**Grade Level:**7-8

**Lesson Overview:** The students will learn how to evaluate energy related purchases in terms of cost effectiveness.

**TEKS:
**

**Math:**7.3 (A, B), 7.13 (B, F), 8.1 (B), 8.12 (F)

**Science:**7.4 (A), 8.4 (A)

**Social Studies:**7.21 (E)

**Time:** 2-3 class periods

**Vocabulary:** simple payback, cost benefit analysis, rate of return, life cycle costing

**Materials:** one copy of Cost Effective Buying per person, energy rating labels from different appliances, calculators

## Background Information:

When we feel compelled to buy a more fashionable garment or a computer, game console, or boat, we do so with satisfaction in the knowledge that the purchase will enrich our lives. We buy labor-saving appliances because they will minimize our work and give us more time for other activities (e.g. leisure).

Consider the motivational factors for purchasing an “energy-saving” heating or cooling system. One might name convenience, dependability, good servicing support, brand name, low first cost, low cost to operate, and estimated future energy/money savings as factors influencing the decision to purchase. That last factor, estimated future energy/money savings, reflects the consumer’s awareness of the rising cost of energy and his or her determination to reduce energy bills, save money, and as a result, save energy as well.

We expect the heating and cooling system to eventually “pay for itself.” We calculate how much time will pass before the monthly savings offset the purchase price. Simple payback is the quotient of the total installed cost divided by the first year’s dollar savings. If tax credits are available, they should be subtracted from the installed cost. The inverse of simple payback is the first year’s rate of return. An example will help clarify this:

You purchase a high efficiency air-conditioner to replace an older model. It costs $360 installed and is estimated to save you $10 each month it operates, or $40 a year. Simple payback is $360 divided by $40/year, or 9 years. Rate of return for first year is ($40/$360) × 100, or 11.1%.

These cost figures enable us to compare one purchase option against another. A more accurate analysis would take into account factors such as interest, tax, and inflation. Interest, for example, is always a factor because, even if we pay cash, we must consider the interest our capital would have earned had it been otherwise invested. Taxes are a factor because the interest we pay on a loan (finance charge) can be an allowable deduction on our income tax return and the interest which we may receive on our capital, otherwise invested, is taxable. Inflation is a factor because it has been with us a long time and because the limited supply of conventional energy resources will rise.

## Setting the Stage:

Ask students about a recent large purchase they or someone in their family made. Ask if it was to replace something that was worn out or just something fun. Ask how much research they put into their purchase.

### Activity 1: Cost Effective Buying

Explain simple payback and rate of return and write the equations on the board or overhead. Hand out the cost effective buying worksheet and work through one of the problems together and then allow the students to work the others.

## Answers:

1. Payback:

Insulation A =1.67 yrs • Insulation B = 2.24 yrs

Rate of Return on Your Investment:

Insulation A = 60 % • Insulation B = 45%

2. Payback:

Water Heater A =17.11 yrs • Water Heater B =9.83 yrs

Rate of Return on Your Investment:

Water Heater A = 6% • Water Heater B = 10%

3. Payback:

Air Conditioner A =14.67 yrs • Air Conditioner B = 12.43 yrs

Rate of Return on Your Investment:

Air Conditioner A = 7% • Air Conditioner B = 8%

### Activity 2: Energy Rating Labels

Collect the energy rating labels from an appliance store for different appliances. Have your students record the initial cost and expected annual savings to compare different models of the same type of appliance (compare refrigerators to refrigerators). Students then find the payback and rate of return for each and decide which to purchase and why.

### Extension:

Based only on operating costs (e.g. ignoring maintenance cost) determine what the payback would be on a new car of your choice.