Question

During the past year, Stacy McGill planted a new vineyard on 150 acres of land that she leases for \(30,000 a year. She has asked you, as her accountant, to assist her in determining the value of her vineyard operation.

The vineyard will bear no grapes for the first 5 years (1–5). In the next 5 years (6–10), Stacy estimates that the vines will bear grapes that can be sold for \)60,000 each year. For the next 20 years (11–30), she expects the harvest will provide annual revenues of \(110,000. But during the last 10 years (31–40) of the vineyard’s life, she estimates that revenues will decline to \)80,000 per year.

During the first 5 years, the annual cost of pruning, fertilizing, and caring for the vineyard is estimated at \(9,000; during the years of production, 6–40, these costs will rise to \)12,000 per year. The relevant market rate of interest for the entire period is 6%. Assume that all receipts and payments are made at the end of each year.

Instructions Dick Button has offered to buy Stacy’s vineyard business by assuming the 40-year lease. On the basis of the current value of the business, what is the minimum price Stacy should accept?

Short answer

The minimum price Stacy should accept is $291,739.22.

Step-by-step solution

Computation of cashflows

Years	0	1 to 5	6 to 10	11 to 30	31 to 40
Annual revenues		0	60,000	110,000	80,000
Annual cost		-9,000	-12,000	-12,000	-12,000
Annual lease		-30,000	-30,000	-30,000	-30,000
Cashflows		-39,000	18,000	68,000	38,000

Calculation of present value

	0	1 to 5	6 to 10	11 to 30	31 to 40
PV of Cashflow of year 31-40
38,000*7.36009					279,683.42
279,683.42*0.55839	156,172.42
PV of Cashflow of year 11-30
68,000*11.46992				779,954.56
779,954.56*0.31180	243,189.83
PV of Cashflow of year 6-10
18,000*4.21236			75,822.48
75,822.48*0.74726	56,659.11
PV of Cashflow of year 1-5
-39,000*4.21236	-164,282.04
PV of all cash flows	$291,739.22