Question

A project has annual cash flows of $6,500 for the next 10 years and then $9,000 each year for the following 10 years. The IRR of this 20-year project is 13.12%. 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

Computation of initial cost of the project:

NPV of the project at discount rate equals to IRR is 0.

NPV = PV of total cash inflow – Initial investment

PV of total cash inflow at discount rate of IRR = Initial investment

Computation of PV of cash inflows:

Year	Cash Flow (C)	PV Factor Computation	PV Factor @ 13.12 % (F)	PV (C x F)
1	$6,500	1/ (1+0.1312)1	0.884016973126	$ 5,746.110325
2	6,500	1/ (1+0.1312)2	0.781486008775	5,079.659057
3	6,500	1/ (1+0.1312)3	0.690846896017	4,490.504824
4	6,500	1/ (1+0.1312)4	0.610720381911	3,969.682482
5	6,500	1/ (1+0.1312)5	0.539887183443	3,509.266692
6	6,500	1/ (1+0.1312)6	0.477269433737	3,102.251319
7	6,500	1/ (1+0.1312)7	0.421914280177	2,742.442821
8	6,500	1/ (1+0.1312)8	0.372979384881	2,424.366002
9	6,500	1/ (1+0.1312)9	0.329720106861	2,143.180695
10	6,500	1/ (1+0.1312)10	0.291478170846	1,894.60811
11	9,000	1/ (1+0.1312)11	0.257671650323	2,319.044853
12	9,000	1/ (1+0.1312)12	0.227786112379	2,050.075011
13	9,000	1/ (1+0.1312)13	0.201366789586	1,812.301106
14	9,000	1/ (1+0.1312)14	0.178011659818	1,602.104938
15	9,000	1/ (1+0.1312)15	0.157365328693	1,416.287958
16	9,000	1/ (1+0.1312)16	0.139113621546	1,252.022594
17	9,000	1/ (1+0.1312)17	0.122978802640	1,106.809224
18	9,000	1/ (1+0.1312)18	0.108715348868	978.4381398
19	9,000	1/ (1+0.1312)19	0.096106213639	864.9559227
20	9,000	1/ (1+0.1312)20	0.084959524080	764.6357167
			Total PV	$49,268.74779

Initial investment of the project is $ 49,268.74779 or $ 49,268.75

Computation of NPV at discount rate of 8 %:

NPV = PV of future cash flow – Initial investment

Year	Cash Flow (C)	PV Factor Computation	PV Factor @ 8 % (F)	PV (C x F)
0	-$4,9268.75	1/ (1+0.08)0	1	-$4,9268.75
1	6,500	1/ (1+0.08)1	0.925925925926	6,018.518519
2	6,500	1/ (1+0.08)2	0.857338820302	5,572.702332
3	6,500	1/ (1+0.08)3	0.793832241020	5,159.909567
4	6,500	1/ (1+0.08)4	0.735029852796	4,777.694043
5	6,500	1/ (1+0.08)5	0.680583197034	4,423.790781
6	6,500	1/ (1+0.08)6	0.630169626883	4,096.102575
7	6,500	1/ (1+0.08)7	0.583490395262	3,792.687569
8	6,500	1/ (1+0.08)8	0.540268884502	3,511.747749
9	6,500	1/ (1+0.08)9	0.500248967131	3,251.618286
10	6,500	1/ (1+0.08)10	0.463193488085	3,010.757673
11	9,000	1/ (1+0.08)11	0.428882859338	3,859.945734
12	9,000	1/ (1+0.08)12	0.397113758646	3,574.023828
13	9,000	1/ (1+0.08)13	0.367697924672	3,309.281322
14	9,000	1/ (1+0.08)14	0.340461041363	3,064.149372
15	9,000	1/ (1+0.08)15	0.315241704966	2,837.175345
16	9,000	1/ (1+0.08)16	0.291890467561	2,627.014208
17	9,000	1/ (1+0.08)17	0.270268951445	2,432.420563
18	9,000	1/ (1+0.08)18	0.250249029116	2,252.241262
19	9,000	1/ (1+0.08)19	0.231712063996	2,085.408576
20	9,000	1/ (1+0.08)20	0.214548207404	1,930.933867
			NPV	$22,319.37317

NPV of the project is $ 22,319.37317 or $ 22,319.37