## 2 Materials and Methods
### Key Assumptions Used in the Financial Cost Analysis  
The following financial analysis was based on three indicators: LCC, NPV and IRR. According to the ISO 15686-5 standard [30], each LCC analysis should take into account the costs of four components, i.e., construction/initial (material, transport to site, labour), operation, maintenance and disposal (disassembly, transportation, treatment/destruction). The maintenance cost was omitted because in this analysis a single-family house was assumed as the reference building, and no glazing repairs were planned. Of course, in the case of office buildings, such assumptions should not be made. Therefore, the LCC value can be calculated from the following relationship:  
\[LCC=IC+\sum_{i=1}^{i=T}OC(i).\frac{1}{\left(1+r/100\right)^{1}}+DC.\frac{1}{ \left(1+r/100\right)^{T}}, \tag{1}\]  
where  
\(IC\)--initial cost [EUR/m\({}^{2}\)];  
\(T\)--life cycle period [year];  
OC--annual operational costs [EUR/m\({}^{2}\)];  
\(r\)--discount rate [%];  
\(DC\)--disposal cost [EUR/m\({}^{2}\)].  
At this time, in conditions of high economic variability, the discount rate is assumed in a wide range from 2% (optimistic variant) to 7-10% (pessimistic option). In the current analysis, it was decided to perform calculations over the entire range of variability of this parameter, i.e., from 2% to 10%. Based on data obtained from leading manufacturers, it can be stated that the life cycle of PVC windows is between 30 and a maximum of 40 years. Due to the continuous progress in glazing technology, an analysis period of 30 years was assumed. There is a high probability that after this period it will be profitable to replace existing windows with those made to a much higher energy standard. The energy cost associated with heat transport through the glazing system was calculated based on building energy simulations and treated as operating costs. All three cost categories were determined for each window type and converted per m\({}^{2}\) of glazing to make this analysis more universal.  
The initial costs (\(ICs\)) for quadruple-glazed windows were assumed to be 331.3 EUR/m\({}^{2}\), those for triple-glazed windows--276.1 EUR/m\({}^{2}\) and for double-glazed windows--225.4 EUR/m\({}^{2}\). In the case of disposal costs (\(DCs\)) for quadruple-glazed windows, 100 EUR/m\({}^{2}\) was assumed, for triple-glazed windows--200 EUR/m\({}^{2}\) and for double-glazed windows--200 EUR/m\({}^{2}\). Operating costs were additionally increased by the costs related to replacing seals and adjusting windows. This maintenance activity should be carried out on average once every 10 years. It was assumed that the value of these costs are 14.5 EUR/m\({}^{2}\), 13.5 EUR/m\({}^{2}\) and 10.2 EUR/m\({}^{2}\) for quadruple-, triple- and double-glazed windows, respectively.  
The NPV indicator is usually used to assess the feasibility of a specified investment proposal. A positive NPV value indicates the profitability of the project from a financial perspective. The formula for calculating NPV is presented below:  
\[NPV=-\Delta IC+\sum_{i=1}^{i=T}\Delta CF(i).\frac{1}{\left(1+r/100\right)^{i}}, \tag{2}\]  
where \(\Delta CF\)--cash flows assumed as an annual reduction in energy costs [EUR/m\({}^{2}\)].  
The internal rate of return determines the real rate of return from an investment. An investment is profitable if the IRR value is greater than the assumed limit value. Calculating the IRR involves finding the value of the discount rate that meets the following relationship:  
\[-\Delta IC+\sum_{i=1}^{i=T}\Delta CF(i)\cdot\frac{1}{\left(1+r/100\right)^{i}}=0. \tag{3}\]