The Problem With Cost Allocation: The Heart of The Matter (Editor’s note: This is the second in a series of articles on costing and pricing electricity.)

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ost allocations reflected in demand charges for most electric generating facilities do not measure real economic costs of decisions to produce more or less electricity at any particular time. A failure to understand this simple, yet profound, fact makes it impossible to understand what cost means, how to measure costs, or how to price electricity services efficiently.

ican Economic Review, May 1961; “An Analysis of Fully Distributed Cost Pricing in Regulated Industries,” Ronald R. Braeutigam, Bell Journal of Economics, Spring 1980); “Simpson’s Reversal Paradox and Cost Allocation,” Shyam Sunder, Journal of Accounting Research, Spring 1983). The purpose here is to show precisely why common costs of generating facilities cannot be meaningfully allocated. The economic Allocating all costs is not explanation is intertwined with, or the other side of the way to know what is the coin of, the statistical really going on. The only reason why serious probway to know is by looking lems can arise with the allocation of common costs. at marginal or incremental These problems include costs or, more simply, by significant inconsistencies looking at the costs of between cost estimates to outright contradictions in particular decisions. results, depending on the allocation methods used. Though the examples used Demand charges attempt to do the im- here are simplified for exposition, they still possible: allocate the common cost of entail the conceptual principles in all their generating capacity in an economically force. They are not parlor game puzzles; meaningful way. This is because, in eco- rather; they reflect economic and statistinomic terms, most generating facilities cal realities that can be costly if ignored. The problem of how to deal with comrepresent common costs and such costs cannot be traced home and attributed to mon costs has been recognized for particular electric services in the same di- decades, and a controversy over the best rect and obvious way that leather can be approach continues today. Outside the traced to a pair of shoes. An increase or electric utility industry, for example, advodecrease in the output of electric services cates of allocating common costs does not result in a proportionate increase acknowledge that common costs “are a particularly difficult problem for most or decrease in cost. This important fact about common cost companies.” Nonetheless, they argue that was recognized more than three quarters such costs “must be broken down and asof a century ago (Studies in the Economics signed to discrete business units or of Overhead Costs, John Maurice Clark) product lines, even if it means being arbiand reemphasized many times since then trary by some standard.” This must be in leading economic and accounting jour- done because “Allocating all costs is the nals (“Fully Distributed Costs in Utility only way to know what is really going on Ratemaking,” James C. Bonbright, Amer- [Emphases added].” (“Vital Truths about 20

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Managing Your Costs,” Charles Ames and James D. Hlavacek, Harvard Business Review, January-February 1990) The economic approach is opposite. Allocating all costs is not the way to know what is really going on. The only way to know is by looking at marginal or incremental costs or, more simply, by looking at the costs of particular decisions. Critics of cost allocation (fully allocated cost methodologies) argue “not all costs are relevant for every pricing decision.” Relevant costs are those that affect net income. Relevant costs are those that “are incremental (not average), avoidable (not sunk).” (The Strategy and Tactics of Pricing: A Guide to Profitable Decision Making, T. Nagel and R. Holden) A proper understanding of common costs is especially important in the electric utility industry because the industry is so capital-intensive and because a large part of its capital costs are “common.” The treatment of such costs is the central difficulty in designing electric rates. It is at the heart of disagreements over whether one customer class is subsidizing another, and of discussions of issues such as demand-side management and price discrimination. To illustrate, assume there are two separate companies: one produces wool, the other mutton. The wool company requires a sheep for one unit of its output, and the mutton company requires a sheep for one unit of its output. Each company pays $400 for a sheep (a total of $800). The wool company has an additional $100 in processing costs to produce a unit of output while the mutton company incurs a processing cost of $300 for a unit of its output. Together, the total cost of the two outputs is $1,200. This table summarizes these costs: PUBLIC POWER

By John Kelly

Wool Co. Mutton Co. Total Sheep ....................$400............$400............ $800 Processing...............100..............300...............400 Total.......................$500............$700..........$1,200

Now assume that the separate companies decide to merge in order to reduce their costs. The above table would look something like this:

