Fans of the Chevrolet Camaro and Pontiac Firebird mourned when General Motors (GM) announced that these classic muscle cars were headed for that big parking lot in the sky at the end of the 2001 model year. GM management said the Camaro and Firebird had become victims of America’s obsession with sport utility vehicles and light trucks. Management would have us believe that the kids who used to crave inexpensive but fun-to-drive muscle cars were now driving $35,000 Ford Explorers.
The truth is that poor product quality, outdated design, lackluster marketing, and tough competition from foreign rivals killed the Camaro and Firebird. It’s simply not true that young people, and the young at heart, no longer want cars that are fast, loud, and cheap. To convince yourself of this, simply go downtown in almost any city or suburb in America on Friday or Saturday night. It won’t be long before you get nearly blown off the sidewalk by some kid slouched behind the wheel of a “low-rider” with windows vibrating to the thump of ultra-amplified bass. In the 1970s or 1980s, that kid was in a Camaro or Firebird. Today, they probably drive a Honda Civic or Acura Integra. Both are relatively cheap, stylish, and easy to customize. If you’re not into customizing, try a Toyota Celica GT-S 2133 Lift back 2D (6-Spd.). It’s more than a stylish, dependable bargain priced at about $23,000. It’s fun to drive. A high quality car is more than neat looking and dependable; it’s a blast to get behind the wheel of a high-quality car.
Cost estimation and control is part of the continual process of making products that exceed customer expectations. Quick fixes don’t work. This chapter shows how making things faster, cheaper, and better requires a fundamental appreciation of cost concepts.1 1 Karen Lundegaard, “Big Three Trail Their Rivals in Consumer Reports Survey,” The Wall Street Journal Online, March 13, 2002.
WHAT MAKES COST ANALYSIS DIFFICULT?
Cost analysis is made difficult by the effects of unforeseen inflation, unpredictable changes in echnology, and the dynamic nature of input and output markets. Wide divergences between economic costs and accounting valuations are common. This makes it extremely important to adjust accounting data to create an appropriate basis for managerial decisions.
The Link Between Accounting and Economic Valuations
Accurate cost analysis involves careful consideration of relevant decision alternatives. In many instances, the total costs of making a given decision are clear only when viewed in light of what is done and what is not done. Careful decision analysis includes comparing the relative costs and benefits of each decision alternative. No option can be viewed in isolation; each choice plays an important role in shaping the relevant costs and benefits of all decision alternatives.
Evaluation of a proposal to expand output requires that revenues gained from added sales be compared with the higher production costs incurred. In weighing a recommendation to expand, managers must compare the revenues derived from investment and the cost of needed funds. Expected benefits from an advertising promotion must be measured in relation to the costs of personal selling, media romotion, and direct marketing. Even a decision to pave the employees’ parking lot or to refurbish the company lunchroom involves a comparison between projected costs and the expected benefits derived from improved morale and worker productivity. In every case, the decision-making process involves a comparison between the costs and the benefits resulting from various decision alternatives.
Corporate restructuring often involves eliminating nonstrategic operations to redeploy assets and strengthen core lines of business. When nonessential assets are disposed of in a depressed market, there is typically no relation between low “fire sale” proceeds and book value, historical cost, or replacement cost. Conversely, when assets are sold to others who can more effectively use such resources, sale proceeds can approximate replacement value and greatly exceed historical costs and book values. Even under normal circumstances, the link between economic and accounting values can be tenuous. Economic worth as determined by profit-generating capability, rather than accounting value, is always the most vital consideration when determining the cost and use of specific assets.
Historical Versus Current Costs
The term cost can be defined in a number of ways. The correct definition varies from situation to situation. In popular terminology, cost generally refers to the price that must be paid for an item. If a firm buys an input for cash and uses it immediately, few problems arise in defining and measuring its cost. However, if an input is purchased, stored for a time, and then used, complications can arise. The problem can be acute if the item is a long-lived asset like a building that will be used at varying rates for an indeterminate period.
When costs are calculated for a firm’s income tax returns, the law requires use of the actual dollar amount spent to purchase the labor, raw materials, and capital equipment used in production.
For tax purposes, historical cost, or actual cash outlay, is the relevant cost. This is also generally true for annual 10-K reports to the Securities and Exchange Commission and for reports to stockholders.
Despite their usefulness, historical costs are not appropriate as a sole basis for many managerial decisions. Current costs are typically much more relevant. Current cost is the amount that must be paid under prevailing market conditions. Current cost is influenced by market conditions measured by the number of buyers and sellers, the present state of technology, inflation, and so on. For assets purchased recently, historical cost and current cost are typically the same.
For assets purchased several years ago, historical cost and current cost are often quite different. Since World War II, inflation has been an obvious source of large differences between current and historical costs throughout most of the world. With an inflation rate of roughly 5 percent per year, prices double in less than 15 years and triple in roughly 22 years. Land purchased for $50,000 in 1970 often has a current cost in excess of $200,000. In California, Florida, Texas, and other rapidly growing areas, current costs run much higher. Just as no homeowner would sell his or her home for a lower price based on lower historical costs, no manager can afford to sell assets or products for less than current costs.
A firm also cannot assume that the accounting historical cost is the same as the relevant economic cost of using a given piece of equipment. For example, it is not always appropriate to assume that use costs equal zero just because a machine has been fully depreciated using appropriate accounting methods. If a machine could be sold for $10,000 now, but its market value is expected to be only $2,000 1 year from now, the relevant cost of using the machine for one additional year is $8,000.2 Again, there is little relation between the $8,000 relevant cost of using the machine and the zero cost reported on the firm’s income statement.
Historical costs provide a measure of the market value of an asset at the time of purchase. Current costs are a measure of the market value of an asset at the present time. Traditional accounting methods and the IRS rely heavily on the historical cost concept because it can be applied consistently across firms and is easily verifiable. However, when historical and current costs differ markedly, reliance on historical costs sometimes leads to operating decisions with disastrous consequences. The savings and loan (S&L) industry debacle in the United States during the late 1980s is a clear case in point. On a historical cost basis, almost all thrifts appeared to have solid assets to back up liabilities. On a current cost basis, however, many S&Ls proved insolvent because assets had a current market value below the current market value of liabilities.
The move by federal and state bank regulators toward market-value-based accounting methods is motivated by a desire to avoid S&L-type disasters in the future.
Although it is typical for current costs to exceed historical costs, this is not always the case. Computers and many types of electronic equipment cost much less today than they did just a few years ago. In many high-tech industries, the rapid advance of technology has overcome the general rate of inflation. As a result, current costs are falling. Current costs for computers and electronic equipment are determined by what is referred to as replacement cost, or the cost of duplicating productive capability using current technology. For example, the value of used personal computers tends to fall by 30 to 40 percent per year. In valuing such assets, the appropriate measure is the much lower replacement cost—not the historical cost. Similarly, if a company holds electronic components in inventory, the relevant cost for pricing purposes is replacement costs.
