# Should You Raise Prices? Should You Lower Them? Derivation of the Formula For Planning Price Changes

Here's how I used algebra to derive the formula that calculates the breakeven sales volume for a prospective change in product prices.

3706 The article, Should You Raise Prices? Or Should You Lower Them? These Excel Charts Can Help You Answer Those Questions, introduces the Price-Change formula. Before you use the formula, it’s a good idea to assure yourself that it’s accurate. So here’s how I derived it…

Here are the variables used in the formula: Our gross profits before and after the price change are equal to our price minus our product cost, multiplied by our unit sales volume: We’re looking for the gross-profit stay-even point, the point where gross profits after the price change equal gross profits before the price change. That is, we want: We can rearrange this formula to arrive at: We can add zero (P0 – P0) to the bottom-left and zero (V0 – V0) to the top right, giving us: Now we can multiply the left side by 1, in the form of (1/P0) / (1/P0). And we can simplify the right side, to return: The top-left term is our current profit margin. The bottom-left terms are our current profit margin minus our price change as a percentage of the current price. The right-hand term is 1 + our percentage change in volume after the price change. Moving the 1 to the other side of the equation, and simplifying, gives us the Stay-Even Formula for price changes: Keep in mind that this formula doesn’t address other costs that might be affected by your planned price change. Early in my career, I worked nearly 20 years as the CFO of turnarounds and startups. But I eventually got burned out fighting continual struggles with cash flow. That's when I started to write about Lotus 1-2-3, the spreadsheet software that I'd been using most of the time during the CFO days. When Excel was about to be introduced for the PC, one of my magazine editors set up a meeting for me to see the product, talk with the developers, and write a cover story about Excel. So I used the first version of Excel before it was launched. And I had also used the first version of VisiCalc before it was launched. And then,