NET PRESENT VALUE AND OTHER
Answers to Concept 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 biased towards short-term projects; it fully ignores
any cash flows that occur after the cutoff point.
The average accounting return is interpreted as an average measure of the accounting performance
of a project over time, computed as some average profit measure attributable to the project divided
by some average balance sheet value for the project. This text computes AAR as average net
income with respect to average (total) book value. Given some predetermined cutoff for AAR, the
decision rule is to accept projects with an AAR in excess of the target measure, and reject all other
projects. AAR is not a measure of cash flows or market value, but is rather a measure of financial
statement accounts that often bear little resemblance to the relevant value of a project. In addition,