# A Data-Driven Model for the Energy and Economic Assessment of Building Renovations
## 3 Results
### Economic Performance and Sensitivity Analysis of Retrofit Measures  
Figure 6 displays the ROI for each retrofit intervention across the three building clusters, providing a direct measure of economic efficiency. The highest ROI values are observed for Wall Insulation in Critical-consumption buildings (2.40), HVAC System Upgrades in High-consumption buildings (2.39), and Smart Home Systems in Moderate-High-consumption buildings (2.48).  
These findings demonstrate how different building types benefit from targeted intervention strategies: buildings with poor thermal envelopes (Critical consumption) achieve the greatest returns from insulation improvements; buildings with moderate envelope performance but inefficient systems (High consumption) benefit most from mechanical upgrades; while buildings with relatively better baseline performance (Moderate-High consumption) achieve optimal returns through control system optimization. Solar panels consistently show the lowest ROI values (1.15-1.27) across all clusters, indicating that, under current cost structures and without considering incentives, renewable energy generation represents a less financially attractive option compared to energy efficiency measures.  
* Robustness to Financial Assumptions  
To assess the stability and real-world reliability of the economic results, a sensitivity analysis was conducted on two key financial assumptions: the discount rate and energy price levels. These parameters strongly influence long-term investment outcomes and are  
Figure 6: ROI for each retrofit intervention across the three building clusters.  
subject to market fluctuations and policy shifts. This analysis enhances the robustness of the economic model by evaluating whether the identified retrofit priorities remain valid under different financial scenarios.  
This evaluation focuses on the three core economic indicators: NPV, ROI, and payback period.  
NPV estimates the cumulative benefit of a retrofit over its lifetime, accounting for the time value of money. It is calculated as:  
\[NPV=\sum_{t=1}^{n}\frac{Saving_{t}-MaintenanceCost_{t}}{(1+r)}\]  
where:  
* \(\text{Saving}_{t}\) = Annual energy saving in year t.
* MaintenanceCost\({}_{t}\) = Annual maintenance cost in year t.
* r = Discount rate.
* t = Year number (e.g., 1, 2, \(\ldots\), n).
* n = Total lifetime of the retrofit (in years).  
A positive NPV means the investment yields more financial benefit than it costs over time. ROI is calculated as:  
\[ROI=\frac{NPV}{Initial\_Investment}\]  
It expresses how much return is achieved per euro invested. An ROI above 1.0 indicates a profitable measure.  
The payback period is defined by the year when:  
\[\sum_{t=1}^{n}\frac{Saving_{t}-MaintenanceCost_{t}}{(1+r)^{t}}\geq Initial\_Investment\]  
It shows how many years are needed to fully recover the initial investment through annual energy savings.  
* Sensitivity-Based NPV Formulation  
To simulate economic uncertainty, a sensitivity-adjusted version of the NPV formula was used. This accounts for potential variation in key parameters:  
\[NPV(\delta)=\sum_{t=1}^{n}\frac{Saving_{t}\big{(}1+\delta_{energy}\big{)}-MaintenanceCost_{t}(1+\delta_{cost})}{(1+r+ \delta_{rate})^{t}}\]  
where:  
* \(\delta_{\text{energy}}\)= Percentage change in energy prices (e.g., \(\pm\)20%).
* \(\delta_{\text{cost}}\) = Change in maintenance or retrofit costs.
* \(\delta_{\text{rate}}\) = Adjustment to the discount rate.
* r = Baseline discount rate.  
These results demonstrate that the model's economic recommendations remain valid even under significant variations in key financial assumptions. The sensitivity analysis confirms the overall robustness of the proposed methodology, reinforcing its applicability in real-world policy and investment decision making.