FMGT-2294 Chapter 12 — Notes from the Textbook

All credit for this text goes to...

Garrison, R. H., Webb, A., & Libby, T. (2024). Managerial Accounting (13th Canadian ed.). McGraw-Hill Ryerson.

Study Session Meta (delete when complete)

LO Coverage & Mastery

LO	Title	Status	Mastery	Notes Section
1	Distinguish between relevant and irrelevant costs in decision making	✅ Mastered	Explain ✅ (one-sentence definition with both conditions). Apply ✅ (restaurant wedding catering — 5 costs classified correctly with conditional reasoning on rent and florals).	§LO1
2	Prepare analyses for various decision situations	✅ Mastered	Explain ✅ (all 4 types described in own words). Apply ✅: Drop-a-line (Charter Sports trampolines — all classifications correct, segment margin recast recognized). Make-or-buy (Finch Sparks — correctly included 60% avoidable fixed OH, $19.10vs$17 → buy). Special order (Finch foreign distributor — correctly excluded fixed OH as already committed, $17.50flooridentified).Sell-or-process(FinchAlpha—correctlyignoredjointcosts,$7K gain from processing).	§LO2
3	Determine the most profitable use of a constrained resource	✅ Mastered	Apply ✅: Abel Company (textbook foundational exercise 12-11 through 12-15) — computed kg/unit, CM/unit, profitability index, ranked correctly (Regular $10/kg>Deluxe$5.10/kg), allocated 80K kg respecting demand ceilings (30K Regular + 4K Deluxe), total CM $702K. Value of relaxing constraint: correct reasoning chain (find unfilled product → its profitability index = max additional price per unit of constraint).	§LO3
4–7	Appendix 12A (pricing)	❌ SKIPPED	Kai has never been tested on appendices; deliberately out of scope for exam prep	—

Vocabulary Tracker

Term	Tier	Location
Relevant cost	T2	§LO1 Vocab
Avoidable cost	T2	§LO1 Vocab
Differential cost	T2	§LO1 Vocab
Incremental cost	T1	§LO1 Glossary
Sunk cost	T2	§LO1 Vocab
Allocated common cost	T2	§LO1 Vocab
Unitized fixed cost	T2	§LO1 Vocab
Opportunity cost	T2	§LO1 Vocab
Book value (as a sunk-cost disguise)	T2	§LO1 Vocab

Current Position

LO: Ch12 COMPLETE. All 3 LOs ✅ Mastered. All 3 mastery gaps resolved. Ready for Ch10–11 refresher. Last Micro-Test: LO3 Abel Company constrained resource (textbook 12-11 through 12-15). Correctly: computed kg/unit (5 and 2), CM/unit ($25.50and$20), profitability index ($5.10/kgand$10/kg), ranked Regular > Deluxe, allocated 80K kg (30K Regular using 60K kg + 4K Deluxe using 20K kg), total CM $702K. Relaxing constraint: correct reasoning chain — find unfilled product → profitability index = max additional price per unit of constraint. Last Lens Used: Brute-force derivation applied to textbook problem

Parking Lot (Remaining work)

• Ch10–11–12 refresher — exam is in ~2 days. Kai wants a cross-chapter refresher covering all three chapters to lock in understanding and identify remaining gaps. This is the next session’s priority.
• Confirm Ovation homework Q4 and Q5 status.
• All Ch12 mastery checks — COMPLETE. LO1 ✅, LO2 ✅, LO3 ✅.
• All Ch12 mastery gaps — RESOLVED. Book value ✅, same-cost-different-relevance ✅, scope-mismatch ✅.
• LO3 teach — COMPLETE.
• Appendix 12A pricing — DELIBERATELY SKIPPED.

Mastery Gaps (Review Before Exam)

• ✅ Relevant cost definition: RESOLVED. Kai stated both conditions unprompted (“differs between alternatives AND future-oriented”) and applied correctly across 5+ scenarios.
• ✅ Over-including costs as relevant: RESOLVED. Demonstrated correct classification across Charter Sports (4 fixed costs), Finch make-or-buy (4 costs including partial fixed OH), Finch special order (correctly excluded fixed OH that was relevant in make-or-buy but not here), restaurant wedding (5 costs with conditional reasoning). Defence (“keep: ___ / drop: ___”) is now automatic.
• 🔶 Book value intuition: Seeded and reinforced via multiple callbacks. “Books don’t buy, markets buy.” Three-strike test taught. Not yet tested cold under exam pressure in a problem that hands Kai a book value and asks “is this relevant?” — but the concept has been addressed from multiple angles. Exam defence: when book value appears, run three-strike test (past purchase? no salvage? no alternative use? → sunk).
• 🔶 Same cost, different relevance across decisions: Surfaced during Finch mastery checks. Fixed OH was relevant in make-or-buy ($3.60of$6.00 avoidable by stopping production) but irrelevant in special order (already committed, adding production doesn’t change it). Kai initially used the make-or-buy figure, then self-corrected after one probe. Exam defence: before including ANY fixed cost, ask “what is the decision? Am I stopping production (costs might leave) or adding to existing production (costs are already committed)?”
• 🔶 Scope-mismatch (V2 pattern): Tested via Charter Sports drop-a-line. Kai correctly classified allocated factory overhead as irrelevant and correctly recast into segment margin format when prompted. Concept appears understood but hasn’t been tested with a deliberately misleading segment report under time pressure.

