Sunk is gone, allocated is not saved, forgone is a cost

The test

A cost or a revenue is relevant to a decision only if it passes two tests at once: it lies in the future, and it differs between the alternatives. Fail either test and the item is irrelevant — it will be the same whatever you choose, so it cannot help you choose. Everything in this module is that test applied line by line, and the exam’s traps are the lines that look relevant and fail one half of it.

Four words carry the vocabulary. A sunk cost has already been incurred and cannot be changed by any decision now — it fails the future test. A differential (or incremental) cost or revenue is the difference between alternatives — it is what survives the test. An opportunity cost is the benefit forgone by not taking the next-best alternative — it is not in any ledger, but it passes both tests and is counted once, as a cost of the option chosen. An allocated cost that continues whatever you decide fails the differs test.

Harbourline’s contract

Harbourline Logistics Inc., a Hamilton courier, is offered a six-month delivery contract worth 30,000. Its accountant lists what the contract would involve:

Item                                 Future?   Differs?   Relevant?   Amount
Contract revenue                     yes       yes        yes         +30,000
Extra driver wages                   yes       yes        yes         −18,000
Extra fuel                           yes       yes        yes          −4,000
Depreciation on the truck             yes       NO         no           (6,000)
Dispatcher’s salary                  yes       NO         no          (48,000)
Truck could be rented out instead    yes       yes        yes          −5,000
Net differential                                                       +3,000

The truck’s depreciation is a future charge, but Harbourline owns the truck already and will depreciate it whether or not it takes the contract — same under both alternatives, irrelevant. The dispatcher is paid 48,000 either way. The rental income is the subtle line: if the truck does the contract it cannot be rented out, so the 5,000 Harbourline would have received is a cost of accepting — the opportunity cost. Counted once, on the accept side. Net differential +3,000 → accept.

The sunk-cost trap: replacing the sorter

Harbourline bought a parcel sorter two years ago for 80,000; its carrying amount is 48,000 and it could be sold today for 15,000. A new sorter costs 70,000 and would save 20,000 a year in labour for four years. The operations manager refuses: “we cannot afford to book a 33,000 loss on the old machine.”

Run the test. The 80,000 was paid two years ago — sunk. The 48,000 carrying amount is the part of that payment the books have not yet expensed — still the same money, still sunk. The loss on disposal of 33,000 (48,000 − 15,000) is the past purchase price catching up with the books; it is a bookkeeping consequence, not a cost of the decision. What passes the test: the 15,000 proceeds (future, and received only if the old machine is sold), the 70,000 cost of the new machine, and 20,000 × 4 = 80,000 of savings.

$$\text{Net differential}=80,000+15,000-70,000=+25,000\text{(undiscounted)}$$

Replace. The manager who will not book the loss is paying 25,000 to avoid a journal entry. The one thing to keep in view: a four-year stream compared with a payment today is the comparison Module 13 discounts; the undiscounted +25,000 is a first answer, not the final one.

The process

Every decision in this module follows the same six steps: define the alternatives · list every revenue and cost each involves · strike the ones that are past or the same under both · compute the differential · weigh the qualitative factors · decide. The striking step is where the marks are.

The other shapes you will recognise

The same test drives decisions this course does not work through. A special order asks whether a one-off sale below the normal price still covers its incremental cost (fixed overhead already covered is irrelevant). Make-or-buy asks whether a part should be produced in-house or purchased, comparing the avoidable cost of making it with the purchase price. Sell-or-process-further asks whether a product should be sold as it stands or processed further, comparing the added revenue with the added cost — the cost incurred up to the split-off point is sunk. Know the shapes by name; only keep/drop, location and relocation are examined in AFM 182.