Question

What is the discounted payback period using the given discount rate and the cumulative cash flow in the payback period (must get both correct for full credit) of the investment and annual cash flow given below?

Discount Rate	Investment	Annual Income Cash Flow	Useful Life
6%	67,000	12,800	12

Answer 1

The discounted payback period for the project

Year	Annual cash flows ($)	Present Value Factor (PVF) at 6.00%	Discounted cash flows ($) [Annual cash flow x PVF]	Cumulative net discounted Cash flow ($)
0	(67,000)	1.0000000	(67,000.00)	(67,000.00)
1	12,800	0.9433962	12,075.47	(54,924.53)
2	12,800	0.8899964	11,391.95	(43,532.57)
3	12,800	0.8396193	10,747.13	(32,785.45)
4	12,800	0.7920937	10,138.80	(22,646.65)
5	12,800	0.7472582	9,564.90	(13,081.74)
6	12,800	0.7049605	9,023.49	(4,058.25)
7	12,800	0.6650571	8,512.73	4,454.48
8	12,800	0.6274124	8,030.88	12,485.36
9	12,800	0.5918985	7,576.30	20,061.66
10	12,800	0.5583948	7,147.45	27,209.11
11	12,800	0.5267875	6,742.88	33,951.99
12	12,800	0.4969694	6,361.21	40,313.20

Discounted Payback Period = Years before full recover + (Unrecovered cash inflow at start of the year/cash flow during the year)

= 6.00 Years + ($4,058.25 / $8,512.73)

= 6 Years + 0.48 Years

= 6.48 Years

Hence, the discounted payback period for the project will be 6.48 Years

NOTE    

The Formula for calculating the Present Value Factor is [1/(1 + r)ⁿ], Where “r” is the Discount/Interest Rate and “n” is the number of years.