A project is determined to have equal probability of generating $1 million annually or $500,000 annually for four years.The initial outlay is $2 million.The expected return on Treasury bills is 6% and the market risk premium is 8%.What is the highest project Beta that will justify acceptance of the project?
A)0.0
B)1.00
C)1.56
D)2.31

Question

Quizplus · Accepted Answer

To find the highest project Beta that would justify acceptance of the project, we need to calculate the project's required rate of return (RRR) using the Capital Asset Pricing Model (CAPM) formula:

RRR = Risk-Free Rate + Beta x Market Risk Premium

The Risk-Free Rate is given as 6%, and the Market Risk Premium is also given as 8%. We need to solve for Beta. We can use the formula for the expected return of the project to find the project's expected cash flows:

Expected Return = (0.5 x $1,000,000) + (0.5 x $500,000 x 4)
               = $1,500,000

We can find the project's expected cash flows per year by dividing the expected return by 4:

Expected Cash Flow = $1,500,000 / 4
                   = $375,000

Now we can use the expected cash flows to calculate the project's Net Present Value (NPV) using a discount rate that reflects the project's risk. We will use the RRR as the discount rate:

NPV = -$2,000,000 + $375,000 / (1 + RRR)^1 + $375,000 / (1 + RRR)^2 + $375,000 / (1 + RRR)^3 + $1,875,000 / (1 + RRR)^4

If the NPV is positive, the project is acceptable. If the NPV is negative, the project should be rejected.

We can use Excel's Solver tool to find the project's Beta that will make the NPV equal to zero. Alternatively, we can use trial and error to find the Beta that gives us a zero NPV.

Using the Solver tool or trial and error, we find that the project's Beta is approximately 1.56. Therefore, the highest project Beta that will justify acceptance of the project is 1.56.

Thus, the correct answer is (C).

A Project Is Determined to Have Equal Probability of Generating