Question

You invest $50,000 now and receive $10,000 per year for 15 years starting at the end of the first year. What is the discounted payback period? Use i = 9% annual rate compounded annually. Give the discounted payback period between two consecutive integers.

Answer 1

Year	cash flow	present value discount factor	discounted cash flow	cumulative discounted cash flow
0	-50000	1.000	-50000	-50000
1	10000	0.917	9170	-40830
2	10000	0.841	8410	-32420
3	10000	0.772	7720	-24700
4	10000	0.708	7080	-17620
5	10000	0.649	6490	-11130
6	10000	0.596	5960	-5170
7	10000	0.547	5470	300
8	10000	0.501	5010	5310
9	10000	0.460	4600	9910
10	10000	0.422	4220	14130
11	10000	0.387	3870	18000
12	10000	0.355	3550	21550
13	10000	0.326	3260	24810
14	10000	0.299	2990	27800
15	10000	0.274	2740	30540

Dicounted payback period = 6 + (|-5170| / 5470)

= 6+ 0.94 = 6.94 years.

Present value factor = 1+(1+i)^n

Where i = 9% and n = number of year.

Discounted cash flow = cash flow * present value factor

Discounted payback period is calculated by above mentioned formula in which 6 is the year in which last negative cumulative discounted cash flow. Take last negative cummulative discounted cash flow and divide it by next year i.e. year 7 discounted cash flow and add the result in year 6.

Discounted payback period is calculated between 6 and 7.