In a more typical example, consider a construction company that has an inventory of 1,000,000 board feet of lumber, purchased at a historical cost of $200,000, or $200 per 1,000 board feet (a board foot of lumber is 1 square foot of lumber, 1 inch thick). Assume that lumber prices rise by 50 percent, and the company is asked to bid on a construction project that would require lumber. What cost should the construction company assign to the lumber—the $200,000 historical cost or the $300,000 replacement cost? The answer is the replacement cost of $300,000. The company will have to pay $300,000 to replace the lumber it uses on the new construction project. In fact, the construction company could sell its current inventory of lumber to others for the prevailing market price of $300,000. Under current market conditions, the lumber has a worth of $300,000. The amount of $300,000 is the relevant economic cost for purposes of bidding on the new construction project. For income tax purposes, however, the appropriate cost basis for the lumber inventory is still the $200,000 historical cost.
When a firm uses resources, it bids against alternative users. To be efficient, a resource’s value in use must be at least as much as its value in alternative opportunities. The role played by choice lternatives in cost analysis is formalized by the opportunity cost concept.
Opportunity Cost Concept
Opportunity cost is the foregone value associated with the current rather than next-best use of an asset. In other words, cost is determined by the highest-valued opportunity that must be foregone to allow current use. The cost of aluminum used in the manufacture of soft drink containers, for example, is determined by its value in alternative uses. Soft drink bottlers must pay an aluminum price equal to this value, or the aluminum will be used in the production of alternative goods, such as airplanes, building materials, cookware, and so on.
Similarly, if a firm owns capital equipment that can be used to produce either product A or product B, the relevant cost of product Aincludes the profit of the alternative product B that cannot be roduced because the equipment is tied up in manufacturing product A.
The opportunity cost concept explains asset use in a wide variety of circumstances. Gold and silver are pliable yet strong precious metals. As such, they make excellent material for dental fillings.
However, when speculation drove precious metals prices skyrocketing during the 1970s, plastic and ceramic materials became a common substitute for dental gold and silver.
More recently, lower market prices have again allowed widespread dental use of both metals. Still, dental customers must be willing to pay a price for dental gold and silver that is competitive with the price paid by jewelry customers and industrial users.
Explicit and Implicit Costs
Typically, the costs of using resources in production involve both out-of-pocket costs, or explicit costs, and other noncash costs, called implicit costs. Wages, utility expenses, payment for raw materials, interest paid to the holders of the firm’s bonds, and rent on a building are all examples of explicit expenses. The implicit costs associated with any decision are much more difficult to compute. These costs do not involve cash expenditures and are therefore often overlooked in decision analysis. Because cash payments are not made for implicit costs, the opportunity cost concept must be used to measure them. The rent that a shop owner could receive on buildings and equipment if they were not used in the business is an implicit cost of the owner’s own retailing activity, as is the salary that an individual could receive by working for someone else instead of operating his or her own establishment.
An example should clarify these cost distinctions. Consider the costs associated with the purchase and operation of a law practice. Assume that the minority partners in an established practice, Donnell, Young, Doyle & Frutt, can be bought for $225,000, with an additional $25,000 needed for initial working capital. Lindsay Doyle has personal savings of $250,000 to invest in such an enterprise; Bobby Donnell, another possible buyer, must borrow the entire $250,000 at a cost of 15 percent, or $37,500 per year. Assume that operating costs are the same no matter who owns the practice and that Doyle and Donnell are equally capable of completing the purchase. Does the $37,500 in annual interest expenses make Donnell’s potential operating cost greater than that of Doyle? For managerial decision purposes, the answer is no. Even though Donnell has higher explicit interest costs, true financing costs may well be the same for both individuals. Doyle has an implicit interest cost equal to the amount that could be earned on an alternative $250,000 investment. If a 15 percent return can be earned by investing in other assets of equal risk, then Doyle’s implicit investment opportunity cost is also $37,500 per year.
In this case, Doyle and Donnell each have a financing cost of $37,500 per year. Doyle’s cost is implicit and Donnell’s is explicit.
Will total operating costs be identical for both individuals? Not necessarily. Just as the implicit cost of Doyle’s capital must be included in the analysis, so too must implicit labor costs be included for each individual. If Doyle is a senior partner earning $250,000 a year and Donnell is a junior partner earning $150,000 annually, implicit labor costs will be different.
When both individuals have ready employment alternatives, the implicit labor expense for each potential buyer is the amount of income forfeited by foregoing such alternative employment. Thus, implicit labor costs are $250,000 for Doyle and $150,000 for Donnell. On an annual basis, Doyle’s total capital plus labor costs are $287,500, all of which are implicit.
Donnell’s total annual costs are $187,500, including explicit capital costs of $37,500 plus implicit labor costs of $150,000.
INCREMENTAL IN DECISION ANALYSIS
Relevant costs and benefits for any decision are limited to those that are affected by it. To limit the confounding influence of irrelevant cost information, it is helpful to focus on the causal relation between costs and a given managerial decision, as well as on the reversible or nonreversible nature of some cost categories.
Incremental cost is the change in cost caused by a given managerial decision. Whereas marginal cost is the change in cost following a one-unit change in output, incremental costs typically involve multiple units of output. For example, incremental costs are the relevant consideration when an air carrier considers the cost of adding an additional departure from New York’s La Guardia Airport to upstate New York. When all current departures are full, it is impractical to consider adding a single passenger-mile unit of output. Similarly, the incremental cost concept comes into play when judging the costs of adding a new product line, advertising campaign, production shift, or organization structure.
Inappropriate managerial decisions can result when the incremental concept is ignored or applied incorrectly. Consider, for example, a commercial real estate firm that refuses to rent excess office space for $750 per month because it figures cost as $1,000 per month—or incremental operating costs of $150 plus interest and overhead charges of $850. If the relevant incremental cost is indeed only $150 per month, turning away the prospective renter causes a $600 (= $750 – $150) per month loss in profit contribution, or profit before fixed charges.
Interest and overhead charges will be incurred irrespective of whether the excess space is rented. By adding the prospective renter, the landlord has the same interest and overhead expenses as before, plus $600 in added revenues after incremental operating expenses. The net effect of rejecting such a renter would be to reduce profit contribution and net profits by $600.
Care must be exercised to ensure against incorrectly assigning a lower than appropriate incremental cost. If excess capacity results from a temporary reduction in demand, this must be taken into account. Accepting the $750 per month renter in the previous example is a mistake if doing so causes more profitable renters to be turned away. When excess capacity is caused by a temporary drop in demand, only short-term or month-to-month leases should be offered at the bargain price of $750 per month. In this way, pricing flexibility can be maintained while the net cost of temporary excess capacity is inimized. In any event, all incremental costs, including those that might be incurred in the future, must be considered.
SUNK COSTS IN DECISION ANALYSIS
Inherent in the incremental cost concept is the principle that any cost not affected by a decision is irrelevant to that decision. A cost that does not vary across decision alternatives is called a sunk cost; such costs do not play a role in determining the optimal course of action.
