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 $1600 per ton but Syrah sells for $2800 per ton, those prices are expected to remain stable, and you produce 50 tons per year. Either way, you plan to sell the vineyard 5 years from today (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 were to switch to Syrah, switching will cost you $109,000 today and the vines won’t produce any grapes until the end of 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 10% 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 will be positive (years 4 and 5)]

Answer 1

Total production=50 tons per year
Investment=$109000

a. For Syrah:
Income in year 1-3=0
Income in year 4= 2800 * 50 =140000
Income in year 5= 2800 * 50 =140000
Proceeds from sale of land = 140000 * 5 = 700000

Year	1	2	3	4	5
Annual cash flow	0	0	0	140000	140000
Proceeds from sale of land					700000
Net Annual cash flow	0	0	0	140000	840000
PV of $1 Factor for 10%	.909	.826	.751	.683	.621
Discounted Cash Flow	0	0	0	95620	521640

Net Discounted Cash Flow = 617260

Initial investment = $109000

NPV =Net Discounted Cash Flow - Initial investment

NPV = $617260 - $109000

NPV = 508260

b.For Merlot:
Income in year 1-5=1600 * 50 =80000

Proceeds from sale of land = 80000 * 5 = 400000

Year	1	2	3	4	5
Annual cash flow	80000	80000	80000	80000	80000
Proceeds from sale of land					400000
Net Annual cash flow	80000	80000	80000	80000	480000
PV of $1 Factor for 10%	.909	.826	.751	.683	.621
Discounted Cash Flow	72720	66080	60080	54640	298080

Net Discounted Cash Flow = 551600

Initial investment = 0

NPV =Net Discounted Cash Flow - Initial investment

NPV = 551600 - 0

NPV = 551600

if we switch from Merlot to Syrah grapes the NPV will be lower. the NPV before switching is 551600 and NPV after switching is 508260.

therefore NPV became lower by amount 43340 so switching is not profitable.