ACCA Applied Skills · Performance Management

Budgetary systems and types of budget: formula sheet

Full chapter guide

Key formulas

Variance: Variance = Actual result − Budgeted result; Label each variance as favourable (F) or adverse (A) by its effect on profit. Variance calculations are covered in later topics.
Budgetary control cycle: Plan → Record actual → Compare → Investigate variances → Act → Revise; Control only exists when the comparison leads to action.
Purposes checklist: Planning, Coordination, Communication, Motivation, Authorisation, Control, Evaluation; A memory list for written answers. Use only those relevant to the scenario.
Production budget (units): Sales units + closing inventory of finished goods − opening inventory of finished goods; Use units, not money. Closing inventory is the target level at the end of the period.
Material purchases budget (units): Material needed for production + closing material inventory − opening material inventory; Material needed for production = production units × material per unit. Allow for normal losses if told.
Principal budget factor test: Compare the maximum activity allowed by sales demand, materials, labour, machine capacity and cash; the lowest is the principal budget factor; Compare in the same unit, such as units of finished product.
Order of building budgets: Principal budget factor budget → other functional budgets → cash budget → master budget (income statement and statement of financial position); For most manufacturers the principal budget factor is sales, so the sales budget comes first.
Incremental budget: New budget = Previous budget or actual × (1 + expected % change); Adjust for inflation and any known volume or policy changes. Check whether the base is last year's budget or actual, as the question states.
ZBB decision package ranking: Rank packages by benefit relative to cost; fund from the top until the budget is used; Minimum-level packages come first. Increments above the minimum are separate packages ranked on their own merit.
Activity-based budget: Activity budget = Forecast cost driver volume × Cost per driver unit; Cost per driver unit = activity cost pool ÷ driver volume. Driver volume comes from planned output.
Flexed budget cost (variable): Flexed variable cost = budgeted variable cost per unit × actual activity; Use the actual units produced or sold, not budgeted units.
Flexed budget cost (fixed): Flexed fixed cost = original budgeted fixed cost; Fixed costs do not change within the relevant range.
Semi-variable cost: Total cost = fixed element + (variable rate × activity); Split the cost first, often using the high-low method, then flex only the variable part.
Flexed sales revenue: Flexed revenue = budgeted selling price per unit × actual units sold; Sales revenue is also flexed to actual volume.
Variance against flexed budget: Variance = actual result − flexed budget result; Label it favourable (F) or adverse (A) based on the effect on profit.
Imposed (top-down) budget: Set by senior management → issued to budget holders; Pros: fast, strategy-aligned, less slack. Cons: low commitment, may be unrealistic, demotivating.
Participative (bottom-up) budget: Prepared by budget holders → reviewed and approved by senior management; Pros: local knowledge, ownership, motivation. Cons: slow, slack, may conflict with strategy.
Negotiated budget: Senior management proposal ↔ budget holder proposal → agreed compromise; Outcome depends on bargaining power. Slack can be challenged but time is needed.
Budgetary slack: Slack = budgeted cost − the cost the manager really expects (or the revenue they expect − budgeted revenue); Deliberate padding to make targets easier. It is a risk of participation. It distorts resource allocation and variances.
Budget versus forecast: Budget = planned target (what we want). Forecast = expected outcome (what we think will happen).; Use this contrast whenever the question asks for the difference.
Feed-forward control: Forecast outcome compared with target, then action taken before the event.; Feedback control compares actual with plan after the event.
Beyond budgeting core features: Rolling forecasts + relative targets + team rewards + flexible resources + devolved decisions; List these when asked what beyond budgeting replaces the annual budget with.
High-low variable cost per unit: Variable cost per unit = (Cost at high activity − Cost at low activity) ÷ (High activity − Low activity); Use the highest and lowest activity levels, not the highest and lowest costs. Take the costs that belong to those activity levels.
High-low fixed cost: Fixed cost = Total cost at either point − (Variable cost per unit × Activity at that point); Check by calculating at the other point. You should get the same fixed cost.
Regression line: y = a + bx; y is the dependent variable (cost or sales), x is the independent variable (activity or time period). b is the slope and a is the intercept.
Regression slope and intercept: b = (nΣxy − ΣxΣy) ÷ (nΣx² − (Σx)²); a = (Σy − bΣx) ÷ n; n is the number of pairs of data. Work out b first, then a.
Correlation coefficient and coefficient of determination: r lies between −1 and +1; r² = proportion of the variation in y explained by x; The closer r is to +1 or −1, the stronger the linear relationship. A value near 0 means a weak linear relationship.
Time series models: Additive: Y = T + S + R. Multiplicative: Y = T × S × R; Y is actual, T is trend, S is seasonal, R is random. Seasonal variations should add to zero (additive) or average 1 (multiplicative) over a full cycle, so adjust the averages if they do not.
Seasonal variation from the trend: Additive: S = Actual − Trend. Multiplicative: S = Actual ÷ Trend; Average the figures for each season over all cycles, then adjust so the total is correct. Forecast = Projected trend + S (additive) or Projected trend × S (multiplicative).
Learning curve (cumulative average time model): Y = aX^b, where b = log r ÷ log 2; Y is cumulative average time per unit for X units, a is time for the first unit, r is the learning rate as a decimal. For an 80% curve, b ≈ −0.322.
Total and incremental time: Total time for X units = X × Y. Time for later units = Total for X units − Total for earlier units; Always work with totals before subtracting. Never subtract averages.