Session Log

Date	LOs Covered	Mastery Results	Key Clarifications
2026-04-11 (1st pass)	LO1 (partial)	🔄 In Progress	ONE RULE locked; sunk costs locked; allocated common costs locked; unitized-average trap concept landed but one-sentence compression not yet clean; book value probe incomplete. Session halted for context window reset.
2026-04-11 (2nd pass — fresh restart)	LO1 → 🔶 Understood; entering LO2	LO1 one-sentence definition locked via bus-vs-car self-retrieval. Trap list: 1 of 5 retrieved unaided (unitized, stated cleanly as “making a fixed cost look variable”); remaining 4 taught. Book value probe: Kai pushed back hard on “book value is irrelevant” framing — surfaced his actual mental model that book value is a market-value signal. Reframe arrived at: depreciation schedules run on autopilot regardless of market; market value (dealer trade-in offer) is the real number. “Books don’t buy, markets buy.” Kai explicitly parked further drilling to revisit from LO2 scenarios. Entering LO2 drop-a-line next.
2026-04-11 (2nd pass continued)	LO2 drop-a-line 🔶 + make-or-buy 🔄 (taught, not drilled)	Drop-a-line taught via AFM Electronics worked example. Ch11→Ch12 bridge locked: “drop a segment only if its segment margin is negative.” Virtual Learning Instant Quiz 12-2 micro-test: Kai computed $28K real contribution via Formulation B (revenue − avoidable costs), correctly recommended keep. Mid-drill Kai clarified that his method WAS correct and Claude had lost the thread by forcing CM-lost-vs-fixed-saved framing where the data didn’t separate cleanly — acknowledged and owned. Process feedback from Kai (twice in session): “you’re ascribing understanding rather than probing” — Claude drifting into lecture mode instead of probing Kai’s actual mental model before correcting. Defence going forward: before correcting anything Kai says, first restate what Kai said and confirm, THEN correct only if there’s actually an error. Make-or-buy taught via OSN Cycles including opportunity cost twist + book value callback (sunk depreciation on special equipment, three-strike test). Cascadia Foods cold micro-test set up but not executed — Kai paused for mid-session synthesis.
2026-04-11 (2nd pass, LO2 finished)	LO2 🔶 complete — all 4 types; Appendix 12A skipped	Cascadia make-or-buy classification: Kai correctly classified all 6 cost lines. Special order (OSN Case A + Case B): Counter-intuitive result locked. Discrimination question (recurring wholesaler): correctly identified as NOT special order. Sell-or-process-further (St. Thomas Wool + lumber mill): All classifications correct. Kai flagged $5K per-log imprecision. LO2 marked 🔶 Understood. Appendix 12A deliberately skipped.
2026-04-11 (2nd pass, mastery checks)	LO1 ✅, LO2 ✅, LO3 pending	LO1: definition + restaurant wedding (5 costs, conditional reasoning). LO2: Charter Sports + Finch make-or-buy ($19.10vs$17) + Finch special order ($17.50vs$18, self-corrected fixed OH) + Finch sell-or-process ($45Kvs$52K). Key insight: same cost, different relevance. Kai feedback: skip traps, focus on procedures.
2026-04-12 (gaps + LO3 check)	All 3 gaps ✅, LO3 ✅ — Ch12 COMPLETE	Gap 1 (book value): Rivera Transport, 5 numbers classified instantly. Gap 2 (same cost, different relevance): Rivera driver salary, correctly irrelevant in keep-vs-replace, relevant in shutdown. Gap 3 (scope-mismatch): Greenfield Electronics, immediately asked for segment margin before accepting CFO’s recommendation. LO3: Abel Company (textbook 12-11 to 12-15) — kg/unit (5, 2), CM/unit ($25.50,$20), profitability index ($5.10/kg,$10/kg), ranked Regular > Deluxe, allocated 80K kg (30K Regular + 4K Deluxe), total CM $702K. Relaxing constraint: correct reasoning chain. All 3 LOs mastered. All 3 gaps resolved. Next: Ch10–11–12 refresher.

Note on Organization — TEMPORARY (pre-refactor state)

This note is currently in LO-linear order matching Garrison’s LO structure. The teaching-flow refactor happens AFTER all LOs are complete, not during. Until then, sections map 1:1 to the textbook LOs. This is the opposite of the Ch10/Ch11 final form — those were refactored into teaching flow at the end of their respective study sessions. Expect this note to be similarly restructured once all LOs have been taught.

Section	What It Covers	Textbook LOs
§LO1	The two-condition test: differs between alternatives AND is a future cost. Sunk costs, allocated common costs, unitized averages, book value.	LO1
§LO2	Drop-a-line, special order, make-or-buy, sell-or-process-further, joint products	LO2
§LO3	Constrained resource analysis — ranking by contribution margin per unit of the constraint	LO3
§LO4-7	Appendix 12A: absorption/variable pricing, price sensitivity, value-based pricing, target costing	LO4-7

Pending restructure (expected teaching-flow shape after Phase F):

• # 1. The Foundation — One Rule for Every Decision (LO1 + whole-company scope discipline from LO2)
• # 2. The Decision Types — Same Rule, Different Costumes (LO2)
• # 3. Constrained Resources — Ranking by the Real Bottleneck (LO3)
• # 4. Pricing the Output (App 12A / LO4–7)

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LO 1. Distinguish between relevant and irrelevant costs in decision making

What is a relevant cost?

A relevant cost is a cost that (a) differs between the alternatives under consideration AND (b) is a future cost that has not yet been incurred. Both conditions must be true. Fail either one and the cost is irrelevant — it cannot influence the decision and must be thrown out of the analysis. (Garrison line 55, 80)

Garrison introduces the concept by pointing out that the same cost can be relevant in one decision and irrelevant in another. There is no such thing as a “relevant cost” in the abstract — relevance is always defined with respect to a specific decision between specific alternatives.

The textbook notes that the terms “avoidable cost,” “differential cost,” “incremental cost,” and “relevant cost” are often used interchangeably (Garrison line 78). They all point at the same idea: the costs that actually matter when choosing between courses of action.

The two-condition test gives you the mechanical procedure. For every cost the problem presents, ask:

1. Does this cost differ between the alternatives? If yes → keep investigating. If no → throw it out.
2. Is this cost in the future (not yet incurred)? If yes → relevant. If no → it’s sunk, throw it out.

Both conditions must pass. A cost that differs but is already sunk (rare but possible) is still irrelevant. A cost that is in the future but is identical in both alternatives is also irrelevant. Only the intersection counts.

Why does the two-condition test work?

The test is not arbitrary. It flows directly from what a decision actually IS: a choice between futures.

Imagine you face two alternatives, A and B. Picking A leads to Future A; picking B leads to Future B. The only thing that matters in deciding between them is how the two futures differ. Any cost that exists identically in both futures cannot influence that difference — it’s present no matter what you choose, so it has zero causal power over the outcome.

• A cost that doesn’t differ between alternatives is identical in both futures → zero influence → irrelevant.
• A cost that is already incurred (sunk) is identical in all possible futures by definition — you already paid it, you can’t un-pay it by making a different decision today → zero influence → irrelevant.

The two-condition test is the definition of what “matters to a decision,” not a convenience rule.

The label on a cost does not determine its relevance

Words like “depreciation,” “overhead,” “fixed cost,” and “allocation” do NOT tell you whether a cost is relevant. Only the two-condition test does. Run the test on what the cost actually does (does the cash flow change between alternatives?), not on what the cost is called.

Example from the Cynthia Moncton case in Garrison: “depreciation on the car” sounds like a fixed cost that should be thrown out. But if the depreciation is usage-based (wear from extra kilometres driven), it only happens if you drive — so it DOES differ between “drive” and “take the train” → it’s relevant. The word “depreciation” was misleading; the underlying cost behaviour is what counts.

Why do sunk costs disappear from the analysis?

A sunk cost is a cost that has already been incurred and cannot be changed by any decision made now or in the future. Sunk costs are irrelevant to any decision because they exist identically in every possible future, so they cannot tilt the choice.

Examples of sunk costs:

• Rent already paid
• A machine purchased 3 years ago (purchase price is sunk, regardless of today’s book value)
• R&D spent last quarter developing a prototype
• Manufacturing costs already spent making defective inventory sitting in the warehouse

The airtight argument for why sunk costs are irrelevant: consider any decision between Alternative A and Alternative B. In Future A, the sunk cost has already been paid. In Future B, the sunk cost has also already been paid. The sunk cost is present, identically, in every branch of the decision tree. No choice made today can unspend that money. Therefore, the sunk cost cannot influence which branch is better — it’s mathematically incapable of tilting the comparison.

The defective-speakers example (from our session, 2026-04-11)

Swift Manufacturing has 1,200 defective speakers in a warehouse. The speakers cost $26eachtomanufacture\ast \ast .Aliquidatoroffers\ast \ast$11 per unit. The variable selling expense for defective units is **$2perunit\ast \ast (lowerthanthenormal$5 because defective units skip the regular distributor channel). Should Swift accept?

