Question

You own a 10-acre vineyard and earn income by selling your grapes to wineries. Your vineyard is currently planted to Merlot grapes, but you are thinking of replanting with Syrah grapes because they are commanding a higher market price per ton. Merlot fetches $1800 per ton but Syrah sells for $2500 per ton, those prices are expected to remain stable, and you produce 5 tons per year per acre (so 50 tons per year total). Either way, you plan to sell the vineyard 5 years from now (at the end of the year) for 5-times (5x) the annual income (in year 5) from the sale of grapes (that is, you'll get the income from grape sales and then sell the vineyard for 5 times that amount at the end of year 5). However, if you switch to Syrah, it will cost you $91,000 immediately and the vines won’t produce any grapes until year 4 (that is, years 1-3 will have no sales if you plant Syrah, but years 4 and 5 will). The applicable discount rate is 12% per year. What is the NPV of switching? Round to the nearest cent. ​[Hint: Create a timeline showing the incremental annual cash flows from switching and find their NPV. Some cash flows will be negative (first 3 years) and some (years 4 and 5) will be positive.]

Answer 1

Step 1: Identification of Cash Flows:

Plan 1. Merlot Grapes

Year	Particulars	Workings	Amount
1	Grape Sales	1,800 * 5 * 10	90,000
2	Grape Sales	1,800 * 5 * 10	90,000
3	Grape Sales	1,800 * 5 * 10	90,000
4	Grape Sales	1,800 * 5 * 10	90,000
5	Grape Sales	1,800 * 5 * 10	90,000
5	Sale of Vineyard	90,000*5	450,000

Plan 2. Switching to Syrah Grapes

Year	Particulars	Workings	Amount
0	Cost of Replanting		- 91,000
1	No Income	-	-
2	No Income	-	-
3	No Income	-	-
4	Grape Sales	2500 * 5 * 10	125,000
5	Grape Sales	2500 * 5 * 10	125,000
5	Sale of Vineyard	125,000 * 5	625,000

Step 2: Calculation of NPV

Year	Cash Flow Plan 1	Cash Flow Plan 2	Incremental Cash Flow (Plan 2 - Plan 1)	Present Value Factor @ 12%	Present Value
0	-	-91,000	-91,000	1.000	-91,000.00
1	90,000	-	-90,000	0.892857	-80,357.13
2	90,000	-	-90,000	0.797194	-71,747.46
3	90,000	-	-90,000	0.711780	-64,060.20
4	90,000	125,000	35,000	0.635518	22,243.13
5	540,000	750,000	210,000	0.567427	1,19,159.67
				NPV	-1,65,761.99

note: The cash flow for the 5th year above is the aggregate of income from the sale of grapes for the 5th year and receipt from sale of the vineyard at the end of year 5.

Since the NPV of the switching plan is negative, it is not advised to proceed for switching.