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 Elementary Math Fractions, Percentages, Word Problems, Equations, Inequations, Factorization, Expansion

November 15th, 2016, 06:32 AM   #1
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Hello,

Hoping someone in this forum can Help me; I work in finance, and am working on a report looking at the cost of products vs sales as a ratio.

The problem I am having is how to articulate the impact on a sales change has to the total variance on Cost/Sales LY vs Cost/Sales TY.

As the sales is a denominator, there is a compound effect I need to consider.

In the example below, I know my variance for volume price and mix and product and total level, but the compound effect on % is harder. Hoping someone can help?

Thanks in advance.
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Last edited by skipjack; November 22nd, 2016 at 10:36 AM.

 November 15th, 2016, 08:59 AM #2 Senior Member   Joined: May 2016 From: USA Posts: 1,029 Thanks: 420 This is a standard problem in presenting an analysis of variance. Let's take an example. I am not taking your example because I am not sure what exactly you are trying to do. $Sales\ last\ year\ = 12000,\ cost\ last\ year = 9000,\ cost\ to\ sales = \dfrac{9000}{12000} =75\%.$ $Sales\ this\ year\ = 15000,\ cost\ this\ year = 10500,\ cost\ to\ sales = \dfrac{10500}{15000} =70\%.$ The increase in sales was $\dfrac{15000 - 12000}{12000} = +\ 25\%.$ The increase in costs was $\dfrac{10500 - 9000}{9000} \approx +\ 16.7\%.$ The decrease in cost to sales, measured intuitively, is $-\ 5\ percentage\ points.$ Obviously, $-\ 5 \not \approx 16.7 - 25.0 = -\ 8.3.$ The problem, as you quite clearly understand, is that the interaction between changes in sales and changes in costs changes your ratio, but not in an arithmetically obvious way. And that represents a problem in PRESENTATION, not in math. One way around it is to break the cost ratio up into fixed and variable ratios, which lets you show the effect of sales increases (as reducing fixed costs per sales dollar) and changes in efficiency with respect to variable costs. But without understanding better what you are trying to explain, it is impossible for me to help with finding an easy way to explain the numbers.
November 22nd, 2016, 03:24 AM   #3
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Quote:
 Originally Posted by JeffM1 This is a standard problem in presenting an analysis of variance. Let's take an example. I am not taking your example because I am not sure what exactly you are trying to do. $Sales\ last\ year\ = 12000,\ cost\ last\ year = 9000,\ cost\ to\ sales = \dfrac{9000}{12000} =75\%.$ $Sales\ this\ year\ = 15000,\ cost\ this\ year = 10500,\ cost\ to\ sales = \dfrac{10500}{15000} =70\%.$ The increase in sales was $\dfrac{15000 - 12000}{12000} = +\ 25\%.$ The increase in costs was $\dfrac{10500 - 9000}{9000} \approx +\ 16.7\%.$ The decrease in cost to sales, measured intuitively, is $-\ 5\ percentage\ points.$ Obviously, $-\ 5 \not \approx 16.7 - 25.0 = -\ 8.3.$ The problem, as you quite clearly understand, is that the interaction between changes in sales and changes in costs changes your ratio, but not in an arithmetically obvious way. And that represents a problem in PRESENTATION, not in math. One way around it is to break the cost ratio up into fixed and variable ratios, which lets you show the effect of sales increases (as reducing fixed costs per sales dollar) and changes in efficiency with respect to variable costs. But without understanding better what you are trying to explain, it is impossible for me to help with finding an easy way to explain the numbers.
I don't understand why the cost is on top in the 1st equation but on the bottom in the 2nd equation.

 November 22nd, 2016, 10:31 AM #4 Senior Member   Joined: May 2016 From: USA Posts: 1,029 Thanks: 420 I do not understand your question. I have four equations, not two. Equation 1: $\dfrac{cost = 9000}{sales = 12000}$ for last year. Equation 2: $\dfrac{cost = 10500}{sales = 15000}$ for this year. These are ratios of cost over sales because that is what the original post was asking about. Cost is not in either denominator, and sales are not in either numerator. Equation 3: $\dfrac{sales\ this\ year\ minus\ sales\ last\ year = 15000 - 12000}{sales\ last\ year = 12000}.$ The above is the relative change in sales year to year. Sales are in both numerator and denominator. Costs appear nowhere because costs are not sales. Equation 4: $\dfrac{cost\ this\ year\ minus\ cost\ last\ year = 10500 - 9000}{cost\ last\ year = 9000}.$ The above is the relative change in costs year to year. Costs are in both numerator and denominator. Sales appear nowhere because sales are not costs. I'd be happy to answer your question if you would be so kind as to make it clearer. As I explained in my original answer, our intuition about how to decompose the change in cost to sales ratio is that it should be some simple addition of the changes in sales and costs, but that intuition is incorrect. That leads to an issue in how to present a decomposition so that it is arithmetically correct and yet intuitively understandable. If that is what you are asking about, please let me know. Last edited by JeffM1; November 22nd, 2016 at 10:39 AM. Reason: Syntax and punctuation errors
 November 22nd, 2016, 02:33 PM #5 Banned Camp   Joined: Nov 2016 From: St. Louis, Missouri Posts: 28 Thanks: 4 Math Focus: arithmetic, fractions I now understand that the final figures represent ratios concerning sales and costs.

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