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 0.7. How much is the firm worth if the risk-free rate is 3% and the expected market risk premium is 8%? (Round your answer to the nearest cent.)
	The value of the firm    $

b.	By how much will you misvalue the firm if its beta is actually 1? (Round your answer to the nearest cent. Enter your answer as positive value.)
	By underestimating beta, you would overvalue or undervalue the firm by $

Answer 1

Requirement (a)

Required Rate of Return (Ke) as per CAPM Approach = Risk-free Rate + )Beta x Market Risk Premium)

= 3% + (0.70 x 8%)

= 3% + 5.60%

= 8.60%

If the cash flows are occurring for infinity period, then the value of the firm = Cash Flow / Required rate of return

= $11,000 / 0.0860

= $1,27,906.98

“The Value of the firm = $1,27,906.98”

Requirement (b)

Required Rate of Return (Ke) if the Beta is actually 1

Required Rate of Return (Ke) = Risk-free Rate + )Beta x Market Risk Premium)

= 3% + (1 x 8%)

= 3% + 8%

= 11%

The Value of the firm = The value of the firm = Cash Flow / Required rate of return

= $11,000 / 0.11

= $100,000

The amount overvalued is the difference between the value computed in (a) and (b).

= $1,27,906.98 - $100,000

= $27,906.98

“Therefore, by underestimating beta, you would overvalue or undervalue the firm by $27,906.98”