Question

Xcel is considering a project that has a cost of $12mi, and subsequent cash flows of 3.9mi. for the next 5 years. The firm recognizes that if it waits 1 year, it would have more information about the project, but the cost can go up to $13 mi. There is a 70% chance that market conditions will be favorable if Xcel waits a year, in which case the project will generate net cash flow of $4.6mi. for 5 years. There is a 30% chance that market conditions will be poor, in which case the project will generate net cash flow of $2.5mi. for 5 years. Assume the discount rate is 9%.

a.) Calculate NPV of the project if the firm decides to invest today.

b.) Calculate NPV of the project at t= 0 if the firm decides to wait a year.

Answer 1

a.) Calculation of NPV if firm decides to invest today:

Initial investment today or at t=0 is $12 million

Cash inflows starting from year t=1 for 5 years are, $3.9 million per annum

PV of cash inflows = $3.9 million x PVAF(9%,5years) = $15.1696 million

NPV = PV of cash inflows - Initial investment today = $15.1696 million - $12 million = $3.1696 million

Answer is $3.1696 million

b.) Calculation of NPV of the project at t= 0 if the firm decides to wait a year:

Initial investment today or at t=1 is $13 million

Cash inflows starting from year t=2 for 5 years are:

= $4.6 million x 70% probability of favorable conditions + $2.5million x 30% probability of poor conditions

= $3.97 million

PV of cash inflows = $3.97 million x PVAF(9%,5years) = $15.4419 million

NPV at t=1 = $15.4419 million - $13 million = $2.4419 million

NPV at t=0 = (NPV at t=1) / (1+9%) = 2.4419 / 1.09 = $2.2402 million

Answer is $2.2402 million