EXHIBIT 9-1 Analysis of Music Festival Revenue Options
Analyzing Costs and Profits for Pricing
It was only a sunny smile and little it cost in the giving but like morning light it scattered the night and made the day worth living.
F. Scott Fitzgerald1
Internal financial considerations and external market considerations are, at many companies, antagonistic forces in pricing decisions. Financial managers allocate costs to determine how high prices must be to achieve profit objectives. Marketing and sales staff analyze buyers to determine how low prices must be to achieve sales objectives. Neither approach will lead to optimizing the firm’s profitability and growth. An effective pricing strategy requires taking account of, and making trade-offs between, both internal financial and external market constraints.
This chapter describes how managers can make that integration. It describes a simple, logically intuitive procedure for quantitatively evaluating the potential impact of a price level change on profitability, even if their knowledge of price elasticity is imprecise and qualitative. Although the accuracy of the resulting decision will be only as good as the accuracy of the information used to reach it, the process we propose helps ensure that a decision about what price level to set for any targeted segment is the best possible given the available information and previously chosen price metric.
A company’s margin goals, return on capital goals, and operating profit goals are, or at least should be, entirely irrelevant to pricing decisions. They are quite relevant for determining whether a company should invest to enter a market or to offer a line of products or services. Thus, a company should anticipate the prices it expects will be possible before making such investments, and reject those investments where it seems that viable price scenarios will be inadequate to generate an adequate return on investment. Having made that investment, however, the best choice between two or more alternative price points is determined entirely by which one will generate the most profit contribution—revenue minus incremental, avoidable costs.
This makes evaluating price levels much easier than most people imagine as they go through various means to allocate costs under different scenarios. There are only two things that need to be considered when comparing alternative price level proposals: What is the difference in revenue expected and what is the difference in costs that will be incurred to generate that revenue. In most cases, the difference in costs is the easier of the two to estimate, but even there it is possible to make mistakes that can lead to poor decisions. Consequently, we will begin with guidance on how to select the appropriate costs for price analysis.
Not all costs are relevant for every pricing decision. A first step in pricing is to identify the relevant costs: Those that actually determine the profit impact of the pricing decision. In principle, identifying the relevant costs for pricing decisions is actually fairly straightforward. They are the costs that are incremental (not average) and avoidable (not sunk). In practice, identifying costs that meet these criteria can be difficult unless a company has a good managerial accounting system in place. If one must rely on financial accounts, which describe past averages and include costs that are no longer avoidable, a pricing manager will need to create a “roughly right” approximation of the incremental, avoidable costs in order to create a pricing capability. We will now explain each of these distinctions in detail and illustrate it in the context of a practical pricing problem.
Pricing decisions affect whether a company will sell less of the product at a higher price or more of the product at a lower price. In either scenario, some costs remain the same (in total). Consequently, those costs do not affect the relative profitability of one price versus another. Only costs that rise or fall (in total) when prices change affect the relative profitability of different pricing strategies. We call the costs that change with the change in a pricing decision “incremental” to that decision.
Incremental costs are the costs associated with changes in pricing and sales. The distinction between incremental and non-incremental costs parallels closely, but not exactly, the more familiar distinction between variable and fixed costs. Variable costs, such as the costs of raw materials in a manufacturing process, are costs of doing business. Because pricing decisions affect the amount of business that a company does, variable costs are always incremental for pricing. In contrast, fixed costs, such as those for product design, advertising, and overheads, are costs of being in business.2 They may be incremental when deciding whether to be in the business of selling a particular type of product or, in some cases, to serve a particular segment of customers. But fixed costs that are not affected by how much a company actually sells (such as R&D and corporate overhead) are not incremental and therefore not relevant when management must decide what price level to set to maximize profit.
Some fixed costs, however, are incremental for pricing decisions, and they must be appropriately identified. Incremental fixed costs are those that directly result from implementing a price change or from offering a version of the product at a different price level. For example, the fixed cost for a restaurant to print menus with new prices or for a public utility to gain regulatory approval for a rate increase would be incremental when deciding whether to make those changes. The fixed cost for an airline to advertise a new discount service or to upgrade its planes’ interiors to offer a premium-priced service would be incremental when deciding whether to offer products at those price levels.
To further complicate matters, many costs are neither purely fixed nor purely variable. They are fixed over a range of sales but vary when sales go outside that range. The determination of whether such semifixed costs are incremental for a particular pricing decision is necessary to make that decision correctly. Consider, for example, the role of capital equipment costs when deciding whether to expand output. A manufacturer may be able to fill orders for up to 100 additional units each month without purchasing any new equipment, simply by using the available equipment more extensively. Consequently, equipment costs are non-incremental when figuring the cost of producing up to 100 additional units. If the quantity of additional orders increased by 150 units each month, though, the factory would have to purchase additional equipment. The added cost of new equipment would then become incremental and relevant in deciding whether the company can profitably price its units low enough to attract that additional business.
To illustrate the importance of properly identifying incremental costs when making pricing decisions, consider the problem faced by the business manager of an annual one-day music festival produced by a small town near a major metro area. The summertime festival is a source of pride for the town but the event must turn a profit, ideally one sufficient to subsidize other cultural events throughout the year. The festival incurs the following costs.
| Sales | 4,000 units |
| Wholesale price | $10.00 per unit |
| Revenue | $40,000 |
| Variable costs | $5.50 per unit |
| Fixed costs | $15,000 |
When the town’s new business manager came on board a few years ago, she began to increase prices with the festival continuing to sell out capacity at 1,000 tickets. Last year, however, ticket sales fell to only 914 after she increased prices once again, from $90 to $100 per ticket. That price covered all the costs and the town eked out a small profit of $7,260. But the failure of the festival to sell out hurt civic pride, as well as local merchants who rely on the festival for a boost in summer sales.
The town manager is reluctant to roll back prices, believing that the festival should make more of a financial contribution to the town. However, she is under pressure to revive festival attendance. Two proposals were put forward, although both involved selling seats at lower prices.
PROPOSAL A: ADDITIONAL PERFORMANCE Offer the same program of performers on Friday as well as Saturday. The manager expects that making Friday tickets available for $85 would definitely revive interest from patrons who were deterred by the $100 price. Based upon the demand turned away in prior years, she estimates that a Friday program could sell 700 tickets, but as many as 200 of those could be sold to people who would otherwise have attended the higher-priced Saturday performance. The net increase in ticket sales, after accounting for the cannibalization of Saturday sales, would still be 500 tickets, generating a 50% increase in total festival attendance and incremental revenue of $39,500. Performers indicated that they would give a second performance of the same program at half the one-day fee. The cost to set up staging and seating for the venue ($8,000) would not need to be borne again to offer the program two days in a row, reducing the venue cost to $12,000 for the added performance.
PROPOSAL B: STUDENT RUSH DISCOUNT A less ambitious, but not necessarily exclusive, proposal would involve offering half-price tickets to bona fide full-time students for any seat still unsold 24 hours before the festival performance. The manager estimates she could easily sell 100 such tickets, but as many as 20 might be to students who otherwise would have bought a full price ticket rather than waiting for the chance to get one at half price. The net increase in ticket sales from this option, after accounting for cannibalization of full price tickets, is 80 tickets generating incremental revenue of $3,000.
