Chapter Eighteen: CostVolumeProfit and Business Scalability
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“Profitability is just around the corner.” This is a common expression in the business world. But, the reality is that many businesses don’t make it! Business is tough, profits are illusive, and competition has a habit of moving into areas where profits are available. Sometimes revenue growth only seems to bring on waves of additional expenses.
How does one realistically assess the viability of a business? This is perhaps the most critical business assessment a manager must make. Many are taught from an early age to not give up, even in the face of adversity. Certainly there are countless stories of businesses that struggled to survive their infancy, but went on to become highly successful. But, it is equally important to identify business models that simply will not work.
Managerial accounting methods provide techniques for evaluating the viability and ability to grow or “scale” a business. These techniques are called costvolumeprofit analysis (CVP). CVP fundamentally depends upon developing an understanding of the nature and behavior of an entity’s costs. To understand how a business is going to perform over time and with shifts in volume, it is imperative to first consider the cost structure of the business. This requires drilling down into the specific types of costs that are to be incurred and trying to understand their unique attributes.
Variable costs will vary in direct proportion to changes in the level of an activity. For example, direct material, direct labor, sales commissions, and so on, may be expected to increase with each additional unit of output. The opposite of variable costs are fixed costs. Fixed costs do not fluctuate with changes in the level of activity. Examples include administrative salaries, rents, and property taxes.
GoSound produces portable music players. Each unit produced requires a digital chip that costs $11. At right is a table that reveals rising chip costs with increases in production. For example, $1,650,000 is spent when 150,000 units are produced (150,000 X $11).
The data are plotted on the following graphs. One graph reveals that total variable cost increases in a linear fashion. The slope of the line is constant. When plotted on a “per unit” basis, the variable cost is constant at $11 per unit. Increases in volume do not change the per unit cost.
The activity base is the item or event that causes the incurrence of a variable cost. It is easy to think of the activity base in terms of units produced, but it can be more than that. Activity can relate to labor hours worked, units sold, customers processed, or other such “cost drivers.” For instance, a dentist uses a new pair of disposable gloves for each patient seen, no matter how many teeth are being filled. Therefore, disposable gloves are variable and key on patient count. But, the material used for fillings is a variable that is tied to the number of decayed teeth that are repaired. Each variable cost must be considered independently and with careful attention to what activity drives the cost.
Assume that GoSound leases the manufacturing facility where the portable music players are assembled. Rent is $1,200,000 no matter the level of production. The rent is said to be a “fixed” cost, because total rent will not change as output rises and falls. The table at right reveals the factory rent incurred at different levels of production and the resulting “per unit” rent amount. The following graphs show how the fixed cost per unit will decline with increases in production. This attribute of fixed costs is important to consider in assessing the scalability of a business.
The nature of a specific business will have a lot to do with defining its inherent fixed cost structure. Airlines have historically been burdened with high fixed costs related to gates, maintenance, reservation systems, and aircraft. Airlines struggle during lean years because they are unable to cover fixed costs. During boom years, these same companies can be extremely profitable, because many costs do not rise with increases in volume. Basically, there is not much cost difference in flying a plane empty or full. Software companies have a big investment in product development, but very little cost in reproducing multiple electronic copies of the finished product. Their variable costs are low.
Other businesses have attempted to avoid fixed costs so that they can maintain a more stable stream of income relative to sales. For example, a computer company might outsource its tech support. Rather than having a fixed staff that is either idle or overloaded at any point in time, it pays an independent support company a percall fee. The effect is to transform the organization’s fixed costs to variable and better insulate the bottom line from fluctuations brought about by the related ability to cover or not cover the fixed costs of operations.
Every business is unique, and a savvy business person will be careful to understand cost structure. For a long time, the trend for many businesses was toward increased fixed costs. Some of this was the result of increased investment in robotics and technology. However, those components have become more affordable, and there now seems to be more outsourcing, elimination of health insurance, and so forth. These activities suggest attempts to structure businesses with a definitive margin that scales up and down with changes in the level of business activity.
