Divisional performance and transfer pricing: formula sheet

Key formulas

Return on investment

ROI = divisional profit ÷ capital employed × 100%

Use the profit and capital definitions the question gives. Often profit is before interest and tax, and capital employed is total assets less current liabilities.

Capital charge

Capital charge = capital employed × cost of capital

Use the same capital employed figure as in the ROI. Use the rate given, such as the divisional or group cost of capital.

Residual income

RI = divisional profit − capital charge

Profit must be the same measure used for ROI. Positive RI means a return above the required rate.

Project decision rule under ROI

Accept if project ROI > current divisional ROI (manager's likely behaviour)

This can reject projects that beat the cost of capital. It is the source of dysfunctional behaviour.

Project decision rule under RI

Accept if project profit − (project investment × cost of capital) > 0

Equivalent to accepting when project return exceeds the cost of capital.

Contribution

Sales − variable costs

Starting point of the divisional layered report.

Controllable profit

Contribution − controllable fixed costs

Use this to assess the divisional manager.

Divisional (traceable) profit

Controllable profit − traceable non-controllable fixed costs

Use this to assess the division's own economic performance, e.g. whether to keep it open.

Net profit after allocations

Divisional profit − allocated head office costs

Shows whether the division covers its share of group costs. Not a fair test of the manager.

Controllability principle

Assess managers only on items they can influence

Controllability is about authority and time period, not whether a cost is fixed or variable.

Return on investment (ROI)

ROI = Divisional profit ÷ Capital employed × 100%

Capital employed is often net assets. Say which profit and which asset base you use, and use the same basis for every division.

Residual income (RI)

RI = Divisional profit − (Capital employed × Cost of capital)

Absolute figure, so larger divisions tend to show larger RI. Accept a project if it gives positive RI.

Net book value

NBV = Cost − Accumulated depreciation

Falls each year, so ROI rises over time if profit is stable.

Currency translation

Result in home currency = Result in foreign currency ÷ Exchange rate (foreign units per 1 home unit)

Check how the rate is quoted. Use the same rate basis for profit and assets, or be clear about which rates you use.

Investment decision rule

ROI rule: accept if project ROI > divisional ROI. Company rule: accept if project return > cost of capital.

The two rules can conflict. That conflict is the short-termism problem.

Minimum transfer price (general rule)

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

Opportunity cost is the contribution lost on other uses of the resources. With spare capacity it is usually zero, so the minimum is marginal cost.

Maximum transfer price

Maximum price = lower of (net marginal revenue to the buying division) and (cost of buying externally)

Net marginal revenue is the buyer's selling price less its own further costs of processing.

Market price based transfer

Transfer price = external market price (less any savings on internal sales)

Suitable if the market is competitive and the divisions are autonomous.

Cost-plus transfer price

Transfer price = cost (full or marginal) + mark-up

The cost basis and the mark-up must be stated clearly.

Acceptable range

Minimum price ≤ transfer price ≤ maximum price

If minimum exceeds maximum, the transfer is not in the group's interest.

Minimum transfer price

Minimum = marginal cost of the seller + opportunity cost to the group

Opportunity cost is the contribution lost on other uses of the resource, such as outside sales.

Minimum price with spare capacity

Minimum = marginal cost per unit

No outside sales are lost, so opportunity cost is nil. Fixed costs are not relevant.

Minimum price at full capacity with an external market

Minimum = marginal cost + contribution lost per unit on external sale = external market price (less any saved selling costs)

Where the item is sold externally at the same cost, this reduces to the market price net of costs saved on internal sales.

Minimum price with a limited key resource

Minimum = marginal cost + (contribution per unit of scarce resource forgone × scarce resource used per unit)

Use when production of other products is given up to make the transferred item.

Maximum transfer price

Maximum = lower of (net marginal revenue of the buyer) and (external purchase price of an equivalent item)

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

Acceptable range

Transfer is worthwhile for the group if minimum ≤ maximum

Any price within the range is acceptable to both divisions in theory. Negotiation decides the point within it.

