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 $1500 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 4-times (4x) 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 4 times that amount at the end of year 5). However, if you were to switch to Syrah, switching will cost you $111,000 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 9% 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=111000

For Syrah:
Income in year1-3=0
Income in year 4= 2800 * 50 =140000
Income in year 5= 2800 * 50 =140000
Proceeds from sale of land = 140000*4 = 560000

For Merlot:
Income in year 1-5=1500*50 =75000
Proceeds from sale of land = 75000*4 = 300000

incremental Income per year (4-5) =140000-75000 = 65000

incremental loss per year (1-3) = -75000

  incremental  Proceeds from sale of land = 560000 - 300000 =260000

Year	1	2	3	4	5
Annual cash flow	-75000	-75000	-75000	65000	65000
Proceeds from sale of land					260000
Net Annual cash flow	-75000	-75000	-75000	65000	325000
PV of $1 Factor for 9%	0.9174	0.8417	.0.7722	0.7084	0.6499
Discounted Cash Flow	-68805	-63127.5	-57915	46046	211217.5

Net Discounted Cash Flow = 67416 (-68805+-63127.5+-57915+46046 + 211217.5)

Initial investment = $111000

NPV =Net Discounted Cash Flow - Initial investment

NPV = $67416- $111000

NPV = -43584

The NPV of incremental cashflows from switching is -43584, which means switching is not profitable.