## Break-Even Analysis

Performing a break-even analysis is a simple way to determine price levels and to estimate whether an expansion or cost-saving project makes good business sense. Break-even calculations are also a key component of most business plans and are especially important for start-up companies seeking financing or investors.

The goal of a break-even analysis is to determine when sales or revenue equal total expenses; in simple terms, when a business or operation "breaks even." The real value lies in helping you determine the relationships between revenue, fixed costs, and variable costs. Changing one variable changes the results and allows you to model a variety of potential scenarios and make better business decisions. You can use a break-even analysis to:

- Make pricing decisions
- Determine the feasibility of selling new products
- Evaluate a project

Simple Pricing Decisions

We'll start with a basic scenario. Assume you plan to sell printers and you want to determine how many units you need to sell to break even. The formula is simple:

Revenue(X) = Fixed Costs + Variable Costs(X)

**Revenue:**Sales price per unit.**Fixed Costs:**Expenses that don't depend on business activities. For example, rent and salaries are fixed costs; you'll pay rent and salaries even if you don't make any sales.**Variable Costs:**Expenses that change based on activity. Shipping costs, for example, increase or decrease when you ship more or less products.**X:**The number of units you need to sell to break even.

Now let's work through an example. You estimate fixed costs like rent and insurance at $10,000 per month. You estimate variable costs at $85 per unit, including the wholesale cost of the printer and packaging and shipping charges. Based on extensive market research and competitive analysis you set your retail price at $145 per printer, including shipping.

Here's the formula:

$145X = $10,000 + $85X

- $145X = total revenue produced by selling X number of printers
- $10,000 = fixed costs
- $85X = variable costs incurred for X printers

Now for the math:

$145X = $10,000 + $85X

$60X = $10,000 (subtract $85X from both sides)

X = 167 (divide both sides by 60)

To cover fixed and variable costs and break even you'll need to sell 167 printers. If you sell more printers, as long as your fixed costs don't increase, each additional sale will generate an incremental gross profit of $60.

On the other hand, if you sell less than 167 printers you won't cover your fixed costs and will operate at a loss.

You can use the same formula to determine the effects of raising or lowering prices. What if you decide to compete on price and lower your retail price to $135 per printer? Here's the formula:

$135X = $10,000 + $85X

Your fixed and variable costs don't change; all that changed was the retail price. Now for the math:

$135X = $10,000 + $85X

$50X = $10,000 (subtract $85X from both sides)

X = 200 (divide both sides by 50)

Lowering the price requires you to sell 200 printers per month to break even; every additional printer sold will generate $50 in gross profit. Will a lower price generate increased sales?

Selling Additional Products

You can also use a break-even analysis to determine when adding a new product line to an existing business makes sense. How? Let's extend the example we just used.

You currently sell printers and would like to expand into selling black ink cartridges. Instead of adding up all your fixed costs again, you only need to know what *additional *costs you will incur by adding a new product line.

In terms of fixed costs, say you have open warehouse space in your current building and rent and utility costs will not go up, but you will have to add a part-time employee to your shipping department, so salary costs will rise by $1,000. You estimate variable costs at $10 per unit, including the wholesale cost of the cartridge along with shipping costs. You set your price at $14 per cartridge.

Here's the formula:

$14X = $1,000 + $10X

$4X = $1,000

X = 250

To break even, you'll need to sell 250 cartridges per month. Any additional sales will result in gross profit of $4 per unit, assuming your part-time employee can handle the additional workload.

Keep in mind we only factored in the *additional *fixed and variable costs incurred as a result of selling a new product line; current fixed and variable costs are covered by current operations.

Projects

You can use a break-even analysis to determine if a project makes sense. You're still in the printer business, and your sales have grown to the point you need to rent additional warehouse space at a cost of $3,000 per month. To make things simple, we'll assume all other costs remain the same. Should you take on the additional expense? Let's find out:

$145X = $13,000 + $85X

- $145X = total revenue produced by selling X number of printers
- $13,000 = current fixed costs ($10,000) + $3,000 for additional warehouse space
- $85X = variable costs incurred for X printers

$145X = $13,000 + $85X

$60X = $13,000 (subtract $85X from both sides)

X = 217 (divide both sides by 60)

To break even you'll need to sell 217 printers per month. If that volume sounds high based on your current retail price, you could take a look at the effect of lowering the price by $10:

$135X = $13,000 + $85X

$50X = $13,000 (subtract $85X from both sides)

X = 260 (divide both sides by 50)

Now you need to sell 260 printers to break even. So should you expand? The answer depends at least in part on your ability to accurately forecast sales – but at least now you know how many units you need to sell to break even under different cost and price scenarios.

Want to take it a step further? Say you can cut your variable costs by $5 per unit if you lease a new shipping system for $500 per month. Is that a good idea? You can perform a break-even analysis using the lower retail price and including the additional warehouse space:

$135X = $13,500 + $80X

$55X = $13,500 ($13,500 + $500 to lease shipping system)

X = 245

What did you learn? Instead of needing to sell 260 printers to break even, you now only need to sell 245 printers; the increase in fixed costs for leasing the shipping system is more than covered by the decrease in variable costs. You can either pocket the additional profits or consider lowering your price slightly to be more competitive while maintaining the same gross profit margin.

Keep in mind real-life situations are rarely as simple as the above examples. When one fixed cost rises other fixed costs often rise as well. For example, adding warehouse space will likely increase utility, insurance, and possibly even administrative costs. Variable costs may rise as well due to the need for additional labor and unforeseen maintenance costs. Work hard to identify and estimate costs so your break-even analysis is as accurate as possible.