Question

An orcharder spends $90,000 to plant pomegranate bushes. It will take four years for the bushes to provide a usable crop. He estimates that every year for 20 years after that he will receive a crop worth $9,500 per year. If the discount rate is 8%​, what is the net present value​ (NPV) of this​ investment?

Answer 1

NPV calculation is as follows:

• The first inflow comes at the end of year 4 and the last at the end of year 23 making it 20 inflows

Year	CF	Discount Factor		Discounted CF
0	$   -90,000.00	1/(1+0.08)^0=	1	1*-90000=	-90,000.00
1	$                    -	1/(1+0.08)^1=	0.925925926	0.925925925925926*0=	-
2	$                    -	1/(1+0.08)^2=	0.85733882	0.857338820301783*0=	-
3	$                    -	1/(1+0.08)^3=	0.793832241	0.79383224102017*0=	-
4	$       9,500.00	1/(1+0.08)^4=	0.735029853	0.735029852796453*9500=	6,982.78
5	$       9,500.00	1/(1+0.08)^5=	0.680583197	0.680583197033753*9500=	6,465.54
6	$       9,500.00	1/(1+0.08)^6=	0.630169627	0.630169626883105*9500=	5,986.61
7	$       9,500.00	1/(1+0.08)^7=	0.583490395	0.583490395262134*9500=	5,543.16
8	$       9,500.00	1/(1+0.08)^8=	0.540268885	0.540268884501976*9500=	5,132.55
9	$       9,500.00	1/(1+0.08)^9=	0.500248967	0.500248967131459*9500=	4,752.37
10	$       9,500.00	1/(1+0.08)^10=	0.463193488	0.463193488084684*9500=	4,400.34
11	$       9,500.00	1/(1+0.08)^11=	0.428882859	0.428882859337671*9500=	4,074.39
12	$       9,500.00	1/(1+0.08)^12=	0.397113759	0.397113758645991*9500=	3,772.58
13	$       9,500.00	1/(1+0.08)^13=	0.367697925	0.367697924672214*9500=	3,493.13
14	$       9,500.00	1/(1+0.08)^14=	0.340461041	0.340461041363161*9500=	3,234.38
15	$       9,500.00	1/(1+0.08)^15=	0.315241705	0.31524170496589*9500=	2,994.80
16	$       9,500.00	1/(1+0.08)^16=	0.291890468	0.291890467561009*9500=	2,772.96
17	$       9,500.00	1/(1+0.08)^17=	0.270268951	0.270268951445379*9500=	2,567.56
18	$       9,500.00	1/(1+0.08)^18=	0.250249029	0.250249029116092*9500=	2,377.37
19	$       9,500.00	1/(1+0.08)^19=	0.231712064	0.231712063996381*9500=	2,201.26
20	$       9,500.00	1/(1+0.08)^20=	0.214548207	0.214548207404057*9500=	2,038.21
21	$       9,500.00	1/(1+0.08)^21=	0.198655748	0.198655747596349*9500=	1,887.23
22	$       9,500.00	1/(1+0.08)^22=	0.183940507	0.183940507033656*9500=	1,747.43
23	$       9,500.00	1/(1+0.08)^23=	0.170315284	0.170315284290422*9500=	1,618.00
				NPV = Sum of all Discounted CF	-15,957.36

As NPV is negative, the project should not be invested in.