The trap: “$11islessthan$26, so we’d lose $15/unit. Reject.”

Why the trap is wrong: The $26/unitwasspentBEFOREthedecision.ItexistswhetherSwiftsellstheunitsfor$11, burns them, or lets them rot. The $26 is identical in both the “accept” and “reject” futures. Sunk. Irrelevant.

The actual analysis: Only the $2/unitsellingcostisafuturecostthatdiffersbetweenalternatives.Acceptthedealwheneverthepriceexceedstheincrementalsellingcost.Since$11 > $2,accept.Minimumbreak-evenprice:$2/unit.

Why do allocated common costs disappear too?

An allocated common cost is a single real expense that the accounting system slices up and distributes across multiple products, departments, or segments using an allocation formula. The slices are not separate costs — they are labels on portions of the same single real expense. At the whole-company level, the real expense does not change when the allocation formula changes.

This is the second-most-common trap after sunk cost confusion. When an accounting report shows “Product X is absorbing $40,000ofCEOsalary,"theinstinctistothink"droppingProductXwillsave$40,000.” That instinct is wrong. Dropping Product X does not fire the CEO. The $400,000CEOsalarycontinues.The$40,000 label simply gets reallocated onto the remaining products on the accounting report.

Garrison confirms this directly (line 274): “Other costs may be allocated common costs that will not differ in total regardless of whether the product line is dropped or retained.”

The key phrase is “will not differ in total” — at the total-company level, the dollars paid to the vendor don’t change. Only the slicing does. And slicing doesn’t count toward the ONE RULE.

Scope matters — the company-level lens

This is where a subtle trap hides. The Rico 6-item drill (session, 2026-04-11) showed that allocated common costs look like they differ at the segment level, because dropping a segment causes the allocation to move. But the decision is made at the company level, not the segment level. At the company level, the total cost is unchanged.

Garrison uses the phrase “the company as a whole” explicitly when setting up drop-a-line analysis (lines 266, 317, 949). That’s the correct scope for any relevant-cost analysis: the whole company, because the decision-maker (management) is choosing between two whole-company futures.

The defence: when applying the ONE RULE, always zoom to the whole-company total. Ask: “At the company level, does total cash paid to this party actually change between the two alternatives?” If no → throw it out, regardless of what the segment report shows.

Confusion Flag — Scope-mismatch (V2 Input Error)

What happened (2026-04-11): During LO1 teaching on allocated common costs, the question came up: “if we drop a product line, the allocated $40,000 CEO salary gets redistributed onto other products, making them look more expensive on the segment report. Doesn’t that matter?” Answered with “yes, there’s a real ripple effect that should factor into the analysis.”

The broken input: Applied the relevance test at the segment reporting level instead of the company level. At the segment level, the $40,000labeldoesmove.Atthecompanylevel,the$400,000 total does not. The mistake was treating segment-report movement as a real cash change when it was only a relabeling.

What landed: The “niggling feeling” was tracking something real — allocated costs DO shift on the segment report. But they shift without changing the company’s total cash outflow. The decision is about total company cash, not about how the total gets sliced on an internal report. Slicing ≠ spending.

Defence: Before marking any cost relevant, zoom to the whole-company level and ask: “Does the company’s total cash paid to this party change between the two alternatives?” If the total doesn’t change, the cost is irrelevant — regardless of how it’s allocated across segments on the internal report.

Pattern match: Same V1-family failure mode as Ch10 (fixed-vs-variable error). Framework was correct, but the INPUT — the level of analysis — was wrong. V1 was “wrong cost classification”; V2 is “wrong scope.” Both are input errors into an otherwise-valid framework. Defence rule for both: check the INPUT before running the framework.

Validated against Garrison: Lines 266 (“profits in the company as a whole”), 274 (“will not differ in total”), 317 (“effects on the company as a whole”), 949 (“Decrease in operating income for the company as a whole — $(33,000)”). The textbook explicitly frames drop-a-line analysis at the whole-company level.

Status: Concept understood during session. NOT drilled under pressure yet. Expect this to resurface when we hit LO2 formally.

When does a per-unit cost lie to you?

A unitized fixed cost (also called an "averaged fixed cost") is a fixed cost that has been divided by a planned activity level to produce a per-unit figure. The per-unit figure is only valid at that exact activity level. At any other volume, it lies — because the fixed portion doesn't actually scale with activity, even though the per-unit form makes it look like it does.

This is the third major trap. Garrison introduces it through the Cynthia Moncton example (line 121): “$0.565 per kilometre to operate.” The number feels precise and usable, but it’s actually a blended figure that hides a fixed cost inside it.

The mechanical example (from the Cynthia case and our courier drill)

Suppose a delivery company reports its cost as $0.80 per parcel delivered, based on 200,000 planned parcels/year:

• Driver wages (variable): $0.35/parcel — actually scales with parcels
• Fuel (variable): $0.15/parcel — actually scales with parcels
• **Truck lease + insurance (fixed $60,000/year,allocatedover200,000parcels):\ast \ast$0.30/parcel — does NOT actually scale; this is $60,000 ÷ 200,000 expressed per-parcel

Now management considers adding 20,000 extra parcels/year. The trap: multiply $0.80\times 20,000=$16,000 extra cost. Wrong.

The actual extra cost: only the variable components ($0.35+$0.15 = $0.50/parcel)scalewithvolume.Thelease+insurancedoes{n}^{\prime }tchangebecausethecompanyisinsidetherelevantrange(nonewtruckneeded).Realextracost:$0.50 × 20,000 = **$10,000\ast \ast .Thetrapansweris$6,000 too high.

Any time a problem presents a cost as "$X per unit of activity," unpack it before using it

Ask: “Is this a pure variable cost, or does it contain a fixed-cost slice that was divided by some planned activity level?” If it’s the latter, the per-unit figure is only valid at that exact volume. For any relevant-cost analysis, break the unitized average back into its variable and fixed components, and treat each piece independently against the ONE RULE.

Where the trap bites hardest

The trap bites hardest when the quoted price sits between the true variable cost and the unitized average. In that zone, the unitized figure tells you to reject a deal that’s actually profitable — flipping a good decision into a bad one.

Example: same courier scenario, but the customer offers only $0.70/parcel.

• **Using $0.80unitized:\ast \ast$0.70 < $0.80\to negative$0.10/parcel → REJECT.
• **Using $0.50actualrelevantcost:\ast \ast$0.70 > $0.50\to +$0.20/parcel × 20,000 = $4,000/year real contribution walked away from.

Where the quoted price is above the unitized average (e.g., $0.85),thedecisiondoes{n}^{\prime }tflip—thecompanyacceptseitherway—butthereportedprofitisbadlywrong(thinks$0.05/parcel when it’s actually $0.35/parcel, a 7x understatement). Same trap, milder symptom. Both versions compromise the quality of managerial thinking.

