Problem

During the past year, Pearl McGill planted a new vineyard on 150 acres of land that she leases for $30,650 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), Pearl estimates that the vines will bear grapes that can be sold for $61,720 each year. For the next 20 years (11-30), she expects the harvest will provide annual revenues of $110,680. But during the last 10 years (31-40) of the vineyard's life, she estimates that revenues will decline to $83,770 per year.

During the first 5 years, the annual cost of pruning, fertilizing, and caring for the vineyard is estimated at $9,750; during the years of production, 6-40, these costs will rise to $11,690 per year. The relevant market rate of interest for the entire period is 5%. Assume that all receipts and payments are made at the end of each year.

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