Which, if either, of these proposals should the town manager adopt if the goal is to maximize net income to the town? An analysis of the alternatives is shown in Exhibit 9-1 and there are a few points that are noteworthy. First, the ticket prices proposed for either proposal do not cover the fully allocated average cost per ticket, a little over $85. At companies that still use the antiquated and flawed practice of “absorption cost” accounting for managerial decisions, both options would be rejected outright as unprofitable unless ticket prices covered that cost. But the advantage of both proposals is that much of the cost of the festival, although necessary for those options, is not incremental to making the additional sales that they would generate. At the proposed ticket prices, the incremental revenue expected to be generated by either proposal more than covers the incremental cost. Also noteworthy is that the Student Rush proposal is expected to be almost as profit-enhancing as the additional Friday performance, even though it generates less than one-tenth of the revenue.
Second, an important cost that is often overlooked in such an analysis is the “opportunity cost” of revenues forgone from other sales: In this case, the forgone sales of some $100 tickets when cheaper tickets are offered under the new proposals. Although the “student rush” option involves selling tickets at the lowest price, that price is easily “fenced” to minimize cannibalization of higher-priced ticket sales by limiting it to bona fide students. Offering discounted student rush tickets enables the potential to sell out the full venue while maintaining the $100 price that most patrons find acceptable, adding over $2,000 to the town’s expected $7,260 income from offering the festival at $100 per ticket to everyone else. The Friday option, however, relies on customers self-segmenting. Considering the greater uncertainty involved in offering the extra Friday performance, with a greater potential for loss if the expected incremental sales are not achieved or if more patrons shift from the Saturday to the cheaper Friday performance, the student rush might well be a better choice.
EXHIBIT 9-1 Analysis of Music Festival Revenue Options
Although the music festival example is hypothetical, the analytical challenges it illustrates are not. Scores of companies add to profit from sales that are priced below average cost, which they can do when that average includes costs that are not incremental to the additional sales:
In each of these cases, the key to getting the business is having a low price. Yet one should never be deceived into thinking that low-price sales are necessarily low-profit sales. In some cases, they make a disproportionately large contribution to profit because they make a small incremental addition to costs. The goal of pricing is not to make higher priced sales; it is to make higher profit sales.
The hardest principle for many business decision-makers to accept is that the costs which are relevant for pricing are the ones that are still avoidable, not the historical ones already incurred. Avoidable costs are those that either have not yet been incurred or can be reversed. The costs of selling a product, delivering it to the customer, and replacing the sold item in inventory are avoidable, as is the rental cost of buildings and equipment that are not covered by a long-term lease. The opposite of avoidable costs are sunk costs— those costs that a company is irreversibly committed to bear. For example, a company’s past expenditures on research and development are sunk costs since they cannot be changed regardless of any decisions made in the present. The rent on buildings and equipment within the term of a current lease is sunk, except to the extent that the firm can avoid the expense by subletting the property.3
The cost of assets that a firm owns may or may not be sunk. If an asset can be sold for an amount equal to its purchase price times the percentage of its remaining useful life, then none of its cost is sunk, since the cost of the unused life can be entirely recovered through resale. Popular models of airplanes often retain their value in this way, making avoidable the entire cost of their depreciation from continued use. If an asset has no resale value, then its cost is entirely sunk even though it may have much useful life remaining. A neon sign depicting a company’s corporate logo may still function for a long time, but its cost is entirely sunk since no other company would care to buy it. Frequently, the cost of assets is partially avoidable and partially sunk. For example, a new truck could be resold for a substantial portion of its purchase price but would lose some market value immediately after purchase. The portion of the new price that could not be recaptured is sunk and should not be considered in pricing decisions. Only the decline in the resale value of the truck is an avoidable cost of using it.
From a practical standpoint, the easiest way to identify the avoidable cost is to recognize that the cost of making a sale is always the current cost resulting from the sale, not costs that occurred in the past. What, for example, is the cost for an oil company to sell a gallon of gasoline at one of its company-owned stations? One might be inclined to say that it is the cost of the oil used to make the gasoline plus the cost of refining and distribution. Unfortunately, that view could lead refiners to make some costly pricing mistakes. Most oil company managers realize that the relevant cost for pricing gasoline is not the historical cost of buying oil and producing a gallon of gasoline, but rather the future cost of replacing the inventory when sales are made. Even LIFO (last-in, first-out) accounting can be misleading for companies that are drawing down large inventories. To account accurately for the effect of a sale on profitability, managers should adopt NIFO (next-in, first-out) accounting for managerial decision-making.4
The distinction between the historical cost of acquisition and the future cost of replacement is merely academic when supply costs are stable. It becomes very practical when costs rise or fall.5 When the price of crude oil rises, companies quickly raise prices, long before any gasoline made from the more expensive crude reaches the pump. Politicians and consumer advocates label this practice “price gouging,” since companies with large inventories of gasoline increase their reported profits by selling their gasoline at much higher prices than they paid to produce it. So what is the real incremental cost to the company of selling a gallon of gasoline?
Each gallon of gasoline sold requires the purchase of crude oil at the new, higher price for the company to maintain its gasoline inventory. If that price is not covered by revenue from sales of gasoline, the company suffers reduced cash flow from every sale. Even though the sales appear profitable from a historical cost standpoint, the company must add to its working capital (by borrowing money or by retaining a larger portion of earnings) to pay the new, higher cost of crude oil. Consequently the real “cash” cost of making a sale rises immediately by an amount equal to the increase in the replacement cost of crude oil.
What happens when crude oil prices decline? If a company with large inventories held its prices high until all inventories were sold, it would be undercut by any company with smaller inventories that could profitably take advantage of the lower cost of crude oil to gain market share. The company would see its sales, profits, and cash flow decline. Again, the intelligent company bases its prices on the replacement cost, not the historical cost, of its inventory. In historical terms, it reports a loss. However, that loss corresponds to an equal reduction in the cost of replacing its inventories with cheaper crude oil. Since the company simply reduces its operating capital by the amount of the reported loss, its cash flow remains unaffected by that “loss.”
The impact of sales on cash is usually a much better gauge of the incremental, avoidable profitability of a sale than the cost of any historical decisions enabling those sales.
Far too often, price changes get made with little or no analysis of their likely financial impact on profitability. Instead, decisions are made to lower prices to protect sales or meet sales goals, and decisions are made to raise prices to recover costs. As a result, price reductions occur without consideration of whether the sales goal is appropriate. And opportunities to raise prices are missed because decision-makers are never confronted with the potential profits that could have been earned if they had acted.
The primary excuse for the failure to estimate and manage pricing for profitability is that it requires estimates of relevant internal costs and of the effect of price on external demand. We have described earlier in this chapter how it is possible to make roughly accurate estimates of relevant costs. We are also sympathetic to the challenge of estimating “demand price elasticities” precisely and cost-effectively, although the cost of doing so for frequently purchased consumer goods has declined immensely due to declines in the cost of technology and the willingness of retailers to sell detailed sales data by brand and package size.
For infrequently purchased products, for products new to the market, and for products where prices are negotiated with large buyers, information about demand price elasticity is rarely precise enough to “optimize” the price. But however difficult it is to know price elasticity with any certainty, it will determine the difference in profitability that could be generated at different price levels. Even if one cannot possibly estimate demand elasticity with a high level of accuracy, it may still be possible to estimate the likelihood that it will be at least whatever it needs to be to prevent a price change from damaging profitability.
