Question

1. Suppose a project has conventional cash flows. (a) If it has a payback less than the project's life, can you definitely state the alge- braic sign of the NPV? Why or why not? (b) If it has a positive NPV, what do you know about its payback? Its IRR? Give some examples, if you have multiple answers.

Answer 1

Part (a)

Conventional cash flows and payback period less than the project's life.

This simply means that only when the discount rate is zero, the project will have a positive NPV. In case discount rate is positive and which will be the case usually, we can't make any claim with absolute certainty, about the sign of the NPV. If discount rate is positive, and the payback period is less than the project's life then:

• NPV will be negative if discount rate > IRR
• NPV will be zero if discount rate = IRR
• NPV will be positive if discount rate < IRR

Part (b)

If a project has positive NPV then:

• Then it will certainly have payback period less than the life of the project. This is because if NPV is positive at some discount rate then NPV will certainly be positive at zero discount rate.
• The Project will certainly have an IRR greater than the discount rate. This is because IRR is that discount rate at which NPV is zero. NPV is inversely related to discount rate. If NPV is positive at a given discount rate and cash flows are conventional, then we need to increase discount rate further to make NPV zero. This implies IRR (the discount rate at which NPV is zero) is greater than discount rate.