Lately I've talked about some home improvements that can help save energy costs. I installed compact fluorescent lights, I bought a programmable thermostat, I installed a water saving device on my shower, I use an electric mower and I've bought a smart power strip. Each of these purchases help save energy costs and give me an ongoing return through lower electricity bills. But they also cost money to buy in the first place. So how exactly do I tell if the energy savings of an item is worth the cost of purchasing it?

I would evaluate energy saving purchases in two ways. First you can look at the annual return rate and payback period. Second you can calculate an estimated rate of return on the investment.

Figuring a Payback Period

This is the simpler method. Basically all you do is figure out how many years it will take to recoup your initial investment. To do this you divide the initial cost by the annual savings. For example if you could spend $150 today to save $50 a year then you can divide the cost by the annual savings or 150 / 50 = 3 years.

Payback period = initial costs / annual savings.

If your payback period is 1-3 years then thats probably a good buy. Payback period can be pretty useful if you're comparing the purchase of multiple alternatives.

Lets look at some examples:

I discussed previously that buying compact fluorescent lamps for my home is saving me about $61 a year. I paid $50-100 for those initially. If we assume the higher cost of $100 then the payback period is: initial cost / savings = 100 / 61 = 1.6 years payback period.

I also bought a shower attachment for $30 that I figure is saving me $20 a year. For that purchase the payback period is = initial cost / savings = $30 / $20 = 1.5 years payback period.

If I compare these two purchases the shower attachment is marginally better with a payback period of 1.5 versus 1.6 for the CFLs. So if I had just $30 to spend then I'd be a little better off putting it into the shower attachment.

Estimating the Annual Rate of Return

For larger purchases that have a longer payback period it might make more sense to look at the annual return rate over the life of the purchase. Buying a large improvement such as a new efficient furnace or a solar array is essentially an investment so you should figure the rate of return on that investment and compare it to other investments.

TO figure what an improvement returns as an investment you have to look at what it will net you financially. Basically with an energy saving improvement you have an item you're buying for a certain amount today which will then give a fixed annual return for a number of years. For example I might pay $150 for an improvement which then saves me $50 a year in electricity and lasts 5 years. If I just took that $50 each year and sat on it at 0% interest then I'd accumulate $250 in a 5 year period. So my $150 investment turned into $250 over 5 years. We can use the formula for compound annual growth rate (CAGR) to figure the rate of return. The formula for CAGR is:

% return = ( (FV / PV ) ^ (1 / # years ) ) -1

For the example that works out to ( ( 250/150 ) ^ (1/5) ) -1 = (1.66)^.2 -1 = 1.107 - 1 = 10.7%

You then have to compare that to what else you could have done with the money. If I had $150 in the bank right now I could easily throw it into my high yield savings account and make 3.5% interest.

For this example paying that $150 will end up netting me a 10% return over 5 years. Thats a good return rate compared to 3.5%.

As a general process for figuring the rate of return on an energy saving investment:

First of all I determine the annual energy savings of the item. This depends on the item you are buying. Hopefully there is enough information on the type of improvement that you can figure the savings. If you are buying an appliance you can compare the energy guide documentation which will tell you the annual energy usage of the item.

Second I determine a lifetime for the item. The lifetime of the item will depend on the nature of the item. I basically take an educated guess to estimate the lifetime roughly based on how long I would expect the item to last. A small item I might figure a life of 5 years. For a large appliance I'd pick a 10 year lifetime. If the item is a major improvement such as a new furnace or something like a solar panel then I might go with 20 years.

Then you simply run the CAGR calculation using a future value of the annual savings * lifetime of the item.

That gives us an equation of:

expected % return = (( annual savings * lifetime in years / cost ) ^ ( 1/lifetime in years) ) -1

If you are not certain on the values then you should run the equations for the minimum and maximum estimates so that you can get a range. For example if you think the item might last 10-20 years then run the equation for 10 years and again for 20 years.

Note that I'm making a couple assumptions in order to simplify the calculation. I'm assuming that the item I buy is not going to retain any costs. In other words I assume it depreciates completely. Basically I figure if I buy a new fridge then over a number of years that fridge will wear out and basically be worthless at the end of its life. The other assumption I'm making is that there is no difference in tax impact from the item. This isn't true exactly but it makes the calculation and comparison simpler.

Lets look at a couple examples:

Example #1 buying a heat pump:

I'm considering buying a new heat pump furnace. For example purposes let say the heat pump costs $5000 to buy and have installed and that I will save around $300 to $500 a year in energy costs. I also figure the heat pump should last me about 10 years minimum.

Given the formula:

expected % return = (( annual savings * lifetime in years / cost ) ^ ( 1/lifetime in years) ) -1

We plug in the numbers for the minimum case to get:

return = (( $300 * 10 / $5000) ^ ( 1/10) ) -1

= .6 ^ .1 -1 = .95 - 1 = - 5%

And the maximum case is :

return = (( $500 * 10 / $5000) ^ ( 1/10 ) ) -1

= 1 ^ .1 - 1 = 0%

So for this example I'd be facing a -5% to 0% return on my money.

The choice of a 10 year lifetime was pretty conservative and its possible the heat pump might last 20 years.

If I figured a $300 annual savings for 20 years then it would be :

(( $300 * 20 / $5000) ^ ( 1/20) -1 = 1.2 ^ .05 - 1 = 0.91%

or at the $500 annual savings over 20 years is :

(( $500 * 20 / $5000) ^ ( 1/20 ) -1 = 2^.05 -1 = 3.5%

Therefore overall if we buy a furnace for $5000 and expect it to give an annual energy savings of $300 to $500 and the furnace will last 10 to 20 years then our expected rate of return on the investment is -5% to 3.5%. I can get 3.75% right now in a CD so this isn't a good investment.

## September 5, 2008

### How to evaluate the return of energy saving home improvements.

Labels:
energy savings,
math,
ROI

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