Exercise 2: Discounting Benefits and Costs

Paul is tired of sitting in the freezing Minnesota winter and is considering insulating his home. It would cost him $4,000 this year to insulate, and the estimated reduction in his yearly fuel costs would be $350 per year. The insulation can be installed immediately and will require a maintenance expense of $1,000 exactly 15 years from today. Assume the discount rate is 5%. Paul plans to live in the house until he retires, 30 years from today, at which point he will sell the house and move to someplace warmer. He has already consulted a real estate agent for advice and was told that insulation will not add anything at all to the value of the house when it is sold.

(a) Calculate the present value of net benefits of insulation assuming that the benefits are realized at the end of each year.

(b) Calculate the present value of net benefits of insulation assuming that the benefits are realized at the beginning of each year.

Suppose the real estate agent is wrong, and that insulation does, after all, add to the value of a house when it is sold, adding then the net present value (discounted) of the reduction in fuel costs over all later times (that is, forever). Note that reaping this reward would require paying the maintenance expense of $1,000 every 15 years (starting at the very beginning once sold). The price of Pauls house will be $500,000 in 30 years from today (without insulation).

(c) Calculate what the house will be worth 30 years from today with insulation. Assume the benefits are realized at the end of each year.

(d) What is the net present value of insulating the house today, allowing for both the reduction in costs and increased value of the house when sold? Assume the benefits are realized at the end of each year.