## 2 Materials and Methods
### DATA4: The M-GRT Computer Support Tool
#### 2.1.2 M-GRCT Financial Control  
The economic viability criteria of the M-GRCT model [23] were built from two waste management business models. The first model was defined considering a linear waste management strategy, in which the operation consists of a waste collection system and final landfilling without obtaining recycled materials. The second model is based on circular economy techniques, which considers obtaining recycled by-products and their reincorporation into production chains. The model was applied to two municipalities (Arbelaez and Tibasosa), so that, in total, the following four scenarios were analyzed: (i) economic valuation of the linear model in Arbelaez; (ii) economic valuation of the circular model in Arbelaez; (iii) economic valuation of the linear model in Tibasosa; and (iv) economic valuation of the circular model in Tibasosa. For the construction of the linear scenarios in each municipality, the income and cost figures reported by the mayors of Arbelaez and Tibasosa were used, and the corresponding projections were produced. For the construction of the scenarios of the circular model with M-GRCT, estimates of income, costs and investments were produced for the implementation of recycling plants for the use of recovered materials. In addition, for all the scenarios, the corresponding cash flows were constructed with a 10-year evaluation horizon. A 10% opportunity rate (or minimum expected return) was used. The results are expressed in EUR, taking a reference exchange rate of COP 4545.45 (Colombian pesos) for EUR 1. In addition, for the calculation of the cash flows, a financing component was assumed through bank credit, since municipalities with low-income levels do not have sufficient resources to carry out the investment with their own resources. The economic valuation criteria used are the net present value (\(NPV\)), the internal return rate (\(IRR\)), the benefit-cost ratio (\(BCR\)) and the return period (payback). These criteria are widely used in the economic valuation literature for the selection and/or prioritization of projects or investment alternatives [44; 45; 46; 47; 48]. \(NPV\) was calculated according to Equation (8) and IRR according to Equation (9). \[NPV=-INV_{0}-\sum_{j=0}^{N}\frac{C_{j}}{(1+OR)^{j}}+\sum_{j=0}^{N}\frac{B_{j} }{(1+OR)^{j}} \tag{8}\]  
\[0=\sum_{j=0}^{N}\frac{B_{j}}{(1+i_{IRR})}-\sum_{j=0}^{N}\frac{C_{j}}{(1+i_{ IRR})^{j}} \tag{9}\]  
where \(NPV\) is defined as the net value of the future cash flows expressed in the base year, \(INV_{0}\) is the investment at initial time, \(C_{j}\) is the net balance of expenses in period \(j\), \(B_{j}\) is the net balance of benefits in period \(j\), \(OR\) is the opportunity rate for a 10% return value (thispercentage is set as a reference, taking into account the average return of investment funds in Colombia), \(j\) are the periods of the evaluation time horizon (10 years), and \(\Sigma_{j=0}^{N}\) is the sum of the cash flows expressed in the base year. On the other hand, \(i_{IRR}\) is the internal return rate and is defined as the rate that converts the \(NPV\) to zero and represents the rate at which the investment returns. The \(IRR\) is calculated through interpolation using the input data to calculate the \(NPV\). To estimate the benefit-cost ratio (\(B/C\)), Equation (10) was used:  
\[B/C=\frac{\sum_{j=0}^{N}\frac{B_{j}}{(1+TO)^{j}}}{\sum_{j=0}^{N}\frac{C_{j}}{(1 +TO)^{j}}} \tag{10}\]  
where \(B/C\) represents the benefits obtained for every EUR of cost in the operation and is defined as the quotient of the present value of income over the present value of costs. To estimate the payback period, Equation (11) was used.