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 $111,000 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

Total production=50 tons per year
Investment=111000

For Syrah:
Income in year1-3=0
Income in year 4= 2800 * 50 =140000
Income in year 5= 2800 * 50 =140000
Proceeds from sale of land = 140000*4
= 560000

So NPV=0/(1.09)^1+0/(1.09)^2+0/(1.09)^3+140000/(1.09)^4+140000/(1.09)^5+560000/(1.09)^5 - 111000
=0+0+0+99220.4+91027.30+364109.232 - 111000
=554356.9 - 111000
=443356.93

For Merlot:
Income inyear 1-5=1500*50
=75000
So Npv=75000/(1.09)...75000/(1.09)^5+75000*4/(1.09)^5
=486703.26

So Switching from Merlot to syrah :
486703.26>443356.93
So NPV gets lower hence Switching is not profitable.