# Optimization of Heat Pump Systems in Buildings by Minimizing Costs and CO\({}_{2}\) Emissions
## 4 Results
### Performance of Economic and Financial Indicators  
The economic performance of heat production and supply systems for different buildings was evaluated by analyzing key financial indicators, such as investment costs, operating costs, and the levelized cost of heat (LCOH). Additionally, the internal rate of return (IRR), net present value (NPV), and payback period (PB) for each heating system were determined using a 5% discount rate. The monthly heat prices of heat suppliers in Lithuania for 2022 were used for the calculations of these financial indicators [56]. The change in heat prices over a 10-year period was projected by assuming that the trend of heat price change is similar to that of electricity prices as presented in Section 3.3. The main results of the economic analysis for each analyzed case are presented in Table 3.  
Figure 9: Comparison of heat production in renovated and unrenovated schools, kindergartens, and supermarket. According to the results of indicators presented in Table 3, the most profitable investments for the analyzed period were in the heating systems of the renovated five-story (no. 3) and unrenovated nine-story (no. 4) apartment buildings, as shown by their low energy costs, short payback periods, and high returns on investment. These buildings had the lowest average heat prices per kWh, with an average of approximately 0.0831 EUR/kWh. These buildings also had the shortest payback periods of 8.55 and 8.89 years, respectively. The internal rate of return (IRR) for these buildings was the highest, indicating a high potential return on investment. Their net present value (NPV) was also highest, meaning the present value of projected cash flows exceeded the cost of investment. The heat production and supply systems in these buildings were determined to be the most economically attractive due to their large volume and resulted in the lowest payback and average heat price. The results revealed that the heating system in the renovated three-story apartment building (no. 6) was not economically viable among the analyzed buildings, and it had the lowest actual heat demand during the analyzed period. The economic performance resulted in an LCOH of 0.0956 EUR/kWh and a payback period of 21.73 years, which was not reached within the modeling period. Negative values of IRR and NPV indicate that the investment in the heating system of this building was unprofitable. Similarly, the renovated school (no. 9) also had poor performance of economic indicators, with a payback period of 17.86 years, a negative IRR and NPV of \(-2.29\%\) and \(-19.59\)k EUR, respectively, and an LCOH of 0.0961 EUR/kWh. In both these cases (buildings no. 6 and 9), the LCOH exceeded the average heat price of the heat supplier. This makes the selected heating systems unprofitable and not worth the investment. The analysis of other buildings revealed varying values for economic indicators, with the LCOH ranging from 0.0847 to 0.0954 EUR/kWh, payback periods ranging from 9.23 to 16.02 years, and the IRR ranging from \(-1.02\%\) to \(6.35\%\). Most of the buildings had a negative NPV, indicating that the optimal heat production and supply systems were not profitable, and the investments were not returned during the analyzed period. However, some of the heating systems in the analyzed buildings demonstrated promising results in terms of economic performance. For example, a positive NPV was obtained for the unrenovated five-story apartment building (no. 2), and other economic indicators for this building also indicated better results. This suggests that the unrenovated five-story apartment building may be a good investment option for heat production and supply systems in addition to other buildings with the best economic indicators. Additionally, the annual operating cost savings for SH and DHW preparation were calculated for the analyzed buildings. It is important to note that these savings were calculated only for operating costs and excluded costs of the heating system itself and its installation.