Divisional Performance: Responsibility Centres, ROI and Residual Income

A holding company in Lagos has two subsidiaries. The cement division reports a profit of ₦1.8 billion on net assets of ₦12 billion. The packaging division reports a profit of ₦0.6 billion on net assets of ₦3 billion. Which division is doing better? The cement division makes three times the profit, but it uses four times the capital.

Judging divisions by profit alone rewards size, not performance, and the managers, who are paid on the numbers, will react accordingly. A large company that delegates authority to divisions needs a way of judging the divisions and their managers that is fair and that encourages decisions in the interest of the whole group.

This topic explains the responsibility centres (cost, revenue, profit and investment centres), the benefits and disadvantages of decentralisation, controllable and traceable profit, and the two main measures of an investment centre: return on investment (ROI) and residual income (RI), including how they are calculated, how they affect investment decisions, the effect of depreciation, and the advantages and disadvantages of each.

It builds on the earlier topic on value for money as a public sector objective. The next topic covers economic value added.

Responsibility centres and decentralisation

Responsibility centres

Every organisation has managers with responsibility for a part of its activity: a responsibility centre. The information a manager needs depends on the scope of the responsibility. There are four types:

• Cost centre: a department or work group for which costs are established. The manager is responsible for costs only and is judged by comparing actual with budgeted costs. A part of the costs, such as salaries, may be outside the manager’s control.
• Revenue centre: a unit for which revenues only are established, such as a sales team or the income office of a hospital. There is no measure of cost or profit.
• Profit centre: a unit for which revenues and costs are both established, so that profit can be measured. A manager responsible for both costs and revenues is responsible for profit.
• Investment centre: a division whose manager is responsible for costs, revenues and decisions on investment in assets, with authority to buy new plant or sell unwanted assets. Its performance is measured by the return on the investment (ROI) or residual income.

These can be nested. A media group may treat each of its divisions as an investment centre; within the magazines division, the fashion, sports and business magazine units may be profit centres; and within the fashion unit, commissioning, editing and printing, and marketing may be cost centres. A responsibility centre should be given information that is relevant to the decisions that it can take.

Decentralisation

Decentralisation is the delegation of authority within an organisation, to the managers of cost, revenue, profit and investment centres. A divisionalised structure is one where each operating unit has its own management team reporting to head office, often by geography or by product line. In a decentralised divisionalised structure, divisional managers decide selling prices, suppliers and output.

Benefits:

• Top management are freed to concentrate on strategy.
• Better decisions at the tactical and operational level, because divisional managers have local knowledge.
• Faster decisions, taken on the spot.
• Motivation from being empowered and rewarded against fair targets.
• Management training: divisions give experience to future senior managers.
• In a multinational group, possible tax advantages or subsidies from locating divisions in particular countries.

Disadvantages:

• Lack of goal congruence: managers put the interests of their division before those of the company, taking decisions that help the division and harm the whole.
• Loss of control by top management, so divisions must be monitored, at a cost.
• Difficulty in finding a measure of investment centre performance that motivates the best decisions: ROI, for example, can encourage poor long-term investment decisions.
• Loss of economies of scale and duplication of functions: three divisions may need three finance directors as well as one at head office, and duplicate IT systems.

Controllable and traceable profit

In evaluating a division it is useful to separate costs controllable by the divisional manager from costs traceable to the division but outside the manager’s control (for example the depreciation of assets allocated by head office), and finally any allocation of general overheads, such as head office costs.

The profit after controllable costs is the controllable profit, used to assess the manager; the profit after traceable costs is the traceable profit, used to assess the division as an investment; the net profit after general overheads is the bottom line for the group. Divisions that trade with each other have internal sales at transfer prices, and external and internal sales should be reported separately.

ROI and residual income

Return on investment (ROI)

ROI (also called the accounting rate of return) is the profit of the division as a percentage of its capital employed. It is used for investment centres because the manager is responsible for both the profit and the assets invested. Profit alone does not make the manager accountable for the use of the assets.

For the earlier example, a division with net assets of ₦5 million and a profit of ₦250,000 has a ROI of 5%, while one with net assets of ₦1 million and a profit of ₦150,000 has a ROI of 15%, so the second performs better, though its profit is smaller.

ROI = divisional profit ÷ divisional capital employed × 100%. The recommended basis:

• profit is accounting profit after depreciation
• capital employed is non-current assets (usually at carrying value, that is cost less accumulated depreciation) plus working capital (inventory plus receivables less payables for a division)
• it may be measured at the start of the year, the end or the average, so read the question carefully

Where possible the profit and capital should be split into controllable (to assess the manager) and traceable (to assess the division). ROI should be supported by other ratios (margins, sales growth), which help to explain a change.

