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
investment. We divide this amount by the discounted amount we will earn in Year 3 to get the
fractional portion of the discounted payback.
If the initial cost is $18,000, the discounted payback is:
Discounted payback = 3 + ($18,000 – 5,701.75 – 5,386.27 – 5,062.29) / $4,736.64 = 3.39 year
s
9.
The NPV of a project is the PV of the outflows minus the PV of the inflows.
Since the cash inflows are an annuity, the equation for the NPV of this project at an 8 percent required return is: