Question

You are considering acquiring a firm that you believe can generate expected cash flows of $11,000 a year forever. However, you recognize that those cash flows are uncertain.
a.Suppose you believe that the beta of the firm is .5. How much is the firm worth if the risk-free rate is 5% and the expected rate of return on the market portfolio is 10%? (Do not round intermediate calculations. Round your answer to 2 decimal places.) Value of the firm$
b.By how much will you overvalue the firm if its beta is actually .7? (Do not round intermediate calculations. Round your answer to 2 decimal places.) Overvaluation$

Answer 1

Answer:

1. $146,666.67

2. $129,411.76

Explanation:

In this question, we apply the Capital Asset Pricing Model (CAPM) formula which is shown below

Expected rate of return = Risk-free rate of return + Beta × (Market rate of return - Risk-free rate of return)

1. For computing the value of the firm, first we have to compute the Expected rate of return  which is shown below:

= 5% + 0.5 × (10% - 5%)

= 5% + 0.5 × 5%

= 5% + 2.5%

= 7.5%

Now the value of firm would be

= Expected cash flows  ÷ Expected rate of return

= $11,000 ÷ 7.5%

= $146,666.67

2. If beta is 0.7, then the expected rate of return and the value of firm would be

= 5% + 0.7 × (10% - 5%)

= 5% + 0.7 × 5%

= 5% + 3.5%

= 8.5%

Now the value of firm would be

= Expected cash flows  ÷ Expected rate of return

= $11,000 ÷ 8.5%

= $129,411.76