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.
