What is Break-Even Analysis?

Break-even analysis is an attempt to identify the level of sales, measured either in units or dollars, at which total revenue equals total costs, or, alternatively stated, whereprofits equal zero.

Break-even analysis provides an indirect way to examine the impact of price on profitability.A more direct approach is to build aproformaincome statement (profit and loss statement) that attempts to project an accurate numerical estimate for expected profits.Proformaprojections, however, rely on obtaining solid estimates of the number of units that would be purchased at different target prices.A reliable projection of the demand curve faced by the firm thus is necessary to produce realistic proformaincome statements.However, predicting the demand curve can prove to be very difficult, requiring too much time and expense, and is prone to error due to the influence of uncontrollable forces.

This is where the need for break-even analysis enters the picture.Break-even analysis does not require the availability of precise estimates of demand at the price under evaluation.This makes break-even analysis an ideal technique for "backing into" profitability estimates when precise estimates of demand are not available and cannot be reasonably developed.But when they know the "break-even point," managers can often estimate the likelihood that actual sales will surpass (or not surpass) the computed break-even point.Projecting the break-even point is easier than precisely pinpointing actual sales anticipated at specific prices.

Assume, for example, the computed break-even point for a product is 100 units.Decision makers then can estimate the likelihood, or probability, that at least 100 units will be sold.If decision makers believe actual sales will likely exceed "break-even," the analysis indicates the price being considered is viable.By contrast, when management believes sales levels likely will not reach the calculated break-even point, alternative prices (or some other change to the marketing mix) should be evaluated.

To re-emphasize, break-even analysis is extremely useful.The tool specifically benefits firms who are uncertain about how much demand will result from charging a specific price.By employing break-even analysis, marketers can acquire general insights about how many units must be sold in order to cover all relevant costs involved in making and marketing the associated product.By knowing the relevant "break-even point," managers can project the likelihood that sales will exceed (not exceed) break-even.

Break-even analysis, therefore, is best described as a technique that allows firms to logically examine the potential profit impact of charging a particular price.The technique is also extensively used to evaluate the profit impact of changing various marketing mix and/or production programs that affect the costs associated with making and marketing products. Marketers may use break-even models to identify the level of sales in units needed to offset increases in advertising or sales promotion expenditures - or to assess the profit impact that would result when personnel are added to the sales force.

The Break-Even Point: Its Relationship to Revenues and Costs

Figure 1 graphically illustrates how a typical break-even analysis is conducted.The "X" axis represents the number of units produced or sold.The "Y" axis represents both costs and total revenues.The cost dimensions on this graph should look familiar.When conducting break-even analyses, the relevant costs are the fixed and variable costs with which you are now quite familiar.Both total fixed costs (TFC) and total variable costs (TVC) at increasing levels of output are summed to generate the total cost (TC) curve.All that needs to be added is the total revenue curve (TR).The TR curve begins at the origin; i.e., where the X and Y axes intersect, and steadily increases to the right as output increases.

Figure 1.Graphic Depiction of the Break-even Point

The break-even point is that level of sales where TR=TC (total revenue equals total costs).Any sales in excess of those required to achieve break-even generate profits.This is illustrated in Figure 1 by the fact that to the right of the break-even point TR>TC (i.e., total revenue exceeds total costs).In contrast, to the left of the break-even point, TR

Mathematics of Break-Even Analysis

The graphic approach to break-even analysis provides a solid conceptual understanding of the break-even point and its relationship to both revenues and costs.However, the break-even point can be found much more easily via direct computation.The formula for break-even in units sold (Q) is:

(1)

The break-even point in units (BE(Q)) is found by dividing total fixed costs (TFC) by the difference between price per unit and average variable cost per unit (P - AVC).The latter difference (P - AVC) is called theunit contribution(UC) or simplycontribution.This is the per unit amount that is available to cover total fixed costs.

An example illustrates the computational procedure and helps clarify the meaning of theunit contribution.If TFC = $200,000, price is $100 per unit, and variable costs per unit are $50, thebreak-evenpoint is computed as in Equation (2):

(2)

The $200,000 in fixed costs is divided by the difference between price and average variable costs.This difference is $50 per unit.Fifty dollars is the contribution per unit that is now available to help cover the $200,000 in fixed costs.Each unit sold contributes $50 to cover fixed costs.This means that 4,000 units ($200,000/$50 = 4,000) must be sold to fully recover the $200,000 in fixed costs.Thus, 4,000 units is the break-even point.