Quick revision

Budget purposes: planning, coordination, communication, motivation, control, evaluation and authorisation.
The principal budget factor is the resource that limits activity, and its budget is prepared first.
Incremental budgeting adds or subtracts a percentage to last period's figures, so it can carry forward inefficiency.
Zero-based budgeting starts from nothing and requires every activity to be justified.
Activity-based budgeting links budgeted costs to the cost drivers of activities.
A fixed budget does not change with activity, while a flexible budget is adjusted to actual activity.
Rolling budgets are updated regularly by adding a new period as one expires.
Participative budgeting involves managers in setting targets and can improve motivation, but may allow budgetary slack.
Imposed budgets come from the top, are quick to set, and may reduce commitment.
High-low: variable cost per unit = change in cost ÷ change in activity, using highest and lowest activity levels.
Learning curve: each time cumulative output doubles, the cumulative average time per unit becomes the learning rate of its previous value. For an 80% rate it becomes 80% of the previous value, a fall of (100% − rate) = 20%.
Beyond budgeting replaces fixed annual budgets with relative targets and adaptive planning.

Common mistakes

Listing purposes with no explanation, for example just writing 'planning, control, motivation'. Fix: Add a sentence explaining each purpose and a link to the scenario. Marks are given for explanation and application.
Confusing coordination with communication. Fix: Coordination means aligning activities so plans fit together. Communication means passing on targets and information. Give a separate example for each.
Assuming the principal budget factor is always sales demand. Fix: Always compare every constraint in the data. Sales is the factor only if it gives the lowest feasible output.
Preparing the production budget before the sales budget when sales is the limiting factor. Fix: Begin with the budget for the principal budget factor. Production depends on sales and inventory targets.
Saying ZBB means every budget is set to zero. Fix: Say it starts from a zero base and requires each activity to be justified. Activities that pass are funded.
Recommending ZBB for direct production costs. Fix: Link ZBB to discretionary and support costs. Production costs are driven by output, so a justification exercise adds little.
Flexing fixed costs along with variable costs. Fix: Tick each line as fixed or variable first. Only variable costs change with activity.
Using budgeted units instead of actual units when flexing. Fix: The flexed budget always uses actual activity. Circle the actual units before you start.
Treating 'participative' as 'no senior involvement'. Fix: Remember that senior management still reviews and approves a participative budget. The difference is where the first draft comes from.
Saying slack only exists in imposed budgets. Fix: Slack is padding added by the budget holder. It is mainly a risk of participative and negotiated budgets, because managers have input into the numbers.

Exam tips

In written answers, tie every purpose to the scenario. Generic lists score poorly.
Always mention the link between the budget and the organisation's corporate objectives or strategic plan.
When asked to discuss, include conflicts between purposes, such as control versus motivation, or the risk of budget slack.
In objective questions, look for the key words in the stem: ahead, aligned departments, permission to spend, target, comparison. They point to the purpose.
Keep each purpose in a separate short paragraph with a clear heading so the marker can award a mark per point.
In objective questions, check every constraint before you choose the principal budget factor. Examiners often make sales the obvious answer and hide a lower limit elsewhere.
Because objective questions are all or nothing, write the units schedule on your scrap paper and check the sign of each inventory change before you answer.
In written answers, name the stages in order and link each to a purpose: for example, the committee coordinates and the manual standardises the process.