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Derivation of the Formula
For Planning Price Changes

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

by Charley Kyd
March, 2008

The article, Should You Raise Prices? Or Should You Lower Them?, 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 it was derived...

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-evem 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.