## Special Report

Break-Even Formula

Introduction

Chances are if you took at least one business course in college that was finance or accounting related, you've seen the break-even formula. The idea is as simple and basic, yet deceptively important, as business math can be. In this article we'll explore the formula and its uses.

Break-Even Theory

The basic concept is simple. Almost all businesses have a certain dollar amount of fixed costs. These are costs that don't vary with the volume of business. In fact, you'll incur these costs whether or not you sell any products or perform any services. It might be rent if the store space is leased, real estate taxes if you own the space, it could be the cost of a clerk or receptionist that has to be in the store or office regardless of volume, etc. You might say that I work out of my house so I pay no rent and have no other fixed costs. Well, you probably do, they're just nominal. You may have a separate telephone line, pay \$30 a month for hosting your web page, etc. But most of your costs are variable. For example, you purchase widgets from a local manufacturer for \$10 and sell them on line for \$17. Your variable costs are \$10 per unit. Your gross margin per unit is \$7.

Some other businesses are just the opposite. A cable-TV company will have to invest an enormous amount in stringing cable, equipment, etc. before it can generate a dollar of revenue. But its variable costs are low. Each \$1 of revenue may cost it only a fraction of that in variable costs.

The idea behind the break-even formula is that you have to sell a certain number of units to cover your fixed costs and the variable costs of those units. The concept and the formula are simple but too often ignored. That can be disastrous if you have substantial fixed costs or your gross margin is low.

Formula

The formula is simple:

`BE = TFC/P-V`

Where:

BE = Break-even point in units
TFC = Total fixed costs
P = Sale price of a unit
V = Variable cost of a unit

Example 1--Madison LLC is considering leasing a new machine and renting additional space for a cost of \$66,000 per year to produce a new product, TCM. The product will sell for \$17 each; the variable costs will be \$7. Plugging into the formula:

```BE = 66,000/17-7

BE = 6,600 units per year ```

The next question, of course, is how many units can Madison sell? Madison isn't sure, since there's no comparable product on the market, so outside of testing, there's no way to gauge demand.

Example 2--Madison LLC has found an alternative to the approach in Example 1. It can buy a cheaper machine and avoid leasing additional space. The fixed cost now is only \$25,000, but variable costs have increased to \$11 because there's more labor involved. The product will still sell for \$17. Plugging into the formula:

```BE = 25,000/17-11

BE = 4,167 units per year ```

The good news is that the breakeven is a lot lower. On the other hand, variable costs are higher. Madison will be break even at lower sales volume, but if sales take off, the higher variable costs with the cheaper machine will produce less profits. If sales go to 10,000 units, the more expensive machine will produce a profit of \$34,000; the cheaper one \$35,000. But if sales hit 15,000 units, the profit from the more expensive machine will be \$84,000; from the cheaper one only \$65,000. Because the fixed costs don't increase (see below) and the gross margin is higher with the expensive machine, the higher sales go using the first option, the faster profits will go up.

You can use a similar approach for a service business.

Example--Chatham Consulting LLC wants to set up a satellite office in a neighboring state. The fixed costs will amount to \$140,000 a year. That includes rent, telephone, internet, a receptionist, a manager and other costs. Chatham bills out consultants at \$105 per hour and their salary plus taxes, benefits, etc. amounts to \$72 per hour. Plugging into the formula:
```BE = 140,000/105-72

BE = 4,243 hours per year```

In theory, as long as the new office can bill more than 4,243 hours in a year, it should break even.

CAUTION 1: Notice here the units were hours per year, not units of product.

CAUTION 2: Be sure you're consistent with your costs. You could define your fixed costs on a monthly basis, but then your break-even point would be on the same basis, units or hours per month.

Limitations and Uses

First, the limitations. There are two axioms to keep in mind. One, in the long run all costs are variable. Two, in the short run many costs are fixed. We can't define long and short run exactly because the definition can vary. But consider rent on your space. It's fixed at \$14,200 per month. Your lease is up in three years at which time you can move into smaller and cheaper space. So the fixed cost isn't totally fixed if your planning horizon is five years. It is fixed if your horizon is one year. Second, you've got four employees assembling widgets. Their cost is theoretically variable, but you don't want to lay off one if you'll need a replacement in three months. So the variable cost isn't totally variable. (Obviously, many other costs such as electric, raw materials, etc. are much more variable.)

There's another issue with costs. They're not as linear as the formula would suggest. For example, the fixed costs of running a machine are \$11,000 per year. But that assumes the machine is making 30,000 units a month. If you crank the machine up to 50,000 units (using overtime) you'll run into additional machine costs because of wear and tear. At 60,000 units you'll have to add another machine, increasing your fixed costs. (The reverse can happen. Running an engine for only a limited number of hours a month can sometimes reduce it's life.) The costs are "lumpy" which restricts the formula to a certain range. The same can be true for variable costs, but to a lesser extent.

Despite these limitations, the break-even formula can be so valuable, you can live with the limitations if you understand and take them into account. Here are some uses.

Decision to manufacture. The classic use of the formula is determine whether it makes sense to engage in production. Using the formula you can quickly find your break-even point. If your best guess as to annual sales exceeds the breakeven, production is a go.

Sensitivity analysis. Chances are your best guess as to annual sales (or costs) won't be on the money. By entering the formula into a spreadsheet you can easily create a model and use different selling prices and fixed and variable costs to see how the break-even point will change based on changes in costs. You should also use sensitivity analysis to see how much your costs and revenue can vary and still allow you to break even. It's highly unlikely you'll cost figures will be right on the money. And even less likely sales projections will. Total fixed costs are likely to be more accurate than variable costs.

Analyzing risk in products or services. While a product or service with a low break-even point may or may not be very profitable, the low breakeven means that it's generally less risky. That's because you simply don't have to sell as many units to break even. You might opt to produce a less risky product if you already have a line of higher risk ones. A high break-even point generally increases your risk because you're faced with higher fixed costs. Should volume decrease below the breakeven, you'll still incur these costs. But a high breakeven generally means your variable costs per unit will be lower. As volume rises over the breakeven you'll make more on every unit sold.

Cash breakeven. In the discussion above the fixed costs in the formula include depreciation and any other noncash outlays. In the long run they have to be included in your analysis. But in some circumstances you might want to just use cash outlays as a measure of your fixed costs. That can be a valid approach if you're in a slow period, the project is only for a short period of time, etc. You can't make a habit of this since failure to cover those noncash costs will catch up eventually.

Quick and dirty. The break-even formula only tells you if you're covering your fixed and variable costs in the first year. It doesn't give you any indication of your return on investment, you'll need another metric for that. And you won't be in business too long if all you do is break even. You've got investors and/or creditors to pay. You should also consider what sales might be in future years. If you don't breakeven this year, might you do so next year? Since the formula is so easy to model, there's no reason not to test a number of scenarios.

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