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The Hidden Magic of Arithmetic Growth

Many investors know about geometric growth, which is what compound interest is.

Investors, for example, know that if you earn an annual 5 percent return on some investment, over time the investment grows large.

Every retirement savings plan employs geometric growth.

But small business owners want to know about another sort of growth, arithmetic growth.

In a manner similar to the way compound interest rewards investors, arithmetic growth rewards new business owners.

But let’s quickly contrast geometric growth and arithmetic growth. Then, we can describe an example of arithmetic growth. Finally, after that, we can discuss some possible actionable insights.

Geometric Growth vs. Arithmetic Growth

Geometric growth grows some value by a percentage.

If you save $10,000 in a retirement account and earn 5 percent interest annually,  the balance grows by a percentage (the interest rate) each year. Or you can say the balance geometrically grows.

At the end of year 1, an initial $10,000 investment earning 5 percent, or .05, grows to $10,500:

$10,000+$10,000*.05=$10,500

That’s geometric growth.

But not all growth is geometric. Some growth, like the growth a new small business experiences, works arithmetically. Meaning, by the simple addition of customers.

If you start a small business and add a customer a week, growth occurs arithmetically. Over five weeks, you accumulate five new customers:

1+1+1+1+1=5

That’s arithmetic growth.

Arithmetic growth sounds a little simplistic. And boring.

But here’s the deal: Arithmetic growth makes all the difference to small business entrepreneurs.

And now let’s talk about my new favorite Mexican restaurant…

The Restaurant Was Nearly Empty

My first visit, I counted four customers eating their lunches.

I expected a full lunchtime crowd. The restaurant served an excellent regional Mexican cuisine. The location? A popular a tourist spot… And then this bit of good luck for the owner: A local weekly newspaper reviewed the place at its opening and called it wonderful.

A little while later, my wife and I finished lunch. And the only unpleasant part of the experience? I felt really bad for the restaurateur who had worked so hard, done so much right, only to seemingly stall at launch.

Early Days Look Bleak

I can only guess what the new restaurant’s daily profit and loss statement looked like with four lunchtime customers.

To make the math easier—and this is rough—I figured about $20 a customer. So $80 from the lunch hour. If the business owner saw similar numbers for the dinner hour–so another four customers and $80 of revenue–the total daily revenue equaled $160.

To keep the numbers simple, I figured a 25% “Cost of Food,” $200 a day for the server and chef, and then $100 for the overhead (rent, utilities and so forth).

Rearranging this information into a little profit and loss statement, I guessed the first day’s results looked bleak:

Revenues (8 customers at $20 each): $160
Less: 25% for Food $40
Less: Waiter and Cook $200
Less: Overhead: $100
The Day’s Loss: ($180)

I honestly wondered how many days the owner would last.

He not only needed enough cash to lose nearly $200 a day, he surely also needed money to pay things like his personal rent and groceries.

Heartbreaking…

Fast Forward A Week

I went back a week later. And the situation seemed almost as dire.

This visit, I counted only eight customers enjoying lunch.

Re-running the same formulas for the daily profit loss only with 16 customers—8 for lunch and 8 for dinner—I estimated this great little restaurant still struggled, sadly:

Revenues (16 customers at $20 each): $320
Less: 25% for Food $80
Less: Waiter and Cook $200
Less: Overhead: $100
The Day’s Loss: ($60)

True, the numbers showed a smaller loss. But people don’t start a business to “only lose a little bit of money.”

And this restaurateur was maybe a couple of weeks into his venture. Ugh.

Fast Forward Another Week

I went back for the third time a week later. Partly because I wondered if the restaurant still operated. Partly for the excellent food.

That visit, the customer counts had slightly grown again. I counted 12 lunchtime customers. Assuming a similar dinnertime crowd of 12 diners, I guessed the daily totals might look like this:

Revenues (24 customers at $20 each): $480
Less: 25% for Food $120
Less: Waiter and Cook $200
Less: Overhead: $100
The Day’s Profit: $60

But that level of daily profit still looked bleak. Nobody starts a business where they lose thousands during the startup phase only to get a job that pays $60 a day.

Then, finally, it dawned on me. This guy’s business worked just fine, thank you.

He only needed to hold out long enough. And the reason? He enjoyed good arithmetic growth rates.

