Math in the Workplace

Preface: 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. 

Math in the Workplace (Segment I)

Credit: Jacob M. Dietz, CPA

Did you ever sit in a math class and ask your teacher “how will this help me in real life when I have a job?” Do you currently wonder how a change in price will affect your net profit or your net profit percentage? The math of a change in price can get complicated. This article explores price changes assuming the same volume of units will be sold. If the number of units sold changes, then it can get even more complicated. Hopefully this article will help demonstrate how math applies to real jobs.

Pricing based on Costs When Costs Increase

For this article, assume John runs a business and sets pricing. When preparing his price list, he realizes that his cost of materials jumped 5% from the year before. His overhead stayed the same. He decides to raise his prices 5% to keep his profits the same. That sounds simple. Is it really that simple?

First, let’s look at how the numbers worked for John’s business last year. Last year, his cost of sales was 70%, his gross profit margin was 30%, his overhead was 15%, and his net income was 15%. For every $100 that John sold, $70 went to cost of sales. Of the remaining $30 gross profit, $15 went to overhead and $15 went to the bank account as net profit.

John calculated his pricing based on costs last year. He took his cost of $70 and divided by .7 to calculate his sales price at $100.

Can John keep his calculations the same, but include the higher direct costs, and get the same profitability? John puts $73.50 into his calculation as the cost of sales (the $70 after the 5% increase.) John divides his cost of $73.50 by .7, and he calculates $105 as the new sales price. His price increased by 5%, which is the same percentage as his cost increased.

“What just happened? By using the same divisor (.7) to calculate his price based on cost when his cost of sales increased, John increased his gross profit, and kept his gross profit percentage the same.”

If John sells the product for $105, with the cost of sales at $73.50, his gross profit per sale is $31.50, or 30%. His net profit is $16.50 ($31.50 gross profit less $15 overhead), or 15.7%.

What just happened? By using the same divisor (.7) to calculate his price based on cost when his cost of sales increased, John increased his gross profit, kept his gross profit percentage the same, and increased both his net profit and net profit percentage.

Because John calculates his sales to earn a 30% gross profit (by dividing by .7) there was no change in the gross profit percentage. Since the sales price increased, however, John’s 30% gross profit percentage is now 30% of $105, not 30% of $100. That additional $5 in sales leads to a $1.50 increase in gross profit, which flows down to the bottom line as a $1.50 increase in net profit.

End of Segment I. To be continued.


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