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 $1700 per ton but Syrah sells for $2700 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 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 switch to Syrah, it will cost you $103,000 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 11% 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

		A	B	C = B-A		D	E = C*D
	Year	Cash flow of Merlot	Cash flow of Syrah	Incremental cash flow	1+r	PVIF = 1/1.11^n	PV = incremental cash flow * PVIF
	-	-	-                     103,000.00	-                          103,000.00	1.11	1.0000	-                                                  103,000.00
Income	1	85,000.00	-	-                            85,000.00		0.9009	-                                                     76,576.58
Income	2	85,000.00	-	-                            85,000.00		0.8116	-                                                     68,987.91
Income	3	85,000.00	-	-                            85,000.00		0.7312	-                                                     62,151.27
Income	4	85,000.00	135,000.00	50,000.00		0.6587	32,936.55
Income	5	85,000.00	135,000.00	50,000.00		0.5935	29,672.57
Sale of vineyard	5	425,000.00	675,000.00	250,000.00		0.5935	148,362.83
						NPV	-                                                     99,743.80

Thus the NPV of switching = - $99,743.80

Calculations:

$85,000 = $1700 per ton * 50 tons

$135,000 = $2700 per ton * 50 tons