# Simple Break-Even

In your business planning, have you ever asked: How much do I have to sell to reach my profit goal? How will a change in my fixed costs (rent, for example) affect my net income? How much do my sales need to increase in order to cover a planned increase in advertising costs? What price should I charge to cover my costs and allow for a planned amount of profit?

These are some of the questions that you can easily answer by using simple break-even analysis. In this guide, you will learn what break-even analysis is; see examples of how the technique works in manufacturing, retailing, and service businesses; and find out how to use it in your own business planning. Break-even analysis is a very useful tool because it can help you understand the sources of profit in your business.

## Basic Definitions

Break-even analysis is the use of a simple. mathematical formula to determine the sales level at which the business neither incurs a loss nor makes a profit. The break-even point, in mathematical terms, is simply the point where:

Total Expenses = Net Sales Revenue

The amount of sales revenue should be readily available on your income statement as net sales. Net sales revenue is all sales revenue (often called "Gross Revenue") less any returns and allowances. If your business is brand new and you have no income statement yet, you will need to use a projected sales figure. This will work for any of the calculations outlined in this guide. Total expenses also appears on your income statement (or projections). You will find most expenses listed under the heading "Operating Expenses" or "General and Administrative Expenses." Additional expenses to include in your analysis are found on the line labeled "Cost of Goods Sold," which appears on income statements for retailers and manufacturers.

To use the break-even technique, you need to do further analysis of your expenses so that you can classify them as either "fixed" or "variable."

Total expenses consist of two cost components: fixed costs and variable costs.

Fixed costs are those expense items which generally do not change in the short run, regardless of how much you produce or sell. These costs are typically the expenses you pay out regularly that do not go up or down with your sales level. Examples of fixed costs include general office expenses, rent, depreciation, utilities, telephone, property tax, salaries of office staff, and the like. Obviously, all expenses vary over the long run. For example, rent and property taxes increase every year. In break-even analysis though, our calculations are based upon those expenses that go up or down "because of" sales.

Variable costs are those expenses that change with the unit level of either production or sales. Generally, these costs increase with increased production or sales because they are directly involved in either making the product or making the sale. Examples of variable costs for manufacturing firms include direct materials used in production and direct labor (wages of production workers). In retail firms, variable costs include the cost of goods (inventory purchased from suppliers), sales commissions, and billing costs. These are only a few of the many kinds of variable costs you will encounter.

Typically, service businesses do not have large variable costs, except for labor. For example, a travel agency's only variable cost may be the expense of billing its clients. Other expenses that may be variable costs for service businesses include: materials routinely given to clients, materials used to offer their service, the cost of hourly labor to provide the service, and commissions paid co individuals who sell the service.

Using the definitions provided above, you should be able to classify all of your expenses as either fixed or variable. To begin the classification process, make two lists. Label one "fixed" and the other "variable." Record each of the expense items that you located on your income statement or projection on one of these lists. If you are not sure which list is right for a particular expense item, use this test to determine if it is fixed or variable. Ask yourself: If I did not sell any of my products or services during the next month, quarter, or year (whichever period is relevant for your break-even analysis), would I still have to pay this expense? If the answer is yes, that item is a fixed cost.

Some items may seem to have both fixed and variable cost characteristics. If that is the case, try to determine what portion of the cost is fixed and what portion is variable for your two lists. For example, you might split telephone costs into 60 percent variable and 40 percent fixed, if you owned a telemarketing firm. This step involves a good deal of judgment, so don't be too concerned about making inexact choices. Just make sure you have good reasons for your classifications. If you truly cannot decide whether an expense is fixed or variable, treat it as fixed. With the information you now have, we can adjust the break-even formula to serve better as a planning tool. Substituting the sum of (Fixed Costs + Variable Costs) for the term "Total Expenses," we get:

