## 3 Results
### Global Cost Robustness of the Baseline  
The secondary objective of this study is to test the robustness of the identified cost-effective package in [28], applied as a baseline for the sensitivity analyses studies in this paper. The robustness analyses are carried out by comparing the resulting variations of the NPV from the MC method to the NPV of renovation packages obtained in [28]. The comparison for the three energy supply systems is shown in Figure 9, where the grey markers depict packages from [28], while the marker types categorize the packages by their achieved energy savings. Packages 1-6 achieve approximately 20% energy savings, Packages 7 and 8 obtain 40%, and 9 and 10 reach 60% energy savings compared to the pre-renovated energy demand of the case study building. The variations attained by the MC method for the baseline (Package 7) are visualized by the box plots in Figure 9. The mid-line in the box plot marks the median of the output data, while \"x\" depicts the mean. The box bounds the first and third quartile (interquartile range, meaning 50% of the observations), whereas the whiskers bound the minimum and maximum data values excluding extremes. A key observation in Figure 9 is a discrepancy in the NPV values of Package 7 from [28] (marked with a black cross) and the baseline values for the studied systems (marked with a horizontal line), even though both models are identical. This is caused by the updated discount rates (DR) from 2018 to 2021. As stated in Section 2, the updated DR are 0.5% points lower than the previously applied values from 2018. As expected and stated in [32], a lower discount factor would result in lower global cost (in this case, the NPV), which is consistent with the results in Figure 9. This leads to the conclusion that the NPV of the different solutions is highly dependent on the DR, which is ultimately a policy decision. In all three cases, the difference due to the updated DR values is larger than the obtained spread from the variated parameters. In the case of the HP, the change in the DR has a significant effect on the result (1.5 MM EUR), while for DH (0.7 MM EUR) and gas (0.18 MM EUR) the difference is still considerable, although to a smaller extent compared to the HP. This shows that the DR significantly influence which technology will be singled out as cost-optimal. For example, with the DR applied in the analysis in [28] (marked in grey in Figure 9), the HP is not competitive with DH or gas. In contrast, the HP is comparable to the other technologies with the updated DR types; in fact, the HP is the solution with the lowest NPV. Suppose the difference stemming from updated DR is corrected, so that the NPV of Package 7 and that of the baseline for the represented variations are equal. Nearly all the package solutions with lower energy reduction targets (Package 1-6) fall in the range of box plot whiskers for all three systems. This is logical, as the NPV of most of these packages is within \(\pm\)5-10% of that of the baseline. Comparing the box plots' interquartile ranges, the number of packages falling within range is reduced to four for DH and gas and two for HP. This indicates that the selection of packages with similar NPVs should be taken with caution as variation in the input may cause the rearrangement of the packages. On the contrary, the NPV of the packages with similar or higher energy-saving targets than the baseline (Packages 8-10) falls outside the respective box plot's ranges. The higher energy savings in Packages 8-10 are achieved by additional or more expensive renovation actions than the baseline. For DH and gas, the NPV of Packages 8-10 is at least 30% costlier than the baseline, whereas the NPV for the same packages combined with the HP is in the range of 20-30%. This indicates that the cost comparison between solutions with a significant difference in NPVs can be taken with certainty, assuming that the LCC approach for all solutions has been consistent.