Question

Suppose you’re evaluating a new project costing 125 and yielding an expected payoff of 75 for the two subsequent years.

You know that the market(portfolio) rate is 0,10 that the covariance of the new investment’s payoff with the market portfolio is 0,2 and that the variance of the market payoff is 0,1.

You also know that the risk-free rate is 0,05. Would you accept the project if you do not account for the risk embodied in the new project? Why? What if you probably accounted for risk, by using CAPM?

Suppose you’re evaluating a new project costing 125 and yielding an expected payoff of 75 for the two subsequent years.

You know that the market(portfolio) rate is 0,10 that the covariance of the new investment’s payoff with the market portfolio is 0,2 and that the variance of the market payoff is 0,1.

You also know that the risk-free rate is 0,05. Would you accept the project if you do not account for the risk embodied in the new project? Why? What if you probably accounted for risk, by using CAPM?

Answer 1

Risk free rate = 5%

Beta = Covariance /Variance = .2/.1 = 2

Risk Premium = Beta*(Market return – risk free rate) = 2*(10-5) = 10%

As per the CAPM,

Cost of capital = Risk free rate + Risk Premium = 5% + 10% = 15%

If risk is not considered,

Then,

R = 5%

Time n = 2 years

Net present value (NPV) = 75*(1-1/(1+5%)^2)/.05 – 125 = 14.46

Since the NPV is positive, the investment project should be accepted.

If risk is considered,

Then,

R = 15% (as per the CAPM model)

Net present value (NPV) = 75*(1-1/(1+15%)^2)/.15 -125 = -3.07

Here the NPV is negative, so the proposal will be rejected.