The environmental protection agency of a county would like to preserve a piece of land as a wilderness area. The current owner has offered to lease the land to the county for 20 years in return for a lump-sum payment of $1.1 million, which would be paid at the beginning of the 20-year period. The agency has estimated that the land would generate $110,000 per year in benefits to hunters, bird watchers, and hikers. Assume that the lease price represents the social opportunity cost of the land and that the appropriate real discount rate is 4 percent.
a. Assuming that the yearly benefits, which are measured in real dollars, accrue at the end of each of the 20 years, calculate the net benefits of leasing the land. Should the environmental protection agency pay for this piece of land?
b. Some analysts in the agency argue that the annual real benefits are likely to grow at a rate of 2 percent per year due to increasing population and county income. Recalculate the net benefits assuming that they are correct. Should the environmental protection agency pay for this piece of land?

a. Assuming that the yearly benefits, which are measured in real dollars, accrue at the end of each of the 20 years, calculate the net benefits of leasing the land. Should the environmental protection agency pay for this piece of land?

the net benefits of leasing the land = the present value of the benefits generated

PV = annual benefit x pv annuity factor

annual benefit = $110,000
pv annuity factor 20 years, 4% = 13.590

PV = $110,000 x 13.59 = $1,494,900

Since the present value of the benefits is higher than the lease price, then this transaction should be carried out.

b. Some analysts in the agency argue that the annual real benefits are likely to grow at a rate of 2 percent per year due to increasing population and county income. Recalculate the net benefits assuming that they are correct. Should the environmental protection agency pay for this piece of land?

this is a growing annuity, therefore we have to use the following formula:

PV = [p / (r - g)] x {1 - [(1 + g)/(1 + r)]ⁿ}

p = $110,000
r = 4%
g = 2%
n = 20

PV = [$110,000 / (4% - 2%)] x {1 - [(1 + 2%)/(1 + 4%)]²⁰} = $5,500,000 x 0.321833005 = $1,770,081.53

Since the present value of the net benefits are even higher now, then the environmental agency should definitely pay.