Solar payback calculator: breakeven years and cost per kWh

Payback is the point at which cumulative avoided electricity spending equals what the system cost after incentives. It sounds like a division -- cost divided by annual saving -- and it is not, because the annual saving does not stay still. Production falls slightly every year as panels degrade, and the value of each kilowatt-hour changes with the price of grid electricity.

This calculator takes a system size in kW, an installed cost per kW, an incentives percentage, an annual production figure per kW installed, an electricity cost per kWh in cents, an assumed annual rate increase and an annual degradation rate. It returns the simple payback period, the gross and post-incentive cost, first-year production and saving, the 25-year saving and net gain, and the average cost of the energy the system produces.

Everything below is a projection under assumptions you supply. The sections explain where each assumption comes from, how much it moves the answer, and the substantial costs and rules the simple model does not capture.

#The formula

Two parts: a cost side that is fixed at purchase, and a benefit side that changes every year.

Formula: gross cost = size in kW x cost per kW. net cost = gross cost x (1 - incentives / 100). year 1 production = size x yield per kW. In year n, production(n) = year 1 production x (1 - degradation)^(n-1) and rate(n) = rate x (1 + escalation)^(n-1), so saving(n) = production(n) x rate(n). Payback is the smallest n where the running total of saving(1) through saving(n) first reaches net cost, with the fractional part interpolated inside that year.

Symbols: size is the DC nameplate rating of the array in kilowatts; yield per kW is annual specific yield in kWh per kW installed; degradation and escalation are decimal fractions per year; rate is the electricity price the system displaces, in dollars per kWh.

The 25-year saving is the running total at year 25, and the net gain is that total minus the net cost. Every figure is nominal, meaning it is not discounted to present value.

#A worked example, done by hand

Worked example: an 8 kW system at an assumed $2,600 per kW, 30% in incentives, an assumed 1,400 kWh per kW per year, an assumed 17 cents per kWh, 2.5% annual rate escalation and 0.5% annual degradation.

1. Gross cost: 8 x 2,600 = $20,800.
2. After incentives: 20,800 x (1 - 0.30) = $14,560.
3. Year 1 production: 8 x 1,400 = 11,200 kWh.
4. Year 1 saving: 11,200 x 0.17 = $1,904.00.
5. The tempting shortcut: 14,560 / 1,904 = 7.65 years. Hold onto that figure.
6. Each following year, production is multiplied by 0.995 and the rate by 1.025, so the saving grows by 1.025 x 0.995 = 1.0199, about 2.0% a year. Year 2 is 11,144 x 0.17425 = $1,941.84.
7. Accumulate: 1,904.00 + 1,941.84 + 1,980.44 + 2,019.80 + 2,059.94 + 2,100.88 + 2,142.64 = $14,149.54 by the end of year 7. Still 14,560 - 14,149.54 = $410.46 short.
8. Year 8 saves 10,813.8 x 0.20208 = $2,185.22. The shortfall is cleared 410.46 / 2,185.22 = 0.19 of the way through, so payback is 7.19 years.

The shortcut in step 5 was 0.46 years too pessimistic here, because it assumed the year-1 saving repeats forever while escalation outpaced degradation. Under different assumptions -- zero escalation, faster degradation -- the shortcut errs the other way.

#Why a cumulative sum rather than a division

A division answers the question only when every year is identical. Once two compounding factors are involved, one shrinking output and one growing price, the cash flows form a geometric series and the crossing point has to be found by accumulation.

By year 25 the array still produces 88.7% of its first-year output, while the assumed rate has risen 81% under a 2.5% escalation. The saving in year 25 is 60% larger than in year 1 in nominal terms, though not in purchasing power -- see the inflation calculator for that distinction.

#Specific yield: the input that matters most

Specific yield is annual production per kW installed, in kWh per kW per year. It is the single biggest driver of the result and the one most often guessed.

It varies with latitude and climate, roof orientation, tilt angle, shading, module temperature, inverter and wiring losses, and soiling. Two identical arrays a few hundred miles apart, or on two roof planes of the same house, can differ by 30% or more. A south-facing plane at a suitable tilt in a sunny region sits near the top of the range; a shaded east or west plane in a cloudy region sits near the bottom.

Do not guess this figure. The National Renewable Energy Laboratory publishes free modeling tools that estimate hourly and annual production for a specific address, roof orientation and tilt using long-run weather data. An installer's proposal should also state expected annual production; divide it by the system size to get the implied specific yield and compare it against an independent model.

