Question

Project M has a cost of $65,125, expected net cash inflows of $13,000 per year for ten years, and a cost of capital of 11%. What is the project’s NPV? What is the project’s discounted payback period?

Answer 1

Project’s Net Present Value (NPV)

Year	Annual Cash Flow ($)	Present Value factor at 11%	Present Value of Cash Flow ($)
1	13,000	0.900901	11,711.71
2	13,000	0.811622	10,551.09
3	13,000	0.731191	9,505.49
4	13,000	0.658731	8,563.50
5	13,000	0.593451	7,714.87
6	13,000	0.534641	6,950.33
7	13,000	0.481658	6,261.56
8	13,000	0.433926	5,641.04
9	13,000	0.390925	5,082.02
10	13,000	0.352184	4,578.40
TOTAL			76,560.02

Net Present Value (NPV) = Present Value of annual cash inflows – Initial Investment

= $76,560.02 - $65,125

= $11,435.02

Discounted Payback Period

Year	Cash Flows ($)	Present Value Factor at 11%	Discounted Cash Flow ($)	Cumulative net discounted Cash flow ($)
0	-65,125	1.000000	-65,125.00	-65,125.00
1	13,000	0.900901	11,711.71	-53,413.29
2	13,000	0.811622	10,551.09	-42,862.20
3	13,000	0.731191	9,505.49	-33,356.71
4	13,000	0.658731	8,563.50	-24,793.21
5	13,000	0.593451	7,714.87	-17,078.34
6	13,000	0.534641	6,950.33	-10,128.01
7	13,000	0.481658	6,261.56	-3,866.45
8	13,000	0.433926	5,641.04	1,774.60
9	13,000	0.390925	5,082.02	6,856.62
10	13,000	0.352184	4,578.40	11,435.02

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

= 7 Year + ($3,866.45 / $5,641.04)

= 7 Year + 0.69 Years

= 7.69 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.