Chillingsworth owns a large, poorly insulated home. His annual fuel bill for home heating averages $300 per year. An insulation contractor suggests to him the following options.
Plan A. Insulate just the attic. If he does this, he will permanently reduce his fuel consumption by 15%. Total cost of insulating the attic is $300.
Plan B. Insulate the attic and the walls. If he does this, he will permanently reduce his fuel consumption by 20%. Total cost of insulating the attic and the walls is $500.
Plan C. Insulate the attic and the walls, and install a solar heating unit. If he does this, he will permanently reduce his fuel costs to zero. Total cost of this option is $7,000 for the solar heater and $500 for the insulating
(a) Assume for simplicity of calculations that the house and the insulation will last forever. Calculate the present value of the dollars saved on fuel from each of the three options if the interest rate is 10%. The present values are: Plan A? ______. Plan B? _____. Plan C? ________.
(b) Each plan requires an expenditure of money to undertake. The difference between the present value and the present cost of each plan is: Plan A? _________. Plan B? _________. Plan C? _________.
(c) If the price of fuel is expected to remain constant, which option should he choose if he can borrow and lend at an annual interest rate of 10%?
(d) Which option should he choose if he can borrow and lend at an annual rate of 5%?
(e) Suppose that the government offers to pay half of the cost of any insulation or solar heating device. Which option would he now choose at interest rates 10%? ____. 5%? ____.
(f) Suppose that there is no government subsidy but that fuel prices are expected to rise by 5% per year. What is the present value of fuel savings from each of the three proposals if interest rates are 10%? (Hint: If a stream of income is growing at x% and being discounted at y%, its present value should be the same as that of a constant stream of income discounted at (y − x) %.) Plan A? ______. Plan B? ______. Plan C? ______. Which proposal should Chillingsworth choose if interest rates are 10%? ______. 5%? ______.