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 $2600 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 $94,000 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 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 will be positive (years 4 and 5)]

Answer 1

Total production=50 tons per year
Investment= $94000

For Syrah:
Income in year1-3=0
Income in year 4= 2600 * 50 =130000
Income in year 5= 2600 * 50 =130000
Proceeds from sale of land = 130000* 5 = 650,000

For Merlot:
Income in year 1-5=1800 * 50 =90000
Proceeds from sale of land = 90000 * 5 = 450,000

incremental Income year (1-3) =0 - 90000 = -90,000

incremental Income year (4-5) =130,000-90000 = 40000

incremental Proceeds from sale of land = 650,000 – 450,000 =200,000

Year	1	2	3	4	5
Annual cash flow	-90000	-90000	-90000	40000	40000
Proceeds from sale of land					200,000
Net Annual cash flow	-90000	-90000	-90000	40000	240,000
PV of $1 Factor for 12%	0.893	0.797	.0.712	0.636	0.567
Discounted Cash Flow	-80370	-71730	-64080	25440	136080

Net Discounted Cash Flow = -54660 (-80370+-71730+-64080+25440+ 136080.5)

Initial investment = $94000

NPV =Net Discounted Cash Flow - Initial investment

NPV = -$54660 - $94000

NPV = -148660

The NPV of incremental cash flows from switching is -148660, which means switching is not profitable.