Why the unitized-average trap is so effective

Three reasons:

1. Per-unit numbers feel authoritative. “$0.80/parcel” looks like a scientific measurement but is actually the output of an arbitrary division (total ÷ planned volume).
2. The fixed component is invisible. Once a cost is collapsed into per-unit form, you can’t tell by looking at it how much is variable and how much is fixed. You have to unpack the original components.
3. Multiplying feels like math. “$0.80\times 20,000=$16,000” is an easy computation, so the mind reaches for it. The hard part is recognising you shouldn’t do the multiplication in the first place.

Is book value ever relevant?

Book value is never relevant to a Ch12 decision. It is a historical accounting calculation — original cost minus accumulated depreciation running on a pre-chosen depreciation schedule. It does not respond to market conditions, physical wear, or any information generated after the schedule was set. No decision made today can change it. It fails the second condition of the ONE RULE (must be a future cash flow).

What IS relevant about an asset: its market value — what a real buyer would pay for it today. When a problem gives you a trade-in offer, a salvage estimate, or a liquidation quote, those are market-value data points and they enter the analysis.

Why book value feels relevant (and why that instinct is wrong)

The instinct “book value is a reasonable estimate of what the asset is worth” is a common starting point, and it’s worth taking seriously before dismissing it. The reasoning looks like: “depreciation tracks the asset’s decline in value, so the book value today is a running estimate of the current value.” If that were true, book value would be a legitimate input to decisions.

It isn’t true. Depreciation is a policy choice made in advance, not a measurement of current value. Companies pick a schedule (straight-line, declining balance, units-of-production, double-declining for tech) at the asset’s purchase date based on a mix of factors that have nothing to do with tracking market value:

• Simplicity and ease of bookkeeping
• Tax strategy (CCA in Canada often accelerates depreciation for tax deductions)
• Financial reporting consistency and GAAP compliance
• Rough average expected life of the asset class, NOT this specific asset

Once the schedule is locked, it runs on autopilot regardless of what happens to the asset in the real world:

• If the asset gets damaged → book value doesn’t drop (unless impairment is explicitly recorded, which is rare and lagging)
• If the market for used versions of the asset crashes → book value unchanged
• If the asset is maintained beautifully and still runs great → book value still ticks down on schedule
• If the asset is used twice as hard as expected → book value unchanged (you just picked the wrong schedule, but the schedule doesn’t self-correct)

Book value is not information about the asset. It’s information about a depreciation policy chosen years ago.

The reframe that dissolves the confusion

Books don't buy. Markets buy.

If the books say the truck is worth $6,000andarealdealeroffers$3,000 cash for it today, the dealer is right and the books are wrong. The dealer is a professional used-truck buyer making a real offer with real money. The books are the output of a formula chosen 5 years ago. When they disagree — and they almost always disagree — the market is the real number.

The accountant’s $6,000 figure isn’t “the truck’s current value as estimated by the accounting system.” It’s the residual of a mechanical calculation: original cost, minus straight-line (or declining-balance) depreciation, tick tick tick for five years. There’s no market input anywhere in that calculation.

The “I don’t want to book a loss” trap

A second instinct surfaces when book value and market value diverge: “if I sell for less than book value, I’m taking a loss — which is bad, so I should avoid the sale.” This is the most expensive version of the trap because it can cause managers to refuse real cash offers to preserve an accounting appearance.

The loss already happened. It happened gradually over the years as the asset wore out faster than the depreciation schedule assumed. The sale just reveals the loss — the accounting system catches up to reality. Refusing to sell doesn’t prevent the loss; it just keeps the loss hidden in the book value for a while longer, until someday when you scrap the asset and the loss gets recorded then instead.

The cash test: If the dealer offers $3,000cashforthetruck,andyourefusebecause"Ido{n}^{\prime }twanttobooka$3,000 loss against a $6,000bookvalue,"youareliterallyburning$3,000 of real cash to avoid a journal entry. The journal entry is a label. The cash is real.

Alternatively, consider taking the $3,000:

• Alternative A (sell): cash +$3,000,truckgone.Booksshow"lossonsale$3,000.”
• Alternative B (keep): cash $0, truck retained. Books show nothing.

In Alternative B, you still have a truck that a real buyer values at $3,000—soyourrealwealthisthesame($3,000 cash vs. $3,000 truck). You haven’t avoided the loss. You’ve just delayed recording it.

What the “loss” IS useful for (different question, different chapter)

The $3,000 “loss on sale” is meaningful managerial information — but it answers a different question than “which alternative maximizes cash.”

Question	Does book value matter?
Ch12: Which alternative maximizes cash going forward?	No. Sunk.
Should I review my depreciation policy? Was I being too optimistic?	Yes. The gap between book value and market value IS the signal.
What’s my equity position for a loan application?	Yes. Banks use book value.
What’s my tax basis on disposal?	Yes. Gain/loss affects taxes. (Ch13 brings taxes in.)
What did this asset cost me historically?	Yes. Running record of spent minus recovered.

Ch12 answers exactly one row of that table — the first one. Book value is legitimate information, just not for THIS question. Garrison isn’t saying book value is worthless — Garrison is saying it doesn’t belong in a differential cash flow analysis.

Applying the rule

When a problem mentions a “book value,” “net book value,” or “carrying value,” immediately classify it as sunk. Then scan the problem for any market-value data point — a trade-in offer, a salvage estimate, a liquidation quote, a dealer bid. That’s the number that enters the analysis on the “dispose” side of the decision.

If no market-value number is given, the asset has no relevant value in the decision at all — the problem has essentially told you to treat the asset as fully sunk.

Session Note (2026-04-11, 2nd pass)

Kai pushed back hard on this concept because his intuition was that book value signals market value. The reframe arrived at — “depreciation runs on autopilot, market value is real, books don’t buy” — is seeded but not locked under pressure. Expect this to re-surface in LO2 make-or-buy (sunk depreciation on equipment), sell-or-process-further, and equipment-replacement scenarios. Each scenario will force the concept from a new angle. Don’t drill in isolation — let the application exercises do the work.

How do you build a relevant-cost table?

How to: Relevant-cost table built for a two-alternative decision

Use when: Given two courses of action and asked to determine which is financially better. The problem will usually present a mixed bag of costs — variable, fixed, allocated, per-unit, sunk — and expect you to filter.

Given: Identify these from the problem before starting:

• The two alternatives, stated as concrete choices (e.g., “make in-house” vs “buy from supplier”)
• Every cost and revenue line item the problem presents
• The activity level for each alternative (important for unpacking unitized averages)

Step	Result	Formula/Action
1	Whole-company scope confirmed	Ask: “What level is this decision being made at?” Default to company-wide. Segment-level costs that get reshuffled don’t count.
2	Unpacked per-unit figures	For every “$X per unit” cost, ask: “Is this pure variable, or does it contain a fixed slice?” If fixed slice exists, split into variable-per-unit and total-fixed components.
3	Sunk costs identified and removed	For each cost, ask: “Has this already been incurred?” If yes → sunk → throw out. Book value is sunk. Past R&D is sunk. Manufacturing cost of existing inventory is sunk.
4	Allocated common costs identified and removed	For each cost, ask: “Is this a slice of a bigger total that stays the same at the company level regardless of the decision?” If yes → throw out.
5	Two-column table built	For each remaining cost, write “Keep: ___" and "Drop/Alt B: ___” with literal numbers. If the two columns match, throw out. If they differ, keep in.
6	Net difference computed	Sum each column. The alternative with the better net is the winner. Magnitude of difference = value of picking correctly.

