Evaluating Return on Solar Investments

Published: Oct. 12, 2009

The time has come, the President said,

To buy so many things.

Renewables like solar power

And graceful wind machines.

So tell us please, the Congress asked,

As our enthusiasm waxes,

How much will all this power cost

And may we pay by cutting taxes?

With apologies to Lewis Carroll, the President and Congress.

It is an auspicious time for renewable energy. Anyone considering investing in a renewable energy system needs to consider many factors including the costs and economic benefits. This article illustrates calculations for return-on-investment for this analysis and provides information and suggestions to allow the calculations to be interpreted.

A spreadsheet has been prepared to calculate the payback time (PBT) and the internal-rate-of-return (IRR) for a proposed photovoltaic (PV) solar project. Values for a specific project are input and the spreadsheet calculates estimates of the costs and benefits of the project and produces values for the PBT and IRR. The inputs and the significance of the parameters are discussed below.

The equations on which this analysis is based follow in word form.

Initial system cost =  (system cost) + (sales tax) + (cost of any extra building or property modifications)

Reductions to system cost =  (rebates – applicable income tax on rebates) – (applicable income tax deduction for sales tax paid)

Net initial system cost = Initial system cost – reductions to system cost

Annual costs = (additional property taxes and insurance) + (operation and maintenance, O&M) + (loan payment, principal plus interest)

Repair & replacement (R&R) costs =  (major repairs)  + (component replacement or upgrading)

Annual savings on energy displaced = (price of energy)*(average annual energy displaced by system).

Added value of system = {either [(value of the property with the system) - (value without)] or [the scrap value of the system]}. The property value with the system may be significantly greater than without, particularly in the near term. However, the added value is only realized if the property is sold. The user must make a guess about when this might occur, or simply leave it out. If the property is not sold, a scrap value is added at the end of the analysis, at 30 years.

Annual benefit = (Annual savings) – (Annual costs)

Total benefits = (Sum of annual benefits over project period)

Total Net Return = (Total benefits) – (Net initial cost) – (R&R costs) + sale or scrap value

It is to be expected that the price of the energy being replaced will increase over time due to general inflation plus escalation of the energy price over-and-above general inflation. Estimates of the rate of increase in energy price can be obtained from the local utility, local Public Utility Commission, or from the U.S. government’s Energy Information Agency. These estimates usually include the anticipated rate of general inflation, but the user should check the source to see if it is included and, if so, what inflation rate is used. If a known value for general inflation is included in the energy price rise, it is used in the calculations to correct future energy costs to dollars of the value at the time of the analysis (time zero). All cash flow streams are converted to dollars at time zero, or constant dollars and the analysis is done with time zero dollars.

Discounting is a calculation used to account for the time-value of money. It reflects how much money would be required at an initial time to produce a certain amount at a time in the future, by allowing the initial amount to grow with compound interest. Discounting is the opposite of compounding and weights later income less than earlier income. It is generally recommended to use a discount rate equal to what the owner-to-be could reasonably expect to earn by investing the money, rather than buying the solar system, in an investment of comparable risk. The risk associated with a solar PV system is low, because the system can be expected to save the owner money for a long time, comparable to the risk associated with home ownership. Thus a relatively low discount rate, such as 4 to 6 percent per year, is appropriate.

The spreadsheet runs calculations for 30 years. The length of analysis does not affect the PBT, but it does affect the IRR

Depreciation is not included in the analysis and spreadsheet discussed here. Depreciation is only considered for income producing properties, such as businesses and rental property. It might be applicable if a homeowner has an office in the home that qualifies for a business deduction. In this case, consult a tax professional to confirm whether a portion of the depreciation applicable to the added solar system could be applied to the home office.

Non-Economic Considerations

The decision to install a solar PV system is usually affected by issues that are not reflected in the economics. For example, concern for the future of the planet or a stable energy supply may influence an individual’s decision. The potential investor must decide how to weigh them alongside the economics to arrive at a final decision.

The spreadsheet has a data input section which is shown at the end of the text. Here the inputs are discussed line-by-line (numbers correspond to row numbers in the spreadsheet). Note that items 4, 5 and 8 are sufficient to do a calculation, but the more data included, the more reliable the results will be.

4. Annual energy output by the solar system is required for the calculations and must be supplied by the user of the spreadsheet. It depends on location, climate, performance of the PV collectors, and on how much of the collected energy can be utilized, either by the owner or the grid (typically systems are sized so that 100 percent utilization is expected). The energy output would typically be obtained from one or more solar-contractor bidders. The energy output will vary from year-to-year, but the vendor should supply an estimate of the average energy obtained from the system--thereby displacing the purchase of energy — based on long-term average conditions.

5. Initial system cost is required for the calculations and should be obtained from bidders. It includes such additional costs as buildings modifications to accommodate system and trimming or removal of trees that might shade the system.

