# Potential Study of Solar Thermal Cooling in Sub-Mediterranean Climate
## 4 Economic Feasibility  
This economic study is intended to evaluate the overall economic viability in-depth. The key financial indicators used for the evaluation include Present Worth (PW), Payback Period, and Internal Rate of Return (IRR).  
The \(PW\) method is the equivalent worth of all cash flows relative to some base or beginning point in time dubbed the present. That is, all cash revenues (incomes, saved energy, reduced CO\({}_{2}\) emissions) and expenses (auxiliary power consumption, maintenance) are discounted to the present point in time at an interest rate [26]. A positive PW for the absorption cooling system will mean that the project is feasible and a profit over the minimum amount required will be achieved. To find the \(PW\) as a function of interest rate (\(i\%\)) of the cash inflows and outflows, the future amounts need to be discounted to the present by applying Equation (1) [27]. To discount future amounts to the present by using the interest rate over the appropriate study period, we used the following:  
\[PW(i\%)=\left[\left(\sum_{k=0}^{N}F_{k}(1+i)^{-k}\right)+\left(A\left[\frac{ \left(1+i\right)^{k}-1}{i\left(1+i\right)^{k}}\right]\right)\right] \tag{1}\]  
where (\(i\%\)) is the effective interest rate; (\(k\)) is the index for each compounding period \(0\leq k\leq N\); (\(F_{k}\)) is future cash flow at the end of period (\(k\)); (\(A\)) is the end-of-period cash flows in a uniform series continuing for a specified number of periods, starting at the end of the first period and continuing through the last period; and (\(N\)) is the number of compounding periods in the study period. In this study, \(N\) was set to 25 years which represents the life expectancy of the system and the interest rate which was set to \(i=6\%\).  
Annual expenses include the maintenance costs and the operating energy and water costs. For maintenance costs, standards like the Association of German Engineers (VDI) 2067 use 2% of the investment costs. Chiller manufacturers calculate maintenance costs by 1% of the investment costs. For large thermal chillers, companies offer constant cost maintenance: the costs vary between 0.5% for large machines (up to 700 kW) up to 3% for lower-power machines [28].  
The payback period is the time required to recover the total investments by profit gaining. The payback period can be calculated by setting PW to 0. The simple payback period, \(\theta\), ignores the time value of money and all cash flows that occur after \(\theta\) (\(\theta\leq N\)) and calculates the number of years  
Figure 6: Water-lithium bromide (H\({}_{2}\)O-LiBr) 160 kW absorption chiller on GJU rooftop.  
required for cash inflows (Rvenues R) to just equal cash outflows (Expenses, E). For this study, where initial investment occurs at time 0, the simple payback period is given in Equation (2) [27]:  
\[\sum_{k=1}^{\theta}(R_{k}-E_{k})-I\geq 0 \tag{2}\]  
In addition, the discounted payback period, \(\theta^{\prime}\) (\(\theta^{\prime}\leq N\)), is calculated so that the time value of money is considered, as given in Equation (3) [27]:  
\[\sum_{k=1}^{\theta^{\prime}}(R_{k}-E_{k})(P/F,i\%,\ k)-I\geq 0 \tag{3}\]