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Calculating payback properly: savings, price, interest, funding

5 min read

The simple payback period, that is the investment divided by the annual saving, delivers a figure but not yet a judgement. Each of the three quantities in it is an assumption, and two of them change over the years. This article presents a calculation model that makes funding, energy price trends and cost of capital visible, using a deliberately neutral numerical example.

The calculation model

  • I: gross investment minus funding, insofar as it is paid out at the start.
  • E: annual saving in kilowatt hours, as the difference between the calculated demand before and after the measure. How far such a calculation carries is covered in the article Heating degree day method: limits.
  • p and g: energy price in the first year in euros per kilowatt hour and the annual price change.
  • z: discount rate, that is the return on the best alternative or the interest rate on a loan.

The saving in year t is E · p · (1 + g)t−1. Divided by (1 + z)t, this gives its present value. The dynamic payback period is the year in which the sum of these present values reaches I. The formal basis for economic viability calculations of building services systems is VDI 2067 Part 1 (edition 2012-09, available for a fee).

Input quantities with documented references

Energy price

For the first half of 2026, the Federal Statistical Office (Destatis) gives an average natural gas price for private households of 11.58 cents per kilowatt hour. The range by consumption band runs from 10.92 cents (over 200 gigajoules a year) to 15.17 cents (under 20 gigajoules). The prices surveyed include the standing charge and unit price as well as network charges, taxes, levies and surcharges.

Compared with the first half of 2021, household gas prices rose by 80.7%; compared with the first half of 2025, they were 4.5% lower. For non-household customers, Destatis already reports initial effects of the crisis in the Strait of Hormuz. A single price for the next 20 years is therefore an assumption, not an observation.

CO2 price

For 2026, § 10(2) of the Fuel Emissions Trading Act (Brennstoffemissionshandelsgesetz, BEHG) sets a price corridor of €55 to €65 per emission allowance. One allowance entitles the holder to emit one tonne of carbon dioxide equivalent. For natural gas, the standard values of the Emissions Reporting Ordinance 2030 (3.2508 GJ/MWh and 0.0558 t CO2/GJ) give a conversion of their own of around 0.18 tonnes per megawatt hour, so about 1.0 to 1.2 cents per kilowatt hour at €55 to €65 per tonne.

Whether this share is already contained in the gas price used must be checked so that it is not counted twice. How the price will be formed from 2027 depends on a statutory ordinance under § 10(3); assumptions about this belong in the calculation expressly as a scenario.

Funding and cost of capital

The BEG grant (federal funding for efficient buildings) for the building envelope is in principle 15% of eligible expenditure and is paid out only after the proof of use. The tax reduction under § 35c EStG (Income Tax Act) is spread over three years at 7, 7 and 6 percent of the expenditure. Both shift the timing of the relief, which matters in a dynamic calculation. There is no official reference value for the interest rate; it follows from the financing or from the forgone investment.

Numerical example with freely chosen assumptions

All values except the gas price are freely chosen and do not represent any product: gross investment €20,000, fully eligible for funding, saving of 8,000 kilowatt hours of natural gas a year, price 11.58 cents per kilowatt hour. The saving in the first year is therefore €926. A grant of 15% reduces I to €17,000.

Calculation method Assumptions Payback period
simple without funding 21.6 years
simple with 15% grant 18.4 years
dynamic with grant, price constant, interest 3% 27.1 years
dynamic with grant, price +2% a year, interest 3% 20.8 years
dynamic without grant, price +2% a year, interest 3% 24.9 years

In the scenario “with grant, price +2%, interest 3%”, the input quantities alone shift the result considerably. With 6,000 instead of 8,000 kilowatt hours saved, it would be 28.8 years; with 10,000 kilowatt hours, 16.3 years. With the Destatis price of 10.92 cents instead of 11.58 cents the result is 22.2 years, and with 15.17 cents it is 15.5 years.

What the simple payback period does not show

  • Time value of money: In the example, the simple value is 2.4 years below the dynamic one, even though the latter already includes a price increase.
  • Service life: The BEG requires at least ten years of use for the intended purpose; whether the measure still works after that is not something the figure tells you.
  • Costs that would arise anyway: Repairs that are due in any case, for example to render or paintwork, belong in the investment only with their additional costs.
  • Funding cap: The BEG limits eligible expenditure per residential unit; anyone who invests more receives no grant on the remainder.
  • Non-energy effects: Comfort, protection against moisture and preservation of value have no price in the formula.
  • Calculated rather than measured: Actual user behaviour and the weather deviate from the calculation assumptions.

What follows from this

A quotation should be calculated with a range: low, medium and high saving, each with a constant and a rising price. A result that holds in only one scenario is a bet on the energy price. In every individual case, the question that remains open is which price path the decision should rest on.

Sources

→ Cut heating costs in an old building

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