Economists speak of the concept of economies of scale. This means that certain efficiencies are achieved as production levels rise. This can take many forms. Fixed costs can be spread over larger production runs, and this causes a decrease in the per unit fixed cost. In addition, enhanced buying power results (e.g., quantity discounts) as volume goes up, and this can reduce the per unit variable cost. These are valid considerations and must be taken into consideration in any business evaluation. However, care must also be exercised to limit one’s analysis to a “relevant range” of activity. At right is an example pricing table for an electronic part. Notice that the per unit cost ranges from $0.44 down to $0.092 each, depending on the quantity purchased.
Despite the large spread in pricing, if a business needed about 250 of these parts, one would study the preceding table and determine that the best quantity to order would be 300 units priced at $13.00 per hundred. As a result, per unit variable cost would be $0.130. The relevant range is the anticipated activity level. Any pricing data outside of this range is irrelevant and need not be considered. This enhanced concept of variable cost is portrayed in the accompanying graphic.
The relevant range must also be considered when evaluating fixed costs. Many fixed costs are only fixed for a certain level of production. For example, a machine can be operating at full capacity. To increase production beyond a certain level, additional machinery must be deployed. This will cause a step upward in the fixed cost. Fixed costs that behave in this fashion are also called step costs. The nature of step costs is illustrated in the accompanying diagram.
The key point is to note that both fixed and variable costs maintain their characteristics over some particular range of activity. It is important to understand the full implications of this observation in managing a business. Adopting a business strategy that results in operating levels outside of the relevant range can significantly upset business results via significant deviations between actual and expected performance.
In an ideal setting, one would try to produce at the rightmost edge of a fixedcost step. This squeezes maximum productive output from a given level of expenditure. For a machine, it is as simple as running at full capacity. However, for a business with many fixed costs, it is more challenging to orchestrate operations so that each component is fully utilized. For example, one employee might be able to operate three machines but only two are in use. It seems simple to assume that a third machine should be installed but that might require additional building space.
Consider that some fixed costs are committed fixed costs arising from an organization’s commitment to engage in operations. These elements include such items as depreciation, rent, insurance, property taxes, and the like. These costs are not easily adjusted with changes in business activity.
On the other hand, discretionary fixed costs originate from top management’s yearly spending decisions; proper planning can result in avoidance of these costs if cutbacks become necessary or desirable. Examples of discretionary fixed costs include advertising, employee training, and so forth. Committed fixed costs relate to the desired longrun positioning of the firm; whereas, discretionary fixed costs have a shortterm orientation. Committed fixed costs are important because they cannot be avoided in lean times; discretionary fixed costs can be altered with proper planning.
Variable costs are also subject to adjustment. In the electronic parts example, it was illustrated how such costs can vary based on quantities ordered. Perhaps one might order and store large quantities of the part for use in future periods. A subsequent chapter shows how to calculate economic order quantities that take into account carrying and ordering costs in balancing these important considerations. Even direct labor cost can be subject to adjustment for overtime premiums, based on whether or not overtime is worked. It may or may not make sense to meet customer demand by ramping up production when overtime premiums must be paid.
The interplay between all of the different costs emphasizes the importance of good planning. The trick is to synchronize operations so that the benefits of each fixed cost are maximized, and variable cost patterns are established in the most economic position. All of this must be weighed against revenue opportunities; one must be able to sell what is produced.
Good managers must not only be able to understand the conceptual underpinnings of cost behavior, but they must also be able to apply those concepts to real world data that do not always behave in the expected manner. Cost data are impacted by complex interactions. Consider the costs of operating a vehicle. Conceptually, fuel usage is a variable cost that is driven by miles. But, the efficiency of fuel usage can fluctuate based on highway miles versus city miles. Beyond that, tires wear faster at higher speeds, brakes suffer more from city driving, and so forth. Vehicle insurance is seen as a fixed cost; but portions are required (liability coverage) and some portions are not (collision coverage). Furthermore, a wreck or ticket can cause the cost of coverage to rise.
The point is that assessing the actual character of cost behavior can be more daunting than might be suspected. Nevertheless, management must understand cost behavior, and this sometimes takes a bit of forensic accounting work. Begin by considering the case of “mixed costs.”
