You are considering acquiring a firm that you believe can generate
expected cash flows of $10,000 a year forever. However, you recognize
that those cash flows are uncertain.

a. Suppose you believe that the beta of the firm is .4. How much is
the firm worth if the risk-free rate is 5 percent and the expected
rate of return on the market portfolio is 15 percent?

b. By how much will you overvalue the firm if its beta is actually .6?

Hello.

Here's the formula for the Capital Asset Pricing Model (CAPM):

Required Return = RF Rate + (Market Return - RF Rate) * Beta  

source: Investopedia.com Concepts: CAPM
http://www.investopedia.com/university/concepts/concepts8.asp

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a.

In the question, you indicate that:

risk-free rate = 5% = .05
market return = 15% = .15
beta = .4

Applying the formula:
Required Return = RF Rate + (Market Return - RF Rate) * Beta  
Required Return = .05 + (.15 - .05) * .4 
Required Return = .05 + (.10) * .4   
Required Return = .09

To calculate the worth of the firm, we divide the cash flows of
$10,000 by the required rate of return (.09):

$10,000/.09 = $111,111.11

So we say that the firm would be worth $111,111.11.

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b.

If beta is actually .6 , we must recalculate the required rate of return:

Applying the formula:
Required Return = RF Rate + (Market Return - RF Rate) * Beta  
Required Return = .05 + (.15 - .05) * .6 
Required Return = .05 + (.10) * .6   
Required Return = .11

Again, we divide the cash flows of $10,000 by the required rate of return (.11):
$10,000/.11 = $90,909.09

The amount overvalued is the difference between the two valuations:
$111,111.11 - $90,909.09 = $20,202.02

Thus, we would have overvalued the firm by $20,202.02.

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search strategy:
capm, "market risk premium", beta

I hope this helps.