Sanity checks:

• Did I run the out-loud “keep: ___, drop: ___” check on every line item before marking it relevant?
• Did I zoom to the whole-company level before applying the differential test?
• Did I unpack every per-unit cost into variable + fixed before using it?
• Did I remove every cost that has already been incurred?
• Does my final table have the shortest possible set of line items? (If there are more than a handful of rows, I’m probably still carrying phantoms.)

Final answer looks like: A small two-column table (often fewer than 5 rows), a net difference, and a one-sentence recommendation stating which alternative is financially better and by how much.

Watch for: The table is always shorter than you think. When in doubt, throw out.

Why the table gets bloated trusting the label on a cost instead of running the two-condition test on the behaviour. Students see "depreciation" or "overhead" or "per-unit cost" and either include it automatically (because it "sounds relevant") or exclude it automatically (because it "sounds fixed"). Neither reaction is the ONE RULE. The ONE RULE ignores labels and looks at cash behaviour.

Bloated relevant-cost tables always come from the same root mistake:

The second most common source of bloat is scope error: including costs that shift at the segment level but stay constant at the company level. Always apply the test at the decision-maker’s scope.

Key Vocabulary (LO1)

Relevant Cost

Definition: A cost that differs between alternatives AND is a future cost that has not yet been incurred. Both conditions must be true. Relevant costs are the only costs that can influence a decision. Example: A courier company considers adding 20,000 parcels/year to its existing volume. Driver wages at $0.35/parcelandfuelat$0.15/parcel are relevant — they only exist if the new contract is taken. Truck lease at $60,000/year is NOT relevant — it’s paid regardless. Trap: The label on a cost (“depreciation,” “overhead,” “fixed cost”) does not determine relevance. Only the two-condition test does. Connects to: Ceteris Paribus — relevant cost analysis is definitionally ceteris paribus. Everything that doesn’t change is held constant; only the differences enter the analysis.

Avoidable Cost

Definition: A cost that can be eliminated (in whole or in part) by choosing one alternative over another. Avoidable costs are the same thing as relevant costs — the two terms are used interchangeably in Garrison (line 78). Example: If a company drops a product line and lays off the line-specific supervisor, the supervisor’s salary is an avoidable cost. If the supervisor is reassigned to another line instead, the salary is NOT avoidable — the company still pays it. Trap: “Avoidable” means “eliminable by the decision,” not “eliminable in theory.” A cost that could theoretically be cut but isn’t affected by this specific decision is still unavoidable for this analysis. Connects to: Garrison line 78 — “the terms avoidable cost, differential cost, incremental cost, and relevant cost are often used interchangeably.”

Differential Cost

Definition: The difference in cost between two alternatives. Same concept as relevant cost, stated from the perspective of comparing rather than filtering. Differential cost analysis focuses on what changes; relevant cost analysis focuses on what to include. Example: Alternative A costs $100,000intotal.AlternativeBcosts$110,000 in total. The differential cost is $10,000, with B being more expensive. Trap: Differential cost CAN be computed using the full-cost approach (list everything, sum it, subtract), but Garrison recommends filtering first — combining irrelevant with relevant data invites errors (line 215). Connects to: Ch2 introduction to differential costs — the foundation for Ch12’s entire framework.

Sunk Cost

Definition: A cost that has already been incurred and cannot be changed by any decision made now or in the future. Sunk costs are always irrelevant because they exist identically in every possible future. Example: A company spent $30,000fiveyearsagoonatruck.Toda{y}^{\prime }sdecisiontorepairorreplacethattruckcannotun-paythe$30,000. The $30,000 is sunk and irrelevant. Trap: Book value is a sunk cost in disguise. It looks like a real number because it’s on the balance sheet, but it’s original cost minus accumulated depreciation — a historical accounting artifact, not a future cash flow. Connects to: Second condition of the ONE RULE (“must be a future cost”). Sunk costs fail this condition by definition.

Allocated Common Cost

Definition: A single real expense that has been sliced up by an accounting formula and distributed across multiple products, departments, or segments. The slices are labels, not separate costs. At the whole-company level, the total does not change when the allocation formula changes. Example: A $400,000CEOsalaryisallocated$40,000 each to 10 product lines. Dropping one line does not fire the CEO. The $400,000stillgetspaid;the$40,000 label just gets reallocated onto the remaining 9 lines. Trap: At the segment-report level, allocated common costs look like they change (they shift between segments). At the whole-company level, they don’t. Scope matters — apply the ONE RULE at the decision-maker’s scope. Connects to: Segment margin analysis (Ch6/Ch11). Segment margin is revenue minus variable costs minus traceable fixed costs only — it deliberately excludes allocated common costs for exactly this reason.

Unitized Fixed Cost (Averaged Fixed Cost)

Definition: A fixed cost that has been divided by a planned activity level and expressed as a per-unit figure. The per-unit form creates the illusion that the cost scales with activity. It doesn’t — it’s still fixed. The per-unit figure is only valid at the exact activity level used in the denominator. Example: $60,000/yeartrucklease÷200,000plannedparcels=$0.30/parcel. This is NOT a variable cost of $0.30perparcel.Ifthecompanydelivers220,000parcels,theleaseisstill$60,000 — and the per-parcel figure drops to $\mathrm{0.272.}The$0.30 was only true at exactly 200,000 parcels. Trap: Multiplying a unitized average across a new activity level. “If we add 20,000 parcels at $0.80each,costgoesupby$16,000.” Wrong — the fixed slice inside the $0.80does{n}^{\prime }tscale.Theactualincreaseisonlythevariableportion($0.50 × 20,000 = $10,000). Connects to: Cost behaviour from Ch2–3 (fixed vs. variable). The unitized trap is a special case of failing to classify costs by behaviour before applying the ONE RULE.

Opportunity Cost

Definition: The cash value of the next-best alternative use of a resource that is given up by choosing one course of action over another. Opportunity costs are relevant whenever an alternative use of a resource exists with a specific, identified value. Example: If dropping a widget line frees floor space that a tenant offers to lease for $12,000/year,the$12,000 is an opportunity cost of keeping the widget line. It enters the analysis as a benefit on the “drop” side — or equivalently as a cost on the “keep” side. Trap: Hypothetical opportunities don’t count. “We could rent this to someone for something” is not an opportunity cost unless the “someone” is identified and the “something” is a specific dollar amount. Don’t include imagined alternative uses in the analysis. Connects to: Will reappear in LO2 (constrained resource shadow prices) and in the the client engagement’s loss-leader analysis (cross-sell opportunity cost as a real future cash flow).

Glossary (LO1)

Incremental cost — another interchangeable term for relevant cost / differential cost / avoidable cost. Garrison uses it when emphasizing the “additional cost of doing something” framing, often in make-or-buy and special-order contexts.

Relevant benefit — the mirror of relevant cost: a revenue or benefit that differs between alternatives and is in the future. Relevant benefits enter the analysis on the “gain” side of whichever alternative receives them.