Many costs contain both variable and fixed components. These costs are called mixed or semivariable. For example, cell phone agreements can provide for a monthly fee plus usage charges for excess minutes, text messages, and so forth. With a mixed cost, there is some fixed amount plus a variable component tied to an activity. Mixed costs are harder to evaluate, because they change in response to fluctuations in volume. But, the fixed cost element means the overall change is not directly proportional to the change in activity.
To illustrate, assume that Butler’s Car Wash has a contract for its water supply that provides for a flat monthly meter charge of $1,000, plus $3 per thousand gallons of usage. Look closely at column B in the following spreadsheet and notice that the “variable” portion of the water cost is $3 per thousand gallons. For example, spreadsheet cell B9 is $2,100 (700 thousand gallons at $3 per thousand). In addition, column C shows that the “fixed” cost is $1,000, regardless of the gallons used. The total in column D is the summation of columns B and C. The graph shows the total cost behavior at various levels of water consumption.
What if one did not know the "formula" by which the water bill was calculated? Instead, the only information is a few past bills. Could one estimate how much the bill should be for a particular level of usage? This type of problem is frequently encountered, as many expenses contain both fixed and variable components. One approach to sorting out mixed costs is the highlow method. It is perhaps the simplest technique for separating a mixed cost into fixed and variable portions. However, beware that it can return an imprecise answer if the data set under analysis has a rogue data point.
Information from Butler’s actual water bills is shown at left. Butler is curious to know how much the September water bill will be if 650,000 gallons are used. With the highlow technique, the highest and lowest levels of activity are identified for a period of time. The highest water bill is $3,550, and the lowest is $2,020. The difference in cost between the highest and lowest level of activity represents the variable cost ($3,550  $2,020 = $1,530) associated with the change in activity (850,000 gallons on the high end and 340,000 gallons on the low end yields a 510,000 gallon difference). The cost difference is divided by the activity difference to determine the variable cost for each additional unit of activity ($1,530/510 thousand gallons = $3 per thousand). The fixed cost can be calculated by subtracting variable cost (perunit variable cost multiplied by the activity level) from total cost.
The table below reveals the application of the highlow method.
As cautioned, the highlow method can be quite misleading. The reason is that cost data are rarely as linear as presented in the preceding illustration, and inferences are based on only two observations (either of which could be a statistical anomaly or “outlier”). For most cases, a more precise analysis tool should be used.
Regression analysis or the method of least squares is ideally suited to cost behavior analysis. This method appears to be imposingly complex, but it is not nearly so complex as it seems. Start by considering the objective of this calculation.
The goal of least squares is to define a line so that it fits through a set of points on a graph, where the cumulative sum of the squared distances between the points and the line is minimized (hence, the name “least squares”).
Simply, if a railroad company was laying out a straight train track to serve a lot of cities, least squares would define a straightline route amongst all of the cities, so that the cumulative distances (squared) from each city to the track is minimized.
Thinking deeper, begin with the characterization of a line. A straight line is a continuous extent of length passing through two points and can be defined on a graph by its intercept with the vertical (Y) axis and its slope along the horizontal (X) axis.
In the diagram at right, observe the red line starting at the Y axis (at the “intercept” value of 2). This line then rises consistently upward to the right as it moves out along the X axis. The rate of rise is called the slope of the line. The slope is 0.8, reflecting that the line is “rising” 8 units on the Y axis for every 10 units of “run” along the X axis. Therefore, the slope is sometimes called rise over run.
In general, a straight line can be defined by this formula:Y = a + bX
where:
a = the intercept on the Y axis
b = the slope of the line
X = the position on the X axis
For the drawing, the formula would be:
Y = 2 + 0.8X
If one wished to know the value of Y, when X is 5 (see the red circle on the line), one would perform the following calculation:
Y = 2 + (0.8 * 5) = 6
Next, move on to fitting a line through a set of points. The following spreadsheet shows an example of monthly unit production and the associated cost (sorted from low to high). These data are also plotted on the graph. Through the middle of the data points is drawn a line, with the formula of:
Y = $138,533 + $10.34X
This formula suggests that fixed costs are $138,533, and variable costs are $10.34 per unit. This means it would cost about $1,276,000 to produce about 110,000 units ($138,533 + ($10.34 * 110,000)).
