NET PRESENT VALUE AND OTHER
Answers to Concepts Review and Critical Thinking Questions
Assuming conventional cash flows, a payback period less than the project’s life means
that the NPV is positive for a zero discount rate, but nothing more definitive can be said.
For discount rates greater than zero, the payback period will still be less than the
project’s life, but the NPV may be positive, zero, or negative, depending on whether the
discount rate is less than, equal to, or greater than the IRR. The discounted payback
includes the effect of the relevant discount rate. If a project’s discounted payback period
is less than the project’s life, it must be the case that NPV is positive.
Assuming conventional cash flows, if a project has a positive NPV for a certain discount
rate, then it will also have a positive NPV for a zero discount rate; thus, the payback
period must be less than the project life. Since discounted payback is calculated at the
same discount rate as is NPV, if NPV is positive, the discounted payback period must be
less than the project’s life. If NPV is positive, then the present value of future cash
inflows is greater than the initial investment cost; thus, PI must be greater than 1. If NPV
is positive for a certain discount rate
, then it will be zero for some larger discount rate
*; thus, the IRR must be greater than the required return.
Payback period is simply the accounting break-even point of a series of cash flows.
To actually compute the payback period, it is assumed that any cash flow occurring
during a given period is realized continuously throughout the period, and not at a
single point in time. The payback is then the point in time for the series of cash
flows when the initial cash outlays are fully recovered. Given some predetermined
cutoff for the payback period, the decision rule is to accept projects that pay back
before this cutoff, and reject projects that take longer to pay back. The worst
problem associated with the payback period is that it ignores the time value of
money. In addition, the selection of a hurdle point for the payback period is an
arbitrary exercise that lacks any steadfast rule or method. The payback period is