Setting out on their task, the accountants confront the central problem: How, exactly, does one allocate common cost? Some argue for an even 50-50 split, while others argue that allocations should be based on proMethod for Allocating portions of processing Common Cost Fully Allocated Cost Profit costs, labor costs, or revWool Mutton. Wool Mutton enues. Such allocations Even Split ...................................$300 ...........$500 .......... $280 ...........$280 produce the following Proportional Processing Cost ......200 .............600 .............380 .............180 fully allocated cost and profit estimates (In this Proportional Labor Cost...............180 .............620 .............400 .............160 example it is assumed Proportional Processing Cost ......270 .............530 .............310 .............250 that the direct labor costs are $50 for wool and $200 for mutton, and revenues are The different methods produce cost es$580 and $780, respectively.): timates that vary significantly, ranging

Here’s Why Cost Allocation Does Not Work

Wool & Mutton Co. Total Sheep .....................$???.............$???............ $400 Processing...............100..............300...............400 Total..........................???...............???.............$800

The question marks indicate uncertainty about what portion of the cost of each single sheep should be assigned to each product. This wouldn’t seem to be a serious concern. The objective was to cut costs and the total cost of the combined output dropped a third, from $1,200 to $800. But, in the words of a recent, popular tune, “there’s always some reason not to feel good enough.” The question marks trouble the cost accountants in the newly merged company and the accountants have convinced management that significant time, money and effort have to be spent trying to replace the question marks with numbers, i.e., numbers that fully allocate common costs. The accountants are prepared to spend a significant part of the $400 in merger savings, (and more if need be) to find out how to allocate the cost of the sheep. www.APPAnet.org

A 1983 accounting journal article (“Simpson’s Reversal Paradox and Cost Allocation,” Journal of Accounting Research, Shyam Sunder, Spring 1983) does a good job explaining why the use of methodologies to allocate common costs can cause a reversal in the movement of unit cost estimates and why such methodologies are unsound. The article contains an excellent business accounting example that is too involved to present here. Instead, the important conceptual point can be illustrated with a simpler, “non-business” example from the same article. Assume there are four boxes with these numbers of black and white chips in them: Boxes 1

2

3

4

1+3

2+4

Black Chips

5

3

6

9

11

12

White Chips

6

4

3

5

9

9

The chance of drawing a black chip from Box 1 is better than from Box 2 (5/11>3/7), and the chance of drawing a black chip out of Box 3 is better than Box 4 (6/9>9/14). Intuitively, we tend to think that if Boxes 1 and 3 are combined, the probability of drawing a black chip is better from this combination than from the combination of Boxes 2 and 4. This is because we tend to assume that each box contains the same number of chips. But in this example they do not, and the chances of drawing a black chip are better from the combination of Boxes 2 and 4. Many who attempt to allocate common costs fail to appreciate the fact that the different weights implicit in different methodologies not only produce costs estimates that can differ significantly, but also lead to estimates that contradict one another.

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The Problem With Cost Allocation

put given the prevailing price for that output. They provide cost estimates that reflect the opportunity cost (for a business, the impact on net income) to produce more or less of a particular good. In the above example, the real costs—those relevant to day-to-day business decision- making—are the processing costs of $100 for wool and $300 for mutton. If the market price exceeds the processing costs, then it is worthwhile to offer these products in the market.1 The basic problem of allocating common cost is the same, regardless of whether the common cost is a sheep or a 500-MW power plant. Demand charges calculated to allocate the cost of a power plant to customer classes use traditional methodologies (e.g., coincident and non-coincident peaks) that have the same shortcomings of the allocation methods used in the wool and mutton example. Consequently, the methods do not provide reliable estimates of the real cost of electricity. Another example illustrates how attempts to force allocations of common costs can lead to contradictory results as well as inconsistent ones. It focuses on the statistical shortcomings of such allocations. (This example is adapted from Managerial Uses of Accounting Information by Joel Demski.) Assume that a company produces products A and B. The variable cost of Product A is $10 and the variable cost of Product B is $1. Also assume that there are two production plans. Under Production Plan 1 the company produces 3,000 units of Product A and 1,000 units of Product B. Common costs are $50,000. What are the unit costs under Production Plan 1? In the table below the common costs are allocated based on the variable costs (e.g., $30,000/$31,000 to Product A under Production Plan 1) and then on output:

