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 50 tons per year. Either way, you plan to sell the vineyard 5 years from today (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 were to switch to Syrah, switching will cost you $111,000 today and the vines won’t produce any grapes until the end of 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 will be positive (years 4 and 5)]

Answer 1

In the given question

Initial cost of switching= $111000

The Cash flows for the foregone sales of merlot sales in Year 1,2&3= 50*1500= 75000/year

Incremental Inflow from extra Syrah sales in 4th year= (2800-1500)*50= 65000

Inflow from extra Syrah sales and extra selling price of farm in 5th year= 65000+ 4*65000=325000

Now we will calculate present values of all cash flow and the sum of these will give the Net present value of incremental cash flows

Present value= Cashflow in the year/(1+r)^n

Where r=9%

n is the year for which cash flow given

The calculations have been given in below table

This gives NPV of incremental cashflows= -43571.76

Year	Parameter	Cash flow	Present value @ 9%
0	Outflow from cost of switching from Merlot to Syrah	-111000	-111000.00
1	Outflow from Foregone Merlot sale	-75000	-68807.34
2	Outflow from Foregone Merlot sale	-75000	-63126.00
3	Outflow from Foregone Merlot sale	-75000	-57913.76
4	Inflow from extra Syrah sales	65000	46047.64
5	Inflow from extra Syrah sales and extra farm selling price	325000	211227.70
NPV incremental cash flows	-43571.76