# How do you decompose the static budget variance?

Static budget variance

The budget we discussed in Chapter 5 is a static budget, i.e. a budget based on a fixed assumption about volumes. The difference between the actual operating income and the static budget operating income, $$OI_\color{red}A - OI_\color{blue}B$$ is called the static budget variance or a first-level variance (L1).

A static budget is a budget based on the level of output initially budgeted; it is not adjusted after it is set, regardless of ensuing changes in actual output.

The static budget variance is the difference between the actual operating income and the static budget operating income (i.e. the operating income initially budgeted).

Useful for planning purposes, the static budget can be misleading for controlling purposes. Indeed, sales forecasts are likely to be incorrect and the budgeted costs are, as a consequence, incomparable to actual costs. Even if employees are extremely efficient, you can expect costs to mechanically increase with volumes. Therefore static budget variance signals that operations did not go as plan, but tells little more.

To make more meaningful comparisons and reduce the ambiguity of the signal, management accountants prepare a flexible budget, which is a revised budget that shows budgeted costs for actual volumes. The flexible budget is an estimate of what revenues and costs should have been, given the actual level of activity for the period. In other words, the flexible budget shows the Operating Income the company would have earned if only volumes had changed compared to budgets. If adjustments for the level of activity are not made, it is very difficult to interpret discrepancies between budgeted and actual costs: comparing revenues and costs at different levels of activity is misleading.

The flexible budget is a budget based on the actual volume of activity, but with budgeted selling prices, unit variable costs, and fixed costs.

From this flexible budget, it is possible to infer two second-level variances (L2): the volume variance and the flexible budget variance.

Volume variance

The only difference between the flexible budget and the static budget is thus the volume of activity. Therefore, the difference between the flexible budget operating income and the static budget operating income, $$OI_\color{purple}F - OI_\color{blue}B$$, called the volume variance, is entirely due to a difference in volumes, $$(Q_\color{red}A - Q_\color{blue}B)$$. When there is a single product, the volume variance is equal to the sales quantity variance and therefore easy to compute: it is the difference in volume multiplied by the budgeted unit contribution margin:

$\text{Sales quantity variance} = (Q_\color{red}A-Q_\color{blue}B) \times UCM_\color{blue}B$

However, when there are multiple products, things are a bit more complex as the volume variance is then equal to the sales quantity variance we just computed plus the product mix variance. You might remember from the multi-product break-even in Chapter 4 that a change in product mix changes the weighted average unit contribution margin even if prices and unit variable costs (i.e. resource usages and resource prices) are constant. To get the product mix variance, you must therefore multiply the actual volume (which has been switched first) by the change in unit contribution margin resulting only from a change in product mix:

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

Be careful: the unit contribution margin of the flexible budget $$UCM_\color{purple}F$$ is neither the actual nor the budgeted unit contribution margin, since the mix has been changed, but not the prices and variable costs:

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

Flexible budget variance

The difference between the actual operating income and the flexible budget operating income, $$OI_\color{red}A-OI_\color{purple}F$$, is called the flexible budget variance. It is the change in profit due to… everything except volumes:

\begin{aligned} \text{Flexible budget variance} & = Q_\color{red}A \times (UCM_\color{red}A - UCM_\color{purple}F)-(FC_\color{red}A-FC_\color{blue}B) \\ & = \text{Static budget variance} - \text{Volume variance} \end{aligned}

In the single product case, there is no mix difference, so $$UCM_\color{purple}F = UCM_\color{blue}B$$.

Illustration

For the exercise on which we will work here, you can download blank file here and the solution file here.

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