How was the formula derived? One approach would be to “eyeball the points” and draw a line through them. One would then estimate the slope of the line and the Y intercept. This approach is known as the scattergraph method, but it would not be precise. A more accurate approach, and the one used to derive the preceding formula, would be the least squares technique.
With least squares, the vertical distance between each point and resulting line (e.g., as illustrated in the drawing that follows by an arrow at the $1,500,000 point) is squared, and all of the squared values are summed. Importantly, the defined line is the one that minimizes the summed squared values! This line is deemed to be the best fit line, hopefully giving the clearest indication of the fixed portion (the intercept) and the variable portion (the slope) of the observed data.
One can always fit a line to data, but how reliable or accurate is that resulting line? The RSquare value is a statistical calculation that characterizes how well a particular line fits a set of data. For the illustration, note (in cell B17) an R^{2} of .798; meaning that almost 80% of the variation in cost can be explained by volume fluctuations. As a general rule, the closer R^{2} is to 1.00 the better; as this would represent a perfect fit where every point fell exactly on the resulting line.
How does one go about finding the line that results in a minimization of the cumulative squared distances from the points to the line? One way is to utilize builtin tools in spreadsheet programs, as illustrated above. Notice that the formula for cell B17 (as noted at the top of spreadsheet) contains the function RSQ(C2:C13,B2:B13). This tells the spreadsheet to calculate the R^{2} value for the data in the indicated ranges. Likewise, cell B16 is based on the function SLOPE(C2:C13,B2:B13). Cell B15 is INTERCEPT(C2:C13,B2:B13). Most spreadsheets provide intuitive popup windows with prompts for setting up these statistical functions.
CVP analysis is used to build an understanding of the relationship between costs, business volume, and profitability. This analysis will drive decisions about what products to offer and how to price them. CVP is at the heart of techniques used to calculate breakeven, volume levels necessary to achieve targeted income levels, and similar computations. The starting point for these calculations is the contribution margin.
The contribution margin is revenues minus variable expenses. Do not confuse the contribution margin with gross profit. Gross profit is calculated after deducting all manufacturing costs associated with sold units, whether fixed or variable.
Instead, the contribution margin reflects the amount available from each sale, after deducting all variable costs associated with the units sold. Some of these variable costs are product costs, and some are selling and administrative in nature. The contribution margin is generally calculated for internal use and is not externally reported.
One might refer to contribution margin on an aggregate, per unit, or ratio basis. This point is illustrated for Leyland Sports, a manufacturer of scoreboards. The production cost is $500 per sign, and Leyland pays its sales representatives $300 per sign sold. Thus, variable costs are $800 per sign. Each signs sells for $2,000. Leyland’s contribution margin is $1,200 ($2,000  ($500 + $300)) per sign. In addition, assume that Leyland incurs $1,200,000 of fixed cost.
Following are schedules with contribution margin information, assuming production and sales of 1,000, 2,000, and 500 units:
Notice that changes in volume only impact certain amounts within the “total column.” Volume changes did not impact fixed costs, nor change the per unit or ratio calculations. By reviewing the data, also note that it is necessary to produce and sell 1,000 units to achieve breakeven net income. At 2,000 units, Leyland managed to achieve a $1,200,000 net income. Conversely, if only 500 units are produced and sold, the result will be a $600,000 loss.
Leyland’s management would probably find the following chart very useful. Dollars are represented on the vertical axis and units on the horizontal.
Be sure to examine this chart, taking note of the following items:
 The total sales line starts at “0” and rises $2,000 for each additional unit.
 The total cost line starts at $1,200,000 (reflecting the fixed cost) and rises $800 for each additional unit (reflecting the addition of variable cost).
 “Breakeven” results where sales equal total costs.
 At any given point, the width of the loss area (in red) or profit area (in green) is the difference between sales and total costs.
