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# Advanced Math/Ratios: Contribution to Change in Weighted Average

Tim wrote at 2015-01-13 22:39:58
I have the same problem when comparing Gross Profit Percentages (GP%).  I wanted to create a "walk" to show the contributing change in GP% changes.

GP% = Gross Profit \$ / Sales \$

I have 100 product categories that equal the total.  The total change for the year involves the numerator changing and denominator changing with each category contributing.  I want to know how each of the 100 product categories contribute to the total GP% change (GP% end - GP% beg).  In another words, what product category caused the GP% to go up and which ones caused it to go down and by how much.

Because the denominator changes, I couldn't do the traditional contribution impact analysis (ex. SalesChng% = SalesChng\$/Sales\$ = (SalesChng\$1 + SalesChng\$2 + SalesChng\$3...) / Sales\$ = SalesChng\$1/Sales\$ + SalesChng\$2/Sales\$ + SalesChng\$3/Sales\$...)

I had to do an "incremental" contribution impact analysis.  Here's what I did.  This ties out so you can create a walk.

LY = Last Year

D = Delta (change in GP or Sales)

# = Category Number (ex. 1 = product category 1)

T = Total (ex. Total Sales or Total GP)

Category1 Impact Contribution = ((LY T GP\$ + D 1 GP\$)/(LY T Sales\$ + D 1 Sales\$)) - LY GP%

Category2 Impact Contribution = ((LY T GP\$ + D 1 GP\$ + D 2 GP\$)/(LY T Sales\$ + D 1 Sales\$ + D 2 Sales\$)) - (LY GP% + Category1 Impact Contribution)

Category3 Impact Contribution = ... Follow the pattern.  Excel will make this formula not that bad.

If you add all your Category impact contributions, they will equal the total GP% change.  Technically, it does matter which category you calculate first (what order you sort... it will still tie out but the categories will be weighted slightly differently by how it is sorted).  The impact of this was very small in my business case (less than a basis point), but I did add a special sort field so my categories would be sorted in impact order.

I do have a spreadsheet example which would help show what I did.

Cheers,

Tim

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#### Scott A Wilson

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