Fully allocated cost methodologies do not yield reliable information about whether it is worthwhile for a business and for society to produce another unit of output given the prevailing price for that output. from $180 to $300 for wool, and from $500 to $620 for mutton. As a consequence, the profit estimates vary significantly. If the merged company decides on a 50-50 split for allocating costs and if the market price for a unit of wool is $580, then the company will continue producing wool because it would make a profit of $280 on each unit. But what if the market price fell by half, to $290 per unit? The company would complain that it would lose money ($10 per unit, $300 unit cost minus $290 market price) if it continued producing and selling wool. However, if any of the other three allocation methods were used to allocate costs, the lower market price would still be regarded as profitable. These inconsistent results illustrate the arbitrariness of attempts to allocate common costs. They are arbitrary not in the sense of being capricious; rather, they are arbitrary in that they are not subject to fixed rules or principles for choosing between methods. The choice of method is left to personal preference. In the worst case, the method chosen may be dictated by the results desired rather than by a genuine interest in ascertaining real cost. So which method yields the real cost of supplying wool and mutton? At this point, adherents to fully allocated cost methodologies typically offer a vague response that never seems convincing, and fails to provide useful guidance for choosing between methods. Fully allocated cost methodologies do not yield reliable information about whether it is worthwhile for a business and for society to produce another unit of out22

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Production Plan 1 Per Unit Cost Based on: Common Cost Common Cost Allocated by Allocated by Relative Relative Percent of Percent of Variable Cost Variable Cost Product A .........$26.13 ....................$22.50 Product B..........$ 2.61 .....................$13.50

That the two methods produce significantly different unit cost estimates is easy to see, but there is also a change in the estimates that is less obvious. The unit cost of Product A decreases when going from allocations based on variable cost to allocations based on output while the unit cost of Product B increases. This inconsistency alone would seem to make the producers and users of common cost allocations estimates skeptical about the reliability of the cost estimates. If not, the additional fact that the inconsistency can easily turn to contradiction should. Assume there is also Production Plan 2. Under this plan 2,500 units of Product A are produced and 2,500 units of Product B. Common costs increase slightly to $55,000. Allocating common costs as before produces these unit costs:

Production Plan 2 Per Unit Cost Based on: Common Cost Common Cost Allocated by Allocated by Relative Relative Percent of Percent of Output Variable Cost Product A .........$30.00 ....................$21.00 Product B..........$ 3.00 .....................$12.00

1

This assumes that the prevailing market price reflects the price of a competitive market. But even if this were not the case, it does not change the fact that the relevant cost to first focus on is the marginal or incremental cost of the decision considered.

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The Problem With Cost Allocation

