Question

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

Answer 1

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