With an estimate of the minimum change in sales necessary to make a price change profitably—what we call the breakeven sales change—it is possible to bring qualitative judgment to bear by, for example, asking a sales or product manager whether she would prefer to retain the current sales goal and target price level, a lower price level with a higher sales goal, or a higher price level with a lower sales goal. It is also possible to track the effect of a price change on sales levels to determine quickly whether the change is meeting the minimum effects necessary for it to be profitable. While the resulting level of uncertainty may be uncomfortable, it is preferable to making decisions blindly or failing to make them out of fear. Over time, as managers learn to think in terms of managing pricing to achieve profit goals, rather than sales or cost-recovery goals, they either become increasingly comfortable incorporating qualitative judgments or they invest to gain more quantitative insight.
The remainder of this chapter describes a simple, logically intuitive procedure to quantitatively evaluate the potential profitability of a price change. First, marketing or pricing managers must define a baseline against which any pricing alternative is to be compared. For example, they might compare the effects of a pending price change with the product’s current level of profitability, or perhaps with a hypothetical scenario that management is particularly interested in exploring. Second, they need to calculate an incremental “breakeven” point for the price change to determine the minimum, or “breakeven” sales response necessary to achieve at least as much profitability at the new price as at the baseline price. Finally, the managers must then decide whether they believe that the sales response will reach at least that breakeven level—a determination that can incorporate both quantitative and qualitative information.
The key to integrating costs and quantitatively assessing the consequences of a price change is the incremental breakeven formula. Although similar in form to the common breakeven points that managers use to evaluate investments, an incremental breakeven for pricing is quite different in practice. Rather than evaluating the sales required for a product to achieve overall profitability, which depends on many factors other than price, incremental breakeven analysis focuses on the incremental effect on profitability of a price change. Consequently, managers start from a baseline then ask whether a change in price could improve the situation. More precisely, they ask:
How much would sales volume have to increase to make a price reduction profitable?
Managers advocating for a lower price can then be asked for evidence and commitment that the higher volume can be achieved and for a credible plan to achieve it.
How much would sales volume have to decline to make a price increase unprofitable?
Managers advocating for a higher price can then be asked for evidence and commitment that sufficient volume can be retained at higher prices and for a credible plan to justify those prices to customers.
The sample problems in this chapter introduce four alternative formulas which, under different circumstances, would be used to answer these questions. To introduce and illustrate the application of these formulas, we will describe the experience of Westside Manufacturing, a company that makes high-quality pillows for sale through specialty bedding and dry-cleaning stores. Although the examples are, for simplicity, based on a hypothetical small manufacturing business, the equations are equally applicable for analyzing any size or type of business that does not negotiate a unique price for each customer.6 If customers are effectively segmented for pricing, the formulas apply to price levels within a segment.
Following are Westside Manufacturing’s income and costs for a typical month:
| Sales | 4,000 units |
| Wholesale price | $10.00 per unit |
| Revenue | $40,000 |
| Variable costs | $5.50 per unit |
| Fixed costs | $15,000 |
Westside is considering a 5 percent price cut, which it believes would make it more competitive with alternative suppliers, enabling it to further increase its sales. Management believes that the company would need to incur no additional fixed costs as a result of this pricing decision. How much would sales have to increase for this company to profit from a 5 percent cut?
To answer Westside’s question, we calculate the breakeven sales change. This, for a price cut, is the minimum increase in sales volume necessary for the price cut to produce an increase in contribution relative to the baseline. Fortunately, making this calculation is simple, as will be shown shortly. First, however, it may be more intuitive to illustrate the analysis graphically (see Exhibit 9-2). In this exhibit, it is easy to visualize the financial tradeoffs involved in the proposed price change. Before the price change, Westside receives a price of $10 per unit and sells 4,000 units, resulting in total revenues of $40,000 (the total area of boxes (a) and (b)). From this Westside pays variable costs of $5.50 per unit, for a total of $22,000 (box b). Therefore, before the price change, total contribution is $40,000 minus $22,000, or $18,000 (box a). In order for the proposed price cut to be profitable, contribution after the price cut must exceed $18,000.
After the 5 percent price reduction, Westside receives a price of only $9.50 per unit, or $0.50 less contribution per unit. Since it normally sells 4,000 units, Westside would expect to lose $2,000 in total contribution (box c) on sales that it could have made at a higher price. This is called the price effect. Fortunately, the price cut can be expected to increase sales volume.
The contribution earned from that increased volume, the volume effect (box e), is unknown. The price reduction will be profitable, however, when the volume effect (the area of box e) exceeds the price effect (the area of box c). That is, in order for the price change to be profitable, the gain in contribution resulting from the change in sales volume must be greater than the loss in contribution resulting from the change in price. The purpose of breakeven analysis is to calculate the minimum sales volume necessary for the volume effect (box e) to balance the price effect (box c). When sales exceed that amount, the price cut is profitable.
EXHIBIT 9-2 Finding the Breakeven Sales Change
So, how do we determine the breakeven sales change? We know that the lost contribution due to the price effect (box c) is $2,000, which means that the gain in contribution due to the volume effect (box e) must be at least $2,000 for the price cut to be profitable. Since each new unit sold following the price cut results in $4 in contribution ($9.50 – $5.50 = $4), Westside must sell at least an additional 500 units ($2,000 divided by $4 per unit) to make the price cut profitable.
The minimum percent change in sales volume necessary to maintain at least the same contribution following a price change can be directly calculated by using the following simple formula (see Appendix 9B for derivation):
In this equation, the price change and contribution margin may be stated in dollars, percentages, or decimals (as long as their use is consistent within the same formula). The result of this formula is a decimal ratio that, when multiplied by 100, is the percent change in unit sales necessary to maintain the same level of contribution after the price change. The minus sign in the numerator indicates a trade-off between price and volume: Price cuts increase the volume and price increases reduce the volume necessary to achieve any particular level of profitability. The larger the price change—or the smaller the contribution margin—the greater the volume change necessary to generate at least as much contribution as before.
Assume for the moment that there are no incremental fixed costs in implementing Westside’s proposed 5 percent price cut. For convenience, we make our calculations in dollars (rather than in percentages or decimals). The contribution margin is:
$CM = $10.00 – $5.50 = $4.50
Given this, we can easily calculate the breakeven sales change as follows:
Thus, the price cut is profitable only if sales volume increases by more than 12.5 percent. Relative to its current level of sales volume, Westside would have to sell at least 500 additional units to maintain the same level of profitability it had prior to the price cut, as shown below:
Unit breakeven sales change = 0.125 × 4,000 = 500 units
If the actual increase in sales volume exceeds the breakeven sales change, the price cut will be profitable. If the actual increase in sales volume falls short of the breakeven sales change, the price change will be unprofitable. If West-side’s sales increase as a result of the price change by more than the break-even amount—say, by an additional 550 units—Westside will realize a gain in profit contribution. If, however, Westside sells only an additional 450 units as a result of the price cut, it will suffer a loss in contribution.
Once we have the breakeven sales change and the profit contribution, calculating the precise change in contribution associated with any change in volume is straightforward: It is simply the difference between the actual sales volume and the breakeven sales volume, times the new contribution margin (calculated after the price change). For Westside’s 550-unit and 450-unit volume changes, the change in contribution equals the following:
(550 – 500) × $4 = $200
(450 – 500) × $4 = –$200
The $4 in these formulas is the new contribution margin ($9.50 – $5.50). You might have noticed that the denominator of the percent breakeven formula is also the new contribution margin.