Unavoidable cost — a cost that remains the same regardless of the decision. Unavoidable costs are irrelevant by definition (they fail the “differs” condition).

Book value — the accounting value of an asset: original cost minus accumulated depreciation. Book value is a historical accounting artifact, not a future cash flow. Always sunk, always irrelevant. (Classic Ch12 trap — don’t confuse with market value.)

Market value — what an asset would actually sell for in the current market. Market value IS relevant to decisions about an asset (e.g., trade-in, sale, scrap) because it represents a real future cash flow. Market value and book value can differ dramatically — don’t conflate them.

Quick Reference: The ONE RULE (LO1)

Trigger: Any problem asking “which alternative is better?” with a mix of costs to filter.

1. A cost is relevant if it differs AND is in the future.
2. Run the two-condition test on every cost, in this order: differs? → future?
3. Throw out sunk costs (fail future condition) and unchanged costs (fail differs condition).
4. Zoom to the whole-company level before running the test. Segment allocations don’t count.
5. Unpack unitized averages into variable-per-unit + total-fixed before using them.
6. Run the out-loud check: “keep: ___, drop: ___” with literal numbers. If the blanks match, throw out.

Watch for: The final table is shorter than you think. Classic traps (exam-critical): Sunk costs disguised as book value. Allocated common costs disguised as segment-specific. Unitized averages disguised as pure variable costs. Scope error (applying the test at segment level when decision is company-level).

Beyond the Textbook

This client engagement is Ch12 applied. Kai is currently running a consulting engagement with a client where the tools from this LO (and LO2, LO3, and Appendix 12A) are directly applicable to real product profitability, ad spend allocation, and pricing decisions. See the client-engagement mapping for the full mapping.

Key connection: Kai’s self-diagnosed “over-including costs as relevant” failure mode is exactly the mistake that would corrupt a real profitability analysis for the client’s product lines. The discipline of running the out-loud “keep: ___, drop: ___” check on every line item is not just an exam technique — it’s the defensive habit that prevents a real client analysis from producing a misleading recommendation. Study this for the exam, use it on the client’s data next month.

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LO 2. Prepare analyses for various decision situations

LO2 takes the ONE RULE from LO1 and applies it to five recurring decision situations: drop-a-line, make-or-buy, special order, sell-or-process-further, and joint products. Each decision has its own trigger phrase, its own trap, and its own procedure — but every one of them reduces to the same rule: compare what actually changes in whole-company cash flow between the alternatives. The vocabulary differs; the tool is identical.

Decision Type 1: Drop-a-Line (Keep or Kill a Segment)

When you use it

The problem gives you a segment — product line, department, store, customer group, service offering — that looks unprofitable on a segment report, and asks: should we drop it?

Trigger phrases to watch for: “operating loss on segment X,” “unprofitable product line,” “should we discontinue,” “is this worth keeping,” “consider eliminating.”

The one question you’re answering

If we drop this segment, does the company as a whole end up better or worse off?

NOT “is this segment profitable in isolation.” NOT “does this segment cover its share of costs.” The only question is whether the whole company comes out ahead. This is where the scope-mismatch trap (V2 input error) bites — a segment can show a loss on the segment report and still be the right thing to keep, because dropping it would destroy more value than it saves.

The decision rule (from Garrison Learning Aid, line 393)

Keep if: CM lost if dropped > Fixed costs avoided if dropped + CM gained on other products

Drop if: CM lost if dropped < Fixed costs avoided if dropped + CM gained on other products

In plain English:

• What you lose by dropping = contribution margin of the segment going away, plus any spillover damage to other segments that depended on it (loss leader effect, brand halo)
• What you save by dropping = the truly avoidable fixed costs (NOT the allocated common costs), plus any boost to other segments

If losses > savings → keep. If savings > losses → drop.

The two equivalent formulations

There are two ways to arrive at the same answer. Use whichever fits the data the problem gives you.

Formulation A — The formal “CM lost vs fixed saved” method:

CM lost if dropped (revenue − variable costs of segment)
Less: Fixed costs actually avoided (line by line classification)
─────────────────────────────────────────────────────────
Net impact of dropping

Formulation B — The “net avoidable benefit” method:

Segment revenue                                 $X
Less: Costs that would actually go away if dropped   (Y)
─────────────────────────────────────────────────
Real contribution to whole company              $X-Y

Both formulations are algebraically identical. Formulation A works when the problem separates variable costs from traceable fixed costs cleanly. Formulation B works when the problem lumps avoidable costs together without separating them (like the Virtual Learning Instant Quiz below).

Which formulation to use

If the problem gives you a traditional contribution-format income statement with variable expenses and fixed expenses separated → Formulation A. If the problem gives you a lump “direct costs” figure or combines variable and traceable fixed costs into one number → Formulation B. Match the method to the data structure. Don’t force a CM comparison when the problem doesn’t give you a clean CM line.

AFM Electronics Worked Example (Garrison Exhibit 12-2)

AFM Electronics has three product lines: TVs, Tablets, Digital Cameras. The fully-allocated segment report shows:

	Total	TVs	Tablets	Digital Cameras
Sales	$340,000	$187,500	$112,500	$40,000
Variable expenses	136,500	75,000	37,500	24,000
Contribution margin	203,500	112,500	75,000	16,000
Fixed expenses (total, allocated)	167,900	88,500	57,000	22,400
Operating income (loss)	$35,600	$24,000	$18,000	$(6,400)

Digital cameras show a $6,400 loss. Drop the line?

Step 1 — CM lost if dropped: Revenue $40,000-variableexpenses$24,000 = $16,000 gone.

Step 2 — Classify each fixed expense:

Fixed cost (cameras)	Allocated	Avoidable?	Reasoning
Salaries	$6,400	Yes	Line-specific employees, will be laid off
Advertising	$5,200	Yes	Line-specific ad spend
Utilities	$800	No	Company-wide, allocated by floor space
Depreciation on fixtures	$1,600	No (SUNK)	Custom fixtures, already paid, no resale, no alternative use
Rent	$3,200	No	Long-term lease on entire building
Insurance	$400	Yes	Per-product-line inventory insurance
Selling & admin	$4,800	No	Central functions, company-wide
Totals	$22,400	$12,000avoidable,$10,400 unavoidable

Step 3 — Compare:

• CM lost: $16,000
• Costs saved: $12,000
• Net change if dropped: company loses $4,000 → KEEP the line

Why the segment report lied

The $(6,400)"loss"onthesegmentreportwasmanufacturedbypushing$10,400 of unavoidable company-wide costs onto digital cameras. Those costs don’t go away when the line dies — they get re-shuffled onto the remaining segments, making those look less profitable. Dropping cameras wouldn’t save the company $10,400; it would just relabel where those costs appear on the report.

Garrison’s recast (Exhibit 12-4) using segment margin format — excluding common allocated costs — shows the real picture: digital cameras have a $2,400segmentmargin(plus$1,600 of sunk depreciation that can’t be avoided either way), totaling $4,000 of real contribution to the company. Exactly the amount the company loses if cameras are dropped.