A Pricing Fable by Mike McMahon Jane operated a nice restaurant and was always on the lookout for ways to earn more profits. One day she decided to sell after-dinner mints. She placed them on the counter next to the cash register so all the customers would see them as they left the restaurant. The mints took up little space and required Jane to incur no new significant expenses other than for the mints. She bought the mints for 30 cents each and sold them for 50 cents each, thereby earning a profit of 20 cents on each mint. The mints were a big hit and soon Jane was selling 1,000 per month, and earning $200 in profits. Jane thought she had a nice moneymaker in mints. Then she talked to her accountant, Joe. Joe pointed out that the mints take up 0.05 percent of the floor space of the restaurant and therefore should be allocated that share of the lighting expense, the mortgage on the building and equipment, the labor benefits on Bill the cook, and all other overhead costs. After spending a few minutes with his pocket calculator Joe informed Jane that she must add 21 cents in overhead costs for each mint. Anything short of this would not recover the full costs of the mint and Jane would be losing money. “You see, Jane,” said Joe with a calm smile on his face, “you haven’t been making $200 per month in profits on your mints. Because you’ve left out all the overhead costs you are actually losing 1 cent on each mint. Therefore, you are losing $10 per month!” Jane trusted Joe. She stopped selling mints. As the years went by Jane took more of Joe’s advice. She often wondered how she could have been so foolish as to think that buying at 30 cents and selling for 50 cents could make her any money. One day Jane realized that her wine list was in the same position as the mints. Up till then she had figured that if she sold each bottle for more than it cost her she would make money. Joe showed her how the picture cleared right up when he allocated overhead costs to the wine. Jane cut wine from her menu. Jane eventually lost her restaurant due to bankruptcy from lack of sales. She now works the cash register on the late shift at another restaurant across town. Her new boss has told her how important it is to push the after-dinner mints prominently displayed on the counter. “You’d be surprised how much money we make off these things,” her boss said her first day on the job. No one is sure where Joe is these days. There are rumors that he went to work for a public utility somewhere in the Northwest. But who knows for sure? He’s somewhere. There’s always a market for a guy who can allocate overhead costs. Mike McMahon is senior manager of economics & business consulting for Snohomish County Public Utility District in Washington and a former chair of the American Public Power Association Pricing & Market Analysis Committee.

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Again, the unit cost estimates between the two allocation methods differ significantly, and the respective estimates for Products A and B again move in different directions. But there is another troubling phenomenon as well. It is not obvious when the cost estimates of the production plans are viewed individually. The following table combines and rearranges them by allocation method and production plan: Variable Cost Allocation Production Plan 1 Production Plan 2 Product A............$26.13 ...................$30.00 Product B ................2.61 .......................3.00 Output Allocation Production Plan 1 Production Plan 2 Product A............$22.50 ...................$21.00 Product B ..............13.50 .....................12.00

In the top, “Variable Cost Allocation” panel, the unit cost estimates of Product A and Product B both increase when moving from Production Plan 1 to Production Plan 2. But estimates for both products decrease, in the bottom panel, when common costs are allocated based on output. Consequently, one allocation method has unit costs increasing while the other has them decreasing. This is a potentially troubling contradiction, to say the least. Both examples illustrate why methodologies that allocate common costs fail on economic grounds: They produce estimates that do not reflect the opportunity cost, the real cost, of a decision to produce another unit of output. For example, the relative output method produces a unit cost of $22.50 for Product A under Production Plan 1. But the economic cost— the cost that will affect net income—is only $10, the variable cost. The expenditure of $50,000 for common costs will not change. In addition, the second example demonstrates why fully allocated cost methodologies are statistically unsound. Inconsistent and contradictory results may occur because different cost allocation PUBLIC POWER

The Problem With Cost Allocation

methods usually entail different weighting factors. For example, the relative proportions of revenues, labor or processing costs will likely differ. In the electric utility industry, the allocation factors (weights) produced by “one-month coincident peak,” “12-month coincident peak,” “average-excess” or other related costing methods usually differ. (The curious or mathematically minded reader can go to the sidebar article on page 21 for a fuller explanation why contradictions in estimates may occur.) The differences between economic and conventional accounting views of cost are not quibbles over fine points. In the electric utility industry, the adoption of one view over the other will affect rate design decisions involving billions of dollars. Expenditures for most generating facilities should properly be viewed as common costs, and the fact that these costs cannot be allocated in any meaningful economic way needs to be realized. Conventional methods that attempt to allocate these costs lead to inefficiencies in the use of ex-

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isting generating facilities and to unneeded construction of new ones. A pattern of rates that better reflects economic costs would make better use of existing facilities, reduce the total amount of capacity required and lower rates. Traditional, fully allocated costing methods do not provide the best practical and useful information for day-to-day business decision-making because they do not provide good indictors of costs. Consequently, a significant part of the time, effort, and money spent on such efforts is wasted. Finally, the economic view of cost and the inherent problems with attempts to allocate common costs are quite instinctive. They are the way most business persons would normally look at cost and allocation questions if they were not caught in a web of accounting conventions that hamper their common sense mental reflexes from working. ● John Kelly is director of economics and research for the American Public Power Association.

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