Budgetary planning and control: formula sheet

Key formulas

Flexed budget cost

Flexed cost = Variable cost per unit × Actual units + Fixed cost

Fixed costs stay at budget level. Only variable costs change with activity. Use this to compare actual and budget fairly.

Flexed budget variance

Variance = Actual cost − Flexed budget cost

A higher actual cost than the flexed budget is adverse. Compare against the flexed figure, not the original fixed budget.

Incremental budget

New budget = Last year's budget × (1 + expected change %)

Adjust for known changes such as inflation. The base itself is not questioned.

Purposes of budgeting

Planning, control, coordination, motivation (also communication and authorisation)

Use these as headings when a question asks why an organisation budgets.

Budget-setting styles

Imposed = top-down | Participative = bottom-up | Negotiated = two-way agreement

Know the main advantages and disadvantages of each and be ready to recommend one for a given scenario.

Budgetary slack

Slack = budgeted target easier than a realistic, achievable target

For example, revenue understated or costs overstated on purpose. It is a behaviour, not a calculation, but you can quantify it if figures are given.

Hopwood evaluation styles

Budget-constrained | Profit-conscious | Non-accounting

Hopwood's three styles of using budget information to evaluate managers. Link each to likely behaviour.

Goal congruence

Manager's goals = organisation's goals

A budget system succeeds when managers acting in their own interest also serve the organisation.

Flexed budget

Flexed budget = budgeted cost per unit × actual activity (variable costs); fixed costs stay as budgeted

Use it to compare actual with budget at the same activity level when volumes are uncertain.

Rolling budget

Each period, drop the period just ended and add a new period at the end

Keeps a constant planning horizon, for example always the next 12 months.

Value for money (3Es)

Economy = inputs at lowest cost; Efficiency = outputs ÷ inputs; Effectiveness = outcomes achieved against objectives

Use it for not-for-profit budgets, where profit does not measure success.

Context-fit rule

Context → problem with standard budget → adapted budget design

A answer structure, not a calculation. Use it for any scenario.

Flexed budget

Flexed budget = budgeted variable cost per unit × actual units; fixed costs stay at budget

Flex to actual activity (output or sales volume). Flex only items that truly vary with that activity.

Sales volume variance (profit or contribution)

(Actual units − budgeted units) × standard profit (or contribution) per unit

Equals flexed budget profit minus original budget profit under marginal costing. Positive means favourable.

Flexed budget variance

Actual result − flexed budget result

Shows price, efficiency and spending effects after removing the volume effect.

Planning price variance

(Original standard price − revised standard price) × standard quantity for actual output

Favourable if the revised price is lower. It compares the original flexed budget with the revised flexed budget, both at actual output. Not usually controllable by the buyer.

Operational price variance

(Revised standard price × actual quantity) − actual cost

Positive means favourable. Judges the buyer against the real market price.

Operational usage variance

(Standard quantity for actual output − actual quantity) × revised standard price

In the operational analysis, usage is valued at the revised standard price. Use the revised quantity standard if one exists. Positive means favourable. Valued at the original price it gives the traditional usage variance, and the difference is the price change × the excess or saved quantity.

Total variance check

Planning price variance + operational price variance + operational usage variance = actual cost − original standard cost of actual output

The same total equals the traditional price variance plus the traditional usage variance. Watch signs when adding favourable and adverse items.

High-low variable cost

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. Then fixed cost = total cost at either point − (variable cost per unit × activity at that point).

Linear cost function

y = a + bx

y is total cost, a is fixed cost, b is variable cost per unit of activity, x is activity.

Regression slope (b)

b = (nΣxy − ΣxΣy) ÷ (nΣx² − (Σx)²)

n is the number of data pairs. Learn the formula and be able to apply it.

Regression intercept (a)

a = (Σy − bΣx) ÷ n

Equivalent to a = ȳ − b × x̄. Calculate b first.

