Divisional Performance Measurement: formula sheet

Key formulas

Cost centre measure

Variance = Actual cost − Budgeted (standard) cost for actual output

Used for cost centres. Compare on a flexed basis where output differs from budget.

Profit centre measure

Divisional profit = Divisional revenue − Divisional costs

Check which costs the manager controls before judging the manager.

Investment centre measure (link)

Return on capital employed = Divisional profit ÷ Capital employed × 100

Basic form of ROI. Detailed treatment sits in the ROI and Residual Income topics.

Controllability rule

Manager performance = Results from controllable items only

Division performance (as an investment) may include non-controllable items; manager performance should not.

Return on Investment

ROI = (Divisional profit ÷ Capital employed) × 100

Use the profit and capital definition given in the question. If none is given, state your assumption.

Profit margin

Profit margin = (Divisional profit ÷ Sales) × 100

Uses the same profit figure as in ROI.

Capital turnover

Capital turnover = Sales ÷ Capital employed

Expressed in times. Uses the same capital figure as in ROI.

DuPont breakdown

ROI = Profit margin × Capital turnover = (Profit ÷ Sales) × (Sales ÷ Capital employed)

Sales cancels out. Use it to check your answer.

Capital employed (asset approach)

Capital employed = Fixed assets + Current assets − Current liabilities

Equals net assets. Check whether the question wants total assets instead.

Average capital employed

Average capital employed = (Opening + Closing) ÷ 2

Use only if the question asks for it or gives both figures.

Residual income

RI = Divisional profit − (Capital employed × Required rate of return)

Use the profit measure the question gives. The product in brackets is the capital charge.

Capital charge

Capital charge = Capital employed × Required rate of return

Use the capital figure stated in the question, such as opening, closing or average.

Return on investment

ROI = (Divisional profit ÷ Capital employed) × 100

Compare with the required rate to judge the division.

Decision rule

Accept a project or division if RI > 0

Equivalent to ROI of the project exceeding the required rate of return.

EVA

EVA = NOPAT − Capital charge

Positive EVA means value creation; negative means value erosion.

NOPAT

NOPAT = EBIT × (1 − tax rate)

EBIT is operating profit before interest. Do not deduct interest again.

Capital charge

Capital charge = WACC × Capital employed

Use the capital employed the question specifies, opening or average, and adjust it if profit is adjusted.

WACC

WACC = (E ÷ V) × Ke + (D ÷ V) × Kd × (1 − t)

E and D are equity and debt, V = E + D. Kd is the pre-tax cost of debt. Use market or stated weights as the question directs.

Alternative EVA form

EVA = (ROCE after tax − WACC) × Capital employed

ROCE after tax = NOPAT ÷ Capital employed. Useful as a quick check.

Minimum transfer price (seller)

Minimum price = Variable (marginal) cost per unit + Opportunity cost per unit

Opportunity cost is the contribution the seller loses by selling internally. It is nil if the seller has spare capacity.

Opportunity cost with full capacity

Opportunity cost = Contribution lost per unit on the external sale given up

So, with no spare capacity and a market for all output, minimum price = external selling price less any cost saved on internal sales.

Maximum transfer price (buyer)

Maximum price = Lower of (net realisable value to the buyer, external purchase price of the same input)

Net realisable value = buyer's selling price less its further processing costs, other than the transferred input.

Acceptable negotiation range

Minimum price ≤ Transfer price ≤ Maximum price

If the minimum exceeds the maximum, the transfer should not happen from the company's viewpoint.

Cost plus price

Transfer price = Cost per unit + Mark-up

Cost may be variable, full or standard. State which basis you use.

Market price less savings

Transfer price = Market price − Costs saved on internal sale

Savings include selling expenses, bad debts and packing the seller avoids.

Four perspectives

Financial + Customer + Internal business process + Learning and growth

Learn the four names in this order. Always give at least one measure under each.

Cause-and-effect chain

Learning and growth → Internal process → Customer → Financial

Use this to show how strategy links to results. Lower perspectives drive the upper ones.

Scorecard structure

Objective → Measure → Target → Action (initiative)

Each perspective is built from these four columns.

Customer retention rate

Customers retained ÷ Customers at start of period × 100

Count only existing customers at the start. Exclude new customers gained in the period.

Defect rate

Defective units ÷ Total units produced × 100

A process measure. Lower is better.

Quick revision

• ROI = Profit ÷ Capital employed × 100; state which profit and capital you use.
• RI = Divisional profit − (Capital employed × Required rate of return).
• A positive RI means the division earns more than the required return.
• ROI can make a manager reject a project that is above the cost of capital but below current ROI.
• RI favours accepting any project earning more than the required rate, so it aligns better with company interest.
• EVA = Net operating profit after tax − (Capital employed × Cost of capital).
• EVA uses adjusted figures, for example treating some spending as investment, so it is closer to economic profit.
• Transfer price should motivate divisions toward decisions good for the whole company.
• With spare capacity, the minimum transfer price is the selling division's marginal cost; without it, add the opportunity cost.
• Market price is a good transfer price when an active external market exists.
• The balanced scorecard has four perspectives: financial, customer, internal business process, and learning and growth.
• Use controllable profit to judge the manager and a fuller profit to judge the division.

Common mistakes

• Calling any department with a budget a profit centre. Fix: A profit centre needs control over both revenue and costs. Apply the control test first.
• Treating division performance and manager performance as the same. Fix: State clearly that the manager is judged on controllable items only, while the division's economic viability is judged on full traceable results.
• Using different profit or capital definitions in margin, turnover and ROI. Fix: Decide profit and capital once at the start and use them in all three ratios. Margin × turnover must equal ROI.
• Forgetting to deduct current liabilities when finding capital employed. Fix: Read the question for the capital definition. If capital employed means net assets, use fixed assets plus current assets minus current liabilities.
• Subtracting the required rate percentage from ROI and calling it RI. Fix: RI is always in rupees. Convert the rate into a capital charge and subtract it from profit.
• Using the wrong capital figure, such as closing capital when average is asked. Fix: Underline the capital basis in the question before calculating.
• Deducting interest before finding NOPAT Fix: Start from operating profit (EBIT). The cost of debt is already inside WACC, so deducting interest double counts it.
• Using pre-tax cost of debt in WACC Fix: Always use Kd × (1 − t) for debt unless the question says the given cost is already after tax.
• Using full cost as the minimum price when the seller has spare capacity. Fix: With spare capacity, fixed cost is incurred whether or not the transfer happens. The minimum is variable cost only.
• Ignoring opportunity cost when the seller is at full capacity. Fix: Always ask whether each internal unit displaces an external sale. If yes, add the lost contribution.

Exam tips

• Section A often tests classification of centres: apply the control test (costs, revenue, investment) and you can answer in seconds.
• In descriptive answers, give balanced points with a one-line reason each. Marks go to explained points, not headings.
• Always say that managers should be judged on controllable items; this single line is often what examiners look for.
• If a case gives figures, link the topic to the right measure (cost variance, profit, ROI or Residual Income) and state your choice before calculating.
• Quote the formula first, then substitute. Even if arithmetic slips, you still earn method marks.
• In MCQs, check which profit and which capital base the options assume. Wrong options often come from using the other base.
• For theory questions on limitations, always include the dysfunctional decision example with numbers if you can.
• When asked to compare divisions, give the ranking and one reason using margin or turnover, not only ROI.