## 2 Materials and Methods
### MFCS Financial Impact Calculation Method  
Discounted Cash Flow Method Analysis  
The primary criterion for assessing the effectiveness of energy conservation investments is the minimization of life cycle costs [76]. For a project to be considered as life-cycle cost (LCC) effective, it must have a net-present value (NPV) greater than or equal to zero, or an internal rate of return greater than the estimated discount rate [77]. Equally, the decision rule can be the choice of a scenario with the lowest LCC as per [PERSON] [78] in [PERSON] et al. [76]. For energy related projects, an LCC study should include the consideration of costs for at least the design, initial construction, energy and utilities, operations and maintenance, repairs, replacement, and salvage [79]. As the MFCS and the two alternative case scenarios do not consider, for instance, the energy for chemical production, they do not qualify as a fully completed LCC analysis. The MFCS and the two alternative case scenarios include the total cost of purchasing and operating the potable and non-potable water system over their assumed lifespan, excluding repairs, replacement and salvage and thus have been analyzed with a discounted cash flow method analysis.  
The simple payback period (SPP) determines the number of years required to recover the initial investment through the project (MFCS, S2, and PRP3) return and is calculated following Equation (19) [79].  
\[\text{SPP = (Initial cost)/(Annual savings)} \tag{19}\]  
The SPP methodology does not consider the time value of money, [PERSON] et al. [76] recommend using a combination of methods that include values such as the discounted cash flow method. The net present value or present worth (PW) can be used as a combination method with SPP [78]. NPV converts future cash flows by using a given discount rate and is used to convert future saving cash flows of the MFCS non-potable water system back to the present, which is then compared to the cost of the two alternative scenarios. If the NPV is positive, the investment is acceptable [80]. The NPV of the MFCS and the two alternative scenarios (S2 and PRP S3) can be calculated using a minimum attractive rate of return (MARR) or discount rate estimated by the Equation (20) mathematical relationship below [78], based on the UAE real interest and inflation rates where i is the market interest rate; f is the inflation rate; and j is the real interest rate.  
\[\text{i}=\text{f}+\text{j}+\text{f}\times\text{j} \tag{20}\]  
Equation (21) (ibid., p. 141) can be used to find the present worth (P) of the MFCS against Scenarios 2 and 3 where i is the interest percentage and A is the initial investment for n years or life span of the project (Equation (21).  
\[\text{P}=\text{A}\;(1+\text{i}\text{'n}) \tag{21}\]  
The reciprocal relationship between P and A is symbolized by the factor (P/A(i,n)) and is called the uniform series, capital recovery factor [79]. The present worth factor (1 + i'n) is extracted from the uniform series tables of (P[A, i, n) in [PERSON] et al. [76] to estimate the annual savings of the MFCS against the two alternative scenarios over 20 years.  
The results are then generated and compared by using Equations (22) and (23) for the MFCS and the two-alternative scenarios.  
\[\text{NPV}=\text{initial cost}-\text{PW of water savings }[\text{P}=\text{A}\;(1+\text{i}\text{'n})]+\text{PW of annual costs }[\text{P}=\text{A}\;(1+\text{i'n})] \tag{22}\]  
\[\text{Benefit/cost ratio }(\text{BC})=\text{Equivalents/Equivalents cost} \tag{23}\]  
where the benefits are the annual savings and the equivalent costs are the maintenance in addition to the energy and water costs. When the BC is greater than 1, the project is deemed economically attractive [78]. The total cost will include the estimated costs of installing and operating a system (including energy and water costs, and maintenance) as per the MFCS operation mode (use of non-potable water and makeup potable water) against a potable water system (S2) and a non-potable water system (PRP S3).