Correlation coefficient

r = (nΣxy − ΣxΣy) ÷ √[(nΣx² − (Σx)²)(nΣy² − (Σy)²)]

r lies between −1 and +1. Values near ±1 show a strong linear relationship.

Coefficient of determination

r² = proportion of variation in y explained by x

If r = 0.9, then r² = 0.81, so 81% of the variation in cost is explained by activity.

Learning curve (cumulative average time model)

Y = aX^b, where b = log(learning rate) ÷ log 2

Y is cumulative average time per unit for X units, a is time for the first unit. For 80%, b = log 0.8 ÷ log 2 = −0.322. When X doubles, Y falls to the learning rate of its previous value.

Time for later units

Time for units m+1 to n = (n × average time for n units) − (m × average time for m units)

Always work from cumulative totals, then subtract.

Expected value

EV = Σ(probability × outcome)

Probabilities must add to 1. The EV may not be a value that can actually occur.

Additive time series forecast

Forecast = Trend + Seasonal variation

Seasonal variations in the additive model should sum to about zero over a full cycle.

Quick revision

• Budget purposes: planning, coordination, communication, motivation, authorisation, control and evaluation.
• Incremental budgets adjust last year's figures. They are simple but can carry forward waste and slack.
• Zero-based budgeting justifies every item from scratch. It is thorough but time-consuming.
• Rolling budgets are updated regularly, which helps in uncertain conditions but takes more effort.
• Beyond budgeting replaces fixed annual targets with relative measures and adaptive forecasts.
• Participation can improve ownership and accuracy, but it also allows slack to be built in.
• Targets that are too easy or impossible both reduce motivation.
• A flexed budget compares actual results with the budget restated for actual activity.
• Variances are signals. Investigate causes, check links between them and consider controllability.
• Public and not-for-profit budgets focus on resource limits and service outcomes, not profit.
• Choose each quantitative technique to suit the data and state its limitations.
• Always end with a clear recommendation tied to the scenario.

Common mistakes

• Listing the definitions of each budget type without using the scenario. Fix: Tie every point to a fact in the case. Say why it matters for this company.
• Comparing actual results with the original fixed budget when activity has changed. Fix: Flex the budget to actual activity first. Only then judge the variance.
• Writing a generic list of budget criticisms with no link to the scenario. Fix: Choose the criticisms that fit the case facts and quote those facts in each point.
• Saying Beyond Budgeting means having no planning, no targets or no control. Fix: Explain that planning continues through rolling forecasts, relative targets and control based on transparency, trust and timely information.
• Saying participation is always better than imposed budgets. Fix: State the costs too: time, slack and pseudo-participation. Say imposed budgets can suit a crisis, a new start-up or a junior team lacking expertise.
• Defining slack but not linking it to the scenario. Fix: Quote the facts that suggest slack, such as budgets always beaten by a wide margin, and name the cause, such as a bonus tied to budget.
• Writing a generic essay on the purposes of budgeting. Fix: Open with the scenario's context and relate every point to it.
• Treating not-for-profit budgets as profit budgets. Fix: Focus on funding limits, allocation, accountability, outputs and value for money.
• Comparing actual results with the original fixed budget and calling the difference performance. Fix: Always flex to actual activity first. Only then do the remaining differences reflect efficiency and prices.
• Flexing fixed costs along with variable costs. Fix: Keep fixed costs at the budgeted total unless the question says activity moves them into a new step. Flex only truly variable items.

Exam tips

• Always answer in the context of the case. Generic lists of advantages earn few marks.
• When a question asks for a recommendation, give a clear choice and state at least one drawback with a mitigation.
• Name the purpose being served, such as control or motivation, and show where purposes conflict.
• If numbers are given, flex the budget before judging performance.
• Use short headings for each system so the marker can see your structure quickly.
• Always tie each criticism or principle to a fact in the scenario. Generic lists earn few marks.
• Use the requirement verb. Evaluate and recommend questions need a judgement and a verdict, not just description.
• Show behavioural insight: link budgets to rewards, gaming and slack. This earns analysis and scepticism marks.