Question

A home construction company offers to sell you energy efficient windows for your home. They claim that the new windows will save you 15% on your electricity bill each year for the next 50 years (which is the life of the windows). For ease of calculation, let's just say that you pay your electric bill at the end of each year and your bill at the end of the first year is $1800. Your electricity savings would then be $1800 * 0.15= $270 for the first year.

Let's also assume that electric bill increases by 3% each year, which means that your savings also increase by 3% each year. For example, your savings for two year would be $270 * (1.03)= $278.10 . The savings for subsequent years are calculated similarly.

For a limited time only, they are offering to install the windows at a cost of only $4000.

Assume that 12% is proper rate to use for evaluating this deal.

Calculate PV of the savings and compare it to the total cost to purchase and decide if it would be financially wise to invest in the new windows for your home. What would be the correct decision?

**Show work please, and calculations, step by step**

Answer 1

Savings for first year=R=$270

Growth rate in savings=g=3%

Time period=n=50 years

Discount rate=i=12%=0.12

It is a case of growing annuity with constant rate.

(1+gn PV (Savings) = 2 i-g"T * 1– (1+i)n)

PV (Savings) = 270 0.12 -0.031 10 -* 11- (1 + 0.03) 50 (1 +0.12)50)]

PV (Savings) = 3000 * 0.98483089 = 2954.49

We can see that PV(Savings) is less than the cost ($4000). So, it is not financially wise to invest in new windows.