Question

A project under consideration has an internal rate of return of 13% and a beta of 0.5. The risk-free rate is 3%, and the expected rate of return on the market portfolio is 13%.

a-1.	Calculate the required return.

Required return

%

a-2.	Should the project be accepted?
	Yes No

b-1.	Calculate the required return if its beta is 1.5.

Required return

%

b-2.	Should the project be accepted?
	Yes No

Answer 1

a-1. As per CAPM equation, required return of the stock is given by:

Required return = Risk free rate + Beta * (Market return - Risk free rate)

Given: Risk free rate = 3, Market return = 13, Beta = 0.5

Putting the given values in the above equation, we get,

Required return = 3 + 0.5 * (13 - 3)

Required return =  3 + (0.5 * 10)

Required return = 3 + 5 = 8%

a-2. Internal rate of return is 13% while required rate of return (as calculated above) is 8%. Since the internal rate of return is more than the required rate of return for the stock, so project should be accepted.

b-1. As per CAPM equation, required return of the stock is given by:

Required return = Risk free rate + Beta * (Market return - Risk free rate)

Given: Risk free rate = 3, Market return = 13, Beta = 1.5

Putting the given values in the above equation, we get,

Required return = 3 + 1.5 * (13 - 3)

Required return =  3 + (1.5 * 10)

Required return = 3 + 15 = 18%

b-2. Internal rate of return is 13% while required rate of return (as calculated above) is 18%. Since the internal rate of return is less than the required rate of return for the stock, so project should not be accepted.