## Math in the Workplace (Segment III)

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%.

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.

## Math in the Workplace (Segment II)

Preface: The inscribed square problem, also known as the square peg problem or the Toeplitz’ conjecture, is an unsolved question in geometry: Does every plane simple closed curve contain all four vertices of some square?  The problem was proposed by Otto Toeplitz in 1911. As of 2017, the general case remains open.

Math in the Workplace (Segment II)

Credit: Jacob Dietz, CPA

Pricing based on Costs When Costs Decrease

Assume the situation is the same as the above example, except John discovers that his cost of sales decreased by 5%. He decides to recalculate his prices.

He uses \$66.50 as the cost, and he calculates a sales price of \$95 (\$66.50 divided by .7.) His sales price is \$95, his cost of sales is \$66.5 (70%), his gross profit is \$28.5 (30%) and his overhead is \$15 (15.8%) and his net profit is \$13.5 (14.2%)

What just happened? Because John calculates his sales to earn a 30% gross profit, there was no change in the gross profit percentage, but there was a change in the gross profit dollars. 30% of \$95 is \$1.50 less than 30% of \$100. John decreased both his gross profit and net profit by \$1.50, and he dropped his net income percentage to about 14.2%.

Takeaways from Pricing

How can John use his knowledge about the effects on profitability of price changes and cost changes? If John’s costs increase, he may not be happy at first. If he can increase his prices using the same divisor (.7 in John’s case) on the new costs, however, John’s net profit can increase if he keeps selling the same quantity.

On the other hand, let’s assume that John faces fierce competition on price, and he cannot keep the same divisor of .7. In that case, he may be able to maintain the same net profit. For example, assume that his costs went up 5%, from \$70 to \$73.50. If John kept his normal divisor, he would then divide \$73.5 by .7 and sell it for \$105.  That would lead to the \$16.50 profit instead of the \$15 profit. If John could not raise the price \$5, however, perhaps he could raise the price by \$3.50 to \$103.50. That would keep his net profit at \$15. The calculation is the \$103.50 sales price less \$73.50 cost of sales less \$15 overhead leaves a \$15 profit.

At first glance, John may decide he makes enough profit at the \$15 net profit even if he does not face withering competition on price.  He may decide only to raise the price to \$103.50 instead of \$105 because he will still come out the same at \$15.

Or will he come out the same? Even though his net profit would still be the same, his cash position may not be the same. He is making the same net profit as before the cost increase, but his cost of sales jumped. If John carries significant inventory, then that additional cost of sales may hurt his cash balance. Each item that use to cost \$70 now costs \$3.50 more, or \$73.50.

## 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.

Preface: Business investment value creation is a most opaque concept and process, even among experienced advisors. Yet, for the business owner with an investor business mind-set, it is of utmost importance.

Credit: Donald J. Sauder CPA |CVA

Business transition advisors are necessary. Yet too often a majority of business owners omit realistic expectations on the investment feature of the transition.

If you think of your business as investment, and are interested in harvesting optimal value, beginning early with the following seven successful steps to the summit of business value creation can assist with a successful transition and an optimized fair market appraisal value to you as a business owner.

I. Adhere to a solid foundation of core values and a core focus (vision) for the business, identifying your business’s unique advantages, opportunities, and niche. Develop a one to three and ten-year plan. When your team strives every day to work purposefully per unified core values, and towards a common core focus, you can achieve great things, as the strong cultural bond of a shared purpose among your team drives the entire organization forward successfully.

II. Hire, train, and retain the best people as you build a talented team on the foundation from Step one. Without the right people, there is no success in business . Businesses thrive with expert, ambitious, talented, purpose driven teams. Your business’s ability to succeed in this area (the right people) is a key to your business’s future value. It is probable that this is where your next generation of transition ownership emerges, i.e., you develop it.

IV. Develop internal KPI’s and business operating systems that create and build value with performance efficiencies, and effective operations scalability. Your business needs to have processes to propel and govern operations and decision making, ranging from efficient and effective onboarding and development of employees to promptly invoicing and collecting on accounts receivable. Developed and implemented business operating systems successfully govern daily operations of the team. Again, this decreases cash flows risks and increases business appraisal value.

V. Further expand top-line sales volume, leveraging the implementation of Steps one, two and three. A great business is continually improving and growing. Successful businesses never stagnate entirely. Yet, growth can be managed with efficiencies and does not need to compound double digits’ sales  volume increases. It can include new technologies for improved product quality or systems for improved sales per employee, or even improved cash flow management. Again, the true value driver of your business (cash flow consistency) is often the core values that are ingrained in your team as they deliver to the marketplace with your products or services.