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 $1600 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 $106,000 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 10% 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

NPV for Option 1 = $1600*50 tonnes=800000 PM

Year 1- 800000*.909 = 7,27,200

Year 2- 800000*.826 = 6,61,090

Year 3- 800000*.751 = 6,00.991

Year 4- 800000*.683 = 5,46,356

Year 5-800000*.621 = 4,96,687

Total 30,32,324

Compounded NPV @ 10% discount Rate = $30,32,324/-

NPV for Option 2 = Outflow $ 1,06,000/- for Year 1 Beginning

Year 4 = 2700*50 = 13,50,000/-*.683 = 9,22,050/-

Year 5 = 13,50,000*.621 = 8,38,350/-

Compounded NPV @ 10% DIscount Rate for Option 2 = $ 16,54,400/-

Incremental Cash Flow for 4th Year : 3,75,694/-

Incremental Cash Flow for 5th Year : 3,41,663/-