The Secret of Arithmetic Growth Rates

You probably quickly saw what happened here: Each week the customer counts grew arithmetically.

When I first visited his excellent little restaurant, he served maybe 8 customers a day. A week later, he served 16 customers a day. A week after that, he served 24 customers a day. And he continued growing this customer base.

One might also say that the business grew by roughly a customer each day: Eight customers added in a week equals roughly one new customer added each day on average.

Note: If a business adds 8 customers in 7 days, the precise arithmetic growth equals 1.14 customers a day. I rounded down to 1.

By the way? The restaurant now serves maybe 40 customers for lunch? A similar number for dinner.

Even with a larger waitstaff and extra help in the kitchen, the profit surely looks good.

I’m not going to guess at their daily profits… That seems a little intrusive. But with maybe $1600 a day in revenues, the business surely works well for the owner. Kudos to him and his family for a well-executed new venture.

But here’s the reason for the story: The business nicely demonstrates the power of steady arithmetic growth.

The story also spotlights some actionable insights…

Arithmetic Growth Matters When You Have Returning Customers

A first insight, for example: The arithmetic growth rate thing shows up in businesses with returning customers.

A restaurant that serves “regulars.” An accounting firm with clients who come back each tax season. A piano teacher who gives weekly music lessons to the same group of students.

Not every small business enjoys returning customers. But many do. And so for many, arithmetic growth matters. A lot.

Arithmetic Growth Rate Drives Forecasted Future Revenues

A second insight: For businesses with returning customers or clients, the owner may be able to forecast revenues at various points in the future using the arithmetic growth rate.

A piano teacher can start his or her business with zero students, for example. But if the teacher adds a student a week, 52 weeks later, he or she may be teaching 52 students. (The arithmetic growth formula is 52 weeks times a student a week.)

An accounting firm may start from scratch but if it adds 2 clients a month, three years later, it may have 72 clients. (The arithmetic growth formula is 2 clients a month times 36 months.)

A restaurant that grows daily customer counts by a patron a day may serve roughly 30 customers after a month in business.

Arithmetic Growth Rate Helps Owner Plan Startup Losses

A related third insight: An entrepreneur may be able to use an estimate of the arithmetic growth rate to plan for those days, weeks and months of startup losses.

The business owner needs to build a detailed spreadsheet to do this. But that isn’t too tricky.

Hopefully the restaurateur I observed did this. And if he did and his estimates were close to reality, he probably worked his way through those first lean weeks with comfort and confidence.

Note: You can download a free profit volume analysis Excel workbook from our CPA firm website. That workbook comes from an old book of mine, the MBA’s Guide to Microsoft Excel, and it lets you determine how revenues, expenses and profit change over a range of sales revenues. The workbook also lets you estimate a venture’s break-even point.

Arithmetic Growth Rate Not Only Input to Revenue Growth

A quick clarification about something obvious once you think about all this a bit.

The arithmetic growth rate explains much of the growth in revenue a new firm experiences. But it doesn’t explain all of the growth.

You can also grow revenues by increasing prices, for example. And you grow revenues by adding products or services.

Finally, some growth a new business experiences looks more like geometric growth than arithmetic growth. Perhaps customer demand for your product or service grows five percent annually because of demographic changes. Or maybe two percent of your customers refer you new customers.

In the case of a new business just starting, however, arithmetic growth probably explains most of the new revenue.

A Closing Comment

Regularly, new business owners don’t think about and watch their arithmetic growth closely enough. (Me included.)

But we all want to do a better job at this when we start new ventures.

Steady arithmetic growth, often hidden at first, may relentlessly push a new business toward profitability and financial success.

Some Related “Grow Your Small Business” Articles

If you’re planning for small business growth, you might find some of the following posts useful or interesting:

In How to Grow a Small Business, I share comments from established small business owners about how they’ve grown their ventures steadily over time.

In Has Your Small Business Stopped Growing?, I discuss a common reason some small businesses see their growth stall–and then a way you can try to fix this problem.

In the slightly theoretical post, Small Business Monte Carlo Simulation, I describe how to simulate small business ownership returns.

Finally, if you’re thinking about all this sort of stuff, you might find the Millionaire Next Door Business Plan blog post useful.

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