Question

A project has annual cash flows of $4,500 for the next 10 years and then $6,000 each year for the following 10 years. The IRR of this 20-year project is 12.64%. If the firm's WACC is 12%, 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 12.64%, 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 12.64%

Year	Annual Cash Flow ($)	Present Value factor at 12.64%	Present Value of Cash Flow ($)
1	4,500	0.887784	3,995.03
2	4,500	0.788161	3,546.72
3	4,500	0.699716	3,148.72
4	4,500	0.621197	2,795.39
5	4,500	0.551489	2,481.70
6	4,500	0.489603	2,203.21
7	4,500	0.434662	1,955.98
8	4,500	0.385886	1,736.49
9	4,500	0.342583	1,541.62
10	4,500	0.304140	1,368.63
11	6,000	0.270011	1,620.06
12	6,000	0.239711	1,438.27
13	6,000	0.212812	1,276.87
14	6,000	0.188931	1,133.59
15	6,000	0.167730	1,006.38
16	6,000	0.148908	893.45
17	6,000	0.132198	793.19
18	6,000	0.117363	704.18
19	6,000	0.104193	625.16
20	6,000	0.092501	555.01
TOTAL			34,819.64

The Initial Investment is $34,819.64

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

Year	Annual Cash Flow ($)	Present Value factor at 12%	Present Value of Cash Flow ($)
1	4,500	0.892857	4,017.86
2	4,500	0.797194	3,587.37
3	4,500	0.711780	3,203.01
4	4,500	0.635518	2,859.83
5	4,500	0.567427	2,553.42
6	4,500	0.506631	2,279.84
7	4,500	0.452349	2,035.57
8	4,500	0.403883	1,817.47
9	4,500	0.360610	1,622.75
10	4,500	0.321973	1,448.88
11	6,000	0.287476	1,724.86
12	6,000	0.256675	1,540.05
13	6,000	0.229174	1,375.05
14	6,000	0.204620	1,227.72
15	6,000	0.182696	1,096.18
16	6,000	0.163122	978.73
17	6,000	0.145644	873.87
18	6,000	0.130040	780.24
19	6,000	0.116107	696.64
20	6,000	0.103667	622.00
TOTAL			36,341.33

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

= $36,341.33 - $34,819.64

= $1,521.69

“Therefore, the Net Present Value (NPV) will be $1,521.69”

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.