Question

You are considering a project that has been assigned a discount rate of 10 percent. If you start the project today, you will incur an initial cost of $1,000 (at t=0) and will receive cash inflows of $500 a year for four years (starting from year t=1). If you wait one year to start the project, the initial cost will rise to $1,300 (at t=1) and the cash flows will increase to $600 a year for four years (starting from year t=2). Should you wait one year to start the project?

		No, because NPV at t=0 is lower by $31.45
		No, because NPV at t=0 is lower by $37.73
		No, because NPV at t=0 is lower by $42.38
		Yes, because NPV at t=0 is higher by $38.65
		Yes, because NPV at t=0 is higher by $46.91

Answer 1

NPV(t=0) = PV of Cash Inflows - PV of Cash Outflows

= [$500 x {(1 - 1.10^-4) / 0.10}] - $1,000

= [$500 x 3.1699] - $1,000 = $1,584.93 - $1,000 = $584.93

NPV(t=1) = PV of Cash Inflows - PV of Cash Outflows

= [$600 x {(1 - 1.10^-4) / 0.10}/1.10] - [$1,300/1.10]

= [($600 x 3.1699)/1.10] - $1,181.82 = $1,729.02 - $1,181.82 = $547.20

Difference = NPV(t=1) - NPV(t=0) = $547.20 - $584.93 = -$37.73

No, you shouldn't wait one year to start the project because NPV at t=0 is lower by $37.73