*Preface: Did Nathan Jacobson thank his schoolmasters? We may never know. Math is good for school students, but it may be even more important in business success. If you’re an entrepreneur, consider writing a thank you note to your former math teacher today.*

**Math in the Workplace (Segment III)**

*Credit: Jacob Dietz, CPA*

**Price Increase Based on Percentage of Old Price**

Now, let’s look at a price increase based on a percentage of the old price, with no change in cost. Last year, John’s cost of sales was 70%, his gross profit margin was 30%, his overhead was 15%, and his net income was 15%. He decided to increase prices because John’s advisor noticed that his income was below the benchmark for his specific industry. John’s advisor said he should be getting a 20% net profit in his industry, and he advised John to raise his prices 5% to increase his net profit from 15% to 20%.

The plan sounds good, but will it work? If John does the math, he will realize that the math does not work. If he raises prices by 5%, then a product that formerly sold for $100 will now sell for $105. That would change his cost of sales from 70% to 66.7% ($70/$105) and his net income from 15% to 19% ($20/$105.)

Why does it work that way? When calculating a net profit percentage, the net profit is divided by sales. Even though he would be making $20 on each sale, it would be $20/$105, which is 19%, not 20%. The increase in sales price therefore makes the additional $5 a smaller percentage of sales.

**Price Decrease Based on Percentage of Old Price**

Now, let’s assume that instead of raising prices, John decided to decrease prices because he is in a price-sensitive market and his prices are currently a little high. John’s cost of sales was 70% last year, and his gross profit margin was 30%, his overhead was 15%, and his net income was 15%.

John decreased his prices by 5%. Therefore, a $100 item’s price changed to $95, but the cost remained steady at $70 (now 73.7% cost of sales), overhead remained steady at $15 (now 15.8% overhead) and net profit dropped to $10 (10.5% net profit percentage.)

Therefore, the net profit dollars dropped by $5, but the net profit percentage dropped by only 4.5%.

**Additional Takeaways from Pricing**

If the prices are changing based off the old price, with no change in cost, then John may want to ask himself what he is trying to accomplish. If he is trying to reach a certain percentage, such as 20% net profit, then he may be disappointed if he only raises prices by 5%.

On the other hand, if he is trying to raise his net income from $15 to $20 for the unit that was selling for $100, then a 5% increase in price should do it.

Although the 5% drop in sales only led to an approximately 4.5% drop in net profit percentage, do not be deceived into thinking it was a small effect on net profit. At first, that may look like his profits only dropped by 4.5%. His net profit percentage decreased by 4.5%, but that is only his net income percentage. His actual profit dollars (assuming no change in volume) decreased by roughly 33% ($5/$15).

Why is there such a significant decrease in net profit dollars? If the sales price decreases, with no other changes, then that decrease in price drops straight to the bottom line. His previous net income was $15, but now it is only $10. In some situations, however, the volume will change which can make up for the loss.

**Math is more than a School Subject**

If you are involved with pricing in your company, do the calculations when changing prices. Math is good for school students, but it may be even more important with a business. Consider writing a thank you note to your former math teacher.

*This article is general in nature, and it does not contain legal advice. Please contact your accountant to see what applies in your specific situation.*