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

Please see the table below for the timeline showing the incremental annual cash flows from switching . Please be guided by the second column titled “Linkage” to understand the mathematics. The last row shows the incremental annual cash flows from switching . Figures in parenthesis, if any, mean negative values. All financials are in $.

Year, n	Linkage	0	1	2	3	4	5
Cash flows in case of Merlot Grapes
From Sale of grapes	A = 50 x 1,500		75,000	75,000	75,000	75,000	75,000
From sale of business	B = 4 x A						300,000
Total cash flows	C = A + B		75,000	75,000	75,000	75,000	375,000
Cash flows in case of Merlot Grapes
From Sale of grapes	D = 50 x 2,800		-	-	-	140,000	140,000
From sale of business	E = 4 x D						560,000
Initial investment	F	(111,000)
Total cash flows	G = D + E + F	(111,000)	-	-	-	140,000	700,000
Incremental cash flows	G - C	(111,000)	(75,000)	(75,000)	(75,000)	65,000	325,000

Hence, the NPV of switching = -C0 + PV of all the future cash flows = -111,000 - 75,000 / (1 + 9%) - 75,000 / (1 + 9%)2 - 75,000 / (1 + 9%)3 + 65,000 / (1 + 9%)4 + 325,000 / (1 + 9%)5 = - $ 43,571.76