Sometimes it is useful to compute the break-even point in dollars rather than units.Of course, a simple way to obtain the dollar break-even point is by first computing break-even in units, as we have already done.The result then is multiplied by the selling price.In our previous example, the dollar break-even is obtained by multiplying 4,000 units by the $100 price tag.The result is $400,000.

Break-even in dollars can also be computed directly by dividing total fixed costs (TFC) by thepercentage contribution margin(also called thecontribution margin).The percentage contribution margin is obtained by dividing the unit contribution (P- AVC) by price (P).The contribution margin is, therefore, a ratio between the dollar unit contribution and the original selling price.The computation is:

(3)

Basic break-even analysis, as presented above, is immensely useful.Even if we stopped here with our presentation of break-even, you will carry away an application that will reside among the most important tools you will use in your business career.However, break-even analysis has many additional applications, or "extensions." For example, the break-even model, with a simple modification, can be employed to solve for the level of unit (or dollar) sales required to achieve some desired level of target profit.The modifications needed in the break-even formula are:

(4)

Note that the desired profit is treated as an additional fixed cost in the revised formula. The numerator in the formula is now TFC + Target Profit.In addition, since the formula is solving for the level of sales required to achieve a target level of profits, it no longer makes sense to call the result 'break-even' or use the variable name BE(Q).We have substituted the variable 'Target Q' for 'BE(Q).'

Conceptually, treating the target profit as an added fixed cost makes sense.Achieving the desired profit requires selling more units beyond those required to break-even. The exact number of extra units that must be sold is a function of the unit contribution (i.e. P-AVC), just as in the standard break-even model.

Our last example can be extended to illustrate how this works.TFC remains at$200,000, but now let's add the stipulation that we want to earn $5,000 in incremental profit - beyond break-even.Unit price is still $100 and AVC is $50.This means that the unit contribution is still $50.The formula becomes:

(5)

Note that the $5,000 target profit is added to the $200,000 fixed costs.The sum ($205,000) is divided by the $50 unit contribution.The result is 4,100 units.Recall from the earlier example (Equation (3)) that 4,000 units were required to break-even.Thus, an additional 100 units must be sold to achieve the $5,000 in profits.Of course, the number of additional units could have been computed directly by dividing the $5,000 by the $50 unit contribution: $5,000 $50 = 100.

Alternative Measures of the Break-Even Point

The discussion of break-even thus far has expressed the break-even point either in units or dollars.These measures make sense.However, break-even can be expressed in other ways that often prove more useful to decision makers.

The market share required to break-even is one such alternative.Market shareis the ratio of the company's sales to total industry sales, where sales can be expressed in either units or dollars:

(6)

Market share, as examined in an earlier exercise, is the firm's "share" of industry sales.Expressing break-even in market share is sometimes more useful than using "units" or "dollars."Management may struggle to judge the likelihood that specific break-even points expressed in units or dollars can be achieved.Essentially, no mental baseline may exist against which the resulting value can be compared.But, when the break-even point is transformed into market share, the required market share may be immediately recognized as reasonable and obtainable, or conversely, as impossible to achieve.This scenario is highly likely to be true when firms are launching new products or entering new markets in which a firm has little prior experience.As an example, assume the estimated break-even point for a newly proposed product as 500,000 units.This may seem like an impossible amount to achieve by just examining the magnitude of the result.Now assume that this break-even estimate is transformed into the market share required and find that the associated break-even market share is only 1%. The outlook now may change dramatically - the 500,000 unit goal may now appear more attainable given the overall size of the market is obviously very large.

In the case of hotels and motels (the lodging industry), break-even can be expressed in terms of room-nights sold or occupancy rates.Room-nights sold is equivalent to computing break-even in units.The result is an estimate of how many rooms must be rented, on average, during a specified period in order to break-even.An alternative measure is "occupancy rate." This is the proportion of rooms in the respective hotel or motel that must be rented, on average, to achieve break-even.Like market share, it is sometimes easier for management to visualize the proportion of rooms that must be rented to break-even instead of the absolute numbers of rooms rented or room-nights that must be sold.

Incremental Break-even Analysis

An additional powerful derivative of break-even analysis involves its use to determine the likely profitability of making changes to aspects of the firm's marketing mix.Adding or modifying advertising and other promotion programs, distribution channel modifications, product modifications, and changes in sales personnel can be costly and incremental break-even analysis can provide insights into the potential profitability of these changes.