Fixed Costs + Variable Costs = Net Sales Revenue

There is something slightly misleading about the formula as it stands, however. As you know, variable costs change with the unit level of production or sales. In general, as the number of units flowing through the firm increases, the variable costs increase. For a manufacturer, the total variable costs increase as the flow of production or sales of the product increases. For a retailer, the total variable costs increases as the time it takes to purchase, inventory, and resell the product increases. So the "Variable Costs" part of the formula should reflect the changing nature of the level of units flowing through the business. That can be done mathematically by expressing the amount of Total Variable Costs as the Variable Cost Per Unit multiplied by the Sales Volume. We now have the final form of the basic break-even formula:

Fixed Costs + (Variable Cost Per Unit in Sales Volume) = Net Sales Revenue

## Break-Even: Basic Example

Now we are ready to try an example of basic break-even analysis. Let's assume that you work for the Reliable Chair Co., a manufacturer of solid wood chairs. You have been asked by the head of the marketing department to calculate a break-even level for monthly sales. In other words, you must determine the number of chairs Reliable needs to sell each month in order to break even. (While this example uses a manufacturing business, remember that break-even analysis can be used for both retail and service businesses as well. A refinement of the analysis for service and retail businesses will follow.)

During this same month last year, Reliable sold 550 chairs. Your business has enjoyed moderate growth over the last year, so you make the reasonable assumption that 600 chairs will be sold this month.

Let's also assume that you have projected your company's income statement, based upon an expected volume of 600 chairs per month. Let's also assume that you have classified each monthly expense as either fixed or variable. This is the classification you have prepared:

Fixed Costs per Month
Month Building Rent \$10,000
Property Tax \$4,000
Utilities \$900
Telephone \$850
Depreciation \$8,000
Insurance \$500
General Office Salaries \$7,000
General Maintenance \$700
Total \$34,950
Variable Costs per Month
Direct Materials
(wood. varnish, etc.)
\$28,800
Direct Labor \$26,400
Overtime Labor \$1,500
Billing Costs \$2,000
General Maintenance \$1,300
Total \$60,000

There are two things to notice about this sample classification of expenses. First, General Office Salaries is included as a fixed cost because in the short run these salaries must be paid regardless of whether any chairs are sold or not during the month. Obviously, if the firm fails to sell chairs for a number of months, the office salaries will decline (because of layoffs) and will no longer be considered fixed. This cost would eventually change with the volume of sales. Remember, though, that break-even analysis focuses only on the short run.

Secondly, notice that General Maintenance Expense appears on both the fixed and variable lists. This is because some maintenance costs will be incurred regardless of how many chairs we sell (the fixed portion). The office wastepaper baskets will still be emptied, floors washed, and windows cleaned. On the other hand, the more chairs we sell, the more the machinery will be used, so the incidence of breakdown is likely to increase, which will require more maintenance (the variable portion). How to divide maintenance costs between fixed and variable costs is an "educated guess". In the above example, we have divided maintenance as 35 percent fixed and 65 percent variable.

You need just one more piece of information, which is readily available from your business records, before you calculate the break-even point: your selling price. The selling price is known for an existing business. You will find, however, as we will see in a moment, that break-even analysis can actually help you determine your selling price.

Currently, Reliable chairs are selling to your dealers for \$250. Let's summarize what we know so far:

\$34,950 = total monthly fixed costs
\$60,000 = total monthly variable costs
\$250 = selling price of one chair
600 = expected number of chairs to be sold this month

Here's where we figure Variable Cost Per Unit. Simply divide the Total Variable Cost by the Number of Units we expect to sell to get the Variable Cost Per Unit. An existing business may use a previously calculated variable cost per unit figure, but it is best to review variable costs and expected sales at least annually to assure the most accurate data in doing your break-even analysis. In general, the formula for figuring Variable Cost Per Unit looks like this:

Variable Cost Per unit = Total Variable Costs / Expected Number of Units to be Sold

The calculation for this example looks like this:

\$60.000 / 600 units = \$100 Variable Cost Per Unit.

## Break-Even in Units

You're now ready to calculate the break-even level of sales for the Reliable Chair Co. We'll let "X" stand for the number of chairs needed to break even in the formula. The net sales revenue at the break-even point will be \$250 times "X" number of chairs. In our formula, then, Net Sales Revenue equals the Selling Price Per Unit times the Number of Units Sold. Similarly, while the Variable Cost Per Unit is \$100, the total Variable Costs equal \$100 times X number of chairs. In our formula, Variable Costs equal Variable Cost Per Unit times the Number of Units Sold. Now, simply plug the values we have previously calculated into the break-even formula.

