Charting Ideas
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, MBA Microsoft Excel MVP, 20052014
The Father of Spreadsheet Dashboard Reports

The article, Should You Raise Prices? Or Should You Lower Them?,
introduces the PriceChange 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 grossprofit stayeven 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 bottomleft 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 topleft term is our current profit margin. The bottomleft terms are our current
profit margin minus our price change as a percentage of the current price. The righthand
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 StayEven Formula for price
changes:
Keep in mind that this formula doesn't address other costs that might be affected by your
planned price change.