An example illustrates the power of incremental analysis.Let's revisit our Pampered Puppy example developed in an earlier exercise.Norton Pet Foods (NPF), the producer of the Pampered Puppy brand of high quality organic canned dog food is interested in penetrating the Dallas - Fort Worth (DFW) market.The producer currently sells the Pampered Puppy brand in other similar markets and possesses, on average, a market share of five percent (5%) of the premium canned organic dog food markets in these areas.Pampered Puppy will be sold through specialty pet food stores and supermarkets in the DFW market area.Sales will be handled by a dog food broker who will be paid a commission of 6% on sales to retailers.Pampered Puppy will be sold in standard 12 ounce cans with a recommended selling price to consumers of $2.40 per can (or, $.20 per ounce).Retailers demand a 40% markup resulting in a selling price to retailers of $2.40 - $.48 = $1.44 per 12oz can or $1.44 x 24 = $34.56 per case of 24.Subtracting the broker's 6% yields revenue to NPF of $32.49 per case of dog food sold.Norton Pet Foods anticipates that variable costs of production for Pampered Puppy will be $.96 per 12oz can, or $23.04 per case.The contribution per case is, therefore, $32.49 - $23.04 = $9.45, or $9.45 $32.04 = .2908 or 29.08%

Management also estimates that the incremental marketing and distribution costs associated with expanding to the DFW market area will be $15,000 per year.These costs will include advertising in local media, slotting fees for retailers, and point of sale materials such as brochures.The resulting incremental break-even in cases of dog food sold is:

(7)

From an earlier Keeping Score exercise, we know that the market potential for premium organic dog food in the DFW area is about 65,000 cases for all producers of this type of dog food.Thus, NPF will need to grab 1,588 65,000 = .0244 or 2.44% market share to cover the incremental expenditures estimated for the expanded distribution program into the DFW area.Since NPF boasts a 5% market share in other market areas similar to the DFW market, management feels that it is quite reasonable that Pampered Puppy can command at least the needed 2.4% market share needed to break-even.It would be a different story is Pampered Puppy averages only, let's say, 1.5% market share in markets it currently serves.Management might not be quite so willing to take the plunge since more market share is needed to just break-even than the 1.5% share it can reasonably expect to achieve.

Now It's Your Turn.Show What You Have Learned

For this exercise we will again use Shannon's Brewery.You will be presented the relevant pricing and cost information needed to address several break-even problems.

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Question 1

10pts

Shannon's distributes its beer through a wholesaler, Miller of Denton.The retail selling price for a six pack of its typical craft beer is $12.00.The retailer's cost per six pack is $8.00.The wholesaler sells the beer to the retailer for this price.Shannon's sells a six pack to the wholesaler for $5.40.Shannon's variable costs of production, packaging, and distribution are $3.60 per six pack.Shannon's has the following annual fixed operating and marketing costs:

Marketing Costs

$58,705

Consumer Advertising

$36,927

Trade Promotion

$30,000

Sales Promotion

$18,000

What is Shannon's annual break-even in six packs of beer sold?

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Question 2

10pts

Given the above information in Q1, Shannon's wants to increase its sales to retailers by 20% in the next year.Management estimates that the incremental promotion program required to generate sufficient demand to boost sales by 20% will be:

Personal Selling Costs

$60,000 (exclusive of commission)

Consumer Advertising

$58,296

Trade Promotion

$41,369

Sales Promotion

$25,000

Shannon's will need to hire an additional salesperson (paid a salary and commission) and provide some added administrative support.The sales person's salary plus administrative support will cost about $60,000 per year.The sales person's commission will be the equivalent of $0.05 per six-pack sold.The incremental costs of consumer advertising, trade promotion, and sales promotion necessary to support sales in the new market will be substantial as indicated in the table above.How many six-packs must be sold to break-even on the incremental costs that are anticipated?

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Question 3

10pts

Let's modify the scenario from Q1 and Q2 a bit.Management estimates that the incremental promotion program required to generate sufficient demand to boost sales by 20% will need to be:

Marketing Costs

$60,000(exclusive of commissions)

Consumer Advertising

$57,829

Trade Promotion

$37,735

Sales Promotion

$25,000

The total market for craft beer sold in six-packs is about 2,500,000 six-packs per year.What market share will Shannon's need to capture in order to break-even on the incremental costs that are anticipated? Express your answer in percent format to two decimal places.For example, 5.00 for five percent or .50 for one-half of one percent.Do not include the percent sign.Use the same contribution from the last question.Assume price and variable costs per six-pack remain the same as in Q2.