ROI and investment decisions

A manager judged by ROI, perhaps with a bonus, will accept investments that increase the division’s ROI in the current year and reject those that reduce it, even if the project is worthwhile over its life. Investment decisions are long-term, and a new asset may lower ROI in the first years (because its carrying value is high and its profits are low) and raise it later.

The manager may reject a good investment because of the short-term effect. Investment decisions should be made on net present value, not on ROI.

Advantages and disadvantages of ROI

Advantages: it relates profit to capital employed, for which the manager is responsible; it is a percentage and so allows comparison of divisions of different size; it is easily understood; it focuses attention on capital and encourages managers to sell off unused assets and to avoid excess inventory and receivables.

Disadvantages: it may lead to rejection of worthwhile investments; capital employed can be measured in different ways, so comparisons between organisations are difficult; it tends to rise as assets depreciate, so managers may keep old assets; it is an accounting measure and ignores non-financial performance (a balanced scorecard may be more suitable); and it may encourage manipulation of profit or of asset values near the year end.

Residual income (RI)

Residual income = divisional profit − notional (imputed) interest on capital employed. It can be calculated as controllable residual income (controllable profit less notional interest on controllable investment) or traceable residual income. The notional interest is capital employed (preferably average) multiplied by the organisation’s cost of borrowing, its weighted average cost of capital, or a special risk-weighted rate for divisions with higher business risk.

A positive RI means that the division’s profit exceeds its cost of capital.

Advantages: it relates profit to capital employed and charges for it; it is in money terms, which some companies prefer; it is flexible, because different rates can be applied to investments of different risk; and it encourages managers to accept any project earning more than the cost of capital, whereas ROI may lead them to reject projects that earn above the cost of capital but below the current ROI.

Disadvantages: it is an accounting measure with the same problems as ROI in defining profit and capital; it is an absolute amount, so large divisions will usually show larger RI than small ones and comparison is difficult (a small division with RI of ₦50,000 may be performing better, by ROI, than a large one with RI of ₦100,000); and it is less easily understood by non-accountants. Both ROI and RI also suffer from the depreciation effect.

Depreciation and the age of assets

If assets are depreciated straight-line, capital employed is based on carrying values, annual profits are constant and assets are not replaced, ROI and RI increase each year. In the early years of a project ROI and RI may be low, and a manager worried about the next year or two may refuse a project that is good over its life.

Managers may also keep ageing assets in use as long as possible, even if replacing them earlier would be better for the company. Remedies: use gross (cost) values or replacement values for capital employed; appraise projects by NPV; judge performance over several years; use a balanced scorecard; use economic value added (the next topic).

Layouts for divisional performance

1. Profit statement: sales; controllable costs; controllable profit; traceable costs; traceable profit; general overhead; net profit.
2. Capital employed on the stated basis (opening, closing or average).
3. ROI = profit ÷ capital employed; RI = profit − (capital employed × cost of capital).
4. Investment decision: project profit after depreciation each year, average net assets, ROI and RI with and without the project; then NPV.
5. Comment on size, risk and which measure favours which division.

Money is in naira (₦m or ₦000); percentages to one decimal place; each answer is rounded once, at the end.

Worked examples

1. Total sales.
   900; contribution 900 − 300 = 600.
2. Controllable profit.
   600 − 150 = 450.
   ROI on controllable investment 450 ÷ 1,500 = 30.0%.
3. Traceable profit.
   450 − 170 = 280.
   ROI on traceable investment 280 ÷ 2,000 = 14.0%.
4. Net profit.
   after the share of general overheads 280 − 60 = 220.
5. Comment. The manager is doing well on what he controls (30%). But the division as an investment earns 14%, which may be below its cost of capital; this does not necessarily mean the manager is at fault.

1. ROI.
   A: 1.8 ÷ 12 = 15.0%.
   B: 0.6 ÷ 3 = 20.0%.
2. RI.
   A: 1.8 − (12 × 11%) = 1.8 − 1.32 = ₦0.48m.
   B: 0.6 − 0.33 = ₦0.27m.
3. Comment. By ROI, B is better (20% against 15%); by RI, A is better (₦0.48m against ₦0.27m) because it is larger. Both add value because both are positive. The two measures give different rankings because ROI ignores size, and RI is affected by it.

