Payback Calculations for Energy-Efficiency Improvements
How to perform a simple payback analysis and calculate net present value
If you are considering investing in an energy-efficiency improvement for your home — for example, additional attic insulation or a photovoltaic(PV) Generation of electricity directly from sunlight. A photovoltaic cell has no moving parts; electrons are energized by sunlight and result in current flow. system — you probably expect the investment will lower your energy bills. So it’s only natural to ask, “Is this a good investment?”
For example, let’s say that you are considering spending $5,000 on an improvement that will save you $350 a year on your energy bills. Does the investment make economic sense? The answer, of course, is “it depends.” Among the factors affecting such a decision:
- How soon do you expect to move? Most people are more likely to invest in home energy improvements if they plan to stay in their house for a long time.
- Will the improvement increase the value of your home?
- Do you expect energy costs to rise in the future? If the cost of energy rises quickly, home energy improvements will prove to be a better investment than if energy costs stay flat.
- Can you finance the work with a low-interest loan? The lower your borrowing costs, the better the investment.
- What is the expected lifetime of the measure you are contemplating? A long-lived measure like attic insulation is likely to be a better investment than the purchase of short-lived equipment like a new water heater.
- Will there be any maintenance costs associated with the energy improvement?
- Do you value the environmental benefits associated with reduced energy use, even if the cost of achieving that goal is high?
- Do you value the peace of mind that comes from lower energy bills?
- Do you value the comfort improvements that may accompany some energy-efficiency improvements?
Some of the items on this list — for example, the interest rate on a loan — are quantifiable. Others — for example, the rate of energy cost inflation — can only be estimated. And some — for example, how much one values having a reduced carbon footprintAmount of carbon dioxide and other greenhouse gases that a person, community, industry, or other entity contributes to the atmosphere through energy use, transportation, and other means. — can’t be quantified at all.
Sick and tired of payback questions
There are so many variables in this list, in fact, that some home performance contractors and solar equipment installers are sick and tired of hearing payback questions. The usual reaction from the sick-and-tired crowd is, “Nobody ever asks what the payback period is for a granite countertop or an SUV!”
(Where would we be without granite countertops? They’re such handy devices for making almost any argument…)
However, I’ve noticed that the people who make this speech are usually people who sell home improvements with a very long payback. You never hear CFLCompact fluorescent lamp. Fluorescent lightbulb in which the tube is folded or twisted into a spiral to concentrate the light output. CFLs are typically three to four times as efficient as incandescent lightbulbs, and last eight to ten times as long. CFLs combine the efficiency of fluorescent light with the convenience of an Edison or screw-in base, and new types have been developed that better mimic the light quality of incandescents. Not all CFLs can be dimmed, and frequent on-off cycling can shorten their life. Concerns have been raised over the mercury content of CFLs, and though they have been deemed safe, proper recycling and disposal is encouraged. manufacturers make the same speech.
Let’s face it: payback matters. It isn’t the only factor in making home improvement decisions — other factors are important, including improved comfort and a smaller carbon footprint — but it’s an important one.
So now we come to the question: How should we calculate payback?
There are many ways to perform these calculations
If you start diving into the world of payback calculations, you quickly learn that there are many ways to perform such an analysis. Among the terms you are likely to encounter:
- Simple payback
- Cash flow analysis
- Net present value
- Internal rate of return
- Return on investment
If you’re an accountant, all of these terms are familiar to you. If you’re like me, however, you may need to study up a little before these terms become clear.
Simple payback analysis
Let’s go back to our original example: you are considering a $5,000 improvement that will save $350 a year on your energy bills. To calculate the simple payback period, just divide the cost of the work by the annual savings to find the payback period in years. In this example, 5000 ÷ 350 = 14.3, so the improvement has a simple payback period of 14.3 years. In a little over 14 years, you will “break even.” If the improvement lasts longer than 14.3 years, then all subsequent savings are gravy.
The main advantage of a simple payback calculation is that it is simple. It may not consider a variety of factors — for example, maintenance costs or energy cost inflation — but it’s quick and easy to understand. And it’s even arguable that, considering the fact that many of the factors it ignores can’t be determined precisely anyway, such a calculation may be accurate enough for many routine decisions we make.