For example, suppose a firm has spent $5,000 on an option to purchase land for a new factory at a price of $100,000. Also assume that it is later offered an equally attractive site for $90,000. What should the firm do? The first thing to recognize is that the $5,000 spent on the purchase option is a sunk cost that must be ignored. If the firm purchases the first property, it must pay a price of $100,000. The newly offered property requires an expenditure of only $90,000 and results in a $10,000 savings. In retrospect, purchase of the $5,000 option was a mistake. It would be a compounding of this initial error to follow through with the purchase of the first property and lose an additional $10,000.
In managerial decision making, care must be taken to ensure that only those costs actually affected by a decision are considered. These incremental costs can include both implicit and explicit costs. If long-term commitments are involved, both current and future incremental costs must also be accounted for. Any costs not affected by available decision alternatives are sunk and irrelevant.
SHORT-RUN AND LONG-RUN COSTS
Proper use of relevant cost concepts requires an understanding of the relation between cost and output, or the cost function. Two basic cost functions are used in managerial decision making: short-run cost functions, used for day-to-day operating decisions, and long-run cost functions, used for long-range planning.
How Is the Operating Period Defined?
The short run is the operating period during which the availability of at least one input is fixed. In the long run, the firm has complete flexibility with respect to input use. In the short run, operating decisions are typically constrained by prior capital expenditures. In the long run, no such restrictions exist. For example, a management consulting firm operating out of rented office space might have a short-run period as brief as several weeks, the time remaining on the office lease. Afirm in the hazardous waste disposal business with 25- to 30- year leases on disposal sights has significant long-lived assets and faces a lengthy period of operating constraints.
The economic life of an asset and the degree of specialization affect the time length of operating period constraints. Consider, for example, a health maintenance organization’s (HMO) automobile purchase for delivering home-based health care. If the car is a standard model without modification, it represents an unspecialized input factor with a resale value based on the used car market in general. However, if the car has been modified by adding refrigeration equipment for transporting perishable medicines, it ecomes a more specialized input with full value only for those who need a vehicle with refrigeration equipment. In this case, the market price of the car might not equal its value in use to the HMO. To the extent that specialized input factors are employed, the short run is lengthened. When only unspecialized factors are used, the short run is condensed.
The amount of time required to order, receive, and install new assets also influences the duration of the short run. Many manufacturers face delays of several months when ordering new plant and equipment. Air carriers must place their equipment orders 5 or more years in advance of delivery. Electric utilities frequently require 8 or more years to bring new generating plants on line. For all such firms, the short-run operating period is an extended period of time.
Long-run cost curves are called planning curves; short-run cost curves are called operating curves. In the long run, plant and equipment are variable, so management can plan the most efficient physical plant, given an estimate of the firm’s demand function. Once the optimal plant has been determined and the resulting investment in equipment has been made, short-run operating decisions are constrained by these prior decisions.
Fixed and Variable Costs
Fixed costs do not vary with output. These costs include interest expenses, rent on leased plant and equipment, depreciation charges associated with the passage of time, property taxes, and salaries for employees not laid off during periods of reduced activity. Because all costs are variable in the long run, long-run fixed costs always equal zero. Variable costs fluctuate with output. Expenses for raw materials, depreciation associated with the use of equipment, the variable portion of utility charges, some labor costs, and sales commissions are all examples of variable expenses. In the short run, both variable and fixed costs are often incurred. In the long run, all costs are variable.
Asharp distinction between fixed and variable costs is not always possible nor realistic. For example, CEO and staff salaries may be largely fixed, but during severe business downturns, even CEOs take a pay cut. Similarly, salaries for line managers and supervisors are fixed only within certain output ranges. Below a lower limit, supervisors and managers get laid off. Above an upper limit, additional supervisors and managers get hired. The longer the duration of abnormal demand, the greater the likelihood that some fixed costs will actually vary. In recognition of this, such costs are sometimes referred to as semivariable.
SHORT-RUN COST CURVES
Ashort-run cost curve shows the minimum cost impact of output changes for a specific plant size and in a given operating environment. Such curves reflect the optimal or least-cost input combination for producing output under fixed circumstances. Wage rates, interest rates, plant configuration, and all other operating conditions are held constant.
Any change in the operating environment leads to a shift in short-run cost curves. For example, a general rise in wage rates leads to an upward shift; a fall in wage rates leads to a downward shift. Such changes must not be confused with movements along a given short-run cost curve caused by a change in production levels. For an existing plant, the short-run cost curve illustrates the minimum cost of production at various output levels under current operating conditions. Short-run cost curves are a useful guide to operating decisions.
Short-Run Cost Categories
Both fixed and variable costs affect short-run costs. Total cost at each output level is the sum of total fixed cost (a constant) and total variable cost. Using TC to represent total cost, TFC for total fixed cost, TVC for total variable cost, and Q for the quantity of output produced, various unit costs are calculated as follows:
These cost categories are portrayed in Table. Using these data, it is possible to identify the various cost relations as well as to examine cost behavior. Table shows that AFC declines.
Short-Run Cost Curves
continuously with increases in output. AC and AVC also decline as long as they exceed MC, but increase when they are less than MC. Alternatively, so long as MCis less than AC and AVC, both average cost categories will decline. When MC is greater than AC and AVC, both average cost categories will rise. Also note that TFC is invariant with increases in output and that TVC at each level of output equals the sum of MC up to that output.
Marginal cost is the change in cost associated with a one-unit change in output. Because fixed costs do not vary with output, fixed costs do not affect marginal costs. Only variable costs affect marginal costs. Therefore, marginal costs equal the change in total costs or the change in total variable costs following a one-unit change in output:
Short-Run Cost Relations
Relations among short-run cost categories are shown in Figure. Figure illustrates total cost and total variable cost curves. The shape of the total cost curve is determined entirely by the total variable cost curve. The slope of the total cost curve at each output level is identical to the slope of the total variable cost curve. Fixed costs merely shift the total cost curve to a higher level. This means that marginal costs are independent of fixed cost.
The shape of the total variable cost curve, and hence the shape of the total cost curve, is determined by the productivity of variable input factors employed. The variable cost curve in Figure increases at a decreasing rate up to output level Q1, then at an increasing rate.
Assuming constant input prices, this implies that the marginal productivity of variable inputs first increases, then decreases. Variable input factors exhibit increasing returns in the range from 0 to Q1 units and show diminishing returns thereafter. This is a typical finding. Fixed
Short-Run Cost Curves
the range of increasing productivity and rises thereafter. This imparts the familiar U-shape to average variable cost and average total cost curves. At first, marginal cost curves also typically decline rapidly in relation to the average variable cost curve and the average total cost curve.
Near the target output level, the marginal cost curve turns up and intersects each of the AVC and AC short-run curves at their respective minimum points.3
LONG-RUN COST CURVES
In the long run, the firm has complete input flexibility. All long-run costs are variable. A long-run cost curve shows the minimum cost impact of output changes for the optimal plant size in the present operating environment.
