Shivers's annual fuel bill for home heating is 800 dollars per year.He considers three alternative plans for insulating his house.Plan A would reduce his annual fuel bill by 15%, plan B would reduce it by 20%, and plan C would eliminate his need for heating fuel altogether.The plan A insulation job would cost Shivers 800 dollars, plan B would cost him 1,100, dollars, and plan C would cost him 8,800 dollars.If the interest rate is 10% and his house and the insulation job last forever, which plan is the best for Shivers?

Question

Quizplus · Accepted Answer

To calculate the present value of each option, we need to use the formula:

Present Value = Future Value / (1+interest rate)^n

where n is the number of years it will take for the option to break even (i.e. for the savings on the fuel bill to equal the cost of the insulation job).

For Plan A:
Savings = $800 x 15% = $120
Present Value = $120 / (1+0.1)^1 = $109.09
Net Present Value (NPV) = -$800 + $109.09 = -$690.91

For Plan B:
Savings = $800 x 20% = $160
Present Value = $160 / (1+0.1)^1 = $145.45
NPV = -$1100 + $145.45 = -$954.55

For Plan C:
Savings = $800
Present Value = $800 / (1+0.1)^1 = $727.27
NPV = -$8800 + $727.27 = -$8072.73

Since Plan B has the highest NPV (i.e. the smallest loss), it is the best option for Shivers.

Shivers's Annual Fuel Bill for Home Heating Is 800 Dollars