rm) – Rf).
the risk of any asset is the risk that it adds to the market portfolio.
 Beta is a measure of the non-diversifiable risk for any asset.
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The Required ROR on an Individual Asset
 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)
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