CHAPTER 9
NET PRESENT VALUE AND OTHER
INVESTMENT CRITERIA
Solutions to Questions and Problems
NOTE: All end of chapter problems were solved using a spreadsheet. Many problems require multiple steps. Due to space
and readability constraints, when these intermediate steps are included in this solutions manual, rounding may appear to
have occurred. However, the final answer for each problem is found without rounding during any step in the problem.
Basic
1.
To calculate the payback period, we need to find the time that the project has recovered its initial investment. After
three years, the project has created:
$1,600 + 1,900 + 2,300 = $5,800
in cash flows. The project still needs to create another:
$6,400 – 5,800 = $600
in cash flows. During the fourth year, the cash flows from the project will be $1,400. So, the payback period will be 3
years, plus what we still need to make divided by what we will make during the fourth year. The payback period is:
Payback = 3 + ($600 / $1,400) = 3.43 years
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 $2,400, the payback
period is:
Payback = 3 + ($105 / $765) = 3.14 years
There is a shortcut to calculate the future cash flows are an annuity. Just divide the initial cost by the annual cash
flow. For the $2,400 cost, the payback period is:
Payback = $2,400 / $765 = 3.14 years
For an initial cost of $3,600, the payback period is:
Payback = $3,600 / $765 = 4.71 years
The payback period for an initial cost of $6,500 is a little trickier. Notice that the total cash inflows after eight years
will be:
Total cash inflows = 8($765) = $6,120
If the initial cost is $6,500, the project never pays back. Notice that if you use the shortcut for annuity cash flows,
you get:
Payback = $6,500 / $765 = 8.50 years
This answer does not make sense since the cash flows stop after eight years, so again, we must conclude the payback
period is never.