While facilitating the Money and Metrics module of the Goldman Sachs 10,000 Small Businesses Program this week, I had a few business owners ask me how to calculate a multi-product or multi-service break-even point. An online search gave me several good explanations, but nothing I thought was comprehensive enough. As I started to write out something to answer these business owners’ questions, I realized I had enough to make a blog post. Here we go…
Understanding the break-even point in any business is critical. While setting ambitious levels for metrics such as ROA (Return On Assets), ROE (Return On Equity), and EVA (Economic Value Added) will yield better performance for your business, understanding the point at which your business can sustain itself without losing money is critical. Break-even can be calculated on a profitability or cash basis. We’ll address profit break-even here, but you can easily turn this into a cash break-even by including only cash items in your calculations.
Regardless of whether you are selling one product or service, or multiple products and services, you start with two simple steps:
1. The first step is to run through your income statement and classify each line item as variable or fixed. Expenses that vary with the amount of revenue will be variable and those that don’t vary with the amount of revenue should be classified as fixed (even if they vary for other reasons).
2. Next look at the last few months of quantity sold data for your business and use it to figure out the price per unit and variable cost per unit the business has been experiencing.
Single product or service Break-even
Once you’ve done this, the basic formula for figuring out break-even for a single product or service is simple enough.
Break-even = Fixed Costs / (Price Per Unit – Variable Cost Per Unit) = Fixed Costs / Contribution Margin
If your fixed costs in a month are $200,000 and you sell your items for a price of $300 each at a cost of $200 each then your break-even number of units will be:
Break-even = 200,000 / ($300 - $200) = 2,000 units. And because the units sell for $300 each, the break-even amount of revenue is $300 x 2,000 units = $600,000
Multi-Product or Multi-Service Break-even
So far so good. But this only works for businesses selling one item. And most businesses sell more than one product or service. To understand the calculation for multiple products or services, we need to dive a bit deeper. We’ll need the below formulas:
Average Revenue Per Unit = Total Revenue / (sum of all quantities sold of all products and services)
Average Cost Per Unit = Total Variable Costs / (sum of all quantities sold of all products and services)
Contribution Margin Ratio = Contribution Margin Per Unit / Average Revenue Per Unit = (Average Revenue Per Unit – Average Costs Per Unit) / Average Revenue Per Unit
Break-even = Expenses / Contribution Margin Ratio
Let’s work through an example. Suppose the below represents either a historic or forecast period of our business where we sell three products, A, B, and C:
First calculate:
Average Revenue Per Unit = Total Revenue / (sum of all quantities sold of all products and services) = $883,750 / 3,250 = $271.92
Average Cost Per Unit = Total Variable Costs / (sum of all quantities sold of all products and services) = $576,000 / 3,250 = $177.23
Contribution Margin Ratio = Contribution Margin Per Unit / Average Revenue Per Unit = (Average Revenue Per Unit – Average Costs Per Unit) / Average Revenue Per Unit = ($271.92 – $177.23) / $271.92 = 0.348
And then the break-even point is:
Break-even = Expenses / Contribution Margin Ratio = $200,000 / 0.348 = $574,712.64.
If we’d like to see this in units we can simply divide our break-even number by the Average Revenue Per Unit. $574,712.64 / $271.92 = 2,114 units.
And if we want to know how much we need to sell of each unit in order to break-even (if the sale mix remains the same) we can multiple each by the Sales Mix Percentage.
Break-even Product A = Breakeven Unites x Product A Sales Mix Percentage = 2,114 x 25% = 529 units
Break-even Product B = Breakeven Unites x Product A Sales Mix Percentage = 2,114 x 37% = 782 units
Break-even Product C = Breakeven Unites x Product A Sales Mix Percentage = 2,114 x 38% = 803 units
Note that you were able to arrive at these numbers while bypassing the need for finding your variable cost per unit. For many businesses finding a variable cost per unit for each of several products of services can be tricky.
The Numbers Explained:
So in layman’s terms, this means that our business needs $574,712.64 in revenue in order to not lose money. Anything less than that puts us into debt. Anything greater, gives us a profit. In terms of units, we need to sell 529 units of Product A, 782 units of Product B, and 803 units of Product C.
And that’s it. If your sales mix or fixed expenses fluctuate you might need a few iterations of this, but this should provide almost everything you need as you evaluate your existing business or plan for capitalizing on your next growth opportunity.