Breakeven occurs when there is no profit or loss. As noted, the breakeven point results where sales and total costs are equal:
BreakEven Sales = Total Variable Costs + Total Fixed Costs
For Leyland, the math works out this way:
(Units X $2,000) = (Units X $800) + $1,200,000
Solving:
Step a:  (Units X $2,000) = (Units X $800) + $1,200,000  
Step b:  (Units X $1,200) = $1,200,000  
Step c:  Units = 1,000 
It is possible to “jump to step b” above by dividing the fixed costs by the contribution margin per unit. Thus, a breakeven short cut is:
BreakEven Point in Units = Total Fixed Costs / Contribution Margin Per Unit
1,000 Units = $1,200,000 / $1,200
Sometimes, one may want to know the breakeven point in dollars of sales (rather than units). This approach is especially useful for companies with more than one product, where those products all have a similar contribution margin ratio:
BreakEven Point in Sales = Total Fixed Costs / Contribution Margin Ratio
$2,000,000 = $1,200,000 / 0.60
Breaking even is not a bad thing, but hardly a satisfactory outcome for most businesses. Instead, a manager may be more interested in learning the necessary sales level to achieve a targeted profit. The approach to solving this problem is to treat the target income like an added increment of fixed costs. In other words, the margin must cover the fixed costs and the desired profit. Assume Leyland wants to know the level of sales to reach a $600,000 target income:
Solving:
Step a:  (Units X $2,000) = (Units X $800) + $1,200,000 + $600,000  
Step b:  (Units X $1,200) = $1,800,000  
Step c:  Units = 1,500 
Again, it is possible to “jump to step b” by dividing the fixed costs and target income by the per unit contribution margin:
Units to Achieve a Target Income
=
(Total Fixed Costs + Target Income) / Contribution Margin Per Unit
1,500 Units = $1,800,000 / $1,200
If one wants to know the dollar level of sales to achieve a target net income:
Sales to Achieve a Target Income
=
(Total Fixed Costs + Target Income) / Contribution Margin Ratio
$3,000,000 = $1,800,000 / 0.60
CVP is more than just a mathematical tool to calculate values like the breakeven point. It can be used for critical evaluations about business viability.
For instance, a manager should be aware of the “margin of safety.” The margin of safety is the degree to which sales exceed the breakeven point. For Leyland, the degree to which sales exceed $2,000,000 (its breakeven point) is the margin of safety. This will give a manager valuable information as he or she plans for inevitable business cycles.
A manager should also understand the scalability of the business. This refers to the ability to grow profits with increases in volume. Compare the income analysis for Leaping Lemming Corporation and Leaping Leopard Corporation:
Both companies “broke even” in 20X1. Which company would one rather own? If one knew that each company was growing rapidly and expected to double sales each year (without any change in cost structure), which company would be preferred? With the added information, one would expect the following 20X2 outcomes:
This analysis reveals that Leopard has a more scalable business model. Its contribution margin is high and once it clears its fixed cost hurdle, it will turn very profitable. Lemming is fighting a neverending battle; sales increases are met with significant increases in variable costs. Be aware that scalability can be a doubleedged sword. Pull backs in volume can be devastating to companies like Leopard because the fixed cost burden can be consuming. Whatever the situation, managers need to be fully cognizant of the effects of changes in scale on the bottomline performance.
Cost structures can be anticipated to change over time. Management must carefully analyze these changes to manage profitability. CVP is useful for studying sensitivity of profit for shifts in fixed costs, variable costs, sales volume, and sales price.
Changes in fixed costs are perhaps the easiest to analyze. To determine a revised breakeven level requires that the new total fixed cost be divided by the contribution margin. Return to the example for Leyland Sports. Recall one of the original breakeven calculations:
BreakEven Point in Sales = Total Fixed Costs / Contribution Margin Ratio
$2,000,000 = $1,200,000 / 0.60
If Leyland added a sales manager at a fixed salary of $120,000, the revised breakeven would be:
$2,200,000 = $1,320,000 / 0.60
In this case, the fixed cost increased from $1,200,000 to $1,320,000, and sales must reach $2,200,000 to break even. This increase in breakeven means that the manager needs to produce at least $200,000 of additional sales to justify his or her post.
