A simple formula method shows utilities exactly how much to discount prices. Electric utilities have drawn attention recently (and criticism from some quarters) for granting off-the-tariff discounts to customers deemed at risk for migration to lower-priced competitive alternatives. Typically, utilities have offered discounts to high-load customers in exchange for a long-term purchase commitment providing either more certain earnings, higher expected earnings, or both. How much utilities should discount rates depends, among other things, upon the likelihood and timing of retail access, the spread between existing tariffs and market power prices, and the likely level of stranded cost recovery.
Utility managers should consider rate discounts as a marketing strategy. They will want to do so to maintain sales, revenues and margins. In fact, a well-crafted agreement can protect a utility against substantial margin losses from market upheavals, such as retail choice for consumers. However, managers and their analysts must define the bounds of such a strategy and ensure that any discounting proposals will prove economically beneficial and consistent with their view of how competition will unfold in the future.
A simple, analytical framework can evaluate the effectiveness of offering discounted rates in exchange for long-term purchase commitments. A numerical example can derive the utility's maximum supportable discount, or MSD. A utility might offer this maximum discount in exchange for long-term purchase commitments. However, the MSD will vary with changes in underlying assumptions.
Trading Price for Security
Many electric utilities charge a bundled retail rate that includes a generation component two- to three-times higher than the market price of wholesale power. Such a rate threatens a significant reduction in the utility's gross margin, with all the attendant consequences for cost recovery and earnings impairment.
One way to hedge this risk is to offer rate discounts tied to long-term purchase commitments from certain high-risk customers. The discount trades off a reduction in price and cash flow for more secure sales and gross margins over the long run.
Customers would have at least two reasons to consider extending their purchase commitments, even if the discounted prices should exceed expected market prices. First, they cannot know with certainty when, or if, changing regulations will provide them with access to power at market prices. The more distant the prospect, the more a customer may prove willing to trade off long-term purchase commitments for immediate rate reductions. Second, customers may wish to hedge the price risk inherent in market-based purchases by signing a more certain, long-term pattern of prices even if they exceed expected market prices.
How should a utility choose a discount? The first step is to determine the maximum supportable discount it is willing to offer given certain assumptions regarding critical variables. These variables may appear complicated, but the key point is simple: How will changes in the regulatory structure alter future revenues and, more importantly, gross margins.
A Hypothetical Example
Suppose a hypothetical utility is concerned that retail wheeling might occur at some point over its five-year planning horizon, giving customers access to power at market prices. It will either lose sales to competitors or will be obliged to cut rates for its generation component. In either case, expected revenues and margins will be reduced from those produced by sales at existing tariff levels.
Assume a utility attempts to forecast total revenues and margins over the next five years from an existing customer who consumes 1 million kilowatt-hours per year at a tariff rate of 5¢/kWh. Assume further that the forecast tariff rate remains constant over the five-year period and that the utility's marginal cost of production is equivalent to the market price of power, or 2¢/kWh for each of the next five years. (Some may question whether the utility's marginal production cost or the market price of power is the appropriate variable to use when calculating gross margin. In this example, we assume they are equivalent, so the question is moot.) Finally, assume the utility's cost of capital is 10 percent.
If the customer has a predictable load, and no possibility exists of lost sales from competition, it is a relatively simple matter to forecast revenue and gross margin values annually and over time. Total annual revenues, marginal costs and gross margins would total $50,000, $20,000 and $30,000, respectively, producing cumulative present value revenues and gross margins of $189,539 and $113,724, respectively. While tariff rates can be forecast with a high degree of certainty, marginal costs are likely to be somewhat more difficult to project, making the calculated gross margins sensitive to this parameter. For example, if marginal costs were forecast to be 3¢/kWh instead of 2¢/kWh, annual margins would fall to $20,000, all other factors remaining equal.
