Battle of the Water Futures 🚰

Inflation Dynamics

Inflation captures the year-over-year change in the general price level. In the BWF, it affects all costs equally except energy prices, which follow different dynamics see ¿sec:energy-model?.

As inflation compounds over time, it can substantially erode water utilities’ purchasing power and alter the financial viability of capital-intensive interventions. While inflation is an exogenous macroeconomic variable beyond the direct control of water utilities, competitors can adopt strategic responses: front-loading major investments to lock in current prices, or stress-testing their masterplan against multiple inflation scenarios to ensure robustness.

In the absence of reliable long-term inflation forecasts, a reasonable baseline assumption is the central bank’s target rate (e.g., 2% for the European Central Bank).

Note that wherever unit prices are given only in base-year terms (e.g., only the value in year 2000 is reported in the input files), their value in year \(y\) (\(C(y)\)) is obtained by multiplying by the cumulative inflation index

\[ C(y) = C(0) \cdot \prod_{\tau = 1}^{y} \bigl(1 + \pi(\tau)\bigr) \qquad{(1)}\]

where \(C(0)\) is the base-year unit price and \(\pi(y)\) is the inflation rate in year \(y\).

Budget Allocation

A national budget (predefined over the planning horizon) is distributed annually across utilities to fund infrastructure interventions and operational expenses.

Competitors must decide how to distribute this budget among utilities in every year. Budget distribution can follow several principled rules: proportional allocation to population size; inverse-proportional schemes favuoring smaller regions; income-based allocations reflecting socioeconomic considerations; inverse-proportional schemes favuoring less wealthy regions; or fully customised schemes.

Water Pricing

Water utilities generate revenue selling water to three types of customers: residential users, businesses, and, possibly, other water utilities. Residential and commercial customers are billed using a two-part pricing scheme: a fixed service charge (\(\text{€}/year\)) and a volumetric charge based on consumption (\(\text{€}/m^3\)). For simplicity, both retail customer types face identical rates within each utility (with also no differentiation by income class or other categories). Water transactions between utilities, however, use only a volumetric charge based on the net exchange at the end of the year.

Thus, the total revenue for a water utility \(w\) in year \(y\) is:

\[ \text{REV}_w(y) = \sum_{m \in \mathcal{M}_w} P_w^\text{fixed}(y) + P_w^\text{variable}(y) \cdot Q^\text{BIL}_m(y) + \sum_{w' \in \mathcal{W}^-} P_w^\text{sell}(y) \cdot Q^{w'+}_w(y) \qquad{(2)}\]

where \(P_w^\text{fixed}(y)\) and \(P_w^\text{variable}(y)\) are the fixed and volumetric components of the retail water price, \(Q^\text{BIL}_m\) is the delivered billable demand in municipality \(m\), \(\mathcal{M}_w\) is the set of municipalities served by water utility \(w\), \(P_w^\text{sell}(y)\) is the volumetric charge that utility \(w\) applies for inter-utility water sales, \(Q^{w'+}_w(y)\) is the net positive volume of water sold by utility \(w\) to utility \(w'\), and \(\mathcal{W}^-\) is the set of water utilities excluding utility \(w\).

The net water exchange between utilities \(w\) and \(w'\) is defined as:

\[ \begin{aligned} \Delta Q_{w}^{w'}(y) &= \sum_{t \in \mathcal{Y}} \sum_{j \in \mathcal J _ {(w,w')}} Q_{j}(t) \\ Q_{w}^{w'+}(y) &= \max ( \Delta Q_{w}^{w'}(y), 0 ) \\ Q_{w}^{w'-}(y) &= - \min ( \Delta Q_{w}^{w'}(y), 0 ) \end{aligned} \qquad{(3)}\]

where \(t\) is the simulation timestep, \(\mathcal{Y}\) is the set of timesteps in year \(y\), \(Q_j(t)\) the flow over connection \(j\) from the set of connections between the water utilities \(\mathcal J_{(w,w')}\) (with flow direction positive from \(w\) to \(w'\)).