The alternate formulation — mechanics

Reported loss + unavoidable costs added back = real contribution to company

Digital cameras reported loss                        $(6,400)
Add back: unavoidable allocated costs                +$10,400
  (utilities 800 + depreciation 1,600 +
   rent 3,200 + S&A 4,800)
                                                     ─────────
Real contribution to whole-company profit             $4,000

Same answer as Formulation A ($16,000CM-$12,000 saved = $4,000 net loss from dropping), arrived at from the opposite direction. Both methods are algebraically equivalent.

The Ch11 → Ch12 Bridge: Segment Margin IS the Decision Rule

This is the conceptual bridge between Chapter 11 (segment reporting) and Chapter 12 (drop-a-line decisions):

Drop a segment only if its segment margin is negative. If segment margin is positive, dropping it makes the whole company worse off — regardless of what the fully-allocated segment report shows.

Why this works: Segment margin (from Ch11) = revenue − variable costs − traceable fixed costs. It deliberately excludes allocated common costs. That’s not a reporting convenience — it’s the exact quantity that answers “what does this segment genuinely contribute to covering company-wide costs?” A positive segment margin is a positive contribution to the company, regardless of how fully-allocated reports might dress it up as a “loss.”

The two-layer income statement structure:

Sum of all segment margins             ← what each segment genuinely contributes
Less: company-wide common fixed costs  ← costs not caused by any single segment
                                          (central admin, CEO salary, HQ rent)
                                       ───────
Company operating income

Each segment’s job is to generate positive segment margin. The pool of segment margins covers the common fixed costs. Dropping a positive-segment-margin line shrinks the pool without reducing the common costs, so the company ends up worse off.

Virtual Learning Micro-test (Garrison Instant Quiz 12-2) — worked result

Virtual Learning platform results:

• Revenue: $500,000
• Direct costs (all avoidable): $(427,000)
• Allocated costs (50% avoidable): $(90,000)
• Operating loss: $(17,000)

Using Formulation B (better fit for this data structure):

Revenue                                         $500,000
Less: direct costs (all avoidable)              (427,000)
Less: allocated costs — avoidable half (50%)     (45,000)
                                                ─────────
Net avoidable benefit (real contribution)       $28,000

Or the alternate formulation:

Reported operating loss                         $(17,000)
Add back: unavoidable allocated costs            +$45,000   (the 50% that stays)
                                                ─────────
Real contribution to company                    $28,000

Conclusion: Platform is contributing $28,000tothecompanydespiteshowinga$17,000 loss. Drop it and the company is $28,000 worse off. Keep the platform.

Vocabulary precision: "lost" vs "saved"

Under exam pressure, keep these straight. Revenue is LOST if dropped; costs are SAVED if dropped. Mix these up on paper and your signs will flip. When you write the comparison, the revenue line belongs on one side (“what we lose”) and the avoidable cost lines belong on the other (“what we save”). The net is the whole-company impact.

How to: Drop-a-Line decision resolved

Use when: A segment looks unprofitable on a segment report and the question is whether to discontinue it.

Given: Segment revenue, segment variable costs, list of fixed costs allocated to the segment with descriptions of what each one represents, and any cross-segment spillover effects.

Step	Result	Formula/Action
1	Data structure identified	Does the problem give a clean variable/fixed split (Formulation A) or lumped “direct costs + allocated costs” (Formulation B)? Pick your method.
2	Contribution margin lost identified	Revenue − variable expenses = CM that disappears if dropped
3	Each fixed cost classified avoidable vs. unavoidable	For each cost: “Does the whole-company total change if we drop this segment?” Yes = avoidable. No = unavoidable (allocated common cost).
4	Sunk costs flagged and removed	Fixed costs for assets already bought with no alternative use (e.g., custom fixtures) are sunk — unavoidable by definition
5	Total avoidable fixed costs summed	Add up the “yes” column from step 3
6	Spillover effects identified	Does this segment pull traffic to other segments (loss leader, brand halo, bundle anchor)? If yes, add the CM lost on other segments to the left side
7	Comparison computed	CM lost + spillover loss vs. avoidable costs saved

Sanity checks:

• Applied at whole-company scope, not segment level?
• Resisted the urge to treat the segment-report “loss” as proof of unprofitability?
• Asked “would the company total for this cost change?” on every single fixed cost line?
• Method matched to data structure (A or B)?

Final answer looks like: A comparison showing “CM lost: $X|Costssaved:$Y | Company is $Z better/worse off if dropped” and a one-sentence recommendation.

Watch for: The unavoidable costs. Rent, depreciation on sunk fixtures, allocated utilities, central S&A — these almost always look like they “belong” to the segment but don’t actually leave when the segment dies.

Why this decision goes wrong most often

Students see the segment-report “loss” and treat it as proof the segment should die. They forget to ask whether the loss is real (would the costs actually leave?) or allocated (would the costs just move to other segments on the report?). The segment-level view lies because it includes costs that are unavoidable at the company level.

Spillover: The Loss Leader Caveat

Garrison’s final note on drop-a-line (line 383): “Managers may choose to retain an unprofitable product line if the line is necessary to the sale of other products or if it serves to attract customers.”

Bread in a grocery store is the canonical example. Bread itself has thin margins, but customers expect it to be available. Drop the bread and a fraction of shoppers go to a competitor for their entire basket — not just their bread. The “cost of dropping bread” includes not just lost bread contribution margin but also lost contribution margin on everything those customers would have bought alongside the bread.

Kai’s margin note flagged this as “loss leader” and “brand halo effect.” Both phrases are correct. When a segment exists to drive traffic or sales of other segments, the decision to drop it must account for the spillover effect. This adds a term to the left side of the comparison:

CM lost on dropped segment
+ CM lost on OTHER segments that lose sales because of the drop
───────────────────────────────────────────────────────────────
Total contribution lost by dropping

If the problem mentions cross-selling, customer cross-traffic, or “customers who buy X also buy Y,” assume there’s a spillover to quantify. If the problem is silent, assume spillover is zero.

Decision Type 2: Make or Buy

When you use it

Trigger: A company currently produces something in-house (a component, a service, a function). An outside supplier offers to sell the same thing at a quoted price. Should the company keep making it or buy from the supplier?

Examples: A bike company making its own gear shifters vs. buying from a parts supplier. A software firm running its own payroll vs. outsourcing to ADP. A restaurant baking its own bread vs. ordering from a bakery. A consulting firm building its own CRM vs. licensing Salesforce.

The decision rule

Make if: relevant cost of making < outside purchase price

Buy if: relevant cost of making > outside purchase price

Where relevant cost of making = costs that would actually disappear if production stopped, plus any opportunity cost of the resources (space, equipment, labour) that would be freed up.