We have illustrated breakeven analysis using Westside’s proposed 5 percent price cut. The logic is exactly the same for a price increase. Since a price increase results in a gain in unit contribution, Westside can tolerate some reduction in sales volume and still increase its profitability. How much of a reduction in sales volume can Westside tolerate before the price increase becomes unprofitable? The answer is this: Until the loss in contribution due to reduced sales volume is exactly offset by the gain in contribution due to the price increase. As an exercise, calculate how much sales Westside could afford to lose before a 5 percent price increase becomes unprofitable.
It is important to note that the calculation resulting from the break-even sales change formula is expressed as the percent change in unit volume required to break even, not the percent change in monetary sales (for example, the percent change in dollar sales) required to break even. In the case of a price cut, the percent breakeven sales change in units necessary to justify the price cut is larger than the percent breakeven sales change in sales dollars because the price is now lower.
To convert from the percent breakeven sales change in units to the percent breakeven sales change in dollars, you can apply the following simple conversion formula:
% BE($)= % BE(units) + % Price change [1 + % BE(units)]
For example, for Westside’s proposed 5 percent price cut above, the percent breakeven sales change in unit volume terms was 12.5 percent. What is the corresponding percent breakeven sales change in dollar sales terms? The answer is calculated as follows:
% BE($) = 0.125 + (–0.05)(1+0.125)
= 6.88%
Thus, to break even on the proposed 5 percent price cut, Westside would have to increase its total dollar sales by 6.88 percent, which is exactly equivalent to a 12.5 percent increase in unit volume.
Thus far, we have dealt only with price changes that involve no changes in unit variable costs or in fixed costs. Often, however, price changes are made as part of a marketing plan involving cost changes as well. A price increase may be made along with product improvements that increase variable costs, or a price cut might be made to push the product with lower variable selling costs. Expenditures that represent fixed costs might also change along with a price change. We need to consider these two types of incremental costs when calculating the price–volume trade-off necessary for making pricing decisions profitable. We begin this section by integrating changes in variable cost into the financial analysis. In the next section, we do the same with changes in fixed costs.
Fortunately, dealing with a change in variable cost involves only a simple generalization of the breakeven sales change formula already introduced. To illustrate, we return to Westside Manufacturing’s proposed 5 percent price cut. Suppose that Westside’s price cut is accompanied by a reduction in variable cost of $0.22 per pillow, resulting from Westside’s decision to use a new synthetic filler to replace the goose feathers it currently uses. Variable costs are $5.50 before the price change and $5.28 after the price change. By how much would sales volume have to increase to ensure that the proposed price cut is profitable?
When variable costs change along with the price change, managers simply need to subtract the cost change from the price change before doing the breakeven sales change calculation. Unlike the case of a simple price change, managers must state the terms on the right-hand side of the equation in currency units (dollars, euros, yen, and so forth) rather than in percentage changes:
In this equation Δ indicates “change in,” P = price, and C = cost. Note that when the change in variable cost ($ΔC) is zero, this equation is identical to the breakeven formula previously presented. Note also that the term ($ΔP – $ΔC) is the change in the contribution margin and that the denominator (the original contribution margin plus the change) is the new contribution margin. Thus, the general form of the breakeven pricing equation is simply written as follows:
For Westside, the next step in using this equation to evaluate the proposed price change is to calculate the change in contribution margin. Recall that the change in price is $9.50 – $10 (or –$0.50). The change in variable costs is –$0.22. Thus, the change in contribution can be calculated as follows:
$ΔCM = ($ΔP – $ΔC)= –$0.50–(–$0.22)= –$0.28
Previous calculations illustrated that the contribution margin before the price change is $4.50. We can, therefore, calculate the breakeven sales change as follows:
In units, the breakeven sales change is 0.066 × 4,000 units, or 265 units. Given management’s projection of a $0.22 reduction in variable costs, the price cut can be profitable only if management believes that sales volume will increase by more than 6.6 percent, or 265 units. Note that this increase is substantially less than the required sales increase (12.5 percent) calculated before assuming a reduction in variable cost. Why does a variable cost reduction lower the necessary breakeven sales change? Because it increases the contribution margin earned on each sale, making it possible to recover the contribution lost due to the price effect with less additional volume. This relationship is illustrated graphically for Westside Manufacturing in Exhibit 9-2. Westside can realize a gain in contribution due to the change in variable costs (box f), in addition to a gain in contribution due to any increase in sales volume.
So far we have restricted our discussion to proactive price changes, where the firm contemplates initiating a price change ahead of its competitors. The goal of such a change is to enhance profitability. Often, however, a company initiates reactive price changes when it is confronted with a competitor’s price change that will impact the former’s sales unless it responds. The key uncertainty involved in analyzing a reactive price change is the sales loss the company will suffer if it fails to meet a competitor’s price cut, or the sales gain the company will achieve if it fails to follow a competitor’s price increase. Is the potential sales loss sufficient to justify cutting price to protect sales volume? Or is the potential sales gain enough to justify forgoing the opportunity for a cooperative price increase? A slightly different form of the breakeven sales formula is used to analyze such situations.
To calculate the breakeven sales changes for a reactive price change, we need to address the following key questions: (i) What is the minimum potential sales loss that justifies meeting a lower competitive price? (ii) What is the minimum potential sales gain that justifies not following a competitive price increase? The basic formula for these calculations is this:
To illustrate, suppose that Westside’s principal competitor, Eastside, has just reduced its prices by 15 percent. If Westside’s customers are highly loyal, it probably would not pay for Westside to match this cut. If, on the other hand, customers are quite price sensitive, Westside may have to match this price cut to minimize the damage. What is the minimum potential loss in sales volume that justifies meeting Eastside’s price cut? The answer (calculated in percentage terms) is as follows:7
Thus, if Westside expects sales volume to fall by more than 33 percent as a result of Eastside’s new price, it would be less damaging to Westside’s profitability to match the price cut than to lose sales. On the other hand, if Westside expects that sales volume will fall by less than 33 percent, it would be less damaging to Westside’s profitability to let Eastside take the sales than it would be to cut price to meet this challenge.
This analysis has focused on minimizing losses in the face of a competitor’s proactive price reduction. However, the procedure for analysis is the same when a competitor suddenly raises its prices. Suppose, for example, that Eastside raises its price by 15 percent. Westside might be tempted to match Eastside’s price increase. If, however, Westside does not respond to Eastside’s new price, Westside will likely gain additional sales volume as Eastside’s customers switch to Westside. How much of a gain in sales volume must be realized in order for no price reaction to be more profitable than a reactive price increase? The answer is similarly found using the breakeven sales change formula with a reactive price change. If Westside is confident that sales volume will increase by more than 33.3 percent if it does not react, a non-reactive price policy would be more profitable. If Westside’s management does not expect sales volume to increase by 33.3 percent, a reactive price increase would be more profitable.
Of course, the competitive analysis we have done is, by itself, overly simplistic. Eastside might be tempted to attack Westside’s other markets if Westside does not respond to Eastside’s price cut. And Westside’s not matching Eastside’s price increase might force Eastside to roll back its prices. These long-run strategic concerns might outweigh the short-term profit implications of a decision to react. In order to make such a judgment, however, the company must first determine the short-term profit implications. Sometimes long-term competitive strategies are not worth the short-term cost.
