**Simple Payback**

Many people ask about the payback period of a photovoltaic solar system; the total installed cost divided by the annual savings produced from electricity generation.

If an 8kW system were to cost $10,000 after state and federal tax credits and generate $1000 of electricity annually, the simple payback is $10,000 divided by $1000/year, or 10 years. Though an easy calculation to perform, this metric has three significant shortcomings:

First, payback periods do not illustrate a project’s long term profitability, but focus only on how quickly the project delivers a return on investment. With this measure, a solar project’s key benefit – its ability to offset electricity derived from conventional fuels over its entire useful life – will be lost; a system with a useful life of only ten years could be seen as economical as one with the more typical 30 year life. Secondly, simple payback periods do not account for the time value of money – the effects of inflation. Thirdly, simple payback does not recognize the likely increase in purchased power costs over time, which can be significant given the expected life of a photovoltaic solar energy system.

**Accounting Rate of Return (ARR)**

Another way to look at the cost of a photovoltaic solar energy system is to ask the question:

"If, instead of buying a photovoltaic solar energy system, I put the same amount of money into an investment, what return would I have to receive in order to buy the electricity the solar electric system would have provided.......?"

The rate of this return is called the Annual Rate of Return, or ARR, and is another easy way to evaluate an investment in solar energy – but one which allows the comparison between that investment and an investment in stocks, bonds or Certificates of Deposit is the return on investment; the income (or utility bill savings) generated by the system divided by the system cost.

Let's again suppose that that an 8 kW system costs $20,000 after tax credits and generates $1000 in savings the first year. The return on that $20,000 investment is 5%. Let's compare that to recent returns of several other available investments:

This method indicates that this 8 kW solar energy system, after tax credits, has approximately the same ARR as that of tax free municipal bonds – and approachesthat of stocks, with far less volatility or risk. Additionally, taxable investments like most stocks will require a higher rate of return to be comparable to the tax-free savings generated from eliminating utility payments.

Although this method accounts for savings beyond the payback period, it still doesn't account for the time value of money – the effects of inflation that reduces the value of future savings, – nor does it account for future utility rate increases.

**Net Present Value (NPV)**

Given the limitations of simple payback and ARR, the economic viability of solar energy projects should not be measured by either method alone. A "net present value" analysis should be the primary means by which these projects are evaluated, with simple payback period or accounting rate of return used to provide additional information. For solar photovoltaic systems net present value is simply today's value of all future monthly electricity savings generated by the system minus the total cost of installing and maintaining the system. The result is the value – or cost – in today's dollars of deciding to install a photovoltaic system.

where *R _{0}* is the total installed cost,

*i*is the discount rate or annual rate of return that could be earned on an investment in the financial markets with similar risk,

*R*is the savings generated in year

_{t}*t,*and

*N*is the total number of years in the evaluation. We will define N to be 30 years – a reasonable assumption of the expected life of a quality photovoltaic solar energy system.

Let's look at actual usage from a typical suburban home, rather than estimates as we did above. We requested two years of usage data from Rocky Mountain Power and calculated its cost using RMP's Utah Price Summary. Our example home uses, on average, 1,100 kilowatt-hours (kWh) per month, or a "daily AC load" of about 36.2 kWh per day. If our example homeowner were to stop purchasing power from Rocky Mountain Power he would generate a stream of savings of approximately $941 per year, assuming that electricity rates won't go up over the next 30 years. $941 is what we will use for *R _{t}* for all years

*.*If we were to expect utility company rates to increase over the thirty years we would want to increase

*R*by the expected annual increase. For this simplified example we will make the very conservative assumption that rates will not increase over the thirty years.

_{t}If we were to eliminate our purchased power completely we would need to generate 36.2 kilowatt hours, on average, every day. To do that in Salt Lake City, you would need to install about 8.0 kW of photovoltaic equipment. At the current installed price of about $4 per watt, a system of that size would cost about $32,000 which, after federal and state tax credits, is a net cost of $20,400.. While that may seem like a lot, remember that you are prepaying for your next 30 years of electricity.

