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 $1900 per ton but Syrah sells for $2500 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 6-times (6x) 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 6 times that amount at the end of year 5). However, if you switch to Syrah, it will cost you $89,000 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 13% 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

Incremental Cash flow in year 0 = - Initial investment = - 89000

For year 1 to 3, there will be no sales of Syrah Grapes ,

Revenue per year of Syrah Grapes from year 1 to 3 = 0

Revenue per year of Syrah Grapes from year 4 to year 5 = Total ton of grapes sold per year x price per ton = 50 x 2500 = 125000

Revenue per year of Merlot grapes from year 1 to 5 = Total ton of grapes sold per year x price per ton = 50 x 1900 = 95000

Incremental cash flow from sale of Vineyard in year 5 = 6 x Revenue from Syrah Grapes in year 5 - 6 x Revenue from Merlot Grapes in year 5 = 6 x 125000 - 6 x 95000 = 750000 - 570000 = 180000

Incremental cash flow per year from year 1 to 3 = Incremental sales revenue = Sales from Syrah Grapes - Sales from Merlot grapes = 0 - 95000 = -95000

Incremental Cash flow in year in year 4 = Incremental sales revenue = Sales from Syrah Grapes - Sales from Merlot grapes 125000 - 95000 = 30000

Incremental cash flow in year 5 = incremental sales revenue + Incremental cash flow from sale of Vineyard in year 5 = (Sales from Syrah Grapes - Sales from Merlot grapes) + Incremental cash flow from sale of Vineyard in year 5 = (125000 - 95000) + 180000 = 30000 + 180000 = 210000

Hence we get following incremental cash flow from switching

Incremental Cash Flow from Switching
Year	0	1	2	3	4	5
Incremental Cash flow	-89000	-95000	-95000	-95000	30000	210000

NPV of Switching = Incremental Cash flow in year 0 + Sum of present value of incremental cash from year 1 to year 5 discounted at 13% = -89000 - 95000/(1+13%)¹ - 95000/(1+13%)² - 95000/(1+13%)³ + 30000/(1+13%)⁴ + 210000/(1+13%)⁵ = -89000 - 84070.7964 - 74398.9349 - 65839.7654 + 18399.5618 + 113979.5865 = -180930.3484 = -180930.35 (rounded to nearest cent)

Hence NPV of Switching = -180930.35