How do you decompose the flexible budget variance?

The flexible budget variance captures the impact on Operating Income of changes in usages or prices.

The flexible budget variance is difficult to define because it conflates the effects of variations from many different estimates: selling prices, resource usages and resource prices (for many different kinds of resources), and fixed costs. It is therefore also possible to produce less equivocal third-level variances (L3) by switching successively each kind of estimate and looking at the impact on Operating Income.

Selling price variance

The selling price variance is the impact on operating income of a difference between actual and budgeted selling prices, for one or several products.

For a single product, it is given by the following formula:

\[ \text{Selling price variance} = Q_\color{red}A \times (P_\color{red}A - P_\color{blue}B) \]

You may wonder why there is no usage variance in this case: it is because we assume that one product sold at the price \(P_\color{blue}B\) corresponds to one product out of the inventory. As for the multi-product case, the easier way to get the selling price variance is to make the sum of all individual products’ selling price variances. An alternative is to use the change in unit contribution margin caused by the changes in selling price, after accounting for the impact of product mix, but before accounting for changes in unit variable costs.

Resource usage variance

The resource usage variance (sometimes also called input efficiency or quantity variance) is the impact on operating income of consuming an actual quantity of resource per unit of output different from the budgeted quantity of resource per unit of output.

It is a difference between the actual and budgeted use of a resources, given the actual volume and the budgeted price of the resource. Note that the resource can be anything: you can have a material usage variance, a labor usage variance, an energy usage variance, etc.

\[ \text{Resource usage variance} = Q_\color{red}A \times (RU_\color{red}A - RU_\color{blue}B) \times RP_\color{blue}B \]

Resource price variance

The resource price variance (sometimes also called input rate variance) is the impact on operating income of buying a quantity of resource at a price different than the budgeted price for this resource.

The resource price variance (sometimes also called input rate variance) is a difference between the amount paid for the resource and the amount that would have been paid if the resource had been purchased at its standard price. Again, the resource can be anything: you can have a material price variance, a labor price (or rate) variance, an energy price variance, etc.

\[ \text{Resource price variance} = Q_\color{red}A \times RU_\color{red}A \times (RP_\color{red}A - RP_\color{blue}B) \]

Together, resource usage and resource price variances constitute the resource cost variance:

\[ \begin{aligned} \text{Resource cost variance} & = Q_\color{red}A \times (RU_\color{red}A \times RP_\color{red}A - RU_\color{blue}B \times RP_\color{blue}B) \\ & = \text{resource usage variance} + \text{resource price variance} \end{aligned} \]

Fixed costs variance

The fixed cost variance is just the difference between the actual amount of fixed costs and the budgeted amount of fixed costs:

\[ \text{Fixed cost variance} = FC_\color{red}A - FC_\color{blue}B \]

BE CAREFUL! When you compute a cost variance with these formulas (resource usage variance, resource price variance, resource cost variance, or fixed cost variance), a positive number means that costs increase, and therefore operating income decreases. We will see later the impact it has on how you report variances.


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