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 $2000 per ton but Syrah sells for $2400 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 $83,000 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 14% 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

We have an option to switch to Syrah which costs $83,000 immediately at year 0.

At the end of 5 years, we can sell the vineyard at a value of 6 times the value of sales in the year 5.

Also Merlot grapes have sales through the 5 years, but Syrah Grapes are sold only in the 4th and 5th year.

NPV is the sum of discounted cash inflows and cash outflows arising from an investment.

Here we are losing the cash inflows of Merlot(opportunity cost) by switching to Syrah

We are gaining the cash inflows of Syrah.

Incremental Cash flow Pattern and NPV are given as follows :