abare.gov.au - research report 08.07

Results

It is important to note the quantitative results generated by the model (such as the realised price levels and the timing of supply augmentation) are a function of model assumptions and are not intended to be interpreted in any way as predictions or forecasts. A sensitivity analysis contained in appendix B demonstrates how the results change when certain parameter assumptions are altered.

Two scenarios are evaluated with the model: a rain-dependent augmentation scenario and a rain-independent augmentation scenario. This approach was necessary because of the ‘curse of dimensionality’ problem, which meant the inclusion of multiple investment projects would make the problem unfeasibly large. These scenarios are intended to be illustrative and are not meant to represent forecasts of specific ACT circumstances. The model time scale is seasonal (quarterly) and each scenario is run over an arbitrary 25-year time horizon, notionally the period 2000 to 2025.

Scenarios involving a single augmentation option will tend to overstate the extent of water scarcity relative to the case of multiple investment projects. This is because an additional investment project provides an option value benefit that is realised even if the project is not executed within the relevant time frame. For example, a water utility may adopt a more relaxed pricing policy if (following construction of a dam) it maintains an option to construct a desalination plant in the event it is required.

Rain-dependent scenario

This scenario assumes an augmentation project representative of a new dam as defined by the parameters set out in table 2.

The estimated price policy function specifies the optimal price given the time period, the prevailing storage level and the state of supply augmentation (that is, pre augmentation, during augmentation, or post augmentation). Figure e shows the estimated pre augmentation price policy function for an arbitrary time period (2015). As expected, the price policy function demonstrates a clear inverse relationship between price and the storage level.

As the storage level approaches 100 per cent, the price approaches, but does not necessarily reach, the SRMC. The optimal price is seasonal: higher in summer and lower in winter. At low storage levels price increases sharply to the maximum price level. The maximum price is that where non-essential demand is reduced to zero. This maximum price is dependent on the season, being highest in summer and lowest in winter. As discussed earlier, it may not be practical to use scarcity pricing in emergency situations where it is necessary to reduce consumption to essential levels. These maximum prices should therefore be interpreted more as shadow prices, representative of high-level water restrictions. In any event the probability of such prices being realised in the model is extremely low, see for example figure i.

2	Rain-dependent augmentation option parameters

Capital cost

$100 million

Ongoing cost

$1.5 million a year

Proportional increase in mean inflow

0.2

Additional storage capacity

70 000 ML

Lead time

2 years

When interpreting figure f, note the initial storage capacity of 200 gigalitres increases to 270 gigalitres following augmentation. The estimated prices are briefly lower pre augmentation, at around 200 gigalitres, given the higher probability of spills at this storage level.

The estimated optimal price is (for a given storage level and augmentation status) increasing in time as a result of demand growth. The optimal price is also (for a given time and storage level) lower post the completion of an augmentation project. Figure f shows the price policy function (pre and post augmentation for the time period spring 2015).

Figure g shows the estimated investment policy rule as a function of time and the prevailing storage level. For each point in time the investment rule defines a storage trigger point: for storage levels below this point the investment is executed. Over time the storage trigger point increases because of demand growth. The investment rule also displays strong seasonality. The storage trigger point peaks in winter when the project (new dam) will come on line, in time for the winter high rainfall season in two years time. This result is dependent on the assumption of a fixed (two-year) lead time, known with certainty. The investment storage trigger point reaches 100 per cent by winter 2009, rendering the remainder of the investment policy rule trivial.

Given the estimated policy functions, model simulations can be generated by drawing a series of inflow observations from the defined probability distributions. A Monte Carlo analysis can be performed by generating a large number of such simulations and combining the results. Figure h displays an example of a sinlge stochastic simulation. In figure h the increase in storage capacity represents the supply augmentation project (new dam) coming online. The timing of investment varies across simulations depending on the realised conditions (the stochastically generated inflows). The mean year of investment is 2008. Variability in the timing of investment for rain-dependent augmentation is relatively low compared with that of rain-independent augmentation (discussed in the next section).

Figure i shows the mean price level and 90 per cent confidence interval estimated by Monte Carlo analysis. The mean price level is increasing in time because of demand growth. The growth in the mean price level slows around the time of supply augmentation. Figure i also shows how the variability in price increases with the mean level of scarcity (mean price level).

3	Rain-independent augmentation option

Capital cost

$200 million

Ongoing cost

$10 million a year

Additional inflow

6000 ML a season

Additional storage capacity

Lead time

2 years

Rain-dependent scenario

The rain-independent scenario assumes a rain-independent augmentation project as defined by the parameters set out in table 3. In the ACT, water recycling is the most practical form of rain-independent supply, given the distance to the coast. However, it is intended that this scenario be representative of rain-independent augmentation generally, whether that be recycling or desalination.