In recruiting the new sales manager, Leyland became interested in an aggressive individual who was willing to take the post on a “4% of sales” commissiononly basis. Let’s see how this would change the breakeven point:
BreakEven Point in Sales = Total Fixed Costs / Contribution Margin Ratio
$2,142,857 = $1,200,000 / 0.56
This calculation uses the revised contribution margin ratio (60%  4% = 56%), and produces a lower breakeven point than with the fixed salary ($2,142,857 vs. $2,200,000). But, do not assume that a lower breakeven defines the better choice! Consider that the lower contribution margin will “stick” no matter how high sales go. At the upper extremes, the total compensation cost will be much higher with the commissionbased scheme. Following is a graph of commission cost versus salary cost at different levels of sales. Note that the commission begins to exceed the fixed salary at any point above $3,000,000 in sales. In fact, at $6,000,000 of sales, the manager’s compensation is twice as high if commissions are paid in lieu of the salary!
What this analysis does not reveal is how an individual will behave. The sales manager has more incentive to perform, and the added commission may be an excellent inducement. For example, the company will make more at $6,000,000 in sales than at $3,000,000 in sales, even if the sales manager is paid twice as much. At a fixed salary, it is hard to predict how well the manager will perform, since pay is not tied to performance.
Sometimes, a business will contemplate changes in fixed and variable costs. For example, an airline is considering the acquisition of a new jet. The new jet entails a higher fixed cost for the equipment, but is more fuel efficient.
The proper CVP analysis requires that the new fixed cost be divided by the new unit contribution margin to determine the new breakeven level. Such analysis is important to evaluate whether an increase in fixed costs is justified.
To illustrate, assume Flynn Flying Service currently has a jet with a fixed operating cost of $3,000,000 per year, and a contribution margin of 30%. Flynn is offered an exchange for a new jet that will cost $4,000,000 per year to operate, but produce a 50% contribution margin. Flynn is expecting to produce $9,000,000 in revenue each year.
Should Flynn make the deal? The answer is yes. The breakeven point on the old jet is $10,000,000 of revenue ($3,000,000/0.30), while the new jet has an $8,000,000 breakeven ($4,000,000/0.50). At $9,000,000 of revenue, the new jet is profitable while continuing to use the old jet will result in a loss. The primary risk of this decision would relate to a significant drop off in volume, in which case Flynn would remain strapped with the $4,000,000 fixed cost.
Thus far, the discussion has focused on cost structure and changes to that structure. Another approach to changing the contribution margin is via changes in per unit selling prices. So long as these adjustments are made without impacting fixed costs, the results can be dramatic. Return to Leaping Lemming, and see how a 10% increase in sales price would impact the contribution margin and profitability for 20X2.
Notice that this 10% increase in price results in a doubling of the contribution margin and a tripling of the net income. The solution to increasing profits appears to be to raise prices while maintaining the existing cost structure. If only it were this easy!
Customers are sensitive to pricing and even a small increase can drive customers to competitors. Before raising prices, a company must consider the “price elasticity” of demand for its product. This is fancy jargon to describe the simple reality that demand for a product will drop as its price rises.
So, the real question for Leaping Lemming is to assess how much volume drop can be absorbed when prices are increased. The appropriate analysis requires dividing the continuing fixed costs (plus target or current net income) by the revised unit contribution margin. This calculation results in the required sales (in units) to maintain the current level of profitability.
For Lemming to achieve a $500,000 profit at the revised pricing level, it would need to sell 5,000 units:
Units to Achieve a Target Income
=
(Total Fixed Costs + Target Income) / Contribution Margin Per Unit
5,000 Units = ($500,000 + $500,000) / $200
If Lemming sells at least 5,000 units at $1,100 per unit, it will make at least as much as it would by selling 10,000 units at $1,000 per unit. The unknown is what customer response will be to the $1,100 pricing decision. It is possible that an increased price will reduce customer demand.
Some contracts provide for “cost plus” pricing, or similar arrangements that seek to provide the seller with an assured margin. These agreements are intended to allow the seller a normal and fair profit margin, and no more. However, they can have unintended consequences.
