Price Mix Variance - Algebra

Proof of concept, Weight Element of Price Variance

It has become clear over the past year that the business’s price metric is affected not just by the price performance of the individual channels or

divisions, but also by the relative Volume performance of the channel. Less volume in a low price channel causes overall price to rise, all else

remaining equal. This is because the price metric is a weighted average.

The following document aims to provide a tool for separating the effects of Volume performance of individual divisions from the impact on

Price that comes from changes in relative Volume performance (which will here be called weight)

We will use an example

Actuals

Division Volume

1

A

2

B

3

C

Total

V

Price %

L

M

N

P

Plan

Division

1

2

3

Total

Volume

a

b

c

v

Price %

l

m

n

p

Where V = A + B + C and P is calculated as follows:

P = (AL + BM + CN) / (A + B + C)

Similarly for v, p.

Defining Price Variance

This means that my total price variance, ΔPrice[total] can be defined as follows

P - p = [(AL + BM + CN) / (A + B + C)] - [(al + bm + cn) / (a + b + c)]

Putting all these over the same constant, this gives:

Δ Price[total] = [(AL + BM + CN) * (a + b + c)] - [(al + bm + cn) * (A + B + C)]

(a + b + c) * (A + B + C)

Six Sigma & Pricing

Paul Johnson-Ferguson

Questions:

1. What is the impact of price performance (only the “price” element) in Division 1 on my overall price? The amount of Δ Price[total]

explained by variations on price in 1.

Δ Price [division 1] = (L – l ) *a / (a + b + c)

Representing the Difference in price (L-l) * the weight that the Volume [a] of Division 1 represents in the whole

and so

Δ Price [division 2] = (M – m ) *b / (a + b + c)

Δ Price [division 3] = (N – n ) *c / (a + b + c)

Adding the impacts of the price of my individual divisions on the total I get:

Δ Price [division 1+2+3] = (L – l) *a / (a + b + c) + (M – m) *b / (a + b + c) + (N – n) *c / (a + b + c)

Δ...