Question

Suppose you own a house and are considering insulating it against the winter cold at a cost of 300,000HlJF. The insulation will save you annually in heating costs (assume that these benefits are received at the end of the year.) In addition. the insulation will increase the resale value of the house by 240,000HlJF. Further, suppose that you plan to sell your house 5 years after the insulation is installed and that if you do not purchase the insulation. the money needed to buy it would remain in a bank paying 4% interest annually. Finally, assume that the monetary values and the interest rate appearing above are all measured in real terms and the annual rate of inflation is 2 percent. Should you invest in the insulation? As part of your answer, provide me with sufficient information so I can tell how you arrived at your decision.

Answer 1

Real rate of return = rate of return - inflation =4-2=2%

If invested in bank value of 300,000 after 5 years = 300,000*(1.02)⁵=331224.241

total increase in house price after insulation = $240,000

Let x be what you save on heating costs at the end of each year

FV of all savings(savings returned at the end of year) =x(1.02) ⁴ +x(1.02)³ +x(1.02)² +x(1.02) = 4.20x

If these savings greater than the difference then you should invest in insulating

4.20x331224.241-240000

x21,719.34

that is if the savings are greater than 21,719 yearly then you should invest in insulating

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