Relevant costs: only changes get a vote
Introduced| English | Meaning |
|---|---|
| relevant cost | relevant cost |
| sunk cost/sʌŋk kɒst/ | A cost already incurred that cannot be recovered. |
Only the numbers that CHANGE get a vote
- The special order lands at £3.60 against a £6.50 list. The sunk machine whispers "we've invested too much". The absorption cost says £4.10. Neither gets a vote.
- A relevant cost 相关成本 is future AND differential. Everything else is scenery.
The special order, gated
- 800 meals of idle capacity; offer £3.60. Relevant cost: variable £3.10 + £0.15 special packaging = £3.25 → contribution £0.35 × 800 = +£280, accept ✓.
- Two gates BEFORE the verdict: does idle capacity exist (yes — 4,020 planned in a 6,000 range), and will the price leak into normal channels (sold out-of-channel — no erosion)?
Offer 3.60, relevant cost 3.10 + 0.15. The total contribution on 800 meals?
Difficulty 2/5 · 140 coins + a small bonus on first completion today
$(3.60 - 3.25) \times 800 = £280$ - accept, subject to the two gates.
The +280 says accept. Which fact could reverse it?
Difficulty 1/5 · 100 coins + a small bonus on first completion today
Gate 2: erosion. If regular customers learn of 3.60, the order can cost far more than 280 in lost margin - that IS relevant.
Match each term to its test.
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Four terms, two tests - future? differs? - and one discipline.
Sunk costs never argue
- Sunk cost 沉没成本: already incurred, unchanged by the choice. The packaging machine's £9,000 is in every alternative — so it is in none of them.
- "We've spent too much to stop now" is the sunk-cost fallacy wearing a business suit. The question is always forward: what differs between the alternatives from here?
Does this number get a vote?
Classify each cost as relevant, sunk, or allocated-and-silent for the special-order decision.
Co-packer bids 4.40; avoidable internal cost 3.10 + 0.30 freed rent. The decision?
Difficulty 1/5 · 100 coins + a small bonus on first completion today
Only 3.40 truly disappears; the bid of 4.40 exceeds it. The absorption 4.10 mixes in allocated cost the choice never changes.
If the idle line could instead be sublet for 60 a month, the special order's true contribution becomes what, to the nearest pound?
Difficulty 2/5 · 140 coins + a small bonus on first completion today
The 60 sublet is the opportunity cost: $280 - 60 = £220$. Still positive - accept - but now honestly priced.
The 9,000 spent on the packaging machine should appear in the special-order analysis as a cost of 11.25 a meal for the 800 meals.
Difficulty 1/5 · 100 coins + a small bonus on first completion today
Sunk costs are constant across alternatives - excluded entirely. "We've spent too much to stop now" is the fallacy, not the analysis.
Outsourcing: what truly disappears?
- A co-packer bids £4.40 against the £4.10 absorption cost — looks like "buy". But only £3.10 of internal cost is avoidable, plus £0.30 of rent actually freed: £3.40 < £4.40 → keep making ✓.
- Every outsourcing bid is two questions: what truly disappears, and what could the freed space earn instead (the opportunity cost — zero is an assumption, not a law)?
Flour is scarce. Alpha: CM 2.60, uses 0.30 kg. Beta: CM 1.80, uses 0.20 kg. Which mix rule?
Difficulty 1/5 · 100 coins + a small bonus on first completion today
Rank by CM per unit of the BINDING constraint: $2.60/0.30 = 8.67$ vs $1.80/0.20 = 9.00$ - Beta wins the scarce kilo.
A loss-making meal line is considered for dropping. Which number MOST argues for keeping it?
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Drop the line and you lose its contribution while most of the allocated fixed cost stays - the classic keep-or-drop trap. Only freed (avoidable) fixed cost argues for dropping.
Product mix under a constraint
- Flour short: Alpha needs 0.30 kg (CM £2.60 → £8.67/kg), Beta 0.20 kg (CM £1.80 → £9.00/kg). Beta earns more per scarce kilo — bias the mix toward Beta ✓.
- Rank products by CM per unit of the BINDING constraint, not per unit of product. Constraints move; the ranking discipline travels.
Three decision slips
- Sunk costs arguing. They are constant across alternatives — excluded.
- Absorption unit cost as decision cost. £4.10 carries allocations the choice never changes.
- Forgetting opportunity cost of freed capacity. Zero is an assumption.
Recap
- Relevant = future + differential; sunk never, allocation rarely, opportunity always.
- Gates before verdict: capacity, price erosion.
- Rank by CM per binding constraint.