Long-Run Total Costs
Long-run cost curves show the least-cost input combination for producing output assuming an ideal input selection. As in the case of short-run cost curves, wage rates, interest rates, plant configuration, and all other operating conditions are held constant. Any change in the operating environment leads to a shift in long-run cost curves. For example, product inventions and process improvements that occur over time cause a downward shift in long-run cost curves.
Such changes must not be confused with movements along a given long-run cost curve caused by changes in the output level. Long-run cost curves reveal the nature of economies or diseconomies of scale and optimal plant sizes. They are a helpful guide to planning decisions.
If input prices are not affected by the amount purchased, a direct relation exists between longrun total cost and production functions. Aproduction function that exhibits constant returns to scale is linear, and doubling inputs leads to doubled output. With constant input prices, doubling inputs doubles total cost and results in a linear total cost function. If increasing returns to scale are present, output doubles with less than a doubling of inputs and total cost. If production is subject to decreasing returns to scale, inputs and total cost must more than double to cause a twofold increase in output.
Aproduction unction exhibiting first increasing and then decreasing returns to scale is illustrated, along with its implied cubic cost function, in Figure. Here, costs increase less than proportionately with output over the range in which returns to scale are increasing but at more than a proportionate rate after decreasing returns set in.
A direct relation between production and cost functions requires constant input prices. If input prices are a function of output, cost functions will reflect this relationship. Large-volume discounts can lower unit costs as output rises, just as costs can rise with the need to pay higher wages to attract additional workers at high output levels. The cost function for a firm facing constant returns to scale but rising input prices as output expands takes the shape shown in Figure. Costs rise more than roportionately as output increases. Quantity discounts produce a cost function that increases at a decreasing rate, as in the increasing returns section of Figure.
Economies of Scale
Economies of scale exist when long-run average costs decline as output expands. Labor specialization often gives rise to economies of scale. In small firms, workers generally do several jobs, and proficiency sometimes suffers from a lack of specialization. Labor productivity can be higher in large firms, where individuals are hired to perform specific tasks. This can reduce unit costs for large-scale operations.
Technical factors can also lead to economies of scale. Large-scale operation permits the use of highly specialized equipment, as opposed to the more versatile but less efficient machines
Total Cost Function for a Production System Exhibiting Increasing, Then Decreasing, Returns to Scale
At some output level, economies of scale are typically exhausted, and average costs level out and begin to rise. Increasing average costs at high output levels are often attributed to limitations in the ability of management to coordinate large-scale organizations. Staff overhead also tends to grow more than proportionately with output, again raising unit costs. The current trend toward small to medium-sized businesses indicates that diseconomies limit firm sizes in many industries.
Cost Elasticities and Economies of Scale
It is often easy to calculate scale economies by considering cost elasticities. Cost elasticity, _C, measures the percentage change in total cost associated with a 1 percent change in output.
Algebraically, the elasticity of cost with respect to output is
Cost elasticity is related to economies of scale as follows:
With a cost elasticity of less than one (_C < 1), costs increase at a slower rate than output. mGiven constant input prices, this implies higher output-to-input ratios and economies of scale. If _C = 1, output and costs increase proportionately, implying no economies of scale. Finally, if _C > 1, for any increase in output, costs increase by a greater relative amount, implying decreasing returns to scale.
To prevent confusion concerning cost elasticity and returns to scale, remember that an inverse relation holds between average costs and scale economies but that a direct relation holds between resource usage and returns to scale. Thus, although _C < 1 implies falling AC and economies of scale, because costs are increasing more slowly than output, recall from Chapter 7 that an output elasticity greater than 1 (_Q > 1) implies increasing returns to scale, because output is increasing faster than input usage. Similarly, diseconomies of scale are implied by _C > 1, diminishing returns are indicated when _Q < 1.
Long-Run Average Costs
Short-run cost curves relate costs and output for a specific scale of plant. Long-run cost curves identify the optimal scale of plant for each production level. Long-run average cost (LRAC) curves can be thought of as an envelope of short-run average cost (SRAC) curves.
This concept is illustrated in Figure, which shows four short-run average cost curves representing four different scales of plant. Each of the four plants has a range of output over which it is most efficient. Plant A, for example, provides the least-cost production system for output in the range 0 to Q1 units; plant B provides the least-cost system for output in the range
Short-Run Cost Curves for Four Scales of Plant
Long-Run Average Cost Curve as the Envelope of Short-Run Average Cost Curves
Q1 to Q2; plant C is most efficient for output quantities Q2 to Q3; and plant D provides the least-cost production process for output above Q3.
The solid portion of each curve in Figure indicates the minimum long-run average cost for producing each level of output, assuming only four possible scales of plant. This can be generalized by assuming that plants of many sizes are possible, each only slightly larger than the preceding one. As shown in Figure, the long-run average cost curve is then constructed tangent to each short-run average cost curve. At each point of tangency, the related scale of plant is optimal; no other plant can produce that particular level of output at so low a total cost. Cost systems illustrated in Figures and display first economies of scale, then diseconomies of scale. Over the range of output produced by plants A, B, and C in Figure, average costs are declining; these declining costs mean that total costs are ncreasing less than proportionately with output. Because plant D’s minimum cost is greater than that for plant C, the system exhibits diseconomies of scale at this higher output level.
Production systems that reflect first increasing, then constant, then diminishing returns to scale result in U-shaped long-run average cost curves such as the one illustrated in Figure.
With a U-shaped long-run average cost curve, the most efficient plant for each output level is typically not operating at the point where short-run average costs are minimized, as can be seen in Figure. Plant A’s short-run average cost curve is minimized at point M, but at that output level, plant B is more efficient; B’s short-run average costs are lower. In general, when economies of scale are present, the least-cost plant will operate at less than full capacity. Here, capacity refers not to a physical limitation on output but rather to the point at which shortrun average costs are minimized. Only for that single output level at which long-run average cost is minimized (output Q* in Figures) is the optimal plant operating at the minimum point on its short-run average cost curve. At any output level greater than Q*, diseconomies of scale prevail, and the most efficient plant is operating at an output level slightly greater than capacity.
MINIMUM EFFICIENT SCALE
The number of competitors and ease of entry is typically greater in industries with U-shaped long-run average cost curves than in those with L-shaped or downward-sloping long-run average cost curves. Insight on the competitive implications of cost/output relations can be gained by considering the minimum efficient scale concept.
Competitive Implications of Minimum Efficient Scale
Minimum efficient scale (MES) is the output level at which long-run average costs are minimized. MES is at the minimum point on a U-shaped long-run average cost curve (output Q* in Figures) and at the corner of an L-shaped long-run average cost curve.