6. Utility rebate is entirely dependent on the current policy of the local utility, and it can range from 0 to 50+ percent of the cost. A bidder should have the most current information, but the buyer can check with their utility. The rebate can have a large impact of the economic return.

7. Federal income tax credit in 2009 for solar PV systems is 30% of the cost to a maximum of $2,000 (from IRS.gov web site). Again, get current information. The effect of this term on the overall result is quite important.

8. Electricity price is required. It is the price paid by owner at the time of the analysis. Be sure to subtract off the amount of any charges that do not depend on the amount of electricity used (such as a franchise fee).

9. Power rating is not used in the calculation.

10 & 11. State and local sales taxes that can be taken as a deduction on income tax taxes. Owner should check with tax advisor. The effect of this term is rather small.

12 & 13. Is income tax to be paid on the utility rebate? The author has received both “Yes” and “No” answers to this question, so cannot give a definitive answer. It is recommended that that the user run each case with and without income tax on the rebate. If income tax is to be included, the marginal tax rate, line 21 must be included. If the results show a difference sufficient to influence the user’s decision, then a trusted tax advisor should be consulted before a decision is made.

14. Operating & maintenance (O&M) plus property tax and insurance (PTI) increase due to adding a PV system. Ask the vendor for an estimate. The users can check with the vendor, local property tax experts and an insurance agent for these values. As an initial guess, the author suggests 0.2 percent per year of the initial system cost.

15. Electricity price increase is the predicted rate of future increase. Consulting with the vendor, the local utility, and the Energy Information Agency is recommended. If the rate includes the general rate of inflation, as is often the case, then the general rate of inflation used must be input in line 17. If the electricity price increase does not include a general rate of inflation, then leave the general rate of inflation at zero.

16. Discount rate selected by user. The author recommends 4 to 6 percent.

17. General inflation rate is discussed previously. An inflation rate of 2 or 3 percent per year is suggested, although it may vary over a much wider range.

18. Loan amount in $. Set =0 if no loan is taken to finance the project.

19. Length of loan is the years of repayment of the loan, based on the terms the owner can obtain. The program assumes that loan payment (principal plus interest) is a constant annual amount.

20. Loan interest rate. Again, it is based on the terms the user can obtain.

21. Marginal income tax rate is that paid on any addition to owner’s income. Be sure to include both federal and state rates.

22. Performance deterioration should be estimated by an expert or the system contractor. The author recommends 0.1 percent per year if no other information is available.

23 & 24. A one-time amount for replacement or repair as estimated by the vendor (in constant, zero-time dollars).

25 & 26. Year of occurrence of the replacement or repair as estimated by the vendor. Program only accepts one replacement and repair event. Experience suggests that inverters are likely candidates for replacement.

27. Added value upon sale is a guess on how much value the system might add at the time of a sale or the scrap value of the system. The user must make a guess as to when and how much a sale might bring. The vendor may be helpful to estimate scrap value. To be safe, the author suggests inputting the amount that the owner has funded, either by their own funds or loan, or a combination.

28. Year of sale is the number of the year after initiating the project that a sale is predicted. Or it can be the year in which the system is to be scrapped. If it is the latter, the author recommends using 30 years.

The key calculated results are: net system cost, loan funding, owner initial funding, payback time, and internal rate of return. In these calculations, the yearly cash flows are adjusted for inflation and are discounted at the rates input by the user. The net system cost is the total cost of the system less any utility rebate and less the Federal income tax credit. Owner funding is the net system cost less loan funding.

The payback time is the number of years it takes for the total net return (see above under “RETURN”) to equal zero at the user specified discount rate. In other words it is the time when the owner has recovered all expenditures and has earned at the specified discount rate on the money spent and earned. The PBT depends upon the discount rate selected. If a discount rate of zero is used, then the PBT is the simple payback time or the payback time corresponding to zero earning rate on the expenditures and income. If a non-zero discount rate is used, the PBT is the time for the discounted-total net return to equal zero. The lower the PBT the better the project for the owner.

The internal rate of return is the discount rate that makes the sum of the discounted-total net return equal to zero. It can be looked at as the rate at which the owner has earned money on all of the expenditures and revenues for the project. In the earlier years of a project the IRR will surely be negative, meaning that the owner’s discounted expenditures have not been recovered as yet. The time that the IRR becomes zero is the time that the owner’s costs have just been recovered. When the IRR is positive, the owner’s costs have been recovered and the owner has earned a return at a rate equal to the IRR. CAUTION: If the property is sold in a year other than 10, 20 or 30, the blue IRR table will show the year of sale, and “See col. G”  in the IRR row. In order to determine the actual IRR, the user must look at the year-to-year results (column G, rows 34-64) for the year of sale and read off the IRR value in column for the year of sale. Values after the year of sale are meaningless.

