If you haven’t ever seen it, Shark Tank is quickly becoming one of the most popular reality shows on television. On the show, hopeful entrepreneurs pitch their business ideas to “sharks” (which the show describes as self-made millionaires and billionaires and includes Mark Cuban, Barbara Corcoran, Lori Greiner, Ashton Kutcher, and Draymond John).

The entrepreneur can only make a deal if they receive their funding amount. The sharks often counter with offers of their own which include a lot of information sometimes: ($150,000 for 30% of the company plus a $0.75 royalty on each sale…what!?).

Embedded within the show, and also, as the show reveals, within the business world at large, are many different examples of math. I’m going to focus this blog on three: Valuation; Royalties; and Profit Margin.

**Valuation**

The valuation of the company is generally the very first thing out of the entrepreneurs’ mouth, however, they never come right out and say “I think my company is worth $2 million.” Instead, they offer their terms in the hopes of making a deal, and with some simple math, anyone at home can figure out how much they value their company at.

Let’s start simple: an entrepreneur comes out and says, “Sharks, I’d like $100,000 in exchange for 50% of my company.” Logically, this makes sense—the entrepreneur thinks that his business is worth $200,000 because he is offering to give away half of it for $100,000. The math behind this is simple:

$100,000 = 200,000

.50

In any valuation situation, first change the percentage to a decimal. Next, divide the amount asked for by that decimal and then arrive at your valuation. Another example would be, “I’d like to offer 25% of my company for $200,000.”

Following our math from above:

200,000 = 800,000

.25

In this instance, the entrepreneur believes her company is worth $800,000. Generally, the sharks counter this offer with something of their own: “I’ll give you the $200,000, but I’d like 40% of the company.” This back and forth changes the valuation of the company, and is a big part of the show—and it requires mathematical knowledge just to understand the drama unfolding!

**Royalties**

In addition to equity (ownership in the company, the percentage amount from above) sometimes the sharks also ask for a royalty. A royalty is a payment either in a percentage or in a constant amount for each sale that an entrepreneur makes.

Let’s say, for example, a shark asks for a 10% royalty on every sale (in addition to the equity they are asking for). What this means is that for every $1 the entrepreneur makes selling their product, they can only keep 90-cents (the other 10 cents is paid to the shark).

Let’s check the math:

A shark asks for a 12% royalty on every product sold. The entrepreneur sells each of their products for $30. How much does the entrepreneur keep, and how much does the shark keep?

To check this, simply change the percentage to a decimal again, but this time multiply:

Shark: $30 x .12 = $3.60

The shark keeps $3.60 for each $30 sale

Entrepreneur: $30 –$3.60 = $26.70

The entrepreneur gets to keep $26.70 of their sale, or 88%.

Each of these situations, along with a few others, are the most common aspects of “the deal” that the entrepreneur makes with the sharks. After the entrepreneur gives their presentation, there are other questions that the sharks ask the entrepreneur that also involve math!

**Profit Margins**

The sharks are obviously most concerned about money. Their job as venture capitalists is to invest their money into business that are going to succeed so they can get a return.

One question they always asks the entrepreneurs is, “What are your margins?” In this case, margins is short for profit margins. What they are really asking is what percentage of each sale is actually profit?

In this case, let’s assume we are selling beach chairs (thinking summer) and each beach chair sells for $20. Unfortunately for the business, it doesn’t mean that they get to keep $20 every time they sell a beach chair, because it cost them money to make the beach chair (things like materials and labor).

Let’s say that it cost $12 for the company to make the beach chair. What this means is that they are making $8 for every sale (the $20 they earn minus the $12 it cost to make the chair).

To figure out the profit margin, we’re just going to divide the profit by the revenue or:

8 = .4

20

then,

.4 x 100 = 40% margin

This tells the shark that for every sale that an entrepreneur makes, they can keep 40% of the money for the business. Margins vary by industry. Some industries, like retail, have very small margins (meaning the cost to make your jeans and the price they sell them for are very close). Others, like the restaurant business, have relatively high margins (the cost to make the hotdog is nowhere near how much they are charging you for it).

Many of the deals on shark tank hinge on both the sharks and the entrepreneurs understanding some basic math calculations. Next time you watch the show, be sure to keep an ear out for these buzzwords and use your new math skills to figure out exactly what’s going on—it helps to keep the drama high!

**Pro Tip:**

Use the examples from this blog as real world applications of math in your next math class, to help your students understand the ways in which mathematics is interwoven with our daily lives—and can help them succeed at business!

**About the Author**

Chris Brida is a mathematics teacher in Baltimore, MD. He currently teaches 9^{th} grade Algebra. Chris is a regular guest contributor to our blog, and we feel lucky to have him.

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