Generally speaking, competition is vigorous when MES is low relative to total industry demand. This fact follows from the correspondingly low barriers to entry from capital investment and skilled labor requirements. Competition can be less vigorous when MES is large relative to total industry output because barriers to entry tend to be correspondingly high and can limit the number of potential competitors. When considering the competitive impact of MES, industry size must always be considered. Some industries are large enough to accommodate many effective competitors. In such instances, even though MES is large in an absolute sense, it can be relatively small and allow vigorous competition.
When the cost disadvantage of operating plants that are of less than MES size is modest, there will seldom be serious anticompetitive consequences. The somewhat higher production costs of small producers can be overcome by superior customer service and regional location to cut transport costs and delivery lags. In such instances, significant advantages to large-scale operation have little economic impact. Therefore, the barrier-to-entry effects of MES depend on the size of MES relative to industry demand and the slope of the long-run average cost curve at points of less-than-MES-size operations. Both must be considered.
Transportation Costs and MES
Transportation costs include terminal, line-haul, and inventory charges associated with moving output from production facilities to customers. Terminal charges consist of handling expenses necessary for loading and unloading shipped materials. Because terminal charges do not vary with the distance of shipment, they are as high for short hauls as for long hauls.
Line-haul expenses include equipment, labor, and fuel costs associated with moving products a specified distance. They vary directly with the distance shipped. Although line-haul expenses are relatively constant on a per-mile basis, they vary widely from one commodity to another. It costs more to ship a ton of fresh fruit 500 miles than to ship a ton of coal a similar distance. Fresh fruit comes in odd shapes and sizes and requires more container space per pound than a product like coal. Any product that is perishable, fragile, or particularly susceptible to theft (e.g., consumer electronics, cigarettes, liquor) has high line-haul expenses because of greater equipment, insurance, and handling costs.
Finally, there is an inventory cost component to transportation costs related to the time element involved in shipping goods. The time required in transit is extremely important because slower modes such as railroads and barges delay the receipt of sale proceeds from customers.
Even though out-of-pocket expenses are greater, air cargo or motor carrier shipments speed delivery and can reduce the total economic costs of transporting goods to market.
As more output is produced at a given plant, it becomes necessary to reach out to more distant customers. This can lead to increased transportation costs per unit sold. Figure illustrates an L-shaped long-run average cost curve reflecting average production costs that first decline and then become nearly constant. Assuming relatively modest terminal and inventory costs, greater line-haul expenses cause transportation costs per unit to increase at a relatively constant rate. Before transportation costs, Q*A represents the MES plant size. Including transportation expenses, the MES plant size falls to Q*B. In general, as transportation costs become increasingly important, MES will fall. When transportation costs are large in relation to production costs—as is the case with milk, bottled soft drinks, gravel, and cement—even small, relatively inefficient production facilities can be profitable when located near important markets. When transportation costs are relatively insignificant—as is the case of aluminum, electronic components, personal computers, and medical instruments—markets are national or international in scope, and economies of scale cause output to be produced at only a few large plants.
FIRM SIZE AND PLANT SIZE
The cost function for a multiplant firm can be the sum of the cost functions for individual plants. It can also be greater or less than this figure. For this reason, it is important to examine the relative importance of economies of scale that arise within production facilities, intraplant economies, and those that arise between and among plants, or multiplant economies of scale.
Multiplant Economies and Diseconomies of Scale
Multiplant economies of scale are cost advantages that arise from operating multiple facilities in the same line of business or industry.
Multiplant diseconomies of scale are cost disadvantages that arise from managing multiple facilities in the same line of business or industry.
To illustrate, assume a U-shaped long-run average cost curve for a given plant, as shown in Figure. If demand is sufficiently large, the firm will employ n plants, each of optimal size and producing Q* units of output. In this case, what is the shape of the firm’s long-run average cost curve? Figure shows three possibilities. Each possible long-run average cost curve has important implications for the minimum efficient firm size, Q*F. First, the long-run average cost
Effect of Transportation Costs on Optimal Plant Size
curve can be L-shaped, as in Figure, if no economies or diseconomies result from combining plants. Second, costs could decline throughout the entire range of output, as in Figure, if multiplant firms are more efficient than single-plant firms. When they exist, such cases are caused by economies of multiplant operation. For example, all plants may use a central billing service, a common purchasing or distribution network, centralized management, and so on. The third possibility, shown in Figure, is that costs first decline beyond Q*, the output of the most efficient plant, and then begin to rise. In this case, multiplant economies of scale dominate initially, but they are later overwhelmed by the higher costs of coordinating many operating units.
All three shapes of cost curves shown in Figure are found in the U.S. economy. Because optimal plant and firm sizes are identical only when multiplant economies are negligible, the magnitude of both influences must be carefully considered in evaluating the effect of scale economies. Both intraplant and multiplant economies can have an important impact on minimum efficient firm size.
Economics of Multiplant Operation: An Example
An example can help clarify the relation between firm size and plant size. Consider Plainfield Electronics, a New Jersey–based company that manufactures industrial control panels. The firm’s production is consolidated at a single Eastern-seaboard facility, but a multiplant alternative to centralized production is being considered. Estimated demand, marginal revenue, and single-plant production plus transportation cost curves for the firm are as follows:
Three Possible Long-Run Average Cost Curves for a Multiplant Firm
Therefore, profits are maximized at the Q = 15,000 output level under the assumption of centralized production. At that activity level, MC = MR = $640, and Mπ = 0.
To gain insight regarding the possible advantages of operating multiple smaller plants, the average cost function for a single plant must be examined. To simplify matters, assume that multiplant production is possible under the same cost conditions described previously. Also assume that there are no other multiplant economies or diseconomies of scale.
The activity level at which average cost is minimized is found by setting marginal cost equal to average cost and solving for Q:
Average cost is minimized at an output level of 5,000. This output level is the minimum efficient plant scale. Because the average cost-minimizing output level of 5,000 is far less than the single-plant profit-maximizing activity level of 15,000 units, the profit-maximizing level of total output occurs at a point of rising average costs. Assuming centralized production, Plainfield would maximize profits at an activity level of Q = 15,000 rather than Q = 5,000 because market-demand conditions are such that, despite the higher costs experienced at Q = 15,000, the firm can profitably supply output up to that level.
Because centralized production maximized profits at an activity level well beyond that at which average cost is minimized, Plain field has an opportunity to reduce costs and increase profits by adopting the multiplant alternative. Although the single-plant Q = 15,000 profit maximizing activity level and the Q= 5,000 average cost-minimizing activity level might suggest that multiplant production at three facilities is optimal, this is incorrect. Profits were maximized at Q = 15,000 under the assumption that both marginal revenue and marginal cost equal $640.
However, with multiplant production and each plant operating at the Q = 5,000 activity level, marginal cost will be lowered and multiplant production will entail a new, higher profit maximizing activity level. Notice that when Q = 5,000,
MC = $40 + $0.02Q
= $40 + $0.02(5,000)
With multiple plants all operating at 5,000 units per year, MC = $140. Therefore, it is profitable to expand production as long as the marginal revenue obtained exceeds this minimum MC = $140. This assumes, of course, that each production facility is operating at the optimal activity level of Q = 5,000.