In our example, if the customer switches all of his load to another supplier, the utility loses all revenues and margins at existing tariffs. In the alternative, if the utility attempts to retain the customer by reducing rates to market prices, revenues will decline to $20,000 per year, and margins will fall to zero. In either case, the effect on gross margin is the same (em full loss of gross margin. Facing this prospect, the utility might be willing to reduce its tariff rate in advance of retail wheeling, in exchange for purchase commitments that enable it to preserve some portion of its current expected gross margin. But how much should the utility discount the price?
Factoring the Probability of Competition
For a given forecast of market prices, the magnitude of the preemptive rate reduction will depend upon the perceived likelihood and timing of retail access. For example, if the utility manager was absolutely certain that retail access would be implemented immediately, the MSD would be 3¢/kilowatt-hour since it would stand to lose this much without the discount. (However, if the utility believes that for some reason the customer would choose an alternative supply, the MSD would have to be adjusted to reflect this expectation.) If, on the other hand, the utility manager assigned a relatively low probability to the advent of direct access, expected revenues and margins would decline by lesser amounts, and thus the appropriate discount would be correspondingly smaller.
To complete the picture, the utility has to consider the likelihood of direct access. Suppose that the utility believes there is a 50-percent chance that retail access will be implemented by the beginning of the fifth and final year of the analysis period. Assuming that the utility analyst believes there is an equal chance that direct access will occur in any particular year, it can be shown that the cumulative probability of 50 percent implies an annual probability of 12.94 percent. %n1%n Using this information we derive the probabilities that direct access (and customer departure) occurs for each of the five years (see Figure 1).
In Figure 1, the probability values in each circle (node) show the probability that customer departure occurs at the beginning of the first year, beginning of the second year, and so on. The computed values are based on the assumption that the customer does not return to the utility supplier once he has left. The node connected to the rounded rectangle, labeled Yr. 1, shows that there is a 12.94 percent chance of customer departure in the first year. The node connected to Yr. 2 shows a 11.27 percent chance that customer departure will occur at the beginning of year two. This second-year figure is calculated as the product of the probability that the customer stays in year one (87.06 percent) times the probability that of leaving (12.94 percent) in any year. In similar fashion, the probability of customer departure at the beginning of the third year is calculated as the product of the probability that the customer stays the first two years (87.06 percent ' 87.06 percent) and the independent probability of departure (12.94 percent). Given all of these assumptions, the expected gross margins are shown on Table 1.
When Bypass Occurs
In Table 1, Column 2 shows the annual gross margin and the cumulative present value gross margin if the customer continues to take service at the current tariff rates throughout the entire five year period. Column 3 shows the gross margin impacts if the customer should opt for an alternative generation supplier at the beginning of the first year. In that case the utility would recover no gross margin contribution for any year over the five-year period.
Columns 4-7 show the gross margin if the customer opted for a nonutility supplier at the second year, third year, and so on, respectively. The row labeled "Cum PV" refers to the cumulative present value gross margin for each possible outcome, discounted at the assumed 10 percent cost of capital. The row labeled "Prob." refers to the probability of occurrence of each outcome. Since there is a 12.94-percent chance that the customer will seek an alternative supplier each year, the probability that the customer leaves at the beginning of the first year is just that.
The remaining probabilities are determined as described above. That is, each value represents the conditional probability that the customer leaves in any particular year (I), given the cumulative probability that he has remained a utility customer in year (I-1). The row labeled "Prob. Wtd." is just the simple product of the values in the preceding two rows. The final row shows the expected CPVGM, which is the sum of the Prob. Wtd present values. The resulting value, $78,496, denotes the present value gross margin the utility can expect in the absence of a discount from tariff rates in exchange for a fixed commitment from the customer to take service over the five-year period. It is this value of expected gross margin that is used to determine the MSD from existing tariffs that provides for the same cumulative present value gross margin.
Fixing the Discount
To determine the maximum supportable discount, the first variable to solve is price, which, when reduced by marginal cost, multiplied by the annual sales volume and discounted over the five-year period, will provide for the same level of CPVGM ($78,496) as calculated in Table 2, where it was assumed that no discount or contract extension was in place.
