Question

1) 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 payback period in whole number years for this investment? In other words, in what year do you break even on this investment? Use i = 9% annual rate compounded annually, and use the discounted payback approach (not Simple Payback).

Answer 1

Req: Payback period:

Initial Investment: $ 50,000

Annual cash inflows: $ 10,000

Pay back period : Initial Investment / Annual cash inflows = $ 50,000 / $10,000 = 5 years

Req : Discounted Payback period = 6.94 years

The explanation is as follows

YEAR	CASHFLOW	PVF @ 9%	PRESENT VALUE	CUMULATIVE Present value
1	10,000.00	0.917	9174.31	9174.31
2	10,000.00	0.842	8416.80	17591.11
3	10,000.00	0.772	7721.83	25312.95
4	10,000.00	0.708	7084.25	32397.20
5	10,000.00	0.650	6499.31	38896.51
6	10,000.00	0.596	5962.67	44859.19
7	10,000.00	0.547	5470.34	50329.53
8	10,000.00	0.502	5018.66	55348.19
9	10,000.00	0.460	4604.28	59952.47
10	10,000.00	0.422	4224.11	64176.58
11	10,000.00	0.388	3875.33	68051.91
12	10,000.00	0.356	3555.35	71607.25
13	10,000.00	0.326	3261.79	74869.04
14	10,000.00	0.299	2992.46	77861.50
15	10,000.00	0.275	2745.38	80606.88
	Discounted payback period : 6 years + (50,000 -44859.19) /5470.34
			(6 years + 0.94 year) = 6.94 years