All other inputs held at the worked example's values. Across that range of yields, payback moves by more than four years.

#Levelized cost of energy

Payback compresses a 25-year proposition into one number and ignores everything after the crossing point. A better basis for comparison is the levelized cost of energy: total cost divided by total energy produced over the life of the system, expressed in cents per kWh, so it can be set directly against a utility rate.

The quick version shown here divides the net cost by lifetime production estimated as first-year output x 25 x 0.9: 14,560 / (11,200 x 25 x 0.9) = 14,560 / 252,000 = 5.78 cents per kWh. Summing the degraded production year by year gives 263,827 kWh over 25 years and a slightly lower 14,560 / 263,827 = 5.52 cents per kWh.

A full levelized cost calculation discounts both cash flows and energy to present value and adds operating costs, insurance and inverter replacement, all of which push the figure up. Even so, comparing a levelized cost against the rate you currently pay is a more informative test than payback, because it survives changes in the rate assumption.

#Degradation, escalation and how much they matter

Panels lose a small fraction of their output each year, typically a fraction of a percent, and manufacturers commonly warrant a minimum output at year 25. Inverters have shorter service lives than modules.

The rate escalation input is the assumption doing the most quiet work. Nobody knows the path of future electricity prices; the honest approach is to run the calculation at several rates and see whether the conclusion is stable.

Escalation dominates. Doubling degradation from 0.5% to 1.0% costs about a month of payback, while removing escalation entirely adds more than half a year and cuts the 25-year gain by a third.

#Where each input comes from

System size comes from a quote, in kW DC. Installed cost per kW is the total contracted price divided by the size; use the full turnkey figure including permits and electrical work, not the equipment cost.

Incentives should include only what you will actually receive. A tax credit is worth its face value only if you have enough tax liability to absorb it, and rebates may be taxable or may reduce the basis on which a credit is computed. Where an incentive arrives years later, entering it as an upfront percentage flatters the payback.

Yield should come from an address-specific model or a proposal you have sanity-checked. Rate should be your effective rate: divide a bill total by the kilowatt-hours it covers, the same method used in the electricity cost calculator. Escalation and degradation are assumptions; state them rather than defend them.

#How to read the result

Payback is a threshold, not a return. It tells you how long the capital is at risk before the position turns positive under these assumptions, which is useful mainly for comparison: against how long you expect to stay in the house, against the warranty term, and against alternative uses of the same money, which the compound interest calculator can frame.

The 25-year net gain is a nominal, undiscounted figure. Dollars saved in year 22 are not worth what dollars saved in year 1 are worth, so treat it as an upper bound on the economic case rather than a valuation. The average cost per kWh is the number to compare against your current rate, and it is the most portable output on the page.

#What this model leaves out

• Financing costs. A loan changes the cash flows entirely; interest can add years. Model the borrowing separately with the loan calculator.
• Net metering and export rules. Whether exported energy is credited at the retail rate, at a lower export rate, or hardly at all, is the single largest structural uncertainty here. This model implicitly values every kilowatt-hour at the full retail rate.
• Offsetting against exporting. Energy consumed on site as it is produced displaces retail purchases. Energy exported is worth whatever the tariff says it is worth. A household away all day exports far more than one at home.
• Time-of-use pricing, which can make midday production worth less than evening consumption.
• Inverter replacement, a real mid-life cost, and any repairs, insurance or cleaning.
• Roof condition. Reroofing under an existing array means removal and reinstallation.
• Property, resale and tax effects, which vary by jurisdiction.
• Curtailment, outages and snow cover, none of which appear in an annual yield figure.
• Discounting. All future dollars are treated as equal to today's.

#Common mistakes

Dividing cost by first-year saving. That shortcut gave 7.65 years where the accumulation gives 7.19. The direction of the error depends on whether escalation or degradation wins.

Using a national average yield. Specific yield is local, and roof-specific. A model run for the actual address is worth more than any rule of thumb.

Counting an incentive you cannot use. A nonrefundable credit is only worth what your tax situation lets you claim.

Valuing every kilowatt-hour at the retail rate. That holds only where exports are credited at retail. Check the tariff before assuming it.

Comparing the headline tariff rate rather than the effective rate. Delivery and fixed charges usually make the effective rate higher, which shortens payback.

Reading a projection as a promise. Every figure here follows from assumptions you entered. Change the escalation assumption and the 25-year gain moves by tens of thousands of dollars, as the table above shows. More calculators covering the same household arithmetic are in the full index.