Fixed Costs + Variable costs = Net sales revenue
\$34,950 + \$100X = \$250X

And, using a little algebra to solve the equation, we find:

\$34,950 = \$250X - \$100X
\$34,950 = \$150X
233 = X

In other words, Reliable needs to sell 233 chairs during the month just to cover all expected expenses. At the 233 chair point, Reliable will not be making a profit or incurring a loss, but the very next chair they sell will give them a profit.

## Break-Even in Dollars

You can also compute the break-even level in terms of dollars. We know how many chairs need to be sold and how much each chair sells for, so multiplying Chairs times Dollars Per Chair will give us the break-even level of sales dollars. The calculation is:

233 chairs x \$250 per chair = \$58,250

Another way of thinking about this number is that once Reliable's sales for the month have passed \$58,250, they should be making a profit.

The words "should be" are important. Remember that many of the figures we used in determining fixed and variable costs were based upon judgment. For a business still in the planning stage, these figures would be estimates or projections. This means that it is probably best not to rely on a single number like the 233 chairs we calculated as the break-even point. It is better to use the real power of break-even analysis to develop a range of points which better define what might actually happen.

## Break-Even to Set Price

In the above calculation, we assumed the price was set at \$250. What happens to our break-even point if we lower the price to \$225? Use the formula to find the answer:

Fixed Costs + Variable Costs = Net Sales Revenue
\$34,950 + \$100X = \$225X

And, solving as before:

\$34,950 = \$225X - \$100X
\$34,950 = \$125X
279.6 = X
or X = approximately 280 chairs

We find. when we cut our price by 10 percent, that the number of chairs we will have to sell to break even went up just over 20 percent. Because we can't sell six-tenths of a chair, Reliable's break-even is actually 280 chairs in this case.

Now, imagine recalculating the break-even point for a whole range of item prices. You would get a corresponding range of break-even points. You can use that range to judge the feasibility of actually reaching different sales levels. If it seems physically impossible to produce the number of units needed to break even at the lowest item price in your range of reasonable prices in the actual marketplace, this is a good advance indication of a potential problem. Possibly, the project is not feasible.

On the other hand, it could be an indication that your classification of expenses is off. You can try adjusting your estimate of fixed expenses to see how that affects your break-even point.

Let's try another illustration of how to adjust estimates. Let's assume the actual fixed maintenance cost is \$2,000. In other words, there is no variable component to this expense item; all maintenance costs are fixed. This might be the case if, for example, Reliable contracted with the machinery manufacturer to provide maintenance on a contract basis. The reason for contract maintenance, of course, is to keep variable costs from increasing beyond acceptable limits. The fixed and variable cost classifications now look like this:

Fixed Costs per Month
Month Building Rent \$10,000
Property Tax \$4,000
Utilities \$900
Telephone \$850
Depreciation \$8,000
Insurance \$500
General Office Salaries \$7,000
General Maintenance \$2,000
Total \$36,250
Variable Costs per Month
Direct Materials
(wood. varnish, etc.)
\$28,800
Direct Labor \$26,400
Overtime Labor \$1,500
Billing Costs \$21,000
General Maintenance \$0
Total \$58,700

Therefore, the new variable cost per unit will become:

\$58,700 per month / 600 units per month = 97.83 per unit.

(This assumes, of course, that there is no change in the number of chairs Reliable expects to sell this month.)

How does the change in classification affect break-even? Look at the formula:

Fixed Costs + Variable Costs = Net Sales Revenue
\$36,250 + \$97.83X = \$250X

and solving:

\$36,250 = \$250X - \$97.83X
\$36,250 = \$152.17X
238.22 = X
or X = approximately 239 chairs

The new break-even point, as a result of the change in classification of expenses, is calculated to be 239 chairs. Notice that we have to produce more than 238 chairs to break even and since we only produce whole chairs, our break-even point must be 239 chairs.