The optimal multiplant activity level for the firm, assuming optimal production levels of Q = 5,000 at multiple plants, can be calculated by equating MR to the multiplant MC = $140:
Given optimal multiplant production of 20,000 units and average cost-minimizing activity levels of 5,000 units for each plant, multiplant production at four facilities is suggested:
At Q = 20,000, P = $940 – $0.02(20,000) = $540 and π = TR – TC = P _ Q – 4 _ TC per plant = $540(20,000) – 4[$250,000 + $40(5,000) + $0.01(5,0002)] = $8,000,000
Given these cost relations, multiplant production is preferable to the centralized production alternative because it results in maximum profits that are $1.5 million larger. As shown in Figure 8.7, this follows from the firm’s ability to concentrate production at the minimum point on the single-plant U-shaped average cost curve.
Finally, it is important to recognize that the optimal multiplant activity level of 20,000 units described in this example is based on the assumption that each production facility produces exactly 5,000 units of output and, therefore, MC= $140. Marginal cost will only equal $140 with production of Q = 5,000, or some round multiple thereof (e.g., Q = 10,000 from two plants, Q = 15,000 from three plants, and so on). The optimal multiplant activity-level calculation is more complicated when this assumption is not met. Plainfield could not produce Q = 21,000 at MC = $140. For an output level in the 20,000 to 25,000 range, it is necessary to equate marginal revenue with the marginal cost of each plant at its optimal activity level.
Plant Size and Flexibility
The plant that can produce an expected output level at the lowest possible cost is not always the optimal plant size. Consider the following situation. Although actual demand for a product is uncertain, it is expected to be 5,000 units per year. Two possible probability distributions for this demand are given in Figure 8.8. Distribution L exhibits a low degree of variability in demand, and distribution H indicates substantially higher variation in possible demand levels.
Now suppose that two plants can be employed to produce the required output. Plant A is quite specialized and is geared to produce a specified output at a low cost per unit. If more or
Plainfield Electronics: Single Versus Multiplant Operation
Plainfield Electronics: Single Versus Multiplant Operation
less than the specified output is produced (in this case 5,000 units), unit production costs rise rapidly. Plant B, on the other hand, is more flexible. Output can be expanded or contracted without excessive cost penalties, but unit costs are not as low as those of plant A at the optimal output level. These two cases are shown in Figure.
Plant A is more efficient than plant B between 4,500 and 5,500 units of output; outside this range, B has lower costs. Which plant should be selected? The answer depends on the level and
Probability Distributions of Demand
Alternative Plants for Production of Expected 5,000 Units of Output
variability of expected average total costs. If the demand probability distribution with low variation, distribution L, is correct, the more specialized facility is optimal. If probability distribution H more correctly describes the demand situation, the lower minimum cost of more specialized facilities is more than offset by the possibility of very high costs of producing outside the 4,500- to 5,500-unit range. Plant B could then have lower expected costs or a more attractive combination of expected costs and potential variation.
For many manufacturing processes, average costs decline substantially as cumulative total output increases. Improvements in the use of production equipment and procedures are important in this process, as are reduced waste from defects and decreased labor requirements as workers become more proficient in their jobs.
Learning Curve Concept
When knowledge gained from manufacturing experience is used to improve production methods, the resulting decline in average costs is said to reflect the effects of the firm’s learning curve.
The learning curve or experience curve phenomenon affects average costs in a way similar to that for any technical advance that improves productive efficiency. Both involve a downward shift in the long-run average cost curve at all levels of output. Learning through production experience permits the firm to produce output more efficiently at each and every output level.
To illustrate, consider Figure, which shows hypothetical long-run average cost curves for periods t and t + 1. With increased knowledge about production methods gained through the experience of producing Qt units in period t, long-run average costs have declined for every output level in period t + 1, which means that Qt units could be produced during period t + 1 at an average cost of B rather than the earlier cost of C. The learning curve cost savings is BC. If output were expanded from Qt to Qt+1 between these periods, average costs would fall from C to A. This decline in average costs reflects both the learning curve effect, BC, and the effect of economies of scale, AB.
To isolate the effect of learning or experience on average cost, it is necessary to identify carefully that portion of average-cost changes over time that is due to other factors. One of the most important of these changes is the effect of economies of scale. As seen before, the change in average costs experienced between periods t and t + 1 can reflect the effects of both learning and economies of scale. Similarly, the effects of important technical breakthroughs, causing a downward shift in LRAC curves, and input-cost inflation, causing an upward shift in LRAC curves, must be constrained to examine learning curve characteristics. Only when output scale, technology, and input prices are all held constant can the learning curve relation be accurately represented.
Figure depicts the learning curve relation suggested by Figure. Note that learning results in dramatic average cost reductions at low total production levels, but it generates increasingl modest savings at higher cumulative production levels. This reflects the fact that many improvements in production methods become quickly obvious and are readily adopted. Later gains often come more slowly and are less substantial.
Learning Curve Example
The learning curve phenomenon is often characterized as a constant percentage decline in average costs as cumulative output increases. This percentage represents the proportion by which unit costs decline as the cumulative quantity of total output doubles. Suppose, for example, that average costs per unit for a new product were $100 during 2001 but fell to $90 during 2002.
Long-Run Average Cost Curve Effects of Learning
Furthermore, assume that average costs are in constant dollars, reflecting an accurate adjustment for input/price inflation and an identical basic technology being used in production. Given equal output in each period to ensure that the effects of economies of scale are not incorporated in the data, the learning or experience rate, defined as the percentage by which average cost falls as output doubles, is the following:
Thus, as cumulative total output doubles, average cost is expected to fall by 10 percent. If annual production is projected to remain constant, it will take 2 additional years for cumulative output to double again. One would project that average unit costs will decline to $81 (90 percent of $90) in 2004. Because cumulative total output at that time will equal 4 years’ production, at a constant annual rate, output will again double by 2008. At that time, the learning curve will have reduced average costs to $72.90 (90 percent of $81).
Because the learning curve concept is often improperly described as a cause of economies of scale, it is worth repeating that the two are distinct concepts. Scale economies relate to cost differences associated with different output levels along a single LRAC curve. Learning curves relate cost differences to total cumulative output. They are measured by shifts in LRAC curves over time. These shifts result from improved production efficiencies stemming from knowledge gained through production experience. Care must be exercised to separate learning and scale effects in cost analysis.
Research in a number of industries, ranging from aircraft manufacturing to semiconductor memory-chip production, has shown that learning or experience can be very important in some production systems. Learning or experience rates of 20 percent to 30 percent are sometimes reported. These high learning rates imply rapidly declining manufacturing costs as cumulative total output increases. It should be noted, however, that many learning curve studies fail to account adequately for the expansion of production. Therefore, reported learning or experience rates sometimes include the effects of both learning and economies of scale. Nevertheless, managers in a wide variety of industries have found that the learning curve concept has considerable strategic implications.
