Question

If a project costs $70,000 and is expected to return $17,500 annually, how long does it take to recover the initial​ investment? What would be the discounted payback period at i=16​%? Assume that the cash flows occur continuously throughout the year.

Answer 1

(a) Simple (non-discounted) Payback period (PBP) is the time by when cumulative cash flows becomes zero.

Year	Cash flow ($)	Cumulative Cash Flow ($)
0	-70,000	-70,000
1	17,500	-52,500
2	17,500	-35,000
3	17,500	-17,500
4	17,500	0

PBP = 4 years

(b)

Discounted payback period (DPBP) is the time by when cumulative discounted cash flows becomes zero.

Year	Cash flow ($)	PV Factor @16%	Discounted Cash Flow ($)	Cumulative Discounted Cash Flow ($)
0	-70,000	1.0000	-70,000	-70,000
1	17,500	0.8621	15,086	-54,914
2	17,500	0.7432	13,005	-41,908
3	17,500	0.6407	11,212	-30,697
4	17,500	0.5523	9,665	-21,032
5	17,500	0.4761	8,332	-12,700
6	17,500	0.4104	7,183	-5,517
7	17,500	0.3538	6,192	675

DPBP lies between years 6 and 7.

DPBP = 6 + (Absolute value of cumulative discounted cash flow, year 6 / Discounted cash flow, year 7)

= 6 + (5,517 / 6,192)

= 6.89 years