Arden and Boyd: Setting a Transfer Price When Capacity Is Only Partly Idle
Arden Division makes a component: variable cost $38 per unit, fixed cost $14 per unit at its 40,000-unit practical capacity ($560,000 total fixed). Arden currently sells 36,000 units a year to outside customers at $70. Arden's invested capital is $3,700,000 and its manager is evaluated and bonused on divisional ROI. Boyd Division buys 8,000 of the identical component a year from an outside supplier at $60 and has no cheaper source. Boyd has asked Arden to supply all 8,000. Arden's manager refuses to quote below $70, saying "I will not sell at a loss to my own company." Corporate requires a 12% return on investment. Arden's outside demand is firm at 36,000 units at $70; there is no other market price for internal transfers.
1. Compute Arden's current divisional operating income and ROI, and explain why the manager's refusal may be rational for her even if it is wrong for the company.
Read the worked answer
Current income = 36,000 × ($70 − $38) − $560,000 = $1,152,000 − $560,000 = $592,000 ROI = $592,000 / $3,700,000 = 16.0% (against a 12% corporate charge, so the division is comfortably above the hurdle)
The manager's behavior is rational under an ROI metric because every unit transferred displaces a unit she can sell for $70. Her opportunity cost is the $32 contribution she forgoes ($70 − $38). Any transfer price below $70 reduces her reported income and her ROI, with no offsetting benefit to her - she does not see Boyd's $60 purchase as a company cost. Refusing at $70 is a goal-congruence failure created by the performance measure, not necessarily by the manager.
2. Compute the minimum transfer price for each block of the 8,000 units and the average minimum. Then evaluate: if the transfer price is $60, does the company benefit, and does Arden's manager benefit?
Read the worked answer
Segmented minimum transfer price (general rule: variable cost + opportunity cost per unit).
| Units | Capacity used | Opportunity cost | Minimum TP |
|---|---|---|---|
| First 4,000 | Idle capacity (40,000 − 36,000) | $0 | $38 |
| Next 4,000 | Displaces outside sales | $70 − $38 = $32 | $38 + $32 = $70 |
Average minimum = (4,000 × $38 + 4,000 × $70) / 8,000 = $432,000 / 8,000 = $54.00
Company view at a $60 transfer price:
- Company contribution with no transfer: Arden 36,000 × $32 = $1,152,000, less Boyd's outside purchase $480,000 = $672,000.
- With the transfer: company revenue $70 × 32,000 = $2,240,000; variable cost $38 × 40,000 = $1,520,000; contribution = $720,000.
- Company gain: $48,000. Check by block: idle 4,000 × ($60 − $38) = +$88,000; displacing 4,000 × ($60 − $70) = −$40,000; net +$48,000.
Arden's manager at $60: income = $592,000 + $88,000 − $40,000 = $640,000; ROI = $640,000 / $3,700,000 = 17.3%, up from 16.0%.
So both the company and the division gain - the manager's flat refusal at $70 is also against her own interest, because she is protecting the average, not the margin. The corporate controller's job is to make this visible with a segmented analysis rather than to impose a price.
3. State the general transfer-pricing rule and show how your answer changes if Arden's outside demand falls to 30,000 units.
Read the worked answer
General rule: minimum transfer price = variable (outlay) cost per unit + opportunity cost per unit of the transferring division. Maximum transfer price = the lower of the buying division's external purchase price and its own net realizable value contribution. A transfer is company-optimal only when minimum ≤ maximum.
If outside demand falls to 30,000 units: Arden has 10,000 idle units, so all 8,000 units for Boyd come from idle capacity and the opportunity cost is zero.
- Minimum TP = $38 per unit (anything below destroys company value).
- Maximum TP = $60 (Boyd's outside price). Any price in $38–$60 splits the gain.
- Company gain at $60 = 8,000 × ($60 − $38) = $176,000. At $38 the entire gain accrues to Boyd; at $60 it accrues to Arden.
What the exam is testing: a single transfer price applied to all units is a compromise. The $70 refusal and the naive "full cost + markup" answer ($52) are both wrong. Note also that if outside demand is soft, Arden must be careful that a low internal price does not leak into the external market through Boyd's own customers.