Learning Curve on an Arithmetic Scale
Strategic Implications of the Learning Curve Concept
What makes the learning curve phenomenon important for competitive strategy is its possible contribution to achieving and maintaining a dominant position in a given market. By virtue of their large relative volume, dominant firms have greater opportunity for learning than do smaller, nonleading firms. In some instances, the market share leader is able to drive down its average cost curve faster than its competitors, underprice them, and permanently maintain a leadership position. Nonleading firms face an important and perhaps insurmountable barrier to relative improvement in performance. Where the learning curve advantages of leading firms are important, it may be prudent to relinquish nonleading positions and redeploy assets to markets in which a dominant position can be achieved or maintained.
A classic example illustrating the successful use of the learning curve concept is Dallas– based Texas Instruments (TI). TI’s main business is producing semiconductor chips, which are key components used to store information in computers and a wide array of electronic products.
With growing applications for computers and “intelligent” electronics, the demand for semiconductors is expanding rapidly. Some years ago, TI was one of a number of leading semiconductor manufacturers. At this early stage in the development of the industry, TI made the decision to price its semiconductors well below then-current production costs, given expected learning curve advantages in the 20 percent range. TI’s learning curve strategy proved spectacularly successful.
With low prices, volume increased dramatically. Because TI was making so many chips, average costs were even lower than anticipated; it could price below the competition; and dozens of competitors were knocked out of the world market. Given a relative cost advantage and strict quality controls, TI rapidly achieved a position of dominant leadership in a market that became a source of large and rapidly growing profits.
To play an important role in competitive strategy, learning must be significant. Cost savings of 20 percent to 30 percent as cumulative output doubles must be possible. If only modest effects of learning are present, product quality or customer service often plays a greater role in determining firm success. Learning is also apt to be more important in industries with an abundance of new products or new production techniques rather than in mature industries with wellknown production methods. Similarly, learning tends to be important in industries with standardized products and competition based on price rather than product variety or service.
Finally, the beneficial effects of learning are realized only when management systems tightly control costs and monitor potential sources of increased efficiency. Continuous feedback of information between production and management personnel is essential.
ECONOMIES OF SCOPE
Cost analysis focuses not just on how much to produce but also on what combination of products to offer. By virtue of their efficiency in the production of a given product, firms often enjoy cost dvantages in the production of related products.
Economies of Scope Concept
Economies of scope exist when the cost of joint production is less than the cost of producing multiple outputs separately. Afirm will produce products that are complementary in the sense that producing them together costs less than producing them individually. Suppose that a regional airline offers regularly scheduled passenger service between midsize city pairs and that it expects some excess capacity. Also assume that there is a modest local demand for air parcel and small-package delivery service. Given current airplane sizes and configurations, it is often less costly for a single carrier to provide both passenger and cargo services in small regional markets than to specialize in one or the other. Regional air carriers often provide both services. This is an example of economies of scope. Other examples of scope economies abound in the provision of both goods and services. In fact, the economies of scope concept explains why firms typically produce multiple products.
Studying economies of scope forces management to consider both direct and indirect benefits associated with individual lines of business. For example, some financial services firms regard checking accounts and money market mutual funds as “loss leaders.” When one considers just the revenues and costs associated with marketing and offering checking services or running a money market mutual fund, they may just break even or yield only a marginal profit. However, successful firms like Dreyfus, Fidelity, and Merrill Lynch correctly evaluate the profitability of their money market mutual funds within the context of overall operations. These funds are a valuable delivery vehicle for a vast array of financial products and services. By offering money market funds on an attractive basis, financial services companies establish a working relation with an ideal group of prospective customers for stocks, bonds, and other investments. When viewed as a delivery vehicle or marketing device, money market mutual funds may be one of the industry’s most profitable financial product lines.
Exploiting Scope Economies
Economies of scope are important because they permit a firm to translate superior skill in a given product line into unique advantages in the production of complementary products.
Effective competitive strategy often emphasizes the development or extension of product lines related to a firm’s current stars, or areas of recognized strength.
For example, PepsiCo, Inc., has long been a leader in the soft drink market. Over time, the company has gradually broadened its product line to include various brands of regular and diet soft drinks, Gatorade, Tropicana, Fritos and Doritos chips, Grandma’s Cookies, and other snack foods. PepsiCo can no longer be considered just a soft drink manufacturer. It is a widely diversified beverages and snack foods company for whom well over one-half of total current profits come from non–soft drink lines. PepsiCo’s snack foods and sport drink product line extension strategy was effective because it capitalized on the distribution network and marketing expertise developed in the firm’s soft drink business. In the case of PepsiCo, soft drinks, snack foods and sports beverages are a natural fit and a good example of how a firm has been able to take the skills gained in developing one star (soft drinks) and use them to develop others (snack foods, sport drinks).
The economies of scope concept offers a useful means for evaluating the potential of current and prospective lines of business. It naturally leads to definition of those areas in which the firm has a comparative advantage and its greatest profit potential.
Cost-volume-profit analysis, sometimes called breakeven analysis, is an important analytical technique used to study relations among costs, revenues, and profits. Both graphic and algebraic methods are employed. For simple problems, simple graphic methods work best. In more complex situations, analytic methods, possibly involving spreadsheet software programs, are preferable.
A basic cost-volume-profit chart composed of a firm’s total cost and total revenue curves is depicted in Figure. Volume of output is measured on the horizontal axis; revenue and cost are shown on the vertical axis. Fixed costs are constant regardless of the output produced and are indicated by a horizontal line. Variable costs at each output level are measured by the distance between the total cost curve and the constant fixed costs. The total revenue curve indicates the price/demand relation for the firm’s product; profits or losses at each output are shown by the distance between total revenue and total cost curves.
In the example depicted in Figure, fixed costs of $60,000 are represented by a horizontal line. Variable costs for labor and materials are $1.80 per unit, so total costs rise by that amount for each additional unit of output. Total revenue based on a price of $3 per unit is a straight line through the origin. The slope of the total revenue line is steeper than that of the total cost line.
Below the breakeven point, found at the intersection of the total revenue and total cost lines, the firm suffers losses. Beyond that point, it begins to make profits. Figure indicates a breakeven point at a sales and cost level of $150,000, which occurs at a production level of 50,000 units.
Algebraic Cost-Volume-Profit Analysis
Although cost-volume-profit charts can be used to portray profit/output relations, algebraic techniques are typically more efficient for analyzing decision problems. The algebra of costvolume- profit analysis can be illustrated as follows. Let P = Price per unit sold
Linear Cost-Volume-Profit Chart
Q = Quantity produced and sold TFC = Total fixed costs AVC = Average variable cost πC = Profit contribution
On a per-unit basis, profit contribution equals price minus average variable cost (πC = P – AVC).
Profit contribution can be applied to cover fixed costs and then to provide profits. It is the foundation of cost-volume-profit analysis.
