# Calculation Example BBSR-Tool: pitched roofs

The following 2 examples are about the insulation of pitched roofs using a thermal insulation composite system. For two different energy performance levels (for both the situations before and after modernisation) the equivalent energy price, the annuity and the amortisation period are determined using the BBSR calculation tool. as well as the costs and prospective energy savings per square meter modernised pitched roofs.

### Boundary condition used for the calculations

- Period under consideration (“Betrachtungszeitraum“): 25 years
- Interest rate (“Zinssatz nominal”): 4.0% (equals real: 3.0 %)
- Energy carrier (“Energieträger“): natural gas
- Gross current energy price (“Aktueller Energiepreis brutto“): 5.9 cents/kWh
- Future nominal energy price increase (“Zukünftige Energiepreissteigerung nominal“): 2.4% per year (equals real: 1.4% per year)
- Year of calculation (“Jahr der Berechnung”): 2018
- Increase of prices since reference year 2015 (“Zunahme der Preise seit Bezugsjahr 2015): 2 % per year
- Expenditure factor of heating system (“endenergiebezogene Aufwandszahl der Heizung“; demand of delivered energy per unit of useful heating energy): 1,15

These boundary conditions match the default settings of the calculation tool. In order to properly depict the conditions occurring with partial modernisation, the degree days after the measure were assumed – other than the default setting – the same as before the measure:

- Degree days - old – (“Gradtagszahl - alt –“): 3251 Kd
- Degree days - new – (“Gradtagszahl - neu –“): 3251 Kd

The tool calculates the investment costs and the share of costs assigned to repair-/ maintenance using the cost functions developed by IWU. The option to adjust the values for full costs and the share of repair costs individually (e. g. based on tenders or estimates) was not used in the examples below.

### Example

Insulation of a pitched in course of a regular repair-/ maintenance measure (renovation of the roofing including the battens)

- U-value before modernisation: 0,80 W/(m²·K)
- U-value after modernisation: 0.20 W/(m²·K)

Source: [BBSR] Screenshot Berechnungstool

**Conclusion**

In example, with investment costs of approximately 198 €/m² and an average future energy price of 7.8 cents/kWh (nominal) calculated by the tool based on the boundary conditions (cell H 13; not visible in the screenshot), cost-effectiveness is accounted for if the investment costs contain a (not energy-relevant) share assigned to repair / reconditioning of 148 €/m² or more. The proportion of costs the example is based on

- full costs (cell H 23): 198 €/m²,
- share of repair costs (cell H 24): 148 €/m²)

meet these requirements.

Per square meter modernised exterior wall energy savings of 48 kWh per year are estimated (cell C 24).

Method a) “Equivalent Energy Price”

Cost effectiveness is achieved for an energy price of 6.62 ct/kWh or more (cell F 44). The average future energy price of 7.8 cents/kWh (brutto, nominal) for natural gas calculated by the tool fulfils this condition.

Method b)“Annuity”

With the given boundary conditions and the cost from the cost functions, an annuity of 1.00 € per m² renovated wall is calculated; the annual costs for energy and investment are reduced by this amount in comparison to the case without modernisation measure.

Method c) “Amortisation Period”

With the given boundary conditions and the cost from the cost functions, an amortisation period of 18.12 years is calculated. In general, modernisation measures concerning the building’s envelop are considered cost effective if the amortisation period does not exceed 25 years.