# How do you decompose the volume variance?

The volume variance (also called planning variance or activity variance) is the impact on Operating Income of the difference between actual and budgeted levels of activity.

As discussed in the previous subsection, the volume variance (also called sometimes planning variance) reflects the financial consequence of operating at an actual activity level different from that assumed in the master budget. While less equivocal than the static budget variance, the volume variance remains equivocal as volume is itself the product of three distinct estimates: 1) the forecast for the total market size; 2) the market share; and 3) the product mix. Accordingly, specific third-level variances (L3) can be computed by looking at the impact on Operating Income of switching successively each assumptions from its budgeted value to its actual value. By convention, you should start with market size, followed by market share, to finish with product mix.

Market size variance

The market size variance is the impact on Operating Income of operating in a market the actual size of which is different from the budgeted one.

You obtain the market size variance by computing the difference in volume due to the difference in market size, assuming budget market share and a budgeted unit contribution margin (because we still use the budgeted product mix, prices, and unit variable costs which have not been switched to actual yet):

$\text{Market size variance} = (MSI_\color{red}A - MSI_\color{blue}B) \times MSH_\color{blue}B \times UCM_\color{blue}B$

Market share variance

The market share variance is the impact on Operating Income of capturing an actual market share which is different from the budgeted one.

You obtain the market share variance by computing the difference in volume due to the difference in market share, assuming the actual market size (because market size has already been switched to its actual value) but a budgeted unit contribution margin (because we still use the budgeted product mix, prices, and unit variable costs which have not been switched to actual yet):

$\text{Market share variance} = MSI_\color{red}A \times (MSH_\color{red}A - MSH_\color{blue}B) \times UCM_\color{blue}B$

Together, market size and market share variances constitute the sales quantity variance:

\begin{aligned} \text{Sales quantity variance} & = (MSI_\color{red}A \times MSH_\color{red}A - MSI_\color{blue}B \times MSH_\color{blue}B) \times UCM_\color{blue}B \\ & = (Q_\color{red}A - Q_\color{blue}B) \times UCM_\color{blue}B \\ & = \text{Market size variance} + \text{Market share variance} \end{aligned}

Product mix variance

The product mix variance is the impact on Operating Income of selling an actual product mix which is different from the budgeted one.

The product mix has already been introduced in the previous subsection as completing the sales quantity variance to produce the volume variance:

$\text{Product mix variance} = MSI_\color{red}A \times MSH_\color{red}A \times (WUCM_\color{purple}F - WUCM_\color{blue}B)$

where:

$WUCM_\color{purple}F = \sum_{d=1}^{p} \frac{Q_\color{red}A^d \times UCM_\color{blue}B^d}{Q_\color{red}A^d}$

Illustration