In this case, the change in maintenance expense classification didn't have much impact on the break-even point, since it increased by only six chairs. One could conclude then, if the management at Reliable felt that six chairs is not a large amount, that the classification of maintenance expense in this case is not as critical to the determination of feasibility as some other expense items.

The main point to take from this series of examples is that the break-even formula is flexible. You can adjust your estimates and classifications to answer a series of "what if' questions - the kind of "what ifs" that frequently come up in business.

There is an important "what if" question we have yet to address. That is "What if I want to find how much I have to sell to make a certain specified profit?" To answer this, we need to make an adjustment to the basic break-even equation.

## The Profit Break-Even Formula

Profit is what is left of the net sales revenue after all expenses have been covered. The basic break-even formula identifies the point at which all expenses have been covered, but where profit has not yet begun to exist. In other words, implicit in the basic formula is the idea that profit is zero at break-even.

In the original Reliable Chair Company example, break-even looked like this:

Fixed Costs + Variable Costs = Net Sales Revenue
\$34,950 + \$100X = \$250X

Actually, profit was in the formula, but at a zero value:

Profit + Fixed Costs + Variable Costs =Net Sales Revenue
\$0 + \$34,950 + \$100X = \$250X

The general form of the formula above, which we will call the "profit break-even formula", is the form to use when you want to estimate the level of sales necessary to meet a certain profit requirement. Let's look at an example using the Reliable Chair Co. data.

The head of the marketing department at Reliable, who was impressed with your ability to find the break-even level of sales, now gives you the assignment of finding the level of sales necessary to meet desired profit projections. You are told that plans require a profit of \$50,000 for the period under consideration. How many chairs must Reliable sell to make that profit level?

Recall the profit break-even formula and fill in the values we know or have already calculated:

Profit + Fixed Costs + Variable Costs = Net Sales Revenue
\$50,000+ \$34,950 + \$100X = \$250X

and solving:

\$50,000 + \$34,950 = \$250X - \$100X
\$84,950 = \$150X
566.33 = X
or X = approximately 567 chairs

So, in order to make a \$50,000 profit, Reliable must sell 567 chairs this month.

As with the basic break-even formula, the real strength of profit break-even is its ability to give you a range of figures to use in your planning.

What if selling 567 chairs a month is physically impossible for Reliable? Suppose Reliable is only able to produce 500 chairs a month because of production constraints. What price would they then have to charge to make a \$50,000 profit?

First, recognize that the variable cost per unit will not change. Therefore, it will still cost \$100 to produce each chair.

Following the procedure we've been, using, the number of chairs was always represented by "X" because the quantity of chairs was unknown.

Now we know that the number of chairs we can produce is 500, and we want to find the sales price. So, let's let "Y" = sales price and fill in the rest of what we know. The profit break-even formula would then look like this:

Profit + Fixed Costs + Variable Costs = Net Sales Revenue
\$50,000 + \$34,950 + \$100X = \$500X

And solving:

\$50,000 + \$34.950 + \$50,000 = 500Y
\$134,950 = 500Y
\$269.90 = Y
or Y = approximately \$270

The above calculation shows that if we must make a \$50,000 profit and are only able to make 500 chairs in a month, the price that will allow us to meet that goal and stay within our production constraint is \$270. Obviously, charging anything over \$270 would insure meeting the profit goal. However, there is a ceiling price above which Reliable will have priced themselves out of the market." The market ceiling price is unknown without further market research.

## Other Applications of the Profit Break-Even Formula

With a little imagination, the profit break-even formula can provide answers to a variety of questions beyond those we have already explored.

Expansion Decisions: Suppose Reliable Chair needed to expand its warehouse facility by renting additional space. The monthly rent for the new building is \$5000. If nothing else changes, how many chairs must Reliable now sell to meet its profit goal?

