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What is the payback period for the following set of cash flows?
(Round your answer to 2 decimal
places, e.g., 32.16.)
Year
Cash
Flow
0
–$5,400
1
1,475
2
1,675
3
2,075
90.00 ± 1%
45.00 ± 1%
30.00 ± 1%

4
1,575
Payback period
years

Explanation:
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:
$1,475 + 1,675 + 2,075 = $5,225
in cash flows. The project still needs to create another:
$5,400 – 5,225 = $175
in cash flows. During the fourth year, the cash flows from the project will be $1,575. So, the payback
period will be three years, plus what we still need to make divided by what we will make during the fourth
year. The payback period is:
Payback = 3 + ($175 / $1,575) = 3.11 years
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An investment project provides cash inflows of $645 per year for eight years.
What is the project payback period if the initial cost is $1,550?
(Enter 0 if the project never pays back.
Round your answer to 2 decimal places, e.g., 32.16.)
Payback period
years
What is the project payback period if the initial cost is $3,300?
(Enter 0 if the project never pays back.
Round your answer to 2 decimal places, e.g., 32.16.)
2.40 ± 1%

Payback period
years
Explanation:
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 $1,550, the payback period is:
Payback = 2 + ($260 / $645) = 2.40 years
There is a shortcut to calculate the payback period when the future cash flows are an annuity. Just divide
the initial cost by the annual cash flow. For the $3,300 cost, the payback period is:
Payback = $3,300 / $645
= 5.12 years
The payback period for an initial cost of $5,400 is a little trickier. Notice that the total cash inflows after
eight years will be:
Total cash inflows = 8($645) = $5,160
If the initial cost is $5,400, the project never pays back. Notice that if you use the shortcut for annuity
cash flows, you get:
Payback = $5,400 / $645 = 8.37 years =
0 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.
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An investment project has annual cash inflows of $5,100, $3,200, $4,400, and $3,600, for the next four
years, respectively. The discount rate is 15 percent.
What is the discounted payback period for these cash flows if the initial cost is $5,000?
(Do not round
intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)
Discounted payback period
years