# 12_Oheads - Lecture Notes 12 NPV Analysis Accounting for...

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1 Lecture Notes 12 NPV Analysis Accounting for Risk More risk requires a higher expected return • Corporate investments satisfy a risk-return separation theorem . • The expected return on a project has to compensate shareholders for the systematic risk they are bearing. • If the riskless interest rate is r , the required per period expected return over the life of a project must be at least as great as (1) Firm s risk ( β ) SML 5% Good projects Bad projects 30% 2.5 A B C Project IRR Rr β j R j r () j 1 = k + r ρ + =

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2 where, for CAPM, k = 1 and R M r is the only risk factor. • A project with an expected cash flow C t needs a positive risk- adjusted expected NPV: (2) • If the risk of different components of cash flow, or different pe- riods, varies different risk-adjusted discount rates could be used. • However, if many different discount rates are used: i. it is more difficult to explain the basis of the assumptions; ii. it is more difficult to examine the effects of varying the rates; iii. it is more difficult to compare projects. The Risk Premium under 100% Equity Finance • For a project similar to existing business, capital market data can be used to calculate beta. This is usually done via regression. • The current riskless rate and market risk premium are then used to derive R . NPV C 0 C t 1 R + () t ------------------- t 1 = T + C 0 C t 1 r ρ ++ t --------------------------- t 1 = T + ==
3 • The CAPM beta is often measured using monthly or weekly ob- servations over a period of two to six years. - Daily returns are too noisy. - Over periods longer than 2-6 years, the “true” beta is likely to change. In APT terms, the dominant factors affecting returns in one historical period may differ from the important factors in an- other period. The CAPM is useful essentially because the beta coefficients are more stable than r and R M but if the sample peri- od is too long, the CAPM beta coefficients are not stable either. • One should also check the beta coefficients for comparable firms. If the firms are making investments of similar risk, the ad- ditional data may give a better estimate of beta. Example 1 • Quatram Co is 100% equity financed with an estimated β of 1.3. It is considering new projects similar to its existing investments. What is the appropriate discount rate for the new projects if the risk-free rate is 7% and the market risk premium is 8.5%?

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4 • The cost of equity (return on stocks) for Quatram Co is r S = 7% + 1.3 × 8.5% = 18.05% (3) Example 2 • Alpha Air Freight is all-equity with β = 1.21. Suppose r = 6% and R M r = 8.5%. The expected return on Alpha Air Freight’s
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## This note was uploaded on 12/20/2011 for the course ECON 448 taught by Professor Bejan during the Spring '06 term at Rice.

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12_Oheads - Lecture Notes 12 NPV Analysis Accounting for...

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