First, recognize that the new rental cost is going to increase Reliable's fixed costs. We shall assume, in this case, that all other variables remain unchanged. The values in the profit break-even formula will change from this:

Profit + Fixed Costs + Variable Costs =Net Sales Revenue
\$50,000 + \$34,950 + \$100X = \$250X

to this:

Profit + Fixed Costs + Variable Costs = Net Sales Revenue
\$50,000 + \$39,950 + \$100X = \$250X

and solving:

\$50.000 + \$39.950 = \$250X - \$100X
\$89.950 = 150X
\$599.67 = X
or X = approximately 600 chairs

So the \$5,000 expansion is going to require that an additional 33 chairs be sold each month in order to maintain the profit goal. Or alternatively, another:

33 chairs x \$250 per chair = \$8,250

\$8,250 in sales is necessary to cover the additional \$5,000 in fixed costs and maintain the profit level goal.

## Other Increased Costs

Note that this same type of analysis could be done for any planned expenditure that affected fixed costs. For example, a planned increase in advertising or a mandated increase in utility costs could also be handled using this analysis. These examples would increase the fixed costs. Raises given to personnel would increase either fixed or variable costs and possibly both.

As the examples in this article have shown, any change in either fixed or variable expenditures, a change in sales price, in sales volume, or in the profit goal can-be incorporated into the profit break-even formula to determine the impact of the change. All it takes is some basic math and an ability to recognize what part of the formula is affected.

So far the discussion has focused on manufacturing. Break-even analysis applies to retail and service businesses also. To adapt the examples in this guide, simply think about the nature of a retail or service business and what you sell.

For example, if you run a retail store that sells furniture, you will still be able to classify your expenses as fixed or variable. Many of the same type of expense items we saw in the manufacturing example also apply to retailers. Items such as utilities, telephone, depreciation, insurance, advertising, and property tax are all examples of fixed costs for retailers. The majority of variable costs for a retailer may be found in the "Cost of Goods Sold" line item on the income statement. Cost of goods sold for a retailer is the cost of purchasing inventory from suppliers, where cost of goods sold for a manufacturer involved costs such as direct materials and direct labor. Of course, a retailer might also have other variable costs such as billing costs or commissions paid to the sales staff.

You will also be able to calculate a variable cost per unit because you can estimate the number of units you expect to sell. The estimate may be based upon past experience with a particular product or upon projections if you are planning to sell a new product line. Of course, the selling price will also be known or estimated for any of your products.

In a retail business, you are likely to have a variety of products. Break-even is best used on a product-by-product basis. A product-by-product break-even is more meaningful than a store-wide break-even, because not all items have the same level of profitability. Determine the percent of total sales that each product line represents and use the same procedure to look at price changes, cost changes, or new profit requirements.

If you have a service business, it is likely that you have no tangible "units" to sell. You can still use break-even. though. Let's look at an example of how to use break-even in a consulting business.

Suppose a consultant advises clients on marketing strategies for their businesses. She has itemized her monthly expenses as either fixed or variable, based on the definitions of fixed and variable costs we have used in this guide. Fixed costs are fairly easy to identify. Let's assume they total \$4,500 for monthly rent, utilities, telephone, insurance, and the salary of an office assistant.

The variable costs relate to paper, brochures, billing costs, and the shared computer time which she needs to perform the marketing assessment she does for her clients. Based upon experience, or her study of competitors, she concludes she will need to spend 20 hours with each client to adequately address their marketing needs. Using 20 hours per client as a working estimate, she then looks at the costs of computer time, average paper usage, and the time spent billing to determine that total variable costs will be approximately \$800 per month.

So now how does the consultant figure the variable cost per unit? It starts with a definition of what a "unit" is for a service business. For some, it may be the hours of work they can bill. For others, it may be the number of documents they process. Our consultant defines "units" as the number of clients served each month.

Now because our consultant estimates it will take 20 hours to serve each client, approximately how many clients will she be able to serve in a month? Estimating 40 hours per week and four weeks in a month means there are 160 hours available each month. Since each client takes 20 hours, dividing the 160 total hours by 20 hours per client, she could serve eight clients a month (assuming a constant demand for her service existed). Because the consultant often works more than 40 hours a week, there is some built in "downtime" in the estimate of eight clients a month. In other words, the estimate appears realistic, given the conditions under which the consultant works.

Since variable cost per unit for this consultant means variable costs divided by the number of clients served, her variable cost per unit looks like this:

\$800 in Monthly Variable Costs / 8 Clients Served in a Month = \$100 Per Client Served.