It is recommended that the basic spreadsheet, or the entire workbook, be downloaded to the user’s computer. To run a particular case, copy the basic sheet to the next available sheet in the workbook and input the desired information. It is a good idea to save the workbook periodically. It may be useful to save for reference all of the sheets which contain worked-out cases until one has reached a decision. In the basic spreadsheet, all the cells are protected except for the red title and data entry ones. In the example sheets, none of the cells are protected.

A trial case may be identified by an entry into the blank red space in cell A1 of the sheet. The user enters data applicable to their project into the red shaded areas in the spreadsheet. As a minimum, only items 4, 5 and 8 are required to run a case. Clearly though, the more information entered, the more reliable the response. The results of each calculation are shown in the blue boxes on the sheet. These results are: the net system cost (initial system cost less utility rebate and federal income tax credit), loan funding, and owner funding; the payback time for the specified discount rate; and the internal rate of return (IRR) at 10, 20, and 30 years. It may be helpful for the user to examine the “Year-by-year calculations” shown between columns A through G and rows 33 through 64, as discussed below under "Examples."

The entries #NUM! or #Div/0! will sometimes be seen in the spreadsheet. These result from the fact that the Excel function IRR (which calculates the internal-rate-of return) does not handle large negative numbers. Simply ignore these entries.

The user is encouraged to run several cases for a proposed system to see how the values of key parameters affect the economic results. Loan amount and interest rate, added value of the system, electricity escalation, discount rate, etc., are examples of important parameters. Except for the input data, the basic spreadsheet is protected so that equations cannot be changed. The examples are not protected, so the user may see and change equations if desired. Note that columns after M contain some of the more detailed calculations, but the user need not be concerned about them, unless more details of how the calculations are done are desired.

It should be noted that although the spreadsheet is written for a solar-PV system, it can be applied to solar-water or solar-space heating as follows: the annual energy output should be entered as the annual heat supplied to the load, in millions of Btu, and the electricity price should be entered as the cost of supplying the heat via electricity or gas in $/million Btu (remember to factor in the efficiency of supplying the heat from the meter to the load). The rest of the inputs will be as normal and the calculated results will apply to the solar-heating system.

The basic spreadsheet contains no data and is on the tab labeled "BASIC."

Five examples are included on the sheets labeled Ex. 1, through Ex. 5. The system cost and performance values in these examples are based on an actual installation in Boulder, Colorado in 2008.

Example 1 uses only the first 5 input entries (numbers 4 through 8). The results show that the owner’s initial funding is $10,000, the payback time is 17 years, and the IRR is -8 percent at year 10, 2 percent at year 20 and 4.5 percent at year 30. These results suggest that the project is a marginal economic success.

Example 2 uses the same system information as 1, but added to the input of Ex. 1 are: sales tax deduction on income tax, operation & maintenance, electric-price increase (with general inflation included), general inflation, and discount rates, plus the marginal income tax rate. These changes increase the PBT to 21 years. The IRR values become -5.9 percent at year 10, 4.7 percent at year 20 and 7.6 percent at year 30. So, although the PBT is longer, the overall economics have improved.

Example 3 has the same information as Ex.2, but the question, is income tax to be paid on utility rebate, is answered “yes” rather than “no.”  The PBT has now increased dramatically to 29 years. The IRR values now are -9.8 percent at 10 years, 2.2 percent at 20 years, and 5.4 percent at 30 years. This decline in economics is enough to make the income-tax question significant and to demand a definitive answer.

Example 4 is similar to 3, but with the answer to the income tax question changed to “no” and the funding changed to a $10,000 loan at 5 percent for 20 years, so the owners’ initial funding is zero. A glance at column X, starting in row 35, shows that the owner pays $ 805 in current $ for each of the 20 years of the loan, at 5 percent interest. The owners cumulative total of net expenditures (in constant $ discounted at 5 percent) never exceeds $831 over the first 20 years (see column E, starting at row 34)! Once the loan has been paid off at 20 years, the net constant-dollar cash flow turns positive at 22 years, and the IRR increases from -0.5 percent at 20 years and 13.5 percent at 30 years. This case looks very attractive over the long term, and even in the short term the owners’ cumulative net outlay is at most very small.

Example 5 adds to Ex. 4 an R&R expenditure of $1,000 (current $) at year 12 and sale of the property in year 18, with an added value due to the PV-system of $10,000 (the initial loan funding), the program reduces this amount by the balance of loan principal that must be paid at the time of sale. This example shows a PBT of 18 years and IRR value of almost 15 percent at 18 years (obtained from the year-to-year table). This shows that sale of the property, even with a modest added value, has a large positive effect on the economics. It yields a very favorable return after sale of the property, with a maximum cumulative net outlay of $1,391 (constant $ at percent discount rate) by the owner.

----------

About the author: Ronald E. West is professor emeritus of chemical engineering at the University of Colorado-Boulder.