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.
7.3
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 = $7,000/1.14 = $6,140.35
Value today of Year 2 cash flow = $7,500/1.14
2
= $5,771.01
Value today of Year 3 cash flow = $8,000/1.14
3
= $5,399.77
Value today of Year 4 cash flow = $8,500/1.14
4
= $5,032.68
To find the discounted payback, we use these values to find the payback period. The discounted first
year cash flow is $6,140.35, so the discounted payback for an $8,000 initial cost is:
Discounted payback = 1 + ($8,000 – 6,140.35)/$5,771.01 = 1.32 years
For an initial cost of $13,000, the discounted payback is:
Discounted payback = 2 + ($13,000 – 6,140.35 – 5,771.01)/$5,399.77 = 2.20 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.