Based upon the consultant's experience and her review of the going rate for marketing consulting services in her area, she has decided to charge clients \$70 per hour for her services. (As an aside, setting prices is a marketing issue based on factors such as knowledge of your customers, the competition, and historical prices to judge what price is reasonable). In this case, since a "unit" is defined as one client served, we need to relate the price per hour to sales revenue per client. It takes 20 hours to serve a client and, at \$70 per hour, the sales revenue per client is estimated to be \$1,400.

To use the profit break-even formula, the consultant needs to determine what profit level she requires. Let's assume that she decides, based on her own needs, that a monthly profit of \$8,000 is a reasonable profit goal. All the variables of the profit break-even formula have been estimated.

Let's summarize the relevant facts the consultant has assembled:

\$1,400 = selling price for one unit (client)
\$4,500 = fixed costs
\$800 = total variable costs (based upon 8 clients per month)
\$100 = variable cost per unit (client)
\$8,000 = monthly profit goal

It's now a matter of plugging in the values:

Profit + Fixed Costs + Variable Costs = Net Sales Revenue
\$8,000 + \$4,500 + \$100X = \$1,400X

and solving:

\$12,500 = \$1,400X - \$100X
\$12,500 = \$1,300X
9.62 = X
or X = approximately 10 clients

In other words, the consultant is going to have to serve 10 clients per month if she is going to make her profit goal. Since by her best estimate it is possible to serve only eight clients a month, this situation is probably not feasible. Note that break-even analysis effectively identified the feasibility of this project. This is another example of how useful the technique is.

So what is the consultant to do? Maybe her profit goal can be reduced. On the other hand, this lack of feasibility is also the result of her estimate of fixed costs, her estimate of variable costs, her estimate of how long it takes to serve one client, and her projected hourly rate. Any of those factors could be changed and the resulting answer judged for feasibility.

For example, what happens to feasibility if the consultant decides to raise her price per hour to \$90? The sales revenue per unit will be:

\$90 per hour x 20 hours per client = \$1,800 per client

And the new profit break-even will look like this:

Profit + Fixed Costs + Variable Costs = Net Sales Revenue
\$8,000 + \$4,500 + \$100X = \$1,800

and solving:

\$12,500 = \$1,800X - \$100X
\$12,500 = 1700X
7.35 = X
or X = approximately 8 clients

The result is that with a higher price, the consultant can reach her profit goal and cover her costs with a feasible number of clients per month. Whether or not such a price will take her out of the market is another question that should be addressed. And will the consultant actually be able to find eight clients per month? The point here, though, is that once again break-even analysis can help set prices.

It should be clear that service businesses can benefit from break-even analysis in every way that retail and manufacturing firms do. It simply requires a little deeper thinking about what it is that a service firm sells.

## The Last Word: Limitations of Break-Even Analysis

Break-even analysis has three important limitations. First, break-even analysis requires estimated projections of expected sales, fixed costs, variable costs, and any costs that have both fixed and variable characteristics. You must not be lulled into a false sense of security regarding your mathematically-sound results which are, after all, based upon projections.

Second, break-even analysis is useful only over a limited range of sales volume extending not too far from the expected level of sales. Moving much beyond that range will require additional capital expenditures for more floor space, more machinery, or more sales people, which will distort the estimates of fixed and variable costs.

Finally, break-even analysis assumes that the cost-revenue relationship is linear. This may or may not be the case for any particular business. For example, many businesses experience a reduction in fixed and variable costs per unit as the overall scale of the business increases. This is referred to as "economies of scale." Most very small businesses do not experience significant economies of scale.

Despite its limitations, break-even analysis is a very useful tool with which to approach a variety of decision problems. Such questions as the costs of expansion, evaluation of sales or profit performance, estimation of the impact of various expenses on profit, setting prices, and financial analysis in general are appropriately addressed using break-even analysis. But it is not a panacea. It is only one of the many tools available to the decision maker. It is best used in conjunction with other financial analysis techniques or as a screening device to determine whether more study is needed. In any case, familiarity with break-even analysis is essential for