For example, Pioneer Plastics sells trash bags to Heap Compacting Service. Heap and Pioneer have entered into an agreement that provides Pioneer with a contribution margin of 20% on 1,000,000 bags. Originally, the bags were anticipated to cost Pioneer $1 each to produce, plus a fixed cost of $100,000. However, increases in petroleum products necessary to produce the bags skyrocketed, and Pioneer’s variable production cost was actually $3 per unit. See how Pioneer fared under the agreement:
Notice the astounding change in Pioneer’s net income from $150,000 to $650,000. Such “cost plus” agreements must be carefully constructed, else the seller has little incentive to do anything but let costs creep up. Sometimes that company may complain about cost increases negatively affecting its margins. Before assuming the worst, take a closer look to see how the bottom line is being impacted. Even if Pioneer agreed to cut Heap a break and reduce the margin in half, Pioneer's bottom line profit would still soar in the illustration.
In the illustration, the contribution margin was 20% of sales. Accordingly, variable costs are 80% of sales. If total variable costs were $1,000,000, then sales would be $1,250,000 ($1,000,000/0.80).
How many businesses sell only one product? The reality is that firms usually offer a diverse product line, and the individual products will have different selling prices, contribution margins, and contribution margin ratios. Yet, the firm’s total fixed cost picture may be the same, no matter the mix of products sold. This can cloud the ability to perform simple CVP analysis. To lift this cloud requires some knowledge of the product mix.
Assume Hummingbird Feeders produces and sells a brightly colored feeding container for $15 (variable cost of production is $10, and contribution margin is $5) and a nectar formula for $3 per packet ($1 variable cost to produce, resulting in a $2 contribution margin). Hummingbird Feeders sells 10 packets of nectar for every feeder sold. Its fixed cost is $100,000.
How many feeders and packets must be sold to break even? To answer this question requires a redefinition of the “unit.” Assume the “unit” is 1 feeder and 10 packets. See that each “unit” would have a contribution margin of $25, as shown.
To recover $100,000 of fixed cost, at $25 of contribution per “unit,” would require selling 4,000 “units” ($100,000/$25). To be clear, this translates into 4,000 feeders and 40,000 packets of nectar. Total breakeven sales would be $180,000 (($15 X 4,000 feeders) + ($3 X 40,000 packets)).
Of course, the validity of this analysis depends upon actual sales occurring in the predicted ratio. Changes in product mix will result in changes in breakeven levels.
If Hummingbird Feeders sold $180,000 in feeders, and no packets of nectar, it would come nowhere near breakeven (because the contribution margin ratio on feeders is much lower than on the packets of nectar).
Note that one could also get the $180,000 result by dividing the fixed cost by the weightedaverage contribution margin ($100,000/0.555 = $180,000). The weightedaverage contribution margin of 0.555 is calculated as follows:
Businesses must be mindful of the product mix. Automobile manufacturers have a broad range of products, some at high margin and some at lower levels. If customers unexpectedly substitute economy cars for sport utility vehicles or basic models for luxury models, the resulting bottom line impacts can be significant.
Product mix can also be important for companies that sell a base product and a related disposable. For example, a printer manufacturer may sell “unprofitable” printers along with large quantities of high margin ink cartridges.
Selling expenses may be variable. For example, a salesperson may be paid a designated percentage of total sales. Such schemes have the potential to be counterproductive in a multipleproduct setting.
For example, assume that a company sells two products. Product A has a per unit sales price of $120, and Product B has a per unit sales price of $100.
A salesperson, earning a commission calculated as 5% of total sales, would prefer to sell product A. However, the company is better off when Product B is sold, because it has a higher contribution impact ($30 vs. $20). As a result, when a business manager considers its program of compensation for its sales staff, care should be given to align the interests of the sales force and the company. For the preceding example, it may make better sense to tie the commission to the contribution effects rather than the sales price.
This chapter has presented information on how to apply CVP for business analysis. Most of this analysis is keyed to a model of how profitability is impacted by changes in business volume. Like most models, there are certain inherent assumptions. Violating the assumptions has the potential to undermine the conclusions of the model. Some of these assumptions have been touched on throughout the chapter:
 Costs can be segregated into fixed and variable portions
 The linearity of costs is preserved over a relevant range (i.e., variable cost is constant per unit, and fixed cost is constant in total)
 Revenues are constant per unit and multipleproduct firms meet the expected product mix ratios
One additional assumption is that inventory levels are fairly constant, with the number of units produced equaling the number of units sold. If inventory levels fluctuate, some of the variable and fixed product costs may flow into or out of inventory, with a variety of potential impacts on profitability.