To grasp fully the potential impact of a price change, especially when the decision involves incremental changes in fixed costs, it is useful to calculate the profit impact for a range of potential sales changes and to summarize them with a breakeven table and chart. Doing so is relatively simple after having calculated the basic breakeven sales change. Using this calculation, one can then simulate “what if” scenarios that include different levels of actual sales volume following the price change.
EXHIBIT 9-3 Breakeven Sales Analysis and Simulated Scenarios: Westside Manufacturing’s Proposed 5 Percent Price Reduction
The top half of Exhibit 9-3 is a summary of the basic breakeven sales change analysis for Westside’s 5 percent price cut, with one column summarizing the level of contribution before the price change (the column labeled “Baseline”) and one column summarizing the contribution after the price change (the column labeled “Proposed Price Change”). The bottom half of Exhibit 9-3 summarizes nine “what if” scenarios, showing the profitability associated with changes in sales volume ranging from 0 to 40 percent given incremental semifixed costs of $800 per 1,000 units. Columns 1 and 2 show the actual change in volume for each scenario. Columns 3 through 5 calculate the change in profit that results from each change in sales.
EXHIBIT 9.4 Breakeven Analysis of a Price Change
To illustrate how these breakeven sales-change scenarios are calculated, let us focus for a moment on scenario 6, where actual sales volume is projected to increase 20 percent. A 20 percent change in actual sales volume is equivalent to an 800-unit change in actual sales volume, since 800 units is 20 percent of the baseline sales volume of 4,000 units. How does this increase in sales translate into changes in profitability? Column 3 shows that a 20 percent (or an 800-unit) increase in sales volume results in a change in contribution after the price change of $1,200. This is calculated by taking the difference between the actual unit sales change (800 units) and the breakeven sales change shown in the top half of Exhibit 9-3 (500 units) and multiplying by the new contribution margin after the price change ($4). However, the calculations made in column 3 do not take into account the incremental fixed costs required to implement the price change (shown in column 4). Column 5 shows the change in profit after subtracting the change in fixed costs from the incremental contribution generated. Where there is inadequate incremental contribution to cover the incremental fixed costs, as in scenarios 1 through 4, the change in profit is negative. Scenario 5 illustrates the breakeven sales change. Scenarios 6 through 9 are all profitable scenarios, since they result in greater profit after the price change than before.
The interrelationships among contribution, incremental fixed costs, and the sales change that results from a price change are often easier to comprehend with a graph. Exhibit 9-4 illustrates the relationships among the data in Exhibit 9-3.
So far we have discussed breakeven sales analysis in terms of a single change in price and its resultant breakeven sales change. In the example above, Westside Manufacturing considered a 5 percent price reduction, which we calculated would require a 17.5 percent increase in sales volume to achieve enough incremental contribution to cover the incremental fixed cost. (As shown in Exhibit 9-3, scenario 5.) However, what if the company wants to consider a range of potential price changes? How can we use breakeven sales analysis to consider alternative price changes simultaneously? The answer is by charting a breakeven sales curve, which summarizes the results of a series of breakeven sales analyses for different price changes.
Constructing breakeven sales curves requires doing a series of “what if” analyses, similar to the simulated scenarios discussed in the last section. Exhibits 9-5 and 9-6 show numerically and graphically a breakeven sales curve for Westside Manufacturing, with simulated scenarios of price changes ranging from +25 percent to –20 percent. Note in Exhibit 9-6 that the vertical axis shows different price levels for the product, and the horizontal axis shows a volume level associated with each price level. Each point on the curve represents the sales volume necessary to achieve as much profit after the price change as would be earned at the baseline price. For example, Westside’s baseline price is $10 per unit, and baseline sales volume is 4,000 units. If, however, Westside cuts the price by 15 percent to $8.50, its sales volume would have to increase 70 percent to 6,800 units to achieve the same profitability, to cover both the decrease in contribution as well as the incremental fixed costs. Conversely, if Westside increases its price by 15 percent to $11.50, its sales volume could decrease 25 percent to 3,000 units and still allow equal profitability.
The breakeven sales curve is a simple, yet powerful tool for synthesizing and evaluating the dynamics behind the profitability of potential price changes. It presents succinctly and visually the dividing line that separates profitable price decisions from unprofitable ones. Profitable price decisions are those that result in sales volumes in the area to the right of the curve. Unprofitable price decisions are those that result in sales volumes in the area to the left of the curve. What is the logic behind this? Recall the previous discussion of what happens before and after a price change. The breakeven sales curve represents those sales volume levels associated with their respective levels of price, where the company will make just as much net contribution after the price change as it made before the price change. If the company’s sales
EXHIBIT 9-5 Breakeven Sales Curve Calculations (with Incremental Fixed Costs)
EXHIBIT 9-6 Breakeven Sales Curve: Trade-Off Between Price and Sales Volume Required for Constant Profitability
volume after the price change is greater than the breakeven sales volume (that is, actual sales volume is to the right of the curve), the price change will add to profitability. If the company’s sales volume after the price change is less than the breakeven sales volume (that is, the area to the left of the curve), the price change will be unprofitable. For example, for Westside a price of $8.50 requires a sales volume of at least 6,800 units to achieve a net gain in profitability. If, after reducing its price to $8.50, management believes it will sell more than 6,800 units (a point to the right of the curve), then a decision to implement a price of $8.50 per unit would be profitable.
The breakeven sales curve also clearly illustrates the relationship between the breakeven approach to pricing and the economic concept of price elasticity. Note that the breakeven sales curve looks suspiciously like the traditional downward-sloping demand curve in economic theory, in which different levels of price (on the vertical axis) are associated with different levels of quantity demanded (on the horizontal axis). On a traditional demand curve, the slope between any two points on the curve determines the elasticity of demand, a measure of price sensitivity expressed as the percent change in quantity demanded for a given percent change in price. An economist who knew the shape of such a curve could calculate the profit-maximizing price.
Unfortunately, few firms use economic theory to set price because of the unrealistic expectation that they first have to know their demand curve, or at least the demand elasticity around the current price level. To overcome this shortcoming, we have addressed the problem in reverse order. Rather than asking, “What is the firm’s demand elasticity?” we ask, instead, “What is the minimum demand elasticity required?” to justify a particular pricing decision. Breakeven sales analysis calculates the minimum or maximum demand elasticity required to profit from a particular pricing decision. The breakeven sales curve illustrates a set of minimum elasticities necessary to make a price cut profitable, or the maximum elasticity tolerable to make a price increase profitable. One is then led to ask whether the level of price sensitivity in the market is greater or less than the level of price sensitivity required by the firm’s cost and margin structure.
This relationship between the breakeven sales curve and the demand curve is illustrated in Exhibits 9-7 and 9-8, where hypothetical demand curves are shown with Westside’s breakeven sales curve. If demand is more elastic, as in Exhibit 9-7, price reductions relative to the baseline price result in gains in profitability, and price increases result in losses in profitability. If demand is less elastic, as in Exhibit 9-8, price increases relative to the baseline price result in gains in profitability, and price reductions result in losses in profitability. Although few, if any, managers actually know the demand curve for their product, we have encountered many who can comfortably make judgments about whether it is more or less elastic than is required by the breakeven sales curve. Moreover, although we have not found any market research technique that can estimate a demand curve with great precision, we have seen many (described in Chapter 8 on measuring price sensitivity) that could enable management to confidently accept or reject a particular breakeven sales level as achievable.
