# Interesting Math

## For Determining Pricing Increases

Recently, I read an interesting article by Charles Kyd, who publishes a lot of great Microsoft Excel help ideas for spreadsheets. He shared formulas for charts showing how increasing or decreasing prices can be analyzed.

Many times we either think about raising prices but we fear the consequence of raising them too far. Or what about the effect of lowering prices – will that help to attract more customers? Let’s take a look at the math using Company X as an example.

Last year Company X sold **$100,000** in custom framing. They paid **$28,000** for the materials to make those products, giving them **$72,000** in gross profit dollars to cover operating expenses. This **$72,000** represents a gross margin percentage of **72% ($72,000/$100,000)**. The company has an average ticket of **$150**, meaning they do **667** projects per year.

Company X, like all of us, wishes to maximize their profits on the **$100,000** in sales and management is considering a **15%** **overall price increase,** but they wonder what will the impact of higher prices will be on sales…

Using this formula, we can determine how far sales would need to drop before the **15%** **increase** actually hurts the profitability of their business.

**[Gross Margin %/ (Gross Margin %+Price Change %)] -1 =
Sales Change %**

So, with our example, Gross Margin Percentage is **72%**. The price change is **15%**. Working the formula would look like this:

**72% / (72%+15%) – 1 x 100%= -17%**

What this math tells us is if company X increases prices **15%**, it will take more than a** 17%** **loss** in sales to cause a decrease in gross profit. This means sales would need to decline from **$100,000** a year to below **$83,000** before this price increase would be detrimental to company profits. Because average ticket will raise from **$150** to **$172.50**, the company could do nearly **100** fewer projects per year and still make the same profit. This means labor can be reduced because many less projects can be created to create the same profit margin.

Now, company X wants to consider the effects of** reducing prices by** **15%**. That math is the same formula except the “**+**” sign now becomes a “**–**” :

**72% / (72% – 15%) -1 = 26%**

So cutting prices **15%** would mean that company X would have to grow sales by **26%** to make the gross profit they are making now, meaning sales would need to grow **$126,000** to stay even with current profits. Since average ticket also falls by **15**%, it would now take more than **300** additional projects to achieve this level of gross profit, meaning that labor costs will be much higher.

It’s interesting to see the impact price increases and decreases can have on your business. Doing the math as part of making pricing decisions can help you see the effect on future profits.

Claudia Roblee

Wow, very interesting Ken. Going to plug some of my own numbers into this as we have a higher average sale. But I’m sure this will still make sense.

Jody niklaus

Great article!