(1) CPVGM ($78,496) =
(Pi - MCi) ' Si /(1+d)I
P = leveled discounted price
MC = marginal production cost
d = discount rate
I = year
S = sales
Recognizing that P is assumed to be constant throughout the entire period and rearranging terms we find that:
(2) CPVGM =
PSi/(1+d)I - (Mci ' Si)/(1+d)I
(3) P = [CPVGM +
CPVMC] / CPVS
In this example, P is equal to 4.07¢/kWh. Given this value, the MSD is an 18.59-percent reduction from the tariff rate of 5.0¢/kWh. Equation (3) shows that it is calculated as the sum of the CPVGM and the cumulative present value marginal cost (CPVMC) divided by the cumulative present value sales volume (CPVS). Table 2 verifies that this is the correct value.
As can be seen from Table 2, the cumulative present value margin ($78,496) is equal to the expected cumulative present value margin derived in Table 1 where it was assumed that no discount and contract extension was in place. Thus, a discounted fixed price of 4.07¢/kWh produces the same CPVGM the utility can expect to receive by maintaining its current tariff at 5¢/kWh given the assumed probabilities that direct access will occur over the forecast period. %n2%n
Fixing the Discount
The appropriate discount is a function of the anticipated path of competition, and the spread between tariff rates and market prices. %n3%n The MSD (18.59 percent) derived above, assumes there is a 50-percent cumulative probability of customer departure and a 3¢/kWh spread between tariff and market price. Varying these assumptions produces significantly different results. This effect is illustrated in Table 3.
The columns labeled 25 percent, 50 percent, and 75 percent refer to different assumed values for the cumulative probability of retail access (and customer departure) over the analysis period. The rows containing the values 3.5¢/kWh, 3¢/kWh, and 2.5¢/kWh reflect alternate values for the difference between the tariff rate (5¢/kWh) and market price. Given each cumulative probability value, we derive the corresponding probability of retail access for each year assuming, consistent with the original example, that there is an equal chance that direct access will occur in any particular year.
The data show MSDs under varying assumptions regarding spreads and the probability of retail competition. These results indicate that the MSD can vary significantly as the assumptions change, with the highest MSD (35.43 percent) occurring where the spread is highest (3.5¢/kWh) and the cumulative probability is highest (75 percent). The lowest MSD (7.32 percent) is obtained where the spread between tariff and market price is lowest (2.5¢/kWh) and the cumulative probability is lowest.
It is interesting to note that the MSD varies more widely across cumulative probability values than it does across changes in the spread between tariff and market prices. This can be seen by noting that the MSD varies from 7.32 percent to 25.31 percent given a spread of 2.5¢/kWh. At a spread of 3.5¢/kWh, the MSD varies from a low of 10.25 percent to a high of 35.43 percent. Conversely, the MSD varies much less with changes in spread for each given cumulative probability value. At 25 percent, the MSD goes from a low of 7.32 percent to a high of 10.25 percent. With a cumulative probability of 75 percent, the MSD varies from a low of 25.31 percent to a high of 35.43 percent. Clearly, the MSD is highly dependent on the assumptions one uses. These results suggest that errors in anticipating the likelihood of regulatory changes that allow for direct access may be more costly than errors in accurately forecasting market prices over time. t
James C. Cater is director of strategic analysis at Central Vermont Public Service Corp. Cater is a Chartered Financial Analyst and holds a BA and MA in economics.
