Simple payback period

What dividing a price by a year of savings can honestly tell you

The denominator is a year of production converted into money: annual kilowatt-hours times a tariff. For a self-consuming household that tariff is the retail price NOT paid to the utility — avoided cost, which is why rooftop solar economics track retail prices rather than wholesale ones. Divide the installed cost by that annual value and the quotient is years: how long the system takes, at current prices and current output, to hand back what it cost.

“Simple” means the division deliberately ignores time. No discounting of future savings, no tariff escalation, no decay of output as modules age, no maintenance or inverter replacement along the way. Every one of those omissions bends the true figure — some in the system’s favour, some against — and the honest use of simple payback is comparison and screening, where the same omissions land on both sides of the comparison and largely cancel.

The single tariff hides a real subtlety: it prices every kilowatt-hour identically. A household that consumes its solar directly avoids retail; one that exports much of it is paid an export rate that is typically far lower; most are somewhere between. The right input is a blended value that reflects the actual split — and a payback computed entirely at retail for a system that exports half its output is optimistic in a way no later arithmetic repairs.

The denominator also inherits the whole cluster. The annual energy came from the yield estimate, which leaned on a peak-sun-hours figure and an assumed performance ratio; the chain from sun data to payback is linear at every link, so a flattering assumption upstream shortens the payback downstream by exactly the same fraction. When a metered year later disagrees with the estimate, this page is where that disagreement turns into money.

When this calculation is used

• Comparing installer quotations on one scale, where identical omissions cancel and the division does exactly what it should.
• Screening whether a site’s combination of sun, consumption and prices makes PV worth a detailed financial workup at all.
• Solving backwards — the declared reverse workflow — for the breakeven tariff that reaches a target payback, which is a useful way to test a decision against future price scenarios.
• Translating a performance shortfall into consequence: rerun with the metered year instead of the estimated one and watch the horizon move.

Worked example

Price the cluster’s reference system: the 5 kWp array installed for $6,000 all-in, its production taken as the 8,030 kWh the pack’s anchor year records, valued at a tariff of $0.15 per kilowatt-hour.

The engine returns the payback horizon in years. Read it against two clocks: the decades a modern module keeps producing, which is what makes a single-digit horizon attractive, and the tenure the owner actually expects at the property, which is what makes a long one a real risk rather than a bookkeeping detail.

Now run the declared reverse: fix the horizon you would accept and let the engine find the tariff that reaches it. If today’s price already exceeds that breakeven, the decision has slack against falling tariffs; if it only works at prices higher than today’s, the case is a bet on escalation and should be named as one.

What each input represents

Assumptions and limits

• Output is treated as constant for the whole horizon: no module degradation, no downtime beyond what the yield figure already conceded.
• The tariff neither escalates nor is discounted — a unit of savings in a distant year counts the same as one this year.
• Every kilowatt-hour is valued at the single entered tariff, so the self-consumption/export split must already be blended into it.
• Running costs are outside the division: maintenance, insurance and a mid-life inverter replacement all lengthen the true horizon.

What the guards protect against

• A zero tariff is refused — the pack declares that refusal as a test vector — because worthless electricity pays nothing back and the division has no finite answer; the refusal surfaces the modelling problem instead of an unusable figure.
• The tariff is capped at a bound no retail price approaches, which catches the classic slip of entering cents per kilowatt-hour where the unit is currency per kilowatt-hour — a hundredfold error that would otherwise return a payback of weeks.
• System cost and annual yield must both be positive: a free system or a dark one leaves nothing meaningful to divide, and each is refused as a domain error rather than answered.

Provenance

Simple payback relation, years = system cost / (annual yield × tariff)

The installed system cost is divided by the product of annual energy yield and electricity tariff, returning the payback period in years; the declared reverse workflow solves for the breakeven tariff that achieves a target payback.

Screening and reference material, to be checked against the governing standard and a qualified engineer; not a design determination. The signed pack carries its own citation, and the page reports the verification state of the release it mounted.