Question

A project has annual cash flows of $9,500 for the next 8 years and then $10,500 each year for the following 8 years. The IRR of this 16-year project is 12%. If the firm's WACC is 10.5%, what is the project's NPV?

Answer 1

Given :

Cash Flows for 8 years = $9500
Cash Flows for next 8 years = $10500
IRR = 12%
WACC = 10.5%

Step 1 : Calculation of Present value of cash inflows (PVCI) at IRR = 12%

Year	Cash Inflows	PVF @ 12%	Present Value
1	$9,500	0.89285714	$8,482.14
2	$9,500	0.79719388	$7,573.34
3	$9,500	0.71178025	$6,761.91
4	$9,500	0.63551808	$6,037.42
5	$9,500	0.56742686	$5,390.56
6	$9,500	0.50663112	$4,813.00
7	$9,500	0.45234922	$4,297.32
8	$9,500	0.40388323	$3,836.89
9	$10,500	0.36061002	$3,786.41
10	$10,500	0.32197324	$3,380.72
11	$10,500	0.2874761	$3,018.50
12	$10,500	0.25667509	$2,695.09
13	$10,500	0.22917419	$2,406.33
14	$10,500	0.20461981	$2,148.51
15	$10,500	0.18269626	$1,918.31
16	$10,500	0.16312166	$1,712.78
		PVCI	$68,259.21

Present value of cash inflows (PVCI) at IRR @ 12% = $68,259.21

Step 2:  Calculation of Present value of cash outflows

We know that IRR is the Rate at which NPV = 0

NPV= Present value of cash inflows - Present value of cash outflows

If NPV = 0

Present value of cash inflows =  Present value of cash outflows

Therefore, Present value of cash outflows =  $68,259.21

Step 2 : Calculation of NPV at WACC =10.5%

NPV= Present value of cash inflows - Present value of cash outflows

Year	Cash Inflows	PVF @ 10.5%	Present Value
1	$9,500	0.90497738	$8,597.29
2	$9,500	0.81898405	$7,780.35
3	$9,500	0.74116204	$7,041.04
4	$9,500	0.67073487	$6,371.98
5	$9,500	0.60699989	$5,766.50
6	$9,500	0.54932116	$5,218.55
7	$9,500	0.49712323	$4,722.67
8	$9,500	0.44988527	$4,273.91
9	$10,500	0.40713599	$4,274.93
10	$10,500	0.36844886	$3,868.71
11	$10,500	0.33343788	$3,501.10
12	$10,500	0.30175374	$3,168.41
13	$10,500	0.27308031	$2,867.34
14	$10,500	0.2471315	$2,594.88
15	$10,500	0.22364842	$2,348.31
16	$10,500	0.20239676	$2,125.17
		PVCI	$74,521.14

Present value of cash inflows =  $74,521.14

Present value of cash outflows =  $68,259.21

NPV = $74,521.14 - $68,259.21

NPV = $6261.92

Note :

PVF(r, t) = (1/1+r)^n
Where r = required rate of return or WACC
t = Time period