Table 1. Cumulative Present Value of Margin vs. Year of Bypass
Year Margin Margin Margin Margin Margin Margin
Stay Leave Yr. 1 Leave Yr. 2 Leave Yr. 3 Leave Yr. 4 Leave Yr. 5
(1) (2) (3) (4) (5) (6) (7)
1 $30,000 $0 $30,000 $30,000 $30,000 $30,000
2 $30,000 $0 $0 $30,000 $30,000 $30,000
3 $30,000 $0 $0 $0 $30,000 $30,000
4 $30,000 $0 $0 $0 $0 $30,000
5 $30,000 $0 $0 $0 $0 $0
Cum PV $113,724 $0 $27,273 $52,066 $74,606 $95,096
Prob. 50.0 percent 12.9 percent 11.3 percent 9.8 percent 8.5 percent 7.4 percent
Prob Wtd. $56,878 $0 $3,072 $5,107 $6,370 $7,069
Expect Value $78,496
Table 1 depicts all of the possible outcomes that could occur given the assumption that there is a 12.94-percent probability that retail choice (and customer departure) occurs in any single year over the course of five years.
Table 2. Cumulative Present Value
of Margin w/No Discount.
Year Revenues Marginal Costs Margins
1 $40,707 $20,000 $20,707
2 $40,707 $20,000 $20,707
3 $40,707 $20,000 $20,707
4 $40,707 $20,000 $20,707
5 $40,707 $20,000 $20,707
CUM PV $154,312 $75,816 $78,496
Table 2 shows that the cumulative present value margin is equal to the expected cumulative present value margin (derived in Table 1), where it is assumed that no discount and contract extension was in place.
Table 3. Price Spread
(Tariff - Market)
vs. Probability of Bypass.
SPREAD (¢/kWh) 25% 50% 75%
3.5 10.25% 21.68% 35.43%
3.0 8.79% 18.59% 30.38%
2.5 7.32% 15.49% 25.31%
Table 3 illustrates that the appropriate discount is a
function of the anticipated path of competition and the spread between tariff rates and market prices.
The Analytical Framework
The rate discount depends on the cumulative present value of gross margin.
MSD. The maximum supportable discount is defined as the percentage discount from tariff rates that would produce the same CPVGM (see below) with or without the contract extension. It represents a point of equivalent mathematical expectation. A discount greater than the MSD would produce a CPVGM that is lower than the expected value assuming no-discount. A discount below the MSD threshold level would yield a higher CPVGM compared to the no-discount case. The smaller the discount offered, all other factors remaining equal, the larger the expected benefit to the utility.
CPVGM. The cumulative present value of gross margin is derived by first calculating the expected (i.e., probability weighted) gross margin, assuming no contract extension, given forecast tariff rates, and market prices over the relevant period of analysis. The resulting value for CPVGM is dependent upon the probability of losing customer load through competition. This value is then used to determine the discounted price that would yield the same CPVGM over the contract period, assuming a long-term purchase commitment from the customer. The benchmark CPVGM represents the probability weighted gross margin, assuming that direct access is possible at any time over the relevant planning horizon. In other words, it is necessary to identify all the possible gross-margin outcomes and their associated probabilities, over the entire period of analysis.
1Given a cumulative probability of departure CP and I number of years in the planning horizon, the annual probability of departure P is determined by the following formula:
P = 1 - (1 - CP)1/I
The analysis is based on the assumption that the annual probability of departure is constant through time. However, the analysis can be easily modified to account for annual probabilities that vary through time.
2In our example, the MSD is expressed as a discount to the leveled tariff rate, and we have demonstrated that the new leveled price yields the same CPVGM. As a practical matter, there is no reason why the discount would have to be structured in this form. The utility could offer the same effective discount in a variety of ways (e.g., lump sum rebate, annual rebates, front-loaded or back-loaded rate discounts). Thus, the analytical results could be utilized in the context of various marketing programs.
3Our analysis implicitly assumes that once a customer has left the system, the utility absorbs the entire financial consequences of the reduced gross margins. To the extent that the utility is allowed to recover the otherwise lost gross margin through a non-bypassable charge, the MSD would be lower than the 18.59 percent figure derived above and for those set forth below, in the sensitivity analysis section. For example, if t he utility could recover 50 percent of the lost gross margin occasioned by customer departure, the MSD would fall from 18.59 percent to 9.29 percent for our base case result.
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