Cash flow analysis
If you are borrowing the money to pay for the home improvements, a cash flow analysis probably makes more sense than a simple payback analysis. For example, let’s say that the $5,000 measure is being rolled into a new home mortgage. Since you know your mortgage interest rate and term, it’s fairly easy to calculate the annual cost to borrow $5,000. (One easy way to do this is with an online mortgage calculator.) If it’s a 20-year mortgage at 6% interest, the cost to borrow $5,000 is $35.82 per month, or $430 per year. If the $5,000 improvement saves you only $350 per year on your energy bill, then borrowing money to pay for the improvement doesn’t work out on a cash-flow basis.
But if the $5,000 improvement saves you at least $431 a year on your energy bills, then the improvement is “cash flow positive” from Day One. If the cost of energy increases, your cash flow position improves.
Integrating inflation considerations into a cash flow analysis
The cash flow example I provided is fairly simple, but a cash flow analysis can account for more factors than I included. For example, if you are considering the purchase of a solar hot water system, it would be wise to budget for system maintenance. Maintenance costs are a negative cash flow, just like a mortgage payment.
It’s also possible to include inflation assumptions in a cash flow analysis. Let’s assume that a homeowner borrows $5,000 to install a solar hot water system that saves $350 on energy bills during the first year of operation. The homeowner wants to budget $50 per year for system maintenance, and assumes that maintenance costs will rise at the rate of 3% per year.
Let's also assume that this homeowner wants to account for energy cost inflation. Of course, the future cost of energy is hard to predict. Building scientist John Straube has argued that the cost of energy has increased 8% per year in recent decades — a rate that is higher than the underlying rate of inflation. However, this conclusion depends on your time frame; from 1981 to 2009, for example, energy cost inflation was actually lower than the general rate of inflation.
In this example, we'll assume that energy cost inflation is 7% per year. What would a cash flow analysis look like over the next 20 years? One way to answer this question is to create a table that breaks down cash expenses and savings by year. (If you create this table on a spreadsheet program, you’ll save yourself a lot of data entry.)
Table 1 - Cash flow analysis assuming 7% energy cost inflation
This investment begins generating a positive cash flow in Year 6, and continues to generate a positive cash flow through the end of Year 20. If we total all of the annual cash flow amounts, we discover that after 20 years, the homeowner has saved $4,405. So far, so good.
However, let’s perform the same exercise with a different assumption. What if the cost of energy only increases at a rate of 3% a year instead of 7% a year?
Table 2 - Cash flow analysis assuming 3% energy cost inflation
In this case, even though this investment is cash flow positive in Year 14 and subsequent years, the outlays are greater than the credits. If we total all of the annual cash flow amounts, we discover that after 20 years, the homeowners have shelled out $539 more than they saved.
These two different results — one showing an investment that yields $4,405 in savings, and another showing an investment that results in a loss of $539 — demonstrate how our conclusions about payback depend heavily on our assumptions.
Or, as a cynic might say, all you have to do is tweak your assumptions, and you can prove any conclusion you want.
Net present value
Alert readers will note a problem with both methods of analysis introduced so far: they fail to account fully for the fact that the value of money changes with time. If we total all of the positive and negative cash flows in the last column of our table, the calculation assumes that $100 in Year 2 has the same value as $100 in Year 19. Of course, it doesn’t; because of inflation (or, to put it another way, to account for the opportunity cost incurred by spending money on an energy improvement instead of on a potentially more profitable investment), money held today is worth more than the same amount in the future.
If we go back to Table 2, we see energy savings of $371 in Year 3. For a homeowner who might earns 4% interest on a certificate of deposit, the present value of $371 received in three years is only $330 in today’s dollars.
To compare cash flows that occur in different years, we need to discount the cash flows in future years to calculate the present value of these cash flows. This is the first step in performing a net present value analysis. We use a “discount rate” to perform the calculation; a discount calculation is simply the reverse of an interest rate calculation. (In the previous paragraph, I assumed a discount rate of 4%. The cash flow of $371 three years from now must be discounted to determine its present value of $330.)
Once all of the anticipated cash flows over the life of an energy improvement measure have been discounted, we can add them all up and determine the net present value of the proposed improvement. (In other words, net present value is defined as the sum of the discounted net cash flows.)
