Math/Work Question

[TheSaxRunner05]

I know this is just algebra, but I was struggling a bit to find the formula for this.

Using brute force methods, I've found that between pricing at 37% Gross Margin and 40.5% GM, you'd have to sell at least 16.2% more product at the lower GM to make more profit. What formula gets you to this number? When I try my hand at it, all I can come up with is that one price is 5.88% higher than the other.

If someone could help me derive the formula that outputs my brute force value of 16.2%, I'd be greatful.

Basically, how much more do you have to sell at Gross Profit % A than Gross Profit % B to make more Gross Profit Dollars? Where A<B.

For reference, Gross Margin is (Price - Cost)/Price

[Rapta]

Re: Math/Work Question

brute force methods

[TheSaxRunner05]

Re: Math/Work Question

Nvm I think I figured it out -
Where A is the lower GM and B is the higher one (written as decimals)
(1-A)/(1-B)/A/(1-B)
It's hard to do math notation on here

[Arntonach]

Re: Math/Work Question

Something tells me you need to set up some slope formulas to compare your number of sales and profits to your gross margins.

[TheSaxRunner05]

Re: Math/Work Question

I was just looking at ratios for this question. We can then look at the actual numbers to see how it played out.

The question was: how much more do we have to sell at a lower gross margin to make the same profit? As a ratio, it can be calculated without looking at a specific item.