One useful application of cost-volume-profit analysis lies in the determination of breakeven activity levels. Abreakeven quantity is a zero profit activity level. At breakeven quantity levels, total revenue (P _ Q) exactly equals total costs (TFC + AVC _ Q):
Total Revenue = Total Cost P *Q = TFC + AVC *Q
(P – AVC)Q = TFC
It follows that breakeven quantity levels occur where
QBE = TFC/ P – AVC
Thus, breakeven quantity levels are found by dividing the per-unit profit contribution into total fixed costs. In the example illustrated in Figure, P = $3, AVC = $1.80, and TFC = $60,000.
Profit contribution is $1.20 (= $3.00 – $1.80), and the breakeven quantity is
Q = $60,000
= 50,000 units
Textbook Publishing: A Cost-Volume-Profit Example
The textbook publishing business provides a good illustration of the effective use of cost-volumeprofit analysis for new product decisions. Consider the hypothetical cost-volume-profit analysis data shown in Table. Fixed costs of $100,000 can be estimated quite accurately.
Variable costs are linear and set by contract. List prices are variable, but competition keeps prices within a sufficiently narrow range to make a linear total revenue curve reasonable.
Variable costs for the proposed book are $92 a copy, and the price is $100. This means that each copy sold provides $8 in profit contribution. Applying the breakeven formula from Equation, the breakeven sales volume is 12,500 units, calculated as
Q = $100,000/$8
= 12,500 units
Publishers evaluate the size of the total market for a given book, competition, and other factors. With these data in mind, they estimate the probability that a given book will reach or exceed the breakeven point. If the publisher estimates that the book will neither meet nor exceed the breakeven point, they may consider cutting production costs by reducing the number of illustrations, doing only light copyediting, using a lower grade of paper, negotiating with the author to reduce the royalty rate, and so on.
Assume now that the publisher is interested in determining how many copies must sell to earn a $20,000 profit. Because profit contribution is the amount available to cover fixed costs and provide profit, the answer is found by adding the profit requirement to the book’s fixed costs and then dividing by the per-unit profit contribution. The sales volume required in this case is 15,000 books, found as follows:
Consider yet another decision problem that might confront the publisher. Assume that a book club has offered to buy 3,000 copies at a price of $77 per copy. Cost-volume-profit analysis can be used to determine the incremental effect of such a sale on the publisher’s profits.
Because fixed costs do not vary with respect to changes in the number of textbooks sold, they should be ignored. Variable costs per copy are $92, but note that $25 of this cost represents bookstore discounts. Because the 3,000 copies are being sold directly to the club, this cost will not be incurred. Hence, the relevant variable cost is only $67 (= $92 – $25). Profit contribution per book sold to the book club is $10 (= $77 – $67), and $10 times the 3,000 copies sold indicates that the order will result in a total profit contribution of $30,000. Assuming that these 3,000 copies would not have been sold through normal sales channels, the $30,000 profit contribution indicates the increase in profits to the publisher from accepting this order.
Degree of Operating Leverage
Cost-volume-profit analysis is also a useful tool for analyzing the financial characteristics of alternative production systems. This analysis focuses on how total costs and profits vary with operating leverage or the extent to which fixed production facilities versus variable production facilities are employed.
Cost-Volume-Profit Analysis for Textbook Publishing
The relation between operating leverage and profits is shown in Figure, which contrasts the experience of three firms, A, B, and C, with differing degrees of leverage. The fixed costs of firm B are typical. Firm A uses relatively less capital equipment and has lower fixed costs, but it has a steeper rate of increase in variable costs. Firm Abreaks even at a lower activity level than
Breakeven and Operating Leverage
does firm B. For example, at a production level of 40,000 units, B is losing $8,000, but A breaks even. Firm C is highly automated and has the highest fixed costs, but its variable costs rise slowly.
Firm C has a higher breakeven point than either A or B, but once C passes the breakeven point, profits rise faster than those of the other two firms.
The degree of operating leverage is the percentage change in profit that results from a 1 percent change in units sold:
Degree of Operating Leverage = Percentage Change in Profit/Percentage Change in Sales
= Δπ/π / ΔQ/Q
= Δπ/ ΔQ π * Q/ π
The degree of operating leverage is an elasticity concept. It is the elasticity of profits with respect to output. When based on linear cost and revenue curves, this elasticity will vary. The degree of operating leverage is always greatest close to the breakeven point.
For firm B in Figure, the degree of operating leverage at 100,000 units of output is 2.0, calculated as follows:
Here, π is profit and Q is the quantity of output in units.
For linear revenue and cost relations, the degree of operating leverage can be calculated at any level of output. The change in output is ΔQ. Fixed costs are constant, so the change in profit Δπ = ΔQ(P – AVC), where P is price per unit and AVC is average variable cost.
Any initial profit level π = Q(P – AVC) – TFC, so the percentage change in profit is
The percentage change in output is ΔQ/Q, so the ratio of the percentage change in profits to the percentage change in output, or profit elasticity, is
Using Equation 8.8, firm B’s degree of operating leverage at 100,000 units of output is calculated as
Equation 8.8 can also be applied to firms A and C. When this is done, firm A’s degree of operating leverage at 100,000 units equals 1.67 and firm C’s equals 2.5. With a 2 percent increase in volume, firm C, the firm with the most operating leverage, will experience a profit increase of 5 percent. For the same 2 percent gain in volume, the firm with the least leverage, firm A, will have only a 3.3 percent profit gain. As seen in Figure, the profits of firm C are most sensitive to changes in sales volume, whereas firm A’s profits are relatively insensitive to volume changes. Firm B, with an intermediate degree of leverage, lies between these two extremes.
Limitations of Linear Cost-Volume-Profit Analysis
Cost-volume-profit analysis helps explain relations among volume, prices, and costs. It is also useful for pricing, cost control, and other financial decisions. However, linear cost-volumeprofit analysis has its limitations.
Linear cost-volume-profit analysis has a weakness in what it implies about sales possibilitiesfor the firm. Linear cost-volume-profit charts are based on constant selling prices. To study profit possibilities with different prices, a whole series of charts is necessary, with one chart for each price. With sophisticated spreadsheet software, the creation of a wide variety of cost-volume-profit charts is relatively easy. Using such software, profit possibilities for different pricing strategies can be quickly determined. Alternatively, nonlinear cost-volumeprofit analysis can be used to show the effects of changing rices.
Linear cost-volume-profit analysis can be hampered by the underlying assumption of constant average costs. As unit sales increase, existing plant and equipment can be worked beyond capacity, thus reducing efficiency. The need for additional workers, longer work periods, and overtime wages can also cause variable costs to rise sharply. If additional plant and equipment is required, fixed costs will also rise. Such changes influence both the level and the slope of cost functions.
Although linear cost-volume-profit analysis has proven useful for managerial decision making, care must be taken to ensure that it is not applied when underlying assumptions are violated. Like any ecision tool, cost-volume-profit analysis must be used with discretion.