1.
To calculate the payback period, we need to find the time that the project has recovered its initial
investment. After two years, the project has created:
$1,500 + 2,600 = $4,100
in cash flows. The project still needs to create another:
$4,800 – 4,100 = $700
in cash flows. During the third year, the cash flows from the project will be $3,400. So, the payback
period will be 2 years, plus what we still need to make divided by what we will make during the
third year. The payback period is:
Payback = 2 + ($700 / $2,900) = 2.24 years
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 = $6,500/1.14 = $5,701.75
Value today of Year 2 cash flow = $7,000/1.14
2
= $5,386.27
Value today of Year 3 cash flow = $7,500/1.14
3
= $5,062.29
Value today of Year 4 cash flow = $8,000/1.14
4
= $4,736.64
To find the discounted payback, we use these values to find the payback period. The discounted first
year cash flow is $5,701.75, so the discounted payback for an $8,000 initial cost is:
Discounted payback = 1 + ($8,000 – 5,701.75)/$5,386.27 = 1.43 years
For an initial cost of $13,000, the discounted payback is:
Discounted payback = 2 + ($13,000 – 5,701.75 – 5,386.27)/$5,062.29 = 2.38 years
Notice the calculation of discounted payback. We know the payback period is between two and three
years, so we subtract the discounted values of the Year 1 and Year 2 cash flows from the initial cost.
This is the numerator, which is the discounted amount we still need to make to recover our initial