Arden Instruments: A Cost-Plus Transfer Price That Destroys Group Profit
Arden Instruments is a listed group with two divisions. Division A manufactures a precision sensor at a variable cost of €22 and fixed costs of €8 per unit at its practical capacity of 100,000 units; all 100,000 units can be sold externally at €45 and A currently does so. Division B assembles the sensor into a finished unit, incurs additional variable cost of €38 and sells at €95. B currently buys an identical sensor from an external supplier at €47 and can source up to 30,000 units a year there. Group policy sets internal transfers at full cost plus 10%, which for the sensor is €33. A's manager is measured on divisional operating margin and refuses to supply B at €33. B's manager is measured on divisional return on investment and prefers to continue buying externally. Group profit before tax is €180m and the CEO wants 'a ruling by Friday' on whether internal supply should be mandated and at what price.
1. Quantify the group profit effect of B sourcing internally instead of externally, and state the transfer price range that makes both divisions better off.
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Compare group contribution, not divisional profit.
B sources externally: A sells 100,000 units outside at €45 → 100,000 × (45 − 22) = €2.30m contribution. B makes 30,000 units at €95 − 38 − 47 = €10 each → €0.30m. Group total = €2.60m.
B sources internally: A sells 70,000 externally and 30,000 to B → 70,000 × €23 = €1.61m. B's contribution per unit is €95 − 38 − 22 = €35 → 30,000 × €35 = €1.05m. Group total = €2.66m.
The group gains €60,000, which is exactly 30,000 × (47 − 45): the internal sensor costs €22 of real resource plus €45 of lost external margin = €45 opportunity cost, against a €47 external purchase price.
Range: A's minimum is its variable cost plus opportunity cost = €22 + €23 = €45. B's maximum is the external price it would otherwise pay = €47. Any price between €45 and €47 shares the €60,000 gain. There is no price at which the group optimum is achieved and both divisions are worse off - the conflict is created entirely by the measurement system, not by economics.
2. Explain why the €33 cost-plus price produces a dysfunctional decision, and recommend a transfer pricing policy.
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At €33, A earns €11 per unit (33 − 22) against €23 selling outside, so it loses €12 per unit - €360,000 a year - by supplying B. A's manager is behaving rationally against the measure he is judged on when he refuses. B, meanwhile, earns €24 per unit buying at €33 against €10 buying at €47, so it would happily take the volume. The policy therefore guarantees deadlock.
The root error is that full cost plus a mark-up ignores the opportunity cost of constrained capacity. A cost-plus rule is only sound where the selling division has spare capacity and the variable cost is the true incremental cost of the group; here capacity is fully utilised.
Recommended policy, in order of preference:
- Market-based transfer price with an opportunity-cost floor. Set the price at the external market price (€45–47), with a documented rule that where capacity is constrained the minimum price is market price, and where there is idle capacity the floor falls to variable cost.
- Two-part tariff or dual pricing. Charge B €47 and credit A €45, with the €2 per unit (€60,000) retained centrally. This preserves both divisions' incentives and keeps the group gain visible rather than buried in one division.
- Mandate internal supply only with a compensating adjustment to the bonus pools, so A is not penalised for a decision taken for group benefit.
The policy should state the capacity rule explicitly, because the answer flips the moment A has spare capacity - the floor then becomes €22.
3. Critique the two divisional performance measures and propose changes that would support goal congruence.
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Both measures are single-metric, short-term and controllable in ways that damage the group.
A on divisional operating margin: margin percentage rewards high-price external sales and penalises internal sales at any price below market, regardless of whether the internal sale creates group value. It also rewards A for not using capacity if the fixed cost per unit can be spread differently. Fixed costs of €8 per unit at capacity are largely sunk and should not drive the transfer decision at all.
B on ROI: ROI encourages B to shrink the asset base and to reject investments that dilute the ratio, and it makes B indifferent to whether the group earns €2.66m or €2.60m. It also gives B an incentive to hold the cheapest input, which happens to be the externally sourced one under the current transfer price - a coincidence, not an alignment.
Proposed changes:
- Measure divisions on contribution or residual income after a capital charge, which removes the ROI disincentive to invest and stops margin percentage from driving sourcing decisions.
- Weight bonuses 50% divisional and 50% group profit, so both managers have a direct stake in the €60,000.
- Add a capacity utilisation measure for A that gives credit for internal sales at opportunity cost, not at cost-plus.
- Require any transfer price dispute above a threshold to be resolved by a group pricing committee against the capacity rule, so the decision is not settled by whichever manager has more negotiating leverage.