EXHIBIT 9-7 Breakeven Sales Curve: Relationship Between Price Elasticity of Demand and Profitability
EXHIBIT 9-8 Breakeven Sales Curve: Relationship Between Price Elasticity of Demand and Profitability: Changes in Profit with More Inelastic Demand
In the preceding examples, the level of baseline sales from which we calculated breakeven sales changes was assumed to be the current level. For simplicity, we assumed a static market. In many cases, however, sales grow or decline even if price remains constant. As a result, the baseline for calculating breakeven sales changes is not necessarily the current level of sales. Rather, it is the level that would be expected to occur if no price change were made.
Consider, for example, a company in a high-growth industry with current sales of 2,000 units on which it earns a contribution margin of 55 percent. If the company does not change its price, management expects that sales will increase by 20 percent (the projected growth of total industry sales) to 2,400 units. However, management is considering a 5 percent price cut in an attempt to increase the company’s market share. The price cut would be accompanied by an advertising campaign intended to heighten consumer awareness of the change. The campaign would take time to design, delaying implementation of the price change until next year. The initial sales level for the constant contribution analysis, therefore, would be the projected sales in the future, or 2,400 units. Consequently, the breakeven sales change would be calculated as follows:
Or:
0.10 × 2,400 = 240 units
If the current sales level is used in the calculation, the unit breakeven sales change is calculated as 200 units, understating the change required by 40 units.
By this point, one might be wondering about the non-incremental fixed and sunk costs that have been ignored when analyzing pricing decisions. A company’s goal must surely be to cover all of its costs, including all fixed and sunk costs, or it will soon go bankrupt. This concern is justified and is central to pricing for profit, but it is misguided when applied to justify higher prices.
Note that the goal in price setting is to determine the price level that maximizes a product’s profit contribution. Profit contribution, you will recall, is the income remaining after all incremental, avoidable costs have been covered. It is money available to cover non-incremental fixed and sunk costs with, ideally, a lot left over for profit. When managers consider only the incremental, avoidable costs in making pricing decisions, they are not saying that other costs are unimportant. They simply realize that the level of those costs is irrelevant to decisions about which price will generate the most money to cover them. Since non-incremental fixed and sunk costs do not change with a pricing decision, they do not affect the relative profitability of one price versus an alternative. Consequently, consideration of them simply clouds the issue of which price level will generate the most profit.
All costs are important to profitability since they all, regardless of how they are classified, have to be covered before profits are earned. At some point, all costs must be considered. What distinguishes value-based pricing from cost-driven pricing is when they are considered. A major reason that this approach to pricing is more profitable than cost-driven pricing is that it encourages managers to think about costs when they can still do something about them. Every cost is incremental and avoidable at some time. For example, even the cost of product development and design, although it is fixed and sunk by the time the first unit is sold, is incremental and avoidable before the design process begins. The same is true for other costs. The key to profitable pricing is to recognize that customers in the marketplace, not costs, determine what a product can sell for. Consequently, before incurring any costs, managers need to estimate how much customers can be convinced to pay for an intended product, given their alternatives. Management must then decide, while all costs are still avoidable, what costs they can profitably incur given the expected revenue.
Of course, no one has perfect foresight. Managers must make decisions to incur costs without knowing for certain how the market will respond and what alternatives competitors will offer. When their expectations are accurate, the market rewards them with sales at the prices they expected, enabling them to cover all costs and to earn a profit. When they overestimate a product’s value, profit contribution may prove inadequate to cover all the costs incurred. In that case, a good manager seeks to minimize the loss. This can be done only by maximizing profit contribution (revenue minus incremental, avoidable costs). Short-sighted efforts to build non-incremental fixed and sunk costs into a price to justify regretted investments made in the past will only reduce volume further, making the losses worse.
The profitability of pricing decisions depends largely on the product’s incremental cost structure and the market’s response to the change in price. We discuss the importance of identifying the costs that are most relevant to the profitability of a pricing decision, namely, incremental and avoidable costs. Having identified the right costs, one must also understand how to use them. The most important reason to identify costs correctly is to be able to calculate an accurate contribution margin. An accurate contribution margin enables management to determine the amount by which sales must increase following a price cut, or by how little they may decline following a price increase for any price change to at least maintain the profit level that would have been achieved without the change. Understanding how changes in sales will affect a product’s profitability is the first step in pricing the product effectively.
1. Elizabeth Drake, “F. Scott Fitzgerald: 10 Quotes on His Birthday,” The Christian Science Monitor, September 23, 2012. Accessed April 21, 2017 at www.csmonitor.com/Books/2012/0923/F.-Scott-Fitzgerald-10-quotes-on-his-birthday/A-smile.
2. Beware of costs classified as “over-head.” Often costs end up in that classification, even though they are clearly variable, simply because “overhead” is a convenient dumping ground for costs that one has not associated with the products that caused them to be incurred. A clue to the existence of such a misclassification is the incongruous term “variable overhead.”
3. Most economics and accounting texts equate avoidable costs with variable costs, and sunk costs with fixed costs, for theoretical convenience. Unfortunately, those texts usually fail to explain adequately that this is an assumption rather than a necessarily true statement. Consequently, many students come away from related courses with the idea that a firm should always continue producing if price at least covers variable costs. That rule is correct only when the variable costs are entirely sunk. In many industries (for example, airlines) the fixed costs are often avoidable, since the assets can be readily sold. Whenever the fixed costs are avoidable if a decision is not made to produce a product, or to produce it in as large a quantity, they should be considered when deciding whether a price is adequate to serve a market.
4. LIFO and NIFO costs are the same in any accounting period when a firm makes a net addition to its inventory. In periods during which a firm draws down its inventory, LIFO will understate costs after the firm uses up the portion of its inventory values at current prices and begins “dipping into old layers” of inventory valued at unrealistic past prices.
5. Sam Peltzman, “Prices Rise Faster Than They Fall,” Journal of Political Economy 108(3) (June 2000), pp. 466–502.
6. The rule for analyzing the profitability of independently negotiated prices is simple: A price is profitable as long as it covers incremental costs. Unfortunately, many managers make the mistake of applying that rule when prices are not independent across customers. They assume, mistakenly, that because they negotiate prices individually, they are negotiating them independently. In fact, because customers talk to one another and learn the prices that others pay, prices are rarely independent. The low price you charge to one customer will eventually depress the prices that you can charge to others.
7. This equation can also accommodate a change in variable cost by simply replacing the “change in price” with the “change in price minus the change in variable cost.” One can also add to it the breakeven necessary to cover a change in fixed costs.
Ritter & Sons, an illustrative company, is a wholesale producer of potted plants and cut flowers. Ritter’s most popular product is potted chrysanthemums (mums), which are particularly in demand around certain holidays, especially Mother’s Day, Easter, and Memorial Day, but they maintain a high level of sales throughout the year. Exhibit 9A-1 shows Ritter’s revenues, costs, and sales from mums for a recent fiscal year. After attending a seminar on pricing, the company’s chief financial officer, Don Ritter, wondered whether this product might somehow be priced more profitably. He then began a serious examination of the effect of raising and lowering the wholesale price of mums from the current price of $3.85 per unit.
