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 $2000 per ton but Syrah sells for $2400 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 6-times (6x) 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 6 times that amount at the end of year 5). However, if you switch to Syrah, it will cost you $80,000 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 14% 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

Cash flows
Without switching
Year	0	1	2	3	4	5
Income		100000	100000	100000	100000	100000
Cash from selling						600000
Total	0	100000	100000	100000	100000	700000
With switching
Year	0	1	2	3	4	5
Expense upfront	-80000
Income					120000	120000
Cash from selling						720000
Total	-80000	0	0	0	120000	840000
Incremental cash flow from switching
Inc. cash flow	-80000	-100000	-100000	-100000	20000	140000
PV @ 14%	-80000.00	-87719.30	-76946.75	-67497.15	11841.61	72711.61
NPV	-227609.98
Since NPV is negative, it does not make sense to switch