Question

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?

Answer 1

Answer: Check explanation

Step-by-step explanation:

a. For this scenario, it should be noted that the net benefits for the land lease will be equal to the present value of the benefits that are generated. This will be the annual benefit multiplied by the present value of annuity factor. This will be:

= $110,000 x 13.59

= $1,494,900

From the calculation, we can see that the lease price is less than the present value calculated, this implies that the transaction will incur a profit and should be undertaken.

b. For the growing annuity here, the calculation will be:

= [$110,000/(4% - 2%)] x [1 - [(1 + 2%)/(1 + 4%)]²⁰]

= [$110,000/2%] × [1 - (1 + 0.02)/(1 + 0.04)²⁰]

= $5,500,000 x 0.321833005

= $1,770,081.53

The environmental agency should pay for the piece of land as the present value calculated is higher.

Note that the present value of the annuity factor for 20 years at 4% = 13.59