1. Profit after depreciation from the project: 3, 7, 11, 15; total divisional profit 67, 71, 75, 79.
2. Average net assets of the project:
   Year 1 (60 + 45) ÷ 2 = 52.5; Year 2 37.5; Year 3 22.5; Year 4 7.5.
   Divisional average net assets 452.5, 437.5, 422.5, 407.5.
3. ROI:
   67 ÷ 452.5 = 14.8%
   71 ÷ 437.5 = 16.2%
   75 ÷ 422.5 = 17.8%
   79 ÷ 407.5 = 19.4%.
   Without the project ROI is 16.0%, so ROI falls in Year 1.
4. RI at 12%: notional interest 54.3, 52.5, 50.7, 48.9; RI 12.7, 18.5, 24.3, 30.1. Without the project RI is 16, so RI also falls in Year 1 (by 3.3) and rises in later years (by 2.5, 8.3 and 14.1).
5. Project ROI.
   Average annual profit 36 ÷ 4 = 9; average carrying value 60 ÷ 2 = 30; ROI of the project 30%, far above 16%.
6. NPV at 12%:
   18 ÷ 1.12 + 22 ÷ 1.2544 + 26 ÷ 1.4049 + 30 ÷ 1.5735 = 71.18
   less 60 = ₦11.18m.
7. Comment. A manager who cares about next year’s ROI or RI may reject the project, though its NPV is positive and its own return is 30%: the measures conflict with the company’s interest. Project appraisal should use NPV, and the manager’s assessment should allow for the long term.

Expect variants: ROI based on opening or closing capital, a part of a longer question that asks for ratios to explain the change in ROI, a requirement to compare divisions of different risk with different rates, and discussion of advantages and disadvantages.

Setting a price to meet a residual income target

To find the price that achieves a target residual income, work backwards:

• required profit = target residual income + capital employed × cost of capital
• contribution needed = required profit + divisional fixed costs
• price = variable cost per unit + contribution needed ÷ units

Example. Division A: capital ₦2.5m at 10%, target RI ₦400,000, fixed costs ₦150,000, variable cost ₦3.20, 500,000 units. Required profit = 400,000 + 250,000 = ₦650,000; contribution needed = ₦800,000; per unit ₦1.60; price ₦4.80.

Division B buys these as a component, adds ₦1.50 a unit, has fixed costs ₦100,000, capital ₦1.8m at 9% and a target RI of ₦250,000. Required profit = 250,000 + 162,000 = ₦412,000; contribution needed = ₦512,000; per unit ₦1.024; B’s selling price = 4.80 + 1.50 + 1.024 = ₦7.324. A transfer price set this way can be a poor one for the group: if the component can be bought outside for less than ₦4.80, B will buy outside and A’s spare capacity is wasted.

A transfer price for idle capacity, set to a residual income target

When a division has idle capacity, its transfer price can be set to recover what the division needs after external sales. Example. Capacity 600,000 units; external sales 450,000 at ₦7.40; variable cost ₦6.10; fixed costs ₦90,000; capital ₦2m at 10%; target RI ₦300,000. Required profit = 300,000 + 200,000 = ₦500,000; plus fixed costs ₦590,000; variable cost of all units 600,000 × 6.10 = ₦3,660,000; total revenue needed ₦4,250,000; less external revenue 450,000 × 7.40 = ₦3,330,000, leaving ₦920,000 to come from the 150,000 units transferred: ₦6.13 a unit.

The buying division treats this price, which includes the seller’s fixed costs, interest charge and required profit, as a variable cost; it is above the variable cost of ₦6.10 and may be above the market price for the component, so the buyer may buy outside and the group lose: a sub-optimal decision.

Common mistakes

• Using the wrong profit or capital basis. Controllable with controllable; check opening, closing or average.
• Forgetting the working capital in capital employed.
• Calculating notional interest on profit instead of on capital.
• Judging divisions by profit alone.
• Ignoring the depreciation effect and the short-term bias.
• Recommending decisions on ROI rather than NPV.

Quick revision

• Cost, revenue, profit, investment centres. Decentralisation: local knowledge and motivation v goal congruence and control.
• Controllable profit assesses the manager; traceable profit the division.
• ROI = profit ÷ capital employed; RI = profit − capital × cost of capital.
• Both rise with asset age; both can lead to rejection of good projects; use NPV for decisions.

How the marks are earned

• Correct basis and calculation.
• Comparison and explanation.
• Advantages, disadvantages and behaviour.

Practice questions

These are original questions, written in the style of the Skills examination. Work each one before you open the answer.

Recall check: multiple choice

Section B style: written questions

Model answers

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