You are the mayor of the small town of Wasilla and a landowner has offered to se

Question

You are the mayor of the small town of Wasilla and a landowner has offered to sell you 1,000 hectares of woodland for $2,000,000. You are very tempted because of the wildlife which live there (such as moose) as well as the recreational value to your constituents. You look at the Financial TImes and see that if you borrow money for this project, the interest rate will be 5% per annum, and so conclude the discount rate you should use is 5%. Your Parks department estimates that annual recreational and environmental benefits will be $100,000 a year.

a.) Looking only at the next 50 years, is buying the woodland a good idea?

b.) What is the maximum amount you would be willing to pay the landowner to lease the and for 50 years?

c.) How would your answers to (a) and (b) change if the recreational and environmental benefits increase by 3% per year, reflecting the fact that Wasilla is growing, not only in population but in income of the population?

Explanation / Answer

(a) Buying of land would be good idea if the net present value of benefit is at least equalt to or greater than the present value of cost of land.

Net present value of land = 100,000 (1-1.05-50 ) /0.05

= $1,825,592.54

The cost of land is however $2,000,000. The net present cost of land is greater thna the benefits. Hence it is not agood idea to buy the land.

(b) The maxiimum amount that should be paid should be equal to the net presnet value of benefits, i.e. $1,825,592.54.

(c) If the recreation benefits increase by 3 years then the net present value of benefits for 50 years would be:

= 100,000 x[ 1-(1.03/1.05)50 ] / (0.05-0.03)

=$3088535.28

The land shloudl be bought since the pesent value of benefits is greater than cost.

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