Question

# Assume a world in which the assumptions of the capital asset pricing model (CAPM) hold. A...

Assume a world in which the assumptions of the capital asset pricing model (CAPM) hold. A company can invest in a project which costs today \$5,000, in one year delivers \$2,000 with certainty and in two years delivers -\$1,000 with a probability of 25% and \$8,000 with a probability of 75%. Suppose the annual risk free rate is 3%, the expected return on the market is 10% and the project’s market beta is 1.5. Should the company invest in the project or not? Explain why or why not

First of all lets find cost of equity

Cost of equity = Risk free rate of return + beta(Market return - Risk free rate of return)

=3% + 1.5(10%-3%)

=3%+1.5(7%)

=3%+10.5%

=13.5%

Now lets calculated expected cash flow in year 2

 Cash flow Probability Cash flow x probability -1000 0.25 -250 8000 0.75 6000 Expected cash flow 5750

Thus expected cash flow in year 2 = 5750\$

Now let's calculate NPV

Statement showing NPV

 Year Cash flow PVIF @ 13.5% PV A B C = A x B 1 2000 0.8811 1762.11 2 5750 0.7763 4463.51 Sum of PV of cash inflow 6225.62 Less: Initial Investment 5000.00 NPV 1225.62

Thus NPV = 1225.62 \$

Since NPV is positive , it will add value to the firm and hence investment must be made in the project

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