If we were to compare the economics of installing a photovoltaic system to an investment of similar risk, perhaps a 5 year Certificate of Deposit that carries a yield of 0.84% per year, we would use 0.84% as the discount rate *i*. The value of our savings, in today's dollars, will be a 0.84% less each year. (Remember, we are assuming power company rates won't increase. If they do, the savings will be the annual percentage increase less 0.84%.) Totaling up that 30-year stream of discounted savings and subtracting the initial cost of the system gives a Net Present Value of $4,671. That is the value of deciding to install this 8 kW system instead of investing in a Certificate of Deposit.

Obviously, borrowing money to install a photovoltaic system will be less economical. But how much less? The net present value of a system financed through a home equity loan can be determined by using the annual percentage rate of the loan as the discount rate. As this is written, home equity loans in Salt Lake City can be obtained for 4.0%, so we will use that as the discount rate. Because the value of the stream of savings now decreases by 4% each year, the present value of this stream would be less. When the initial investment is subtracted the Net Present Value becomes negative, at -$3,477. This is the cost of the decision to install an 8kW system in today's dollars.

But electricity rates are expected to climb by up to 6% annually through 2017, and likely beyond. That is higher than the expected overall inflation rate of 3%. With 6% annual increases in rates, the $941 first year savings will grow to $5,098 per year for this power, but then, with 3% annual inflation, that $5,098 thirty years from now will be worth only $2,163 in today's dollars. (Because solar modules degrade in efficiency about 0.6% per year, the actual savings will be slightly less; $4,324 in future dollars, which is worth only $1,835 in today's dollars. As Yogi Berra said of inflation, "A nickel ain't worth a dime anymore.") The NPV function in Excel can calculate the value of your solar energy purchase decision. We are happy to help you with those calculations, using your own assumptions of the growing cost of energy.

In conclusion, if you decide to install an 8kW system that will satisfy your entire electric energy need and can pay cash, that decision is worth approximately $4,671 in today's dollars. If you need to take out a home equity loan for the purchase the cost of that decision to purchase is $3,477. Either way, your days of big electric bills will be behind you.

If cash flow is an issue, you can replace only the higher cost electricity for $13,137 after tax rebates and save a total of $7,289 in today's dollars over the life of the system if you pay cash, or $1,617 if you use a home equity loan. Replacing only the higher cost electricity often makes the most sense; especially because it is these higher tiered rates that typically increase faster than base rates. Often, too, you will be constrained from replacing your entire electric energy need by the amount of space on your roof, unless you specify more efficient – and more expensive – solar modules.

Click to enlarge.

A 5 kW system that eliminates only the higher cost electricity tier has an NPV of $7,289 compared with a 5 year CD, and $1,617 when financed.

**Internal Rate of Return (IRR)**

Internal Rate of Return is simply the Discount Rate *i *that makes Net Present Value equal zero; it is the discount rate in which the sum of all future discounted savings exactly equals the cost of the photovoltaic solar energy system. IRR is helpful when comparing the economic value of competing investments with comparable risks. Because finding IRR is an iterative process it is best to apply Microsoft Excel to a stream of savings your system will generate.

When you invest in a solar system, you receive non-taxable dividends each year in the form of the cash that is no longer being paid to the utility company. Remember that because you pay no tax on the money you no longer pay to Rocky Mountain Power the photovoltaic system has an internal rate of return higher than the yield achievable through most taxable investments. In other words, if you put money equal to the net cost of a solar energy system into an investment, and withdraw the money to pay your utility bills, you have to receive a return equal to the solar IRR on a tax-free investment (or equal to the Taxed Equivalent Rate on a taxable investment) to perform financially as well. For further information, local climate data, and typical energy costs in Utah please read "Payback and Other Financial Tests".

At today's very low interest paid on investments (less than 1% for money market accounts and certificates of deposit), the same amount of money invested in a solar energy system will save you far more on electricity than your money market account can generate, for the same (nearly zero) amount of risk.