Question

Suppose the expected net benefits from a project are continuously rising with calendar time. Suppose also that you expect the present value of the initial costs of the project to fall over time, (evaluated at the time it starts operations), if the project is postponed. Will this cause the optimum time to start the project to be delayed or to be started earlier? Explain why.

Answer 1

Since the expected net benefits from a project increase with calendar time, the benefits from delaying the project by a unit period are more than if the project is started immediately.

Also, the PV of the costs would fall on delaying the project, then the NPV of the project (calculated as PV of benefits - PV of costs) would be higher if the project is delayed than if the project is started immediately. This is based on the assumption that the discount rate is not high enough to reduce the NPV of starting the project later below the NPV of starting the project today.

So,

Expected benefits (t+1) > Expected benefits (t)

PV of costs (t+1) < PV of costs (t)

NPV (t) = PV (Expected Benefits (t)) - PV of costs (t)

NPV (t+1) = PV (Expected Benefits (t+1)) - PV of costs (t+1)

Clearly NPV(t+1) > NPV(t).

However NV(t+1) is evaluated one period later and NPV(t) is evaluated immediately.

Also present value of NPV(t+1) = NPV(t+1)/(1+r)

if r is not big enough, then PV of NPV(t+1) > NPV(t)

So, in that case the optimum time to start the project is delayed.