Question

15.  Problem 11.20 (NPV)

A project has annual cash flows of $7,500 for the next 10 years and then $9,500 each year for the following 10 years. The IRR of this 20-year project is 11.67%. If the firm's WACC is 8%, 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 11.67%, 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 11.67%

Year	Annual Cash Flow ($)	Present Value factor at 11.67%	Present Value of Cash Flow ($)
1	7,500	0.895496	6,716.22
2	7,500	0.801912	6,014.34
3	7,500	0.718109	5,385.82
4	7,500	0.643064	4,822.98
5	7,500	0.575861	4,318.96
6	7,500	0.515681	3,867.61
7	7,500	0.461790	3,463.42
8	7,500	0.413531	3,101.48
9	7,500	0.370315	2,777.36
10	7,500	0.331616	2,487.12
11	9,500	0.296960	2,821.12
12	9,500	0.265927	2,526.30
13	9,500	0.238136	2,262.29
14	9,500	0.213250	2,025.87
15	9,500	0.190964	1,814.16
16	9,500	0.171008	1,624.57
17	9,500	0.153137	1,454.80
18	9,500	0.137133	1,302.77
19	9,500	0.122802	1,166.62
20	9,500	0.109969	1,044.70
TOTAL			60,998.52

The Initial Investment is $60,998.52

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

Year	Annual Cash Flow ($)	Present Value factor at 8.00%	Present Value of Cash Flow ($)
1	7,500	0.925926	6,944.44
2	7,500	0.857339	6,430.04
3	7,500	0.793832	5,953.74
4	7,500	0.735030	5,512.72
5	7,500	0.680583	5,104.37
6	7,500	0.630170	4,726.27
7	7,500	0.583490	4,376.18
8	7,500	0.540269	4,052.02
9	7,500	0.500249	3,751.87
10	7,500	0.463193	3,473.95
11	9,500	0.428883	4,074.39
12	9,500	0.397114	3,772.58
13	9,500	0.367698	3,493.13
14	9,500	0.340461	3,234.38
15	9,500	0.315242	2,994.80
16	9,500	0.291890	2,772.96
17	9,500	0.270269	2,567.56
18	9,500	0.250249	2,377.37
19	9,500	0.231712	2,201.26
20	9,500	0.214548	2,038.21
TOTAL			79,852.24

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

= $79,852.24 - $60,998.52

= $18,853.72

“Therefore, the Net Present Value (NPV) would be $18,853.72”

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.