If an energy-efficiency improvement is expected to last 20 years, we would calculate the net cash flow for each year; then we would discount each amount to determine its present value. Finally, the column of figures can be added up to determine the net present value of the proposed improvement. If the net present value is greater than zero, the proposed investment would be considered profitable. (These calculations are made easier if you use an online calculator.)
Here is the formula to determine net present value (NPV), assuming that r is the discount rate, and n is the number of years under consideration:
When the numbers from Table 2 are entered into a net present value calculator, we learn that the net present value of the project is -$595, which is a lower value than the -$539 total that we obtained by simply adding up the cash flows without discounting them. The reason for the difference is that the present value of the positive cash flows in Year 14 (and subsequent years) is less than the dollar value of the cash flow in Year 14.
One problem with net present value calculations is that we don’t really know what the discount rate should be over time, since it’s hard to anticipate future inflation or future interest rates. Like many other factors under consideration, including energy cost inflation, the discount rate is basically a guess.
Internal rate of return and return on investment
If you love accounting, you can calculate the internal rate of return of a proposed energy improvement, using the net present value formula provided above. The internal rate of return is simply the discount rate (r in the formula) when the net present value is equal to zero.
It's also possible to calculate the return on investment for your proposed energy improvement. To do this you need to calculate your annual net cash flow, which is the sum of the present values of the anticipated cash flows divided by the number of years under consideration. The return on investment (ROI) formula is:
ROI = (annual net cash flow) ÷ (capital cost)
Once you know the internal rate of return or the return on investment for a proposed energy improvement, you could presumably compare the investment with a more conventional investment vehicle — for example, an investment in U.S. government bonds. However, note the following important distinction: if you invest $5,000 in a solar hot water system, the equipment will wear out in 20 years and be carted off to the dump. On the other hand, if your money is invested in a government bond, you might earn 2% interest per year — and you’ll still have the $5,000 of capital at the end of 20 years.
The bottom line
I’m glad that accountants have given us tools to perform a cash flow analysis and to calculate the net present value of a proposed investment. Because these calculations have been made, energy experts can advise homeowners that it always makes sense to swap their incandescent bulbs for CFLs, while window replacement doesn’t make financial sense.
Every few years, it’s important to take a fresh look at these calculations. As Jesse Thompson pointed out in his recent guest blog, falling prices for photovoltaic modules mean that investing in a PV system makes a lot of sense in areas with high electricity costs. Just two years ago, however, it was hard to make the same statement.
Many energy-efficiency measures — for example, installing exterior rigid foam on an existing house — are hard to justify using any economic analysis. But that doesn’t necessarily mean that they aren’t worth considering. Remember, all of these cash flow and net present value calculations include a great many unknowns, most notably our assumptions about energy cost inflation. Whenever we’re making a prediction about future prices, it makes sense to be humble.
On the other hand, many energy-efficiency advocates are overly optimistic in their cash flow predictions. For example, techno-nerds often underestimate maintenance costs and overestimate equipment lifetime — for example, in cash flow predictions for ground-source heat pumps or solar hot water systems. If you are hoping to save $350 a year on your energy bills, a single service call to repair a broken pump can wipe out one or two years of anticipated savings.
Determining the real cost of energy
The exercises presented in this article show how different assumptions about the future cost of energy produce widely differing conclusions about payback. From the perspective of an environmentalist, however, trying to guess the future cost of energy is an irrelevant exercise.
Since the continued burning of fossil fuels at current rates is likely to lead to catastrophic environmental disruptions whose effects could linger for thousands of years, it's fundamentally impossible to choose an appropriate price for fossil fuel. Seen from this perspective, efforts to reduce our use of fossil fuels is a moral imperative, and the actual payback periods for energy efficiency measures are irrelevant.
We still need to make some simple calculations, however, so that we invest our money wisely. Efforts to reduce energy use should always start with the low-hanging fruit. To determine which fruit hangs lowest, it turns out that simple payback calculations are accurate enough for our purposes.
So, here's my advice: sharpen your pencil if you want to, but in the long run, you really don't need a fine point. You can forget the exponents; fourth-grade long division is all you need.
Last week’s blog: “The Third Annual Christmas Parody.”
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