Performance analysis: formula sheet

Key formulas

Controllable profit

Controllable profit = Revenue − Controllable costs

Used to judge the divisional manager. Exclude costs the manager cannot influence, such as allocated head office costs.

Return on investment (ROI)

ROI = Divisional profit ÷ Capital employed × 100%

Used for investment centres. State clearly which profit and which capital figure you use.

Residual income (RI)

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

A positive RI means the division earns more than the required return on its capital.

Cost centre performance

Variance = Budgeted (or standard) cost − Actual cost

Adverse if actual is higher than budget. Flex the budget first if activity levels differ.

Return on investment (ROI)

ROI = Divisional profit ÷ Capital employed × 100%

Profit is usually controllable profit before interest and tax. Capital employed is usually total assets less current liabilities, or the net asset base for the division. Use the definition the question gives.

Imputed interest charge

Imputed interest = Capital employed × Cost of capital (required return)

A notional charge, not a cash cost. Use the same capital employed figure as in ROI.

Residual income (RI)

RI = Divisional profit − Imputed interest charge

Result in money terms. Positive RI means the division earns more than the required return.

ROI decision rule

Accept a project if its ROI ≥ the division's target ROI

Managers often compare with the division's current ROI instead. This is the source of the goal congruence problem.

RI decision rule

Accept a project if it increases RI, that is if project profit > capital invested × cost of capital

Equivalent to the project's return exceeding the cost of capital.

Four perspectives

Financial + Customer + Internal business process + Innovation and learning

Learn the four names exactly. Some books call the last one learning and growth. The two names mean the same perspective.

Question each perspective asks

Financial: how do we look to shareholders? | Customer: how do customers see us? | Internal: what must we excel at? | Innovation and learning: can we continue to improve and create value?

Use these questions to generate goals quickly when you are stuck.

Answer structure for each perspective

Perspective → Goal → Measure → Link to scenario

A measure without a goal and scenario link earns few marks.

Fitzgerald: results

Results = Competitiveness + Financial performance

Outcomes of past strategy choices.

Fitzgerald: determinants

Determinants = Quality + Flexibility + Resource utilisation + Innovation

Drivers of the results. Remember the lists of both groups.

Building Block model

Dimensions + Standards + Rewards

Standards should be ownable, achievable and fair. Rewards should be clear, motivating and controllable.

Performance Pyramid levels

Vision → Market and financial measures → Customer satisfaction, flexibility, productivity → Quality, delivery, cycle time, waste

Top two levels are mainly external. The lower levels are mainly internal.

Flexibility measures

Examples: speed of delivery, ability to handle volume changes, ability to customise

Use these when asked how to measure flexibility.

Economy

Economy = actual cost of inputs compared with the budgeted or benchmark cost of inputs

Lower cost for the same quality means better economy. Example: cost per kg of material, cost per hour of staff.

Efficiency

Efficiency = outputs ÷ inputs (or inputs ÷ outputs)

Example: patients treated per nurse hour, or cost per patient treated. Compare with a target, past period or similar body.

Effectiveness

Effectiveness = actual outcome achieved compared with the objective or target

Example: percentage of students passing, or reduction in waiting list against target. Often not a simple ratio.

Link between the Es

Inputs → (economy) | Inputs to outputs → (efficiency) | Outputs to outcomes → (effectiveness)

Use this chain to decide which E a measure belongs to.

Minimum transfer price

Minimum price = marginal cost of the selling division + opportunity cost to the group

Marginal cost means variable cost of the units transferred. Opportunity cost is the contribution lost on outside sales or other use of resources.

Minimum price with spare capacity

Minimum price = marginal cost

With no lost external sales, the opportunity cost is zero.

Minimum price with no spare capacity

Minimum price = marginal cost + contribution lost per unit on external sales

If the product has a standard external market, this equals the market price (when selling costs are the same).

Maximum transfer price

Maximum price = lower of (net marginal revenue of the buying division, external buying price)

Net marginal revenue = final selling price less the buyer's own further costs.

Acceptable range

Minimum price ≤ transfer price ≤ maximum price

If minimum exceeds maximum, the transfer should not take place from the group's view.

Cost-plus transfer price

Transfer price = cost + mark-up

Standard cost is better than actual cost, so inefficiency is not passed on.

Gross profit margin

Gross profit ÷ Revenue × 100%

Shows pricing and direct cost control.