EXHIBIT 9A-1 Cost Projection for Proposed Crop of Mums
Ritter’s first step was to identify the relevant cost and contribution margin for mums. Looking only at the data in Exhibit 9A-1, Don was somewhat uncertain how to proceed. He reasoned that the costs of the cuttings, shipping, packaging, and pottery were clearly incremental and avoidable and that the cost of administrative overhead was fixed. He was far less certain about labor and the capital cost of the greenhouses. Some of Ritter’s work force consisted of long-time employees, whose knowledge of planting techniques was highly valuable. It would not be practical to lay them off, even if they were not needed during certain seasons. Most production employees, however, were seasonal laborers who were hired during peak seasons and who found work elsewhere in the off-season.
After consulting with the production manager for potted plants, Don concluded that about $7,000 of the labor cost of mums was fixed. The remaining $44,850 (or $0.52 per unit) was variable and thus relevant to the pricing decision.
Don also wondered how he should treat the capital cost of the greenhouses. He was sure that the company policy of allocating capital cost (interest and depreciation) equally to every plant sold was not correct. However, when Don suggested to his brother Paul, the company’s president, that since these costs were sunk, they should be entirely ignored in pricing, Paul found the suggestion unsettling. He pointed out that Ritter used all of its greenhouse capacity in the peak season, that it had expanded its capacity in recent years, and that it planned further expansions in the coming year. Unless the price of mums reflected the capital cost of building additional greenhouses, how could Ritter justify such investments?
That argument made sense to Don. Surely the cost of greenhouses is incremental when they are all in use, since additional capacity would have to be built if Ritter were to sell more mums. But the greenhouses are used to the 45,000-unit capacity in only one of the three growing seasons. In the other two seasons combined, Ritter grew and sold only 41,250 units. During those non-peak seasons, Ritter could grow many more mums. Ritter’s policy of making all mums grown in a year bear a $0.77 capital cost was simply misleading, since additional mums could be grown without bearing any additional capital cost during seasons with excess capacity. Mums grown in peak seasons, however, actually cost much more than Ritter had been assuming, since those mums require capital additions. Thus, if the annual cost of an additional greenhouse (depreciation, interest, maintenance, heating) is $9,000, and if the greenhouse will hold 5,000 mums for three crops each year, the capital cost per mum would be $0.60 ($9,000/ (3 × 5,000)) only if all greenhouses are fully utilized throughout the year. Since the greenhouses are filled to capacity for only one crop per year, the relevant capital cost for pricing that crop is $1.80 per mum ($9,000/5,000), while it is zero for pricing crops at other times.1
EXHIBIT 9A-2 Relevant Cost of Mums
As a result of his discussions, Don calculated two costs for mums: One to apply when there is excess capacity in the greenhouses and one to apply when greenhouse capacity is fully utilized. His calculations are shown in Exhibit 9A-2. These two alternatives do not exhaust the possibilities. For any product, different combinations of costs can be fixed or incremental in different situations. For example, if Ritter found itself with excess mums after they were grown, potted, and ready to sell, the only incremental cost would be the cost of shipping. If Ritter found itself with too little capacity and too little time to make additions before the next peak season, the only way to grow more mums would be to grow fewer types of other flowers. In that case, the cost of greenhouse space for mums would be the opportunity cost (measured by the lost contribution) from not growing and selling those other flowers. The relevant cost for a pricing decision depends on the circumstances. Therefore, one must begin each pricing problem by first determining the relevant cost for that particular decision.
For Ritter, the decision at hand involved planning production quantities and prices for the forthcoming year. There would be three crops of mums during the year, two during seasons when Ritter would have excess growing capacity and one during the peak season, when capacity would be a constraint. The relevant gross margin would be $2.25, or 58.5 percent ($2.25/3.85), for all plants. In the peak season, however, the net profit contribution would be considerably less because of the incremental capital cost of the greenhouses.
Don recognized immediately that there was a problem with Ritter’s pricing of mums. Since the company had traditionally used cost-plus pricing based on fully allocated average cost, fixed costs were allocated equally to all plants. Consequently, Ritter charged the same price ($3.85) for mums throughout the year. Although mums grown in the off-peak season used the same amount of greenhouse space as those grown during the peak season, the relevant incremental cost of that space was not always the same. Consequently, the profit contribution for mums sold in an off-peak season was much greater than for those sold in the peak season. This difference was not reflected in Ritter’s pricing. Don suspected that Ritter should be charging lower prices during seasons when the contribution margin was large and higher prices when it was small. Using his new understanding of the relevant cost, Don calculated the breakeven sales quantities for a 5 percent price cut during the off-peak season, when excess capacity makes capital costs irrelevant, and for a 10 percent increase during the peak season, when capital costs are incremental to the pricing decision. These calculations are shown in Exhibit 9A-3.
EXHIBIT 9A-3 Breakeven Sales Changes for Proposed Price Changes
Don first calculated the percent breakeven quantity for the off-peak season, indicating that Ritter would need at least a 9.3 percent sales increase to justify a 5 percent price cut in the off-peak season. Then he calculated the basic break-even percentage for a 10 percent price increase during the peak season. If sales declined by less than 14.6 percent as a result of the price increase (equal to 6,570 units, given Ritter’s expected peak season sales of 45,000 mums), the price increase would be profitable. Don also recognized, however, that if sales declined that much, Ritter could avoid constructing at least one new greenhouse. That capital cost saving could make the price increase profitable even if sales declined by more than the basic breakeven quantity. Assuming that one greenhouse involving a cost of $9,000 per year could be avoided, the breakeven decline rises to 22.2 percent (equal to 9,990 units). If a 10 percent price increase caused Ritter to lose less than 22.2 percent of its projected sales for the next peak season, the increase would be profitable.
Judging whether actual sales changes were likely to be greater or smaller than those quantities was beyond Don’s expertise. He calculated a series of “what if” scenarios, called breakeven sales change simulated scenarios, and then presented his findings to Sue James, Ritter’s sales manager (see Exhibit 9A-4).
EXHIBIT 9A-4 Breakeven Sales Change Simulated Scenarios (Vertical Orientation)
Sue felt certain that sales during the peak season would not decline by 22.2 percent following a 10 percent price increase. She pointed out that the ultimate purchasers in the peak season usually bought mums as gifts. Consequently, they were much more sensitive to quality than to price. Fortunately, most of Ritter’s major competitors could not match Ritter’s quality since they had to ship their plants from more distant greenhouses. Ritter’s local competition, like Ritter, would not have the capacity to serve more customers during the peak season. The high-quality florists who comprised most of Ritter’s customers were, therefore, unlikely to switch suppliers in response to a 10 percent peak-period price increase. If peak season sales remained steady, profit contribution would increase significantly, by about $50,000. If peak season sales declined modestly, the change in profit contribution would still be positive.
Sue also felt that retailers who currently bought mums from Ritter in the off-peak season could probably not sell in excess of 9.3 percent more, even if they cut their retail prices by the same 5 percent that Ritter contemplated cutting the wholesale price. Thus, the price cut would be profitable only if some retailers who normally bought mums from competitors were to switch and buy from Ritter. This possibility would depend on whether competitors chose to defend their market shares by matching Ritter’s price cut. If they did, Ritter would probably gain no more retail accounts. If they did not, Ritter might capture sales to one or more grocery chains whose price-sensitive customers and whose large expenditures on flowers make them diligent in their search for the best price.
