Answer:
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.
