Answers to End–of–Chapter Problems
B–57
Chapter 7: Net Present Value and Other Investment Rules
7.2
To calculate the payback period, we need to find the time that the project has recovered its initial
investment. The cash flows in this problem are an annuity, so the calculation is simpler. If the initial
cost is $3,000, the payback period is:
Payback = 3 + ($480 / $840) = 3.57 years
There is a shortcut to calculate the payback period if the future cash flows are an annuity. Just divide
the initial cost by the annual cash flow. For the $3,000 cost, the payback period is:
Payback = $3,000 / $840 = 3.57 years
For an initial cost of $5,000, the payback period is:
Payback = 5 + ($800 / $840) = 5.95 years
The payback period for an initial cost of $7,000 is a little trickier. Notice that the total cash inflows
after eight years will be:
Total cash inflows = 8($840) = $6,720
If the initial cost is $7,000, the project never pays back. Notice that if you use the shortcut for
annuity cash flows, you get:
Payback = $7,000 / $840 = 8.33 years.
This answer does not make sense since the cash flows stop after eight years, so there is no payback
period.
7.4.
To calculate the discounted payback, discount all future cash flows back to the present, and use these
discounted cash flows to calculate the payback period. Doing so, we find:
r = 0%:
4 + ($1,600 / $2,100) = 4.76 years
Discounted payback = Regular payback = 4.76 years
r = 5%:
$2,100/1.05 + $2,100/1.05
2
+ $2,100/1.05
3
+ $2,100/1.05
4
+ $2,100/1.05
5
= $9,091.90
$2,100/1.05
6
= $1,567.05
Discounted payback = 5 + ($10,000 – 9,091.90) / $1,567.05 = 5.58 years
r = 15%:
$2,100/1.15 + $2,100/1.15
2
+ $2,100/1.15
3
+ $2,100/1.15
4
+ $2,100/1.15
5
+
$2,100/1.15
6
= $7,947.41; The project never pays back.
7.6
a.
The average accounting return is the average project earnings after taxes, divided by the
average book value, or average net investment, of the machine during its life. The book value
of the machine is the gross investment minus the accumulated depreciation.