MGMT 8605M Week 6 Sensitivity Write-Up Example

Ranked by a One Percent Nudge, Then by What We Actually Know: A Sensitivity Write-Up for a Water Utility's Drought Revenue Shortfall, Where the Mandated Cut Tops the Local Ranking but a Borrowed Price Elasticity Dominates the Uncertainty

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Walden University

MGMT 8605M: Financial Risk Management and Decision Making for Organizations

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Month Day, Year

Ranked by a One Percent Nudge, Then by What We Actually Know: A Sensitivity Write-Up for a Water Utility's Drought Revenue Shortfall, Where the Mandated Cut Tops the Local Ranking but a Borrowed Price Elasticity Dominates the Uncertainty

The Question and the Model

Millbrook Water, a composite municipal utility serving about 260,000 people in central California, faces a state-ordered 20 percent cut in residential use for six months of a drought year. Its finance staff built a model of the resulting revenue shortfall. Normal annual residential revenue is about $80 million, 30 percent of it from fixed monthly charges and 70 percent from volumetric charges. During the restriction, a drought surcharge of 28 percent on the volumetric rate is meant to recover most of the revenue lost to lower use. Customers respond to the surcharge as well as the mandate, so the model applies a price elasticity of residential demand to the surcharge on top of the mandated cut. The base case projects a six-month shortfall of about $1.7 million. This write-up asks one narrow question of that model: which input, moved slightly off its base value, moves the projected shortfall furthest?

One Percent, One Input at a Time

[after]

The fourth column moves each input by 1 percent of its own base value with the others held fixed. The last column moves each input across the range its source supports, explained below.

Table 1

Sensitivity of the Projected Drought Revenue Shortfall to Each Input

Why the Residual Is Fragile

The surcharge was sized to recover most of the revenue the mandated cut removes. A 20 percent cut in volume combined with a 28 percent higher rate would almost exactly restore volumetric revenue if customers did not also respond to the price. The projected shortfall is therefore a small residual left over after two large offsetting effects, and small residuals are fragile: any input that shifts either effect moves the residual by a large percentage. That is why every entry in the fourth column exceeds or approaches 1 percent even though the inputs moved by only 1 percent.

The Local Ranking

By the one-percent test, the depth of the mandated cut ranks first, the surcharge second and the elasticity third. A manager reading only this column would conclude that the mandate's depth is the input to watch.

What a Local Design Misses

A one-percent nudge measures how strongly the shortfall responds to each input near its base value. It says nothing about how uncertain each input is. Saltelli et al. (2008) warned that one-at-a-time local designs explore only a small corner of the space of possible inputs and can mislead badly when some inputs are uncertain over wide ranges. The depth and duration come from a state order and will vary only with compliance, perhaps by two points of depth or a month of duration. The surcharge and fixed-charge share are set by the utility and known. The elasticity is different. It is borrowed from published research, and that research shows a wide spread. Dalhuisen et al. (2003), synthesizing estimates from many studies, found price elasticities varying substantially with rate structure, location and study design, and Espey et al. (1997) found that factors such as season, income and rainfall systematically shifted the estimates. Taken together, the published estimates suggest that a price rise of a tenth trims household use by anywhere from a small fraction of that amount to most of it. Millbrook's −0.35 is a reasonable midpoint, but it is not Millbrook's own measurement.

Across that documented range, from −0.10 to −0.75, the projected shortfall runs from almost nothing to about $4.2 million, a swing larger than all other inputs combined. The local design ranked the elasticity third because a 1 percent change in it is small; the honest ranking puts it first, because its plausible range is wide.

The Top Input Is Borrowed

The input that dominates the uncertainty is the one the utility did not measure. That is a problem rather than a result: the revenue plan, and the reserve the utility holds against the shortfall, rest on a figure taken from other places and other times.

Evidence That Would Narrow It

Millbrook can narrow the range with its own data. Its billing records cover two earlier rate increases, in 2019 and 2023, and comparing use before and after each, adjusted for weather, would give a local elasticity estimate. During the drought itself, monthly billing data will show the response within the first two cycles, allowing the utility to adjust its reserve or the surcharge early.

References

Dalhuisen, J. M., Florax, R. J. G. M., de Groot, H. L. F., & Nijkamp, P. (2003). Price and income elasticities of residential water demand: A meta-analysis. Land Economics, 79(2), 292-308. https://doi.org/10.2307/3146872

Espey, M., Espey, J., & Shaw, W. D. (1997). Price elasticity of residential demand for water: A meta-analysis. Water Resources Research, 33(6), 1369-1374. https://doi.org/10.1029/97WR00571

Saltelli, A., Ratto, M., Andres, T., Campolongo, F., Cariboni, J., Gatelli, D., Saisana, M., & Tarantola, S. (2008). Global sensitivity analysis: The primer. Wiley.