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 $114,000 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)]

The timeline should look like this:
Year 0: Outflow from cost of switching
Year 1: Outflow from the foregone Merlot sales
Year 2: Outflow from the foregone Merlot sales
Year 3: Outflow from the foregone Merlot sales
Year 4: Inflow from the extra Syrah sales
Year 5: Inflow from the extra Syrah sales and extra farm selling price

Answer 1

Year 0 : Cost of switching today = 114,000

If I have replanted with Syrah :

Income in year1= 0

Income in year2= 0

Income in year3= 0

Income in year 4= 2800 * 50 =140000

Income in year 5= 2800 * 50 =140000

Inflow from selling the land in year 5 = 140000*4 = 560000

The NPV is calculated as below:

year	CF	Pv factor	CF* pv factor
1	0	0.917431	0
2	0	0.84168	0
3	0	0.772183	0
4	140000	0.708425	99179.52955
5	140000	0.649931	90990.39408
5	560000	0.649931	363961.5763
Total	554131.5

NPV from switching = 554131.5 -114000 = $ 440131.5

If I am currently planted to Merlot grapes,

My income from years 1 to 5 = 1500*50 = 75000

Inflow from selling the land in year 5 = 75000*4 = 300000

The timeline showing the incremental annual cash flows from switching is shown below :
Year 0: Outflow from cost of switching = -114000

Year 1: Outflow from the foregone Merlot sales = -75000
Year 2: Outflow from the foregone Merlot sales = -75000
Year 3: Outflow from the foregone Merlot sales = -75000
Year 4: Inflow from the extra Syrah sales = 140000-75000 = 65000
Year 5: Inflow from the extra Syrah sales and extra farm selling price = (140000 + 560000)-(75000+ 300000) = 325000

The NPV is calculated as below:

year	CF	Pv factor	CF* pv factor
1	-75000	0.917431193	-68807.33945
2	-75000	0.841679993	-63125.99949
3	-75000	0.77218348	-57913.761
4	65000	0.708425211	46047.63872
5	325000	0.649931386	211227.7005
Total	67428.23932

NPV= 67428.23932 -114000 = $ -46571.76

Since its value is negative, switching to Syrah is not profitable