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 $1400 per ton but Syrah sells for $2900 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 $117,000 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 8% 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 This question the NPV for switching can be solved by 2 methods

Method 1- By calculating the NPV of cash flows for both types of grapes separately and then subtracting them

Method 2 - By calculating Incremental cashflow of Syrah over Merlot for each other and then calculating the NPV for incremental cashflows

Now we can calculate cash flows for merlot grapes in the following way

Initial investment= 0

Year 1 = $1400*50= $70000

Year 2 = $1400*50= $70000

Year 3 = $1400*50= $70000

Year 4 = $1400*50= $70000

Year 5 = $1400*50+ 4($1400*5)= $70000= $350000

Similarly we will find out cashflow for Syrah grapes but in this case Initial investment = $117000

Therefore the NPV is calculated as given in below table

Method 1							Method 2
Merlot Grapes				Syrah Grapes			Incremental cash flow= (a)-(b)	NPV of incremental cash flow
Year	Cash flow(a)	Present value of cashflow	Year	Cash flow(b)	Present value of cashflow
0	0	0.00	0	-117000	-117000.00		-117000.00	-117000.00
1	70000	64814.81	1	0	0.00		-70000.00	-64814.81
2	70000	60013.72	2	0	0.00		-70000.00	-60013.72
3	70000	55568.26	3	0	0.00		-70000.00	-55568.26
4	70000	51452.09	4	145000	106579.33		75000.00	55127.24
5	350000	238204.12	5	725000	493422.82		375000.00	255218.70
NPV Merlot		470053.00	NPV Syrah		483002.15
		NPV switching = NPV Syrah-NPV merlot	12949.15				NPV Switching	12949.15

So as we can see from the table, in both methods the switching NPV=$12949.15