How to calculate volume change from price and gross margin?

Question

I have a matrix that looks like this:

           Gross Margin
           10% 15% 20% 25% 30%
    Price  Volume
    1%     -9% -6% -5% -4% -3%
    2%     -17% -12% -9% -7% -6%
    5%
    10%
    15%

The matrix is not all filled out, but you read it as this: If the price goes up by 1%, and you want to keep you your Gross Margin at 10%, you can manage a -9% decrease in volume.

Likewise, if you experience a -17% volume loss, you must increase price by 2% in order to keep your Gross Margin at 10%.

Now, I can't figure out how to calculate the Changes in volume, only based on price and gross margin percentages?

Answer 1

The only way I can understand the table is to assume the price increase is on the selling price, the buying price stays the same, your current gross margin percentage is the value at the top of the table, and you are trying to maintain the currency value (not percentage) of your gross margin. In that case, taking the upper left corner entry as an example, the price going up by $1\%$ means your gross margin percentage goes up to $11\%$. If your volume goes down by $9\%$, you are selling $0.91$ times as much as before, but you keep $0.11 \cdot 0.91 =1.001$ times as much cash as before. They round this off to $1.00$

To get the formula, let $g$ be your current gross margin, $p$ be the price increase, and $v$ be the volume decrease. The new income is $(g+p)(1-v)$ and we want that to match the current income of $g$, so we set $$(g+p)(1-v)=g\\1-v=\frac g{g+p}\\v=1-\frac g{g+p}=\frac p{g+p}$$ With that formula I was able to reproduce all the values you have once they were rounded to the nearest percent.