The estimated pre-augmentation price policy function for the rain-independent scenario, is essentially identical to that estimated for the rain-dependent scenario. However, post augmentation the estimated optimal prices are lower in the rain-independent scenario (see figure j).

While the rain-independent option provides a smaller increase in mean inflows, it results in a substantial increase in the reliability of inflows. For a given storage level this increase in reliability substantially reduces mean water scarcity. It should be noted that the estimated prices in figure j do not reflect the higher operating and capital costs of rain-independent augmentation. In practice, given the need to recover costs, average water prices may be higher under rain-independent augmentation.

The estimated investment policy function is shown in figure k. The storage trigger points remain lower than in the rain-dependent scenario, peaking at around 60 per cent at the end of the simulation period (2025). With rain-independent augmentation the investment policy essentially involves delaying investment until storage levels decline substantially. There are two reasons for this. Firstly, rain-independent augmentation is more expensive and therefore there is more to be gained by delaying its introduction. Secondly, rain-independent augmentation provides additional inflows with certainty. This certainty allows the water utility to delay investment until storage levels are low, in the knowledge the project will provide inflows sufficient to improve storage levels and ensure the essential water supply is maintained.

The rain-independent augmentation investment rule also displays a degree of seasonality. With rain-independent augmentation the storage trigger point peaks in summer, when the project will come on line in time for the critical summer period in exactly two years time.

Figure l displays a single-example simulation for the rain-independent scenario, showing the realised price and storage levels as well as the augmentation time. In the rain-independent scenario simulations, a substantial drop in the price level is often observed following the introduction of the augmentation project.

Figure m shows the cumulative probability distribution over investment timing for rain-dependent and rain-independent augmentation. Rain-dependent augmentation occurs earlier on average (2008 compared with 2018) and is less variable. The timing of rain-independent augmentation is highly variable, being strongly dependent on realised inflow levels. For example, there remains a positive probability that a series of inflows is realised which allows the rain-independent augmentation project to be delayed beyond the simulation period. The results demonstrate the benefits of delaying investment in rain-independent supply in the face of significant inflow risk, consistent with a real-options approach to irreversible investment under uncertainty. A real-options approach to water infrastructure investment has previously been advocated by Acil Tasman (2007). While not modelled here, urban water utilities can use a number of alternative measures to manage risk and delay investment, including investing in lead time reduction, adopting smaller upgradeable investment projects (where the risk savings outweigh economies of scale) and pursuing temporary supply options such as water trade with rural water holders.

The results are also to some extent consistent with the behaviour of Australian water utilities in that demand management and other supply alternatives have generally been pursued prior to rain-independent augmentation. For example, the NSW Government did at one point have a stated policy that investment in desalination would occur only if storage levels dropped below 30 per cent (NSW Government 2006). However, in recent times most capital cities (including Sydney) have subsequently approved investments in rain-independent supply, although this has not been without controversy (see for example Brennan 2008).
Figure n displays the mean price for the rain-independent scenario. In this scenario the mean price rises quickly at first, given that augmentation is occurring later than in the rain-dependent scenario. The mean price falls gradually after year 17 as the probability of augmentation increases.

A sensitivity analysis over a number of model parameters was also conducted (the details are contained in Appendix B). One of the key results of this analysis is that investment in rain-independent supply is highly marginal, as small increases in the costs (capital or operating) or decreases in the benefits (more elastic demand, higher mean inflows, lower penalty for system failure) result in a large reduction in the probability of investment.

‘Staged’ scarcity pricing

As discussed earlier, scarcity pricing could potentially be implemented using a system of stages similar to that used for water restrictions. A staged scarcity pricing system can be represented in the model by limiting the number of points within the discrete price policy grid. The model results above are based on a 50-point price grid. To estimate the impact of a staged price system, the model was run separately for price grids containing 12 and 6 points. These limited price point simulations should not be interpreted as an implicit representation of water restrictions. Such an interpretation has not been intended and would be an oversimplification of current water restriction systems. A reduction in the number of price points yields a reduction in mean welfare, as measured by the objective value in the model. However, this reduction is relatively small (–0.4 per cent for the 12-point grid and –1.8 per cent for the 6-point grid). An example of a staged price policy function is shown in figure o.

A staged scarcity pricing system could be implemented under a similar framework to that used for water restrictions at present, in terms of the number of stages, the storage trigger points and the quantity targets (see, for example, table 1). The only real difference is that price is used to achieve the quantity targets rather than water restrictions. A staged scarcity pricing system would be simpler for the utility to implement than a fully flexible price, significantly reducing the frequency of price changes required.