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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.
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View Full Document3.
Project A has cash flows of $19,000 in Year 1, so the cash flows are short by $21,000 of
recapturing the initial investment, so the payback for Project A is:
Payback = 1 + ($21,000 / $25,000) = 1.84 years
Project B has cash flows of:
Cash flows = $14,000 + 17,000 + 24,000 = $55,000
during this first three years. The cash flows are still short by $5,000 of recapturing the initial
investment, so the payback for Project B is:
B:
Payback = 3 + ($5,000 / $270,000) = 3.019 years
Using the payback criterion and a cutoff of 3 years, accept project A and reject project B.
4.
When we use discounted payback, we need to find the value of all cash flows today. The
value today of the project cash flows for the first four years is:
Value today of Year 1 cash flow = $4,200/1.14 = $3,684.21
Value today of Year 2 cash flow = $5,300/1.14
2
= $4,078.18
Value today of Year 3 cash flow = $6,100/1.14
3
= $4,117.33
Value today of Year 4 cash flow = $7,400/1.14
4
= $4,381.39
To find the discounted payback, we use these values to find the payback period. The
discounted first year cash flow is $3,684.21, so the discounted payback for a $7,000 initial
cost is:
Discounted payback = 1 + ($7,000 – 3,684.21)/$4,078.18 = 1.81 years
For an initial cost of $10,000, the discounted payback is:
Discounted payback = 2 + ($10,000 – 3,684.21 – 4,078.18)/$4,117.33 = 2.54 years
Notice the calculation of discounted payback. We know the payback period is between two
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 Spring '11
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