CMA Intermediate · Management Accounting

Responsibility Accounting: formula sheet

Full chapter guide

Key formulas

Cost centre performance: Variance = Actual cost − Budgeted (standard) cost; Actual higher than budget is adverse. Compare on the same activity level, so use a flexed budget where output differs.
Revenue centre performance: Sales variance = Actual sales − Budgeted sales; Actual higher than budget is favourable. Revenue centres are judged on revenue, not on profit.
Profit centre performance: Profit = Revenue − Costs charged to the centre; Include only costs the manager controls when judging the manager. Judging the centre itself may include allocated costs.
Return on Investment: ROI = Profit ÷ Capital employed × 100; Used for investment centres. Use the profit and capital definition given in the question.
Residual Income: RI = Profit − (Capital employed × Required rate of return); Used for investment centres. Positive RI means the division earns more than the required return.
Controllability rule: Evaluate a manager only on controllable items; A cost controllable at one level may be non-controllable at a lower level.
Controllability principle: Manager is evaluated on: items the manager can influence at that level and in that period; Non-controllable items are excluded from the manager's evaluation or shown separately.
Controllable cost: Controllable cost = cost whose amount the manager can change by their own decisions; Always state the level (manager) and the time period.
Controllable profit or margin of a centre: Controllable result = Revenue − Controllable costs; Used to assess the manager. Non-controllable costs are then deducted to show the centre's overall result.
Variance on controllable items: Variance = Actual − Budget (or Budget − Actual for costs, stating Favourable/Adverse); For a cost, actual below budget is favourable and actual above budget is adverse.
Minimum transfer price (seller): Minimum price = Marginal (variable) cost per unit + Opportunity cost per unit; Opportunity cost is the contribution lost on external sales given up because of the internal transfer. It is zero when there is spare capacity.
Minimum price with spare capacity: Minimum price = Variable cost per unit; Use this when the seller can supply the buyer without giving up any outside sales.
Minimum price at full capacity: Minimum price = Variable cost + Contribution lost per unit = External selling price (adjusted for savings); If the seller can sell every unit outside, the contribution lost equals the external price less variable cost. Reduce for any cost saved on internal sales.
Maximum transfer price (buyer): Maximum price = Lower of (external purchase price of the same item, net benefit per unit to the buyer from the item); The buyer will not pay more than it would pay outside, or more than the item adds to its own contribution.
Acceptable range: Seller's minimum ≤ Transfer price ≤ Buyer's maximum; If the minimum exceeds the maximum, the internal transfer is not worthwhile for the company.
Cost-plus price: Transfer price = Cost per unit + Mark-up % × Cost per unit; State clearly whether the cost is full cost or variable cost.
Return on Investment: ROI = (Divisional profit ÷ Capital employed) × 100; Use the profit and capital definitions given in the question. Use closing, opening or average capital only as instructed.
Residual Income: RI = Divisional profit − (Capital employed × Required rate of return); The deduction is a notional capital charge. It is not the interest actually paid.
Capital charge: Capital charge = Capital employed × Required rate of return; Calculate this first, then subtract.
ROI decision rule: Accept if project ROI > required rate of return; Divisions often compare with their current ROI instead, which causes the conflict.
RI decision rule: Accept if RI is positive (project return > required rate); Zero RI means the return exactly equals the required rate.
EVA: EVA = NOPAT − (Invested capital × WACC); NOPAT is net operating profit after tax. Adjustments apply only if the question gives them.
Return on Investment (ROI): ROI = Divisional profit ÷ Capital employed × 100; Use the profit and capital definitions the question gives. Be consistent between the two.
Residual Income (RI): RI = Divisional profit − (Capital employed × Required rate of return); The deduction is the imputed interest charge. A positive RI adds value above the required return.
Four balanced scorecard perspectives: Financial | Customer | Internal business process | Learning and growth; Learn the order and one or two measures for each.
Measure rating (percentage of target): Achievement % = Actual ÷ Target × 100; For measures where lower is better (defects, complaints), use Target ÷ Actual × 100 or compare directly.

Quick revision

Responsibility accounting holds each manager accountable only for items they can control.
The four centres are cost, revenue, profit and investment centres.
A cost centre is judged on cost control; an investment centre is judged on profit relative to capital employed.
Controllable costs can be influenced by the manager in the period; allocated head office costs are usually non-controllable.
Transfer price is the internal price at which goods or services move between divisions.
A good transfer price supports goal congruence and keeps divisional autonomy.
With spare capacity, the minimum transfer price is usually the variable cost of the selling division.
ROI = Profit ÷ Capital employed × 100.
Residual income = Divisional profit − (Capital employed × required rate of return).
ROI can make managers reject projects that earn more than the cost of capital but less than current ROI; residual income reduces this problem.
The balanced scorecard has four perspectives: financial, customer, internal business process, and learning and growth.
Always state the assumption you use for profit and capital employed in your answer.

Common mistakes

Calling every department a cost centre or a profit centre without checking what the manager controls. Fix: Apply the control test: costs only, sales only, both, or both plus investment.
Judging a profit centre manager on costs allocated from head office. Fix: Separate controllable and non-controllable items and judge the manager only on the controllable ones.
Treating all fixed costs as non-controllable and all variable costs as controllable. Fix: Decide controllability by who has authority over the cost. A discretionary fixed cost can be controllable. A variable cost with a price set centrally may not be.
Saying a cost is controllable or not without naming the level of management. Fix: Always write 'controllable by the plant manager' or 'non-controllable at departmental level'. The same cost can differ by level.
Using full cost as the minimum price when there is spare capacity. Fix: Fixed costs are already incurred. With spare capacity, only the variable cost is relevant, so the minimum is variable cost per unit.
Forgetting the opportunity cost at full capacity. Fix: Always ask whether the transfer displaces outside sales. If it does, add the lost contribution per unit.
Deducting actual interest paid instead of a capital charge on total capital employed. Fix: Always multiply total capital employed by the required rate. Ignore actual interest unless told otherwise.
Showing RI as a percentage. Fix: Show RI as a rupee amount. Only ROI is a percentage.
Placing measures in the wrong perspective, such as putting defect rate under Customer. Fix: Ask where the measure is controlled. Defect rate is an internal process measure. Customer complaints belong under Customer.
Judging a manager on total divisional profit including allocated head-office costs. Fix: For manager evaluation, use controllable profit. Exclude costs the manager cannot influence.

Exam tips

Begin classification answers with the control test sentence, then name the centre. This earns marks even if the example is imperfect.
For performance reports, always show Actual, Budget, Variance and F or A in a table-like layout, and add one line of interpretation.
If a question mentions allocated head-office costs, show the manager's controllable result separately from the full result.
In MCQs, watch for traps that pair the wrong measure with a centre, such as ROI for a cost centre.
For theory questions on objectives or process, write short numbered points of one sentence each rather than long paragraphs.
In classification questions, write a one-line reason against each item. A bare label earns fewer marks.
Always state the level of manager. Say 'for the departmental manager' in your answer.
In a report, put controllable items first with a clear subtotal, then non-controllable items. This layout earns presentation marks.