ACCA Applied Knowledge · Management Accounting

Flexible budgets: formula sheet

Full chapter guide

Key formulas

Flexed variable cost: Flexed variable cost = budgeted variable cost per unit × actual activity; Use the budgeted rate per unit of activity, not the actual rate.
Flexed fixed cost: Flexed fixed cost = original budgeted fixed cost; Unchanged within the relevant range of activity.
Semi-variable cost: Total cost = fixed element + (variable rate × activity); Split it first, then flex only the variable part.
Variance for control: Variance = actual result − flexed budget; For costs, actual above flexed budget is adverse. For sales and profit, actual above flexed is favourable.
Total cost: Total cost = Fixed cost + (Variable cost per unit × Activity level); Applies to semi-variable costs. Fixed cost is the intercept, variable cost per unit is the slope.
High-low variable cost per unit: Variable cost per unit = (Cost at highest activity − Cost at lowest activity) ÷ (Highest activity − Lowest activity); Use the highest and lowest activity levels, not the highest and lowest costs, unless they coincide.
High-low fixed cost: Fixed cost = Total cost at either level − (Variable cost per unit × Activity at that level); Check by using the other activity level. You should get the same answer.
Flexed variable cost: Flexed variable cost = Budgeted variable cost per unit × Actual activity; Equivalent to budgeted variable cost × (actual activity ÷ budgeted activity).
Flexed budget cost for a semi-variable item: Flexed cost = Fixed element + (Variable rate × Actual activity); Do not scale the whole semi-variable cost by activity. Only the variable part moves.
Variable cost per unit: Variable cost per unit = Budgeted variable cost ÷ Budgeted activity; Find this from the original budget before you flex.
Flexed variable cost: Flexed variable cost = Variable cost per unit × Actual activity; Use actual activity, not budgeted activity.
Flexed fixed cost: Flexed fixed cost = Original budgeted fixed cost; Fixed costs do not change within the relevant range of activity.
Semi-variable cost: Total cost = Fixed element + (Variable rate × Activity); Split the cost first, often with the high-low method, then flex the variable part only.
Flexed budget variance: Variance = Flexed budget − Actual cost (or the reverse for income); Costs: actual below flexed budget is favourable. Income: actual above flexed budget is favourable.
Flexed budget for a variable cost: Flexed cost = budgeted cost per unit × actual activity; Or budgeted cost ÷ budgeted activity × actual activity.
Flexed budget for a fixed cost: Flexed fixed cost = original budgeted fixed cost; Do not flex fixed costs unless the question says they step up.
Cost variance: Cost variance = Flexed budget cost − Actual cost; Positive = favourable. Negative = adverse.
Revenue or profit variance: Variance = Actual − Flexed budget; Positive = favourable. Negative = adverse.
Volume variance (fixed to flexed): Flexed budget profit − Original budget profit; Shows the effect of activity level only.
Semi-variable cost: Flexed cost = fixed element + (variable rate × actual activity); Split the cost first if only totals are given.

Quick revision

A fixed budget is set for one activity level and is not changed.
A flexible budget is restated for the actual activity level.
Variable cost per unit stays constant; total variable cost changes with activity.
Total fixed cost stays constant within the relevant range.
Semi-variable cost = fixed part + variable part.
High-low: variable rate = (high cost − low cost) ÷ (high activity − low activity).
Fixed part = total cost − (variable rate × activity), using either the high or low point.
Flexed budget = variable cost per unit × actual activity + budgeted fixed cost.
Variance = actual result − flexed budget, then judge whether it is F or A.
Higher actual revenue than flexed is favourable; higher actual cost than flexed is adverse.
Compare actual with flexed budget for control, not with the original budget.
Check the activity measure and units in the question before you calculate.

Common mistakes

Flexing fixed costs along with variable costs. Fix: Only scale variable costs. Keep fixed costs at the original figure.
Comparing actual costs with the original fixed budget for control. Fix: Flex the budget to actual activity first, then compare.
Flexing the whole of a semi-variable cost in proportion to activity. Fix: Split it first. Flex only the variable element and keep the fixed element unchanged.
Using the highest and lowest cost figures instead of the highest and lowest activity levels in the high-low method. Fix: Always choose the periods with the highest and lowest activity. Take the costs that go with them.
Flexing fixed costs along with variable costs. Fix: Classify every line first. Only variable parts move with activity.
Using actual cost figures to calculate the rate per unit. Fix: Always calculate the rate from the original budget and then multiply by actual activity.
Comparing actual results with the original fixed budget and calling the gap a variance. Fix: Always check whether actual and budget activity match. If not, flex first.
Flexing fixed costs along with variable costs. Fix: Scale only variable and the variable part of semi-variable costs. Keep fixed costs as budgeted.

Exam tips

Read the question for the word 'flexed' or 'actual activity'. It tells you to scale variable costs.
In multiple response questions, check each statement against the rule: fixed budgets do not change, flexible budgets adjust for activity.
In number entry questions, show the per-unit rate on scrap paper first. It catches most arithmetic slips.
Check the sign and label of every variance before you submit.
Read the activity measure carefully. A question may flex on labour hours rather than units produced.
In multiple response questions, check each statement against the definition. Fixed cost per unit falls as activity rises, but total fixed cost does not change within the relevant range.
For number entry questions, give the answer in the units asked for, such as $ or ₹, and do not round until the final step.
Sketch a quick graph in your head for stepped costs. The cost is flat, then jumps, then flat again.