Don and Sue needed to identify their competitors and ask, “How does their pricing influence our sales, and how are they likely to respond to any price changes we initiate?” They spent the next two weeks talking with customers and with Ritter employees who had worked for competitors, trying to formulate answers. They learned that they faced two essentially different types of competition. First, they competed with one other large local grower, Mathews Nursery, whose costs are similar to Ritter’s. Because Mathews’s sales area generally overlapped Ritter’s, Mathews would probably be forced to meet any Ritter price cuts. Most of the competition for the largest accounts, however, came from high-volume suppliers that shipped plants into Ritter’s sales area as well as into other areas. It would be difficult for them to cut their prices only where they competed with Ritter. Moreover, they already operated on smaller margins because of their higher shipping costs. Consequently, they probably would not match a 5 percent price cut.
Still, Sue thought that even the business of one or two large buyers might not be enough to increase Ritter’s total sales in the off-peak season by more than the breakeven quantity. Don recognized that the greater price sensitivity of large buyers might represent an opportunity for segmented pricing. If Ritter could cut prices to the large buyers only, the price cut would be profitable if the percentage increase in sales to that market segment alone exceeded the breakeven increase. Perhaps Ritter could offer a 5 percent quantity discount, for which only the large, price-sensitive buyers could qualify.2 Alternatively, Ritter might sort its mums into “florist quality” and “standard quality,” if it could assume that its florists would generally be willing to pay a 5 percent premium to offer the best product to their clientele.
Don decided to make a presentation to the other members of Ritter’s management committee, setting out the case for reducing price to large buyers by 5 percent for the two off-peak seasons and for increasing price by 10 percent for the peak season as illustrated in Exhibit 9A-5. After Don’s presentation, Sue James explained why she believed that sales would decline by less than the breakeven quantity if price were raised in the peak season. She also felt sales might increase more than the breakeven percent if price were lowered in the off-peak seasons, especially if the cut could be limited to large buyers.
EXHIBIT 9A-5 Profit Impact of a 10 Percent Increase
Since Ritter has traditionally set prices based on a full allocation of costs, some managers were initially skeptical of this new approach. They asked probing questions, which Don and Sue’s analysis of the market enabled them to answer. The management committee recognized that the decision was not clear-cut. It would ultimately rest on uncertain judgments about sales changes that the proposed price changes would precipitate. If Ritter’s regular customers proved to be more price sensitive than Don and Sue now believed, the proposed 10 percent price increase for the peak season could cause sales to decline by more than the breakeven quantity. If competitors all matched Ritter’s 5 percent price cut for large buyers in the off-peak season, sales might not increase by as much as the breakeven quantity.
The committee accepted the proposed price changes. In related decisions, they postponed construction of one new greenhouse and established a two-tier approach to pricing mums based on selecting the best for “florist quality” and selling the lower-priced “standard quality” mums only in lots of 1,000.
Finally, they agreed that Don should give a speech at an industry trade show on how this pricing approach could improve capital utilization and efficiency. In the speech, he would reveal Ritter’s decision to raise its price in the peak season. (Perhaps Mathews’s management might decide to take such information into account in independently formulating its own pricing decisions.) He would also let it be known that if Ritter were unable to sell more mums to large local buyers in the off-peak season, it would consider offering the mums at discount prices to florists outside of its local market. This plan, it was hoped, would discourage non-local competitors from fighting for local market share, lest the price-cutting spread to markets they found more lucrative.
At this point, there was no way to know whether these decisions would prove profitable. Management could have requested more formal research into customer motivations or a more detailed analysis of non-local competitors’ past responses to price-cutting. Since past behavior is never a perfect guide to the future, the decision would still have required weighing the risks involved with the benefits promised. Still, Don’s analysis ensured that management identified the relevant information for this decision and weighed it appropriately.
1. We are assuming that a greenhouse depreciates no more rapidly when in use than when idle. If it did depreciate faster when used, the extra depreciation would be an incremental cost even for crops grown during seasons with excess capacity.
2. This option could expose Ritter to the risk of a legal challenge if Ritter’s large buyers compete directly with its small buyers in the retailing of mums. Ritter could rebut the challenge if it could justify the 5 percent discount as a cost saving in preparing and shipping larger orders. If not, then Ritter may want to try more complicated methods to segment the market, such as offering somewhat different products to the two segments.
A price change can either increase or reduce a company’s profits, depending on how it affects sales. The breakeven formula is a simple way to discover at what point the change in sales becomes large enough to make a price reduction profitable, or a price increase unprofitable.
Exhibit 9B-1 illustrates the break-even problem. At the initial price P, a company can sell the quantity Q. Its total revenue is P times Q, which graphically is the area of the rectangle bordered by the lines 0P and 0Q. If C is the product’s variable cost, then the total profit contribution earned at price P is (P – C)Q. Total profit contribution is shown graphically as the rectangle left after subtracting the variable cost rectangle (0C, 0Q) from the revenue rectangle (0P, 0Q).
EXHIBIT 9B-1 Breakeven Sales Change Relationships
If this company reduces its price from P to P’, its profits will change. First, it will lose an amount equal to the change in price, ΔP, times the amount that it could sell without the price change, Q. Graphically, that loss is the rectangle labeled A. Somewhat offsetting that loss, however, the company will enjoy a gain from the additional sales it can make because of the lower price. The amount of the gain is the profit that the company will earn from each additional sale, P’ – C, times the change in sales, ΔQ. Graphically, that gain is the rectangle labeled B. Whether or not the price reduction is profitable depends on whether or not rectangle B is greater than rectangle A, and that depends on the size of ΔQ.
The logic of a price increase is similar. If P’ were the initial price and Q’ the initial quantity, then the profitability of a price increase to P would again depend on the size of ΔQ. If ΔQ were small, rectangle A, the gain on sales made at the higher price, would exceed rectangle B, the loss on sales that would not be made because of the higher price. However, ΔQ might be large enough to make B larger than A, in which case the price increase would be unprofitable.
To calculate the formula for the breakeven ΔQ (at which the gain from a price reduction just outweighs the loss or the loss from a price increase just out-weighs the gain), we need to state the problem algebraically. Before the price change, the profit earned was (P – C)Q. After the change, the profit was (P’ – C) Q’. Noting, however, that P’ P + ΔP (we write, “+ΔP” since ΔP is a negative number) and that Q’ Q + ΔQ, we can write the profit after the price change as (P + ΔP – C) (Q + ΔQ). Since our goal is to find the ΔQ at which profits would be just equal before and after the price change, we can begin by setting those profits equal algebraically:
(P–C)Q = (P+ΔP–C)(Q+ΔQ)
Multiplying this equation through yields:
PQ – CQ = PQ + ΔPQ – CQ + PΔQ + ΔPΔQ – CΔQ
We can simplify this equation by subtracting PQ and adding CQ to both sides to obtain:
0 = ΔPQ + PΔQ + ΔPΔQ – CΔQ
Note that all the remaining terms in the equation contain the “change sign” Δ. This is because only the changes are relevant for evaluating a price change. If we solve this equation for ΔQ, we obtain the new equation:
which, in words, is: