Question

Many decisions are made on the basis of the payback period: the time it will take through savings to equal the capital cost of an investment. Acceptable payback times depend upon the business or philosophy one has. (For some industries, a payback period is as small as 2 years.) Suppose you wish to install the extra insulation in the preceding problem. If energy cost $1.00 per million joules and the insulation was $4.00 per square meter, then calculate the simple payback time. Take the average ΔT for the 120-day heating season to be 15.0°C.

a) 2.5 years

b) 3.0 years

c) 4.0 years

d) 5.0 years

Answer 1

The simple payback time for the insulation investment is approximately 2.6 years, calculated by dividing the cost of insulation ($600) by the annual energy savings ($235). The correct answer is a) 2.5 years.

Step-by-step explanation:

The question is asking to calculate the simple payback time for the installation of extra insulation, given the energy savings and cost of insulation. The preceding problem provided us with a total heat loss during the 120-day heating season and an associated cost for the energy needed to compensate for this loss.

The savings from the insulation is a percentage of this cost per year, and by dividing the cost of insulation by the annual savings, we obtain the payback time.

Using the information provided, we found that the baseline energy use during the 120-day heating season, with an average temperature difference (ΔT) of 15.0°C, results in a total heat loss of 1960 x 106 joules. The cost to offset this heat loss at $1.00 per million joules would be $1960.

The yearly savings from the extra insulation is 12% of that cost, which equates to $235. If the attic requires 150 m² of insulation at $4.00 per m², the total cost for the insulation is $600. Therefore, the payback period is calculated as $600 divided by the annual savings of $235, resulting in approximately 2.6 years.