Note that if a water utility has a negative net exchange with another utility (i.e., \(\Delta Q_{w}^{w'}(y) <0\)), that will be regarded as a water import cost:

\[ \text{WIC}_w(y) = \sum_{w' \in \mathcal{W}^-} P_{w'}^\text{sell}(y) \cdot Q^{w'-}_w(y) \qquad{(4)}\]

where \(P_{w'}^\text{sell}(y)\) is the volumetric charge applied by utility \(w'\) for water sales.

Participants must decide the water pricing adjustment strategy. They can either let all three quantities adjust according to inflation, or define a custom policy by specifying the yearly percentage increase for each of them independently.

Bond Issuance

Whenever a water utility is unable to cover its expenditures in a given year, it finances the resulting deficit by issuing nationally backed bonds. Bonds are automatically generated to cover the utility debt in that year.

Specifically, the bond amount is \(\kappa\) times the debt, i.e., \(\mathrm{amount}_i=\kappa \cdot \mathrm{debt}_w(y)\) where \(\kappa \in [1,2.5]\). A value of \(\kappa\) equal to 1, implies that, depending on investor demand and prevailing market conditions, the proceeds from the bond issuance may barely cover the utility’s financing needs, leaving the balance for the following year around 0. In contrast, higher values of \(\kappa\) (closer to 2.5) generate a cash surplus with the downside of a larger principal obligation to be repaid at maturity. Bonds are also characterised by a maturity of \(M\) years, determining when the bond principal must be repaid, a coupon rate (\(\mathrm{coupon}_i\)), which determines the interest payments due each year, and a yield to maturity (\(\mathrm{yield}_i\)), which determines the price of the bond (\(\mathrm{price}_i\)).

Each year, the utility must repay the sum of principal amounts of all bonds reaching maturity plus the annual interest payments and and receives proceeds based on the bond price in that year. Formally:

\[ \begin{aligned} &\text{PRI}_w(y) = \sum_{i \in \mathcal {B}_w(y) : y=\tau_i+M} \mathrm{amount}_i \\ &\text{INT}_w(y) = \sum_{i \in \mathcal{B}_w(y)} \mathrm{amount}_i \cdot \mathrm{coupon}_i \\ &\mathrm{PRO}_w(y) = \mathrm{price}_i/100 \cdot \mathrm{amount}_i \end{aligned} \qquad{(5)}\]

where \(i\) indicates the i-th bond, \(\tau_i\) is the issuance year for bond \(i\), \(\mathcal{B}_w(y)\) is the set of bonds active for water utility \(w\) in year \(y\) and \(\mathcal {B}_w(y) : y=\tau_i+M\) the subset of bonds reaching maturity \(M\).

The i-th bond’s coupon, yield, and price are given by:

\[ \begin{aligned} &\mathrm{coupon}_i=r_f + \hat{\pi}(y=\tau_i) \\ &\mathrm{yield}_i=\mathrm{coupon}_i + a \cdot (1-d(y=\tau_i)) \\ &\mathrm{price}_i=\sum_{y=1}^M \frac{\mathrm{coupon}_i}{(1+\mathrm{yield}_i)^y} + \frac{100}{(1+\mathrm{yield}_i)^M} \end{aligned} \qquad{(6)}\]

where \(r_f\)​ is the risk-free rate (long-term government yield), \(\hat{\pi}(y=\tau_i)\) is the inflationary expectation at issuance year, \(a\) is the sensitivity to investor demand, and \(d(y=\tau_i)\)​ is the uncertain demand factor for bond \(i\) at issuance year.

Strong investor demand (\(d(y) > 1.0\)) increases \(\mathrm{PRO}_w(y)\) (through a lower yield and therefore higher price at issuance), while weak demand (\(d(y) < 1.0\)) decreases it. This simulates real-world bond pricing where investor appetite introduces uncertainty to the utilities budgetting.

While utilities cannot directly control bond yields, they can anticipate debt accumulation through scenario analysis and adopt strategies that maintain financial sustainability. For instance, utilities may design pacing of interventions to minimize borrowing, or evaluate alternative interventions that reduce the likelihood of large bond issuances during periods with unfavorable yield conditions.

The complete list of the bond model properties can be seen in tbl. 4, while the actual values for these variables can be inspected within the data files, which are mapped in Appendix A.