Problem 22-27 walks through the Slate company's Screen Division (SD) and Assembly Division (AD), testing the general transfer-pricing guideline when the supplying division has partial excess capacity. Problem 22-32 covers the UP and DOWN divisions of Baldenius, focusing on how a new external order at a lower price changes the weighted average external price and the discount rate at which the DOWN division breaks even. Together, these two problems cover the full range of exam-style transfer pricing calculations.
Difficulty: Intermediate | Prerequisites: General transfer-pricing guideline, contribution margin
Slate has two divisions: the Screen Division (SD) manufactures screens, and the Assembly Division (AD) uses those screens. Key figures:
SD's variable cost per screen: $65
SD's external selling price: $92 per screen
AD's total cost of purchasing from outside: $107 per screen (including $7 variable purchasing cost)
SD's marketing and distribution cost for external sales: $8 per screen
SD's total output: 20,000 screens
SD's excess capacity: 6,000 screens (30% of output), meaning 14,000 screens (70%) can be sold externally
\text{CM per screen} = \$92 - \$65 = \$27This is the profit SD earns on each screen sold externally, before marketing and distribution costs.
The AD manager will pay at most what it costs to buy from outside: $107 per screen. This is the ceiling for any negotiation.
The minimum TP depends on capacity:
First 6,000 units (excess capacity, 30% of output): opportunity cost is zero because SD has no outside buyer for these units. Minimum TP = $65 (variable cost only).
Remaining 14,000 units (can be sold externally, 70% of output): opportunity cost equals the contribution margin of $27 per screen. Minimum TP = $65 + $27 = $92.
From head office's perspective, all 20,000 screens should be transferred internally. Why:
It avoids the $7 per-screen variable purchasing cost AD incurs when buying externally.
It saves the $8 per-screen marketing and distribution cost SD incurs when selling externally.
Net saving per screen transferred (for the 14,000 that could go either way): $7 + $8 = $15.
The company as a whole is better off keeping the transaction internal.
If the two division managers negotiate, the price will land between the SD's minimum and the AD's maximum ($107).
For the 6,000 excess-capacity units: the range is $65 to $107. "Split the difference" gives ($65 + $107) / 2 = $86.
For the 14,000 externally sellable units: the range is $92 to $107. "Split the difference" gives ($92 + $107) / 2 = $99.50.
Any price within these ranges is acceptable to both divisions and optimal for Slate.
Difficulty: Intermediate-Advanced | Prerequisites: Contribution margin, weighted averages, market-price transfer pricing
The UP division currently produces 30,000 units. It sells 10,000 externally at $16 each and transfers 20,000 to the DOWN division at $16 each (market price). Key cost figures:
Variable manufacturing cost: $9 per unit
Fixed manufacturing costs: $60,000 total
Line | Calculation | Amount |
|---|---|---|
Sales to external customers | 10,000 x $16 | $160,000 |
Sales to DOWN division | 20,000 x $16 | $320,000 |
Total sales revenue | $480,000 | |
Less: variable manufacturing costs | 30,000 x $9 | ($270,000) |
Less: fixed manufacturing costs | ($60,000) | |
Operating income | $150,000 |
Jean Georges offers to buy 4,000 units at $12.50 each. UP has the capacity to fill this order.
Incremental contribution from the new order:
4{,}000 \times (\$12.50 - \$9.00) = 4{,}000 \times \$3.50 = \$14{,}000The new weighted average external price becomes:
\frac{(10{,}000 \times \$16) + (4{,}000 \times \$12.50)}{10{,}000 + 4{,}000} = \frac{\$160{,}000 + \$50{,}000}{14{,}000} = \$15Yes. The order adds $14,000 in contribution margin to UP and $14,000 in firm-wide profit. The variable cost of $9 is well below the $12.50 price, and the order uses otherwise-idle capacity.
If the transfer price to DOWN is based on the weighted average external price, accepting the Jean Georges order drops that price from $16 to $15. The question asks: at what discount rate d is UP indifferent between accepting and rejecting the order?
Without the order, DOWN pays $16, and UP's revenue from DOWN (net of a discount d) is:
20{,}000 \times \$16 \times (1 - d)With the order, the weighted average external price falls to $15, and UP's revenue from DOWN plus the incremental contribution is:
20{,}000 \times \$15 \times (1 - d) + \$14{,}000Setting these equal and solving:
20{,}000 \times \$16 \times (1 - d) = 20{,}000 \times \$15 \times (1 - d) + \$14{,}00020{,}000 \times (1 - d) \times (\$16 - \$15) = \$14{,}00020{,}000 \times (1 - d) = 14{,}0001 - d = 0.70 \quad \Rightarrow \quad d = 0.30At a discount of 30%, the gain from the Jean Georges order exactly offsets the reduction in revenue from DOWN. Below 30%, accepting is worthwhile; above 30%, the lost transfer revenue exceeds the new contribution.
Pattern 1: always identify the range first. In any transfer-pricing problem, pin down the supplying division's minimum (incremental cost + opportunity cost) and the buying division's maximum (outside purchase price). If minimum > maximum, the transfer should not happen.
Pattern 2: capacity drives opportunity cost. The single biggest variable in these problems is whether the supplying division has spare capacity. With spare capacity, opportunity cost is zero and the minimum drops to variable cost. At full capacity, opportunity cost equals the contribution margin forgone.
Pattern 3: company-wide vs. divisional perspective. Problems often ask you to evaluate from both angles. What is optimal for the company (transfer internally to avoid duplicated costs) may not happen voluntarily if the transfer price falls outside the negotiation range.
Pattern 4: new orders change weighted averages. When a division accepts a new external order at a different price, the weighted average external price shifts. If transfer prices are tied to that average, the downstream division is affected. This is the core of Problem 22-32.
Pattern 5: solve for the breakeven parameter. Problems may ask at what discount rate, volume, or price a manager is indifferent. Set the two scenarios equal and solve for the unknown, as in Part 4 of Problem 22-32.
Q: In Problem 22-27, why is the minimum transfer price different for the first 6,000 units vs. the remaining 14,000?
A: Because the first 6,000 units fall within SD's excess capacity, so there is no opportunity cost (no external sale is displaced). The remaining 14,000 units could be sold externally for a $27 contribution margin each, so the opportunity cost is $27, raising the minimum from $65 to $92.
Q: Why does Slate's management want all output transferred internally, even though the minimum TP for 14,000 units ($92) equals the external price?
A: Because internal transfer avoids $7 per screen in variable purchasing costs for AD and saves $8 per screen in marketing and distribution costs for SD. These savings total $15 per screen, which only materialise through internal transfer.
Q: In Problem 22-32, what is the incremental contribution from the Jean Georges order?
A: 4,000 units x ($12.50 - $9.00) = $14,000. The $12.50 price exceeds the $9 variable cost, so the order is profitable on an incremental basis.
Q: How does accepting the Jean Georges order affect the transfer price to DOWN?
A: The weighted average external price drops from $16 to $15, which reduces the market-based transfer price DOWN pays. This costs UP $1 per unit on 20,000 units = $20,000 in lost transfer revenue, partially offset by the $14,000 incremental contribution.
Q: At what discount rate is UP indifferent between accepting and rejecting the Jean Georges order?
A: d = 0.30 (30%). At this discount, the $14,000 gain from Jean Georges exactly offsets the revenue reduction on the DOWN transfer caused by the lower weighted average price.
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