Question

"You invest $8,500 now and receive $3,000 at the end of year 1, $2,800 at the end of year 2, $2,600 at the end of year 3, and so on. In what year do you break even on your investment? Use the discounted payback approach and assume an annual interest rate of 4.5%, compounded annually. Enter your answer as an integer."

Answer 1

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Answer
Payback period is the duration  taken by a project to recovers its initial inestment.Payback period is calculated by using cumulative cash flows. Discounted cumulative cash flows are calculated as follows

All the inflows are discounted at 4.5% by dividing by (1+4.5%)n where n is the year of cash inflow

Example 3000/(1.045) = 2870.813

Year	Cash flow	PV of cash flow	Cumulative cash flows
1	3000	2870.813	2870.813
2	2800	2564.044	5434.857
3	2600	2278.371	7713.228
4	2400	2012.547	9725.776

It is clear that payback period will be between 3 to 4 years
It is calculated as A + B/C
where A is the year before recovery
b is the balance amount recovered
C is the inflow in the recovery year

Discounted . P. B period = 3 + (8500-7713.228)/2012.547
=3+ 786.772/2012.547
= 3+ 0.390
= 3.390 years