# Annuity: Comparing the yearly costs before and after the measure

The costs before the measure are given by the yearly energy costs. It is recommended to form an average value for the consumption from the past years or to carry out a weather adjustment. Energy consultants and certificate issuers can provide advice in on this issue. If there are no consumption values for the past years, the demand values of an EnEV calculation should be used.

The yearly financial effort after realisation of a measure is given by the reduced energy costs and the incurred yearly costs that are a result of the measures on building shell and/or building technology.

In order to determine the yearly energy costs after realisation of a measure, the pre-sumably resulting energy consumption should be determined using realistic assumptions. One should estimate whether and how much the user behaviour will change in in consequence of the measure, e. g. lowering the indoor air temperature (increases energy savings) or change from partial to full heating of the building (reduces the energy savings). The energy costs incurring after realisation of the measures must be supplemented by the financial effort for the intended measures.

One either assumes that the measure is financed via a loan or really does so. Its duration corresponds (fictitiously) to a period under consideration that is often given by the lifetime of the measure. The annual payments for interest and repayment in €/a can be determined using an assumed interest rate. The calculation is carried out by multiplying the amount to be financed or, in the case of the use of capital resources (equity interest) the amount contributed personally, by the annuity factor. Potentially, other annually incurring costs are considered as well (e.g., inspection, maintenance, repair). The amount of the annual costs during the period in €/a is the final result of this calculation.

The equivalent annual cost method allows consideration of reinvestment in certain building components or systems that have a shorter lifetime than the full measure. Example: In course of a heating modernisation, a switch is made to heat pump and floor heating. The lifetime of the heat pump is considerably shorter than that of the new heat exchange surface. During the system’s full lifetime, the heat pump must therefore be renewed repeatedly.

If resulting the annual costs after the measure are lower than before, this modernisation can be assumed to be a cost effective. Consideration of actual interest conditions and durations is possible but makes the calculation more complicated. In this case, the time after the measure is divided into two stages – until expiry of the specific loan financing and for the remaining time until the end of the lifetime.

### Calculation of annuity

**Step 1 – Determining the savings of delivered energy:**

The determination of the energy savings is independent on the chosen method of efficiency calculation. Different calculation methods are described under the menu item Energy savings. The result is a value in kilowatt hours per year (kWh/a).

**Step 2 – Determining the average energy cost savings per year:**

The average annual energy cost savings are calculated by multiplying the savings of delivered energy determined in step 1 with the average price for one kWh of delivered energy. The current price for one kilowatt hour (kWh) of delivered energy can be determined for individual sources of delivered energy or as an average value. For grid-bound energy (e.g., gas, district heat, local heat, electricity), the kilowatt-hour-rate and the (basic-) kilowatt-rate have to be considered. The average future energy price can be calculated from the current energy price and a so-called mean value factor. This can be determined using the interest rate, duration, and future energy price increase or from the Mean value factors table.

**Step 3 – Determining the investment costs for the measure(s):**

The determination of the modernisation costs is independent on the chosen method of efficiency calculation. Different procedures are described under the menu item modernisation costs. Cost functions for frequent measures are summarized under Example of modernisations. One must differentiate between the full costs and the energyrelated additional costs of a measure. If necessary, it should be determined whether and what costs additionally arise from operation, inspection, maintenance, or repair and, in part, also for insurance.

**Step 4 – Determining the annual investment costs:**

In order to be able to compare the costs of the energy modernization with the annual energy savings, it is necessary to calculate the annual costs. The costs per year are determined under the assumption that the measures are financed through a loan. The duration of the loan either corresponds to the lifetime of the measure or to a general recommendation/specification. Often, this is said to be 20-30 years. The assumed or actual financing conditions are expressed through an interest rate in %. The annuity factor can be determined from the interest rate and duration or from the Annuity factors table. If the construction costs are multiplied by this factor, the annual costs throughout the duration are given in €/a. The calculation follows this formula:

Total annual costs of the measure (€/a) = investment costs (€) * annuity factor (1/a) + follow-up costs (€/a)

**Step 5 – Determining the annuity:**

The annuity is the difference between the average energy cost savings and the annual (annuity) costs. Alternatively, the annual costs before and after the measure can be compared (determining the annuity profit).

**Step 6 – Comparison and evaluation:**

If the determined annuity is greater than zero, the measure is economically reasonable. Then the average energy cost savings per year exceed the average costs per year. This is also referred to as "annuity profit", i.e. after the measure is carried out, a profit is achieved on average every year.