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Project A has a beta of 1.7 and an expected rate of rate of return of...

Project A has a beta of 1.7 and an expected rate of rate of return of 16.1%. Project B has a beta of 0.8 and an expected rate of return of 12.1%. What is the risk-free rate?

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Answer #1

According to CAPM model,

ERi = Rf + β(ERm - Rf)

where,

ERi = Expected return of portfolio
Rf = Risk-free rate
β = Beta of the investment
ERm = Expected return of market

For Project A,
ERi = 16.1%
β = 1.7
=> 16.1 = Rf + 1.7(ERm - Rf)
=> (ERm - Rf) = (16.1 - Rf)/1.7 ...... (I)

For Project B,
ERi = 12.1%
β = 0.8
=> 12.1 = Rf + 0.8(ERm - Rf)
=> (ERm - Rf) = (12.1 - Rf)/0.8 ...... (II)

Substituting I and II

=> (16.1 - Rf)/1.7 = (12.1 - Rf)/0.8

=> 12.88 - 0.8Rf = 20.57 - 1.7Rf

=> Rf = (20.57 - 12.88) / (1.7 - 0.8) = 8.54%

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