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 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 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 switch to Syrah, it will cost you $114,000 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 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 (years 4 and 5) will be positive.]

Answer 1

Initial Cost of Switching = C0 = -$114000

Incremental Cashflows in case of switching year 1,2,3, C1=C2=C3 = -$1500/ton*50 tons = -$75000

Incremental Cashflows in year 4,5 . , C4=C5 = ($2800/ton-$1500/ton)*50 tons = $65000

Incremental Cashflows from sale of plant at end of year 5= 4* incremental income in year 5 = 4*$65000 =$260000

So, NPV = -114000-75000/1.09-75000/1.09^2-75000/1.09^3+65000/1.09^4+65000/1.09^5+260000/1.09^5

= - $46571.76

NPV of switching = - $46571.76