Question

A project has annual cash flows of $7,500 for the next 10 years and then $10,000 each year for the following 10 years. The IRR of this 20-year project is 12.88%. If the firm's WACC is 11%, what is the project's NPV? Do not round intermediate calculations. Round your answer to the nearest cent.

Answer 1

Step-1, Calculation of Initial Investment Cost for the Project

The question has given he Internal Rate of Return [IRR] as 12.88%, IRR is the rate at which the present value of the annual cash flow equals to the initial Investment or it can say that at IRR, the present value of the annual cash flow = Initial Investment, or at IRR, NPV will be Zero

Initial Investment = Present Value of the annual cash inflows discounted at 12.88%

Year	Annual Cash Flow ($)	Present Value factor at 12.88%	Present Value of Cash Flow ($)
1	7,500	0.885897	6,644.22
2	7,500	0.784813	5,886.09
3	7,500	0.695263	5,214.47
4	7,500	0.615931	4,619.48
5	7,500	0.545651	4,092.38
6	7,500	0.483390	3,625.43
7	7,500	0.428234	3,211.75
8	7,500	0.379371	2,845.28
9	7,500	0.336083	2,520.63
10	7,500	0.297735	2,233.01
11	10,000	0.263762	2,637.62
12	10,000	0.233666	2,336.66
13	10,000	0.207004	2,070.04
14	10,000	0.183384	1,833.84
15	10,000	0.162459	1,624.59
16	10,000	0.143922	1,439.22
17	10,000	0.127500	1,275.00
18	10,000	0.112952	1,129.52
19	10,000	0.100064	1,000.64
20	10,000	0.088646	886.46
TOTAL			57,126.37

The Initial Investment is $57,126.37.

Step-2, Calculation of the Net Present Value (NPV) of the Project

Year	Annual Cash Flow ($)	Present Value factor at 11.00%	Present Value of Cash Flow ($)
1	7,500	0.900901	6,756.76
2	7,500	0.811622	6,087.17
3	7,500	0.731191	5,483.94
4	7,500	0.658731	4,940.48
5	7,500	0.593451	4,450.88
6	7,500	0.534641	4,009.81
7	7,500	0.481658	3,612.44
8	7,500	0.433926	3,254.45
9	7,500	0.390925	2,931.94
10	7,500	0.352184	2,641.38
11	10,000	0.317283	3,172.83
12	10,000	0.285841	2,858.41
13	10,000	0.257514	2,575.14
14	10,000	0.231995	2,319.95
15	10,000	0.209004	2,090.04
16	10,000	0.188292	1,882.92
17	10,000	0.169633	1,696.33
18	10,000	0.152822	1,528.22
19	10,000	0.137678	1,376.78
20	10,000	0.124034	1,240.34
TOTAL			64,910.20

Therefore, the Net Present Value (NPV) of the Project = Present Value of annual cash inflows – Initial Investment

= $64,910.20 - $57,126.37

= $7,783.83

“Therefore, the Project’s Net Present Value (NPV) will be $7,783.83”

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.