Tax effect of a transfer price

Group tax = (Seller profit × seller tax rate) + (Buyer profit × buyer tax rate)

Recalculate both divisions' profit at each transfer price. Total profit before tax stays the same.

Direction of profit shifting

Seller tax rate < buyer tax rate → set a high transfer price. Seller tax rate > buyer tax rate → set a low transfer price.

The price should push profit to the lower-tax country. This is before tariffs and other constraints. Apply it only if tax is the key driver.

Net saving with tariffs

Net benefit = Tax saved − extra import duty after tax relief. Extra duty after tax relief = change in price × tariff rate × (1 − buyer tax rate) if duty is deductible; otherwise change in price × tariff rate.

A higher price saves tax but raises duty if the duty is charged on the transfer price. Check whether the duty is deductible for tax.

Dual pricing

Seller credited at one price; buyer charged at another; difference = group-level adjustment

Not a numerical formula. Remember the adjustment is eliminated on consolidation.

Quick revision

• ROI = divisional profit ÷ capital employed × 100%.
• RI = divisional profit − (capital employed × required rate of return).
• ROI can make a manager reject a project that is good for the group if it lowers their ROI.
• RI favours accepting any project that earns more than the cost of capital, so it supports goal congruence.
• RI is an absolute figure, so it is hard to compare divisions of different sizes.
• Judge a manager on controllable items only; judge the division on its full results.
• Minimum transfer price = marginal cost of the selling division + opportunity cost to the group.
• With spare capacity, the opportunity cost is usually zero, so the minimum price is the marginal cost.
• Maximum transfer price = the lower of the external market price and the net marginal revenue of the buying division.
• A negotiated price works only if the minimum is below the maximum.
• Good transfer prices aim for goal congruence, fair performance measurement, autonomy and, where relevant, lower tax.
• In multinationals, transfer prices may shift profit to low-tax countries, but tax authorities can challenge this.

Common mistakes

• Using different profit or capital figures for ROI and RI. Fix: Fix the profit and capital employed figures first and use them in both measures.
• Deducting the cost of capital percentage from profit instead of the capital charge in money. Fix: Always multiply capital employed by the rate first. RI is a money amount.
• Treating all fixed costs as non-controllable. Fix: Ask who has the authority. Divisional fixed costs such as local salaries or advertising may be fully controllable by the manager.
• Using net profit after head office allocations to judge the manager. Fix: Stop at controllable profit for the manager. Use later lines only for the division.
• Saying the division with the higher ROI is simply the better performer. Fix: Always ask what is behind the figure: asset age, depreciation policy, currency and market. State the caveat in your answer.
• Thinking NBV lowers ROI over time. Fix: With flat cash profit, NBV falls so ROI rises. State that using NBV rewards holding old assets and discourages replacement.
• Using full cost as the minimum price for the group Fix: Fixed costs are usually unchanged by the transfer. Use marginal cost plus opportunity cost for the group decision.
• Ignoring spare capacity Fix: Ask if the selling division is at full capacity. If it is, add the lost contribution from external sales. If not, add nothing.
• Including fixed costs in the minimum transfer price when there is spare capacity. Fix: Fixed costs are not incremental. With spare capacity use variable cost only, unless the question says fixed costs will rise.
• Forgetting opportunity cost when the seller is at full capacity. Fix: Always ask the capacity question first. At full capacity, add the contribution lost on external sales.

Exam tips

• Write the formulas first, then substitute. Method marks in Section C depend on clear working.
• In objective test questions, check whether the question asks what the manager would do or what is best for the group. The answers differ.
• Keep the profit and capital employed definitions exactly as given, including whether to use opening or closing values.
• For discussion parts, link each point to behaviour: ROI discourages investment above the cost of capital but below current ROI; RI encourages it.
• Mention at least one limitation of each measure, such as the size problem with RI and book value distortion with both.
• Read the verb: 'assess the manager' means stop at controllable profit; 'assess the division' means include traceable costs.
• In OT questions, check who sets the cost. Group-imposed transfer prices and allocated central costs are the usual non-controllable items.
• In Section C, set out the layered profit statement clearly, then write a short comment under it. Marks go to both.