My Love-Hate Relationship with Math

By John V. Guiliana, DPM, MS

Many critical business decisions can actually be made by using math. Now, I know what you are likely thinking…” oh no…I hated math!” Well from a scholastic perspective, so did I. But from a practical and business perspective, I love math!

In business, numbers never lie to you. They never try to sell you anything. Numbers are simply unbiased, genuine, and real. And there are a whole host of ways that numbers and formulas can guide you towards the right decisions…once you understand how to use them.

In this month’s blog, I’m going to highlight a common practice decision point- whether to perform billing in-house, or outsource.

I’m certain that you have read many articles or even past blogs of mine that discussed the advantages of outsourcing. Many authors, including myself, frame their argument to outsource based upon factors such as specialization of labor, lower opportunity costs, lower rejection and denial rates, etc. But today, I’m going to completely ignore all those somewhat intangible advantages and discuss the pure mathematical formula to easily help you understand the tangible. It’s known as the Indifference Point.

In economic terms, the indifference point represents the level of activity at which the cost is the same under either a fixed or variable cost arrangement. In order to demonstrate how the indifference point calculation can help guide you in your decision to outsource, I need to start with some assumptions.

Assumption #1:

The cost associated with the option of outsourcing billing is based upon a percentage of revenue (6% for this exercise).

Assumption #2:

The cost associated with performing billing in-house is a fixed cost ($65,000 in annual salaries and benefits allocated towards billing for this exercise).

The indifference point computation will help you identify the practice’s revenue needed to make each choice (outsource versus in-house) equal (indifferent), as well as which option becomes more or less costly as revenues deviate from the indifference point.

Revenue at Indifference Point = Fixed Cost/Variable Rate
= $65,000/.06
= $1,083,333

The indifference point in this exercise tells us that when the practice is generating $1,083,333 in annual revenues, the variable cost associated with outsourcing billing versus the fixed cost of performing billing in-house are equal. Phrased differently, if the practice generates less than the indifference point revenue, the variable option of outsourcing becomes more attractive (less costly option) and the fixed option becomes less attractive (more costly option). Conversely, if the practice generates more than the indifference point revenue, the variable option of outsourcing becomes less attractive and the fixed option becomes more attractive. Remember that the numbers used in this exercise are purely hypothetical and for demonstration purposes only. You will need to find your practice’s unique indifference point by working with accurate numbers.

And remember that the indifference point and its associated math will help you understand the best option based only on the tangible cost associated with the choices. As discussed in many articles and past blogs, the intangible costs discussed above can be very meaningful… and sometimes even approach or exceed the tangible costs!

While the Indifference Point formula is rather simplistic and intuitive, I’ll discuss more cool things you can learn about your practice by using other formulas in upcoming blogs. Learn to love math my friends!

By John V. Guiliana, DPM, MS