You are considering acquiring a firm that you believe can generate expected cash

Question

You are considering acquiring a firm that you believe can generate expected cash flows of $12,000 a year forever. However, you recognize that those cash flows are uncertain. a. Suppose you believe that the beta of the firm is .6. How much is the firm worth if the risk-free rate is 3% and the expected rate of return on the market portfolio is 8%? (Do not round intermediate calculations. Round your answer to 2 decimal places.) b. By how much will you overvalue the firm if its beta is actually 1.0? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Explanation / Answer

a) Cost of equity using CAPM model is

Cost of Equity = Risk free rate + beta * (Market return - risk free rate) = 3% + 0.6 * (8%-3%) = 6.00%

Value of firm = cash flow / Cost of equity = 12000 / 6.00% = $200,000

b) Cost of equity using CAPM model is

Cost of Equity = Risk free rate + beta * (Market return - risk free rate) = 3% + 1.0 * (8%-3%) = 8.00%

Value of firm = cash flow / Cost of equity = 12000 / 8.00% = $150,000

Firm is over valued by 33.33%

(200000 - 150000) / 150000 = 33.33%

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