Operating profit margin

Profit before interest and tax ÷ Revenue × 100%

Adds the effect of overheads to gross margin.

Net profit margin

Profit after tax ÷ Revenue × 100%

Use the definition given in the question if it states one.

ROCE

Profit before interest and tax ÷ Capital employed × 100%

Capital employed = total assets less current liabilities (equity plus long-term debt).

Asset turnover

Revenue ÷ Capital employed (times)

Revenue generated per $1 of capital employed. ROCE = operating margin × asset turnover.

Current ratio

Current assets ÷ Current liabilities

Liquidity. Do not treat a fixed figure as always right; compare with the industry.

Quick ratio

(Current assets − Inventory) ÷ Current liabilities

Stricter liquidity test that excludes inventory.

Inventory days

Inventory ÷ Cost of sales × 365

Use cost of sales as the base.

Receivables days

Trade receivables ÷ Credit revenue × 365

Use total revenue if credit sales are not given.

Payables days

Trade payables ÷ Cost of sales × 365

Use credit purchases if given.

Gearing

Debt ÷ Equity × 100%, or Debt ÷ (Debt + Equity) × 100%

State which definition you use and keep it consistent.

Interest cover

Profit before interest and tax ÷ Finance costs (times)

Low cover means profit is thin against interest.

Quick revision

• Judge a manager on controllable items only; separate manager performance from division performance.
• ROI = profit ÷ capital employed × 100%. Define profit and capital employed the same way each time.
• RI = profit − (capital employed × required rate of return).
• ROI can make managers reject projects that are good for the group; RI is less likely to do so.
• The balanced scorecard has four perspectives: financial, customer, internal business process, and innovation and learning.
• Every non-financial indicator should link to a strategic aim and be measurable.
• Value for money = economy, efficiency and effectiveness.
• Not-for-profit bodies need measures linked to their objectives, which are often hard to quantify.
• Minimum transfer price = marginal cost + opportunity cost to the group.
• With spare capacity in the selling division, the opportunity cost is nil, so the minimum price is marginal cost.
• Ratios mean little alone; compare with prior years, targets or competitors.
• In written answers, state the point, give the reason, and link it to the scenario.

Common mistakes

• Treating all fixed costs as uncontrollable. Fix: Decide by who can influence the cost. Discretionary fixed costs, like advertising or training set by the manager, are controllable.
• Judging a profit centre manager on profit after apportioned head office costs. Fix: Use controllable profit for the manager's performance. Use profit after allocations to assess the division itself.
• Treating the imputed interest charge as a cash cost or including actual interest paid as well Fix: Use the charge only as a notional deduction in RI. If profit is stated before interest, do not deduct actual interest again.
• Using the wrong capital employed figure, such as opening instead of closing or average Fix: Check the wording. Use exactly the base the question states, and use the same base for ROI and the interest charge.
• Listing generic measures with no link to the scenario. Fix: Name the business in your answer and choose measures that suit it, such as bed occupancy for a hospital or table turnover for a restaurant.
• Putting measures in the wrong perspective, for example new product launches under internal process. Fix: Use the four questions. Anything about future capability, innovation or staff development goes in innovation and learning. Anything about current operations goes in internal process.
• Treating market share or sales growth as a determinant. Fix: In Fitzgerald they are results under competitiveness. Determinants are quality, flexibility, resource utilisation and innovation.
• Saying the Building Block model has the same six items as its three blocks. Fix: The model has three blocks: dimensions, standards and rewards. The six Fitzgerald measures sit inside the dimensions block.
• Treating efficiency and economy as the same thing. Fix: Economy is the price of inputs. Efficiency needs an output in the ratio. If there is no output, it is not efficiency.
• Calling a cost-cutting measure effective. Fix: Effective means objectives are achieved. Check the outcome, not the cost.

Exam tips

• Read the scenario for what the manager can decide. The centre type follows from that, not from the department name.
• In written answers, always separate controllable from uncontrollable items and say why for each.
• When asked to evaluate a manager, mention that ROI and RI can encourage short-term thinking or rejecting good projects.
• In objective questions, watch for apportioned or allocated costs. These are usually the uncontrollable items.
• Show the formula and each figure used in constructed response questions so you earn method marks.
• Show the imputed interest line separately. Method marks are often given for it even if the final RI is wrong.
• In written parts, tie your comment to the scenario. Say which manager would reject which project and why.
• If the question tells you the capital employed definition, follow it exactly, even if it differs from the textbook.