For each individual item (such as demand nodes, transmission links, treatment plants and reservoirs), costs can be entered as capital, fixed operating, and variable operating costs. Capital and fixed operating costs are entered as an annual cost stream (capital costs typically use the LoanPayment function), whereas fixed operating costs are entered as a cost per unit of water (e.g., delivered, pumped, released or treated).
CostItem = CapitalCostItem + FixedOperatingCostItem + VariableOperatingCostItem
VariableOperatingCostItem = VariableCostRateItem * FlowItem
where CapitalCost and FixedOperatingCost are data.
Annual capital and fixed operating costs are spread evenly over the time steps of the year to get a cost per time step.
Benefits can also be entered for each individual item, both as fixed (annual) and variable (per unit flow).
BenefitItem = FixedBenefitItem + VariableBenefitItem
VariableBenefitItem = VariableBenefitRateItem * FlowItem
where FixedBenefit is data.
Annual Benefits are spread evenly over the time steps of the year to get a Benefit per time step.
In addition to itemized costs and Benefits, overall uncategorized system capital and operating costs and benefits can be entered as a whole.
Net cost is the total cost, net of any benefit.
NetCost = SystemCost + CostItem - SystemBenefit - BenefitItem
The net present value of future expenditures for capital and operations costs, net of any benefits. The NPV is the sum of the net present value calculation of the net costs for each of the future years modeled in the scenario
NPV is the future stream of benefits and costs converted into equivalent values today. This is done by discounting future benefits and costs using an appropriate discount rate, and subtracting the sum total of discounted benefits from the sum total of discounted costs. The discount rate is specified under the menu option General, Units, Monetary.
NPV = [ NetCostYear / ((1 + DiscountRate)(Year - BaseYear)) ]
The average cost of water is the net total cost per unit of water delivered to all demand site.
AverageCost = NetCost / DemandSiteInflowDS
Costs are incurred for transmission of supply and treatment of wastewater. Demand Site A has a demand of 100 units, of which only 60 is satisfied from the river. Of the 60 units of supply, half are consumed by the demand site. The other half are sent to Treatment Plant B for treatment, which returns the treated wastewater to the river.
The cost to transmit supply from the river through the transmission link to the demand site is $1000 per unit of water transmitted. The treatment plant was built in 2005 at a cost of $50,000,000, financed through a 30-year loan with a fixed interest rate of 5%. In addition to capital costs (loan payments), the treatment plant incurs ongoing operating and maintenance costs every year. The fixed operating cost is $200,000 per year for labor and maintenance fees; the variable operating cost is $5000 per unit of water treated.
AnnualTreatmentCapitalCost = LoanPayment(50000000, 2005, 30, 5%) = $3,252,571.75
MonthlyTreatmentCapitalCost = AnnualTreatmentCapitalCost / 12 = $271,047.65
MonthlyTransmissionOperatingCost = 60 * $1000 = $60,000
MonthlyTreatmentOperatingCost = (AnnualFixedTreatmentOperatingCost / 12) + MonthlyVariableTreatmentOperatingCost
AnnualFixedTreatmentOperatingCost = $200,000
MonthlyVariableTreatmentOperatingCost = 30 * $5000 = $150,000
MonthlyTreatmentOperatingCost = ($200,000 / 12) + $150,000 = $166,666.67
Total Operating Cost
MonthlyTotalOperatingCost = MonthlyTransmissionOperatingCost + MonthlyTreatmentOperatingCost = $60,000 + $166,666.67 = $226,666.67
MonthlyNetCost = MonthlyTreatmentCapitalCost + MonthlyTotalOperatingCost = $271,047.65 + $226,666.67 = $497,714.32
AnnualNetCost = MonthlyNetCost * 12 = $497,714.32 * 12 = $5,972,571.80
Net Present Value (NPV)
Assuming a base year of 2005, a time horizon of 30 years, a discount rate of 3%, and a constant demand and supply,
NPV = AnnualNetCost2005 / (1 + 3%)(2005 - 2005) + AnnualNetCost2006 / (1 + 3%)(2006 - 2005) + ... + AnnualNetCost2034 / (1 + 3%)(2034 - 2005)
NPV = $5,972,571.80 / 1.030 + $5,972,571.80 / 1.031 + ... + $5,972,571.80 / 1.0329 = $120,576,994.57
Average Cost of Water
AverageCost = $497,714.32 / 60 = $8295.24 per unit of water supplied to demand site