Answers to Concepts Review and Critical Thinking Questions
1.
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.
2.
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 R, then it will be zero for some larger discount rate R*; thus the IRR must
be greater than the required return.
3.
a.
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 payback before this cutoff, and reject projects that take longer to payback.
b.
The worst problem associated with payback period is that it ignores the time value of money. In
addition, the selection of a hurdle point for 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.
c.
Despite its shortcomings, payback is often used because (1) the analysis is straightforward and
simple and (2) accounting numbers and estimates are readily available. Materiality consider-
ations often warrant a payback analysis as sufficient; maintenance projects are another example
where the detailed analysis of other methods is often not needed. Since payback is biased
towards liquidity, it may be a useful and appropriate analysis method for short-term projects
where cash management is most important.
4.
a.
The discounted payback is calculated the same as is regular payback, with the exception that
each cash flow in the series is first converted to its present value. Thus discounted payback
provides a measure of financial/economic break-even because of this discounting, just as regular