Chapter 12 Cash Flow Estimation and Risk Analysis 371some familiarity with Excel access the model and work through it to see how the
table was generated. Anyone doing real-world capital budgeting today would use
such a model; and our model provides a good template, or starting point, if and
when you need to analyze an actual project.
12-2a Effect of Different Depreciation Rates
If we replaced the accelerated depreciation numbers in Table 12-1 with the con-
stant $225 values that would exist under straight line, the result would be a cash
! ow time line on Row 22 that has the same total! ows. However, in the early
years, the cash! ows resulting from straight-line depreciation would be lower
than those now in the table; and the later years’ cash! ows would show higher
numbers. You know that dollars received earlier have a higher present value than
dollars received later. Therefore, Project S’s NPV is higher if the " rm uses acceler-
ated depreciation. The exact effect is shown in the Project Evaluation section of
Table 12-1—the NPV is $78.82 under accelerated depreciation and $64.44, or 18%
less, with straight line.
Now suppose Congress wants to encourage companies to increase their capital
expenditures to boost economic growth and employment. What change in depre-
ciation would have the desired effect? The answer is to make accelerated deprecia-
tion even more accelerated. For example, if the " rm could write off this 4-year
equipment at rates of 50%, 35%, 10%, and 5%, its early tax payments would be
lower, early cash! ows would be higher, and the project’s NPV would be higher
than that shown in Table 12-1.
12-2b Cannibalization
Project S does not involve any cannibalization effects. Suppose, however, that
Project S would reduce the net after-tax cash! ows of another division by $50 per
year. No other " rm would take on this project if our " rm turns it down. In this
case, we would add a row at about Row 18 and deduct $50 for each year. If this
were done, Project S would end up with a negative NPV; hence, it would be
rejected. On the other hand, if Project S would cause additional! ows in some
other division (a positive externality), those after-tax in! ows should be attrib-
uted to Project S.
12-2c Opportunity Costs
Now suppose the $900 initial cost shown in Table 12-1 was based on the assump-
tion that the project would save money by using some equipment the company
now owns and that equipment would be sold for $100, after taxes, if the project is
rejected. The $100 is an opportunity cost, and it should be re! ected in our calcula-
tions. We would add $100 to the project’s cost. The result would be an NPV of
$78.82! $100 "! $21.18, so the project would be rejected.
12-2d Sunk Costs
Now suppose the " rm had spent $150 on a marketing study to estimate potential
sales. This $150 could not be recovered regardless of whether the project is accepted
or rejected. Should the $150 be charged to Project S when determining its NPV for
capital budgeting purposes? The answer is no. We are interested only in incremen-
tal costs. The $150 is not an incremental cost; it is a sunk cost. Therefore, it should
not enter into the analysis.
One additional point should be made about sunk costs. If the $150 expendi-
ture was actually made, in the " nal analysis, Project S would turn out to be a
loser: Its NPV would be $78.82! $150 " !$71.18. If we could somehow back up