OSN Cycles Worked Example (Garrison Exhibit 12-5)

OSN Cycles currently makes heavy-duty gear shifters in-house. Supplier offers to sell them for $19each.Accountingreports$21/unit production cost — looks like buying saves $2/unit.\ast \ast Buthalfthe$21 is phantom.**

Cost per unit	Amount	Relevant?	Why
Direct materials	$6	Yes	Stop making → stop buying materials
Direct labour	$4	Yes	Stop making → labour freed up
Variable overhead	$1	Yes	Indirect costs that scale with production
Supervisor’s salary	$3	Yes (per problem)	Supervisor will be laid off if line closes
Depreciation — special equipment	$2	No — SUNK	Equipment already paid, no salvage, no alternative use
Allocated general overhead	$5	No — allocated common	Factory-wide overhead that gets reallocated elsewhere
Relevant cost of making	$14

Comparison:

• Relevant cost of making: $14/unit
• Outside supplier price: $19/unit
• Difference: $5/unit in favour of making → continue to make in-house

The reported $21wasmisleading.Onceyoustripthe$2 sunk depreciation and the $5allocatedoverhead,therealcostofmakingis$14, and the supplier’s $19isactually$5 worse, not $2 better.

Book Value Callback: Sunk Depreciation on Special Equipment

This is the first real workout of the book-value reframe from LO1. The $2/unitdepreciationonspecialequipment($16,000/year total) is sunk because of three strikes:

1. The equipment was bought in the past → original cost is sunk
2. It has no salvage value → no future cash if sold
3. It has no alternative use → no future cash if repurposed

Every dollar of that depreciation is a historical accounting entry tracking money that’s already left the company. Nothing OSN does today — make, buy, scrap — can bring those dollars back. The depreciation on next year’s income statement is the accounting system closing out spending that already happened.

Now flip it — what if the equipment HAD a $10,000 salvage value? Then:

• The depreciation itself is still sunk
• The $10,000salvagebecomesrelevant,but\ast \ast onlytothe"buy"side\ast \ast —sellingtheequipmentgenerates$10,000 cash inflow that only happens if OSN stops making

Same asset, two different numbers, only one enters the analysis. Equipment book value/depreciation = sunk (always). Salvage value = relevant if the decision involves disposal.

The Opportunity Cost Twist (Garrison line 511)

OSN’s initial analysis concluded “make.” But the $14vs$19 comparison assumes the freed resources have no alternative use. What if they do?

Scenario: Suppose the factory space currently used to produce shifters could be repurposed to produce disc brakes, generating a segment margin of $60,000/year.

Now the “make” decision isn’t free — it costs the $60,000 of segment margin the space could have earned on disc brakes. That’s an opportunity cost: a real future cash benefit forgone by choosing one alternative over another.

With opportunity cost included:

	Make	Buy
Relevant cost of making (8,000 × $14)	$112,000	—
Outside purchase cost (8,000 × $19)	—	$152,000
Opportunity cost — disc brake segment margin forgone	$60,000	—
Total cost	$172,000	$152,000

Difference: $20,000 in favour of BUY. The decision flipped because the freed resource has a specific, identified alternative use.

Critical rule about opportunity costs

An opportunity cost only counts if the alternative use is SPECIFIC and IDENTIFIED — a real, concrete alternative with a known dollar value. Hypothetical “we could do something with this space someday” doesn’t count. If the resource would sit idle, its opportunity cost is zero and shouldn’t enter the analysis.

Opportunity cost is the segment margin of the best alternative use of the resource. This is the second place (after drop-a-line) where Ch11’s segment margin concept does real work in Ch12 — it’s the natural unit for measuring “what the resource could be earning instead.”

Kai’s margin note: risk-adjusted returns

“would you also have risk adjusted returns here because launching a new product line is uncertain”

Yes — real managers would. The textbook’s $60,000opportunitycostassumesthediscbrakelinewillhititssegmentmarginwithcertainty.Inreality,anewproductlaunchhasaprobabilitydistribution(e.g.,60$60K, 25% chance of $30K,15$0). Expected value is lower than $60K, and a risk-averse manager would discount further for variance.

Garrison assumes certainty because the tool is already complex enough. Chapter 13 brings in uncertainty via expected values and scenario analysis for capital budgeting. For Ch12, take the stated opportunity cost as given — understand that real-world decisions layer a risk adjustment on top.

How to: Make-or-buy decision resolved

Use when: A company currently produces something in-house and an outside supplier offers to sell the same item at a quoted price.

Given: Per-unit production cost breakdown, supplier quote, quantity needed, notes about what happens to equipment, staff, and space if production stops.

Step	Result	Formula/Action
1	Each production cost line classified avoidable vs. unavoidable	For each cost: “Does total company cash leaving change if we stop making?” Yes = relevant. No = throw out.
2	Sunk depreciation/book value removed	Equipment bought in past, no salvage, no alternative use → sunk. Throw out.
3	Allocated common costs removed	Factory-wide overhead that gets reallocated if we stop → throw out.
4	Salary/layoff question answered explicitly	Does the supervisor actually get laid off, or reassigned? Reassigned = not avoidable.
5	Relevant cost of making computed	Sum remaining costs × quantity = total relevant cost of making
6	Opportunity cost of freed resources assessed	Do the freed space/equipment/labour have a SPECIFIC IDENTIFIED alternative use? If yes, add its segment margin to the “make” side. If no (or idle), zero.
7	Comparison made	Total cost of making (including opportunity cost) vs. total supplier cost

Sanity checks:

• Threw out sunk depreciation and allocated common costs before comparing?
• Checked whether freed resources have a specific alternative use?
• Opportunity cost is a real identified number, not a hypothetical?
• Salary/layoff disposition answered explicitly (reassignment ≠ layoff)?

Final answer looks like: “Total cost of making $X(includingopportunitycostof$Y) vs. total cost of buying $Z.Companyis$W better off under [make/buy].”

Watch for: The allocated common overhead line. Always the biggest trap in make-or-buy problems — the full reported production cost looks higher than the supplier quote, tempting you to buy. Strip the allocations first.

Why make-or-buy often goes wrong full reported production cost ($21inOSN)tothesupplierquote($19) and conclude "buy, we'll save $2/unit."Thesavingsareillusorybecause$7 of the $21(sunkdepreciation+allocatedoverhead)does{n}^{\prime }tactuallyleavethecompanywhenproductionstops.Realavoidablecostis$14, so buying at $19isanetlossof$5/unit. Always strip the phantoms first.

Students compare the

Decision Type 3: Special Order

When you use it

Trigger: A customer offers a one-time, non-recurring order at a price that’s typically below the company’s normal selling price. The order is outside the normal course of business — different terms, different quantities, different specs, different customer relationship.

Trigger phrases to watch for: “one-time order,” “special order,” “bulk discount request,” “private label,” “non-recurring,” “order from outside our usual market,” “foreign customer / government customer wanting a custom modification.”

The decision rule (Garrison Learning Aid, line 651)

Accept if: Incremental revenues > Total relevant costs

Reject if: Incremental revenues < Total relevant costs

Where total relevant costs = incremental costs of filling the order (variable + any genuinely new fixed costs triggered by this order) + opportunity cost of any normal business that gets displaced.

The critical split: idle capacity vs. at capacity

Single most important distinction in special order problems. The answer changes dramatically based on one question:

Can the company fill the special order without giving up any normal sales?

• Yes (idle capacity) → only costs are the incremental costs of the order. Fixed costs are irrelevant. Low floor price — often well below normal selling price is acceptable.
• No (at capacity) → accepting the special order means turning away regular-price customers. Contribution margin lost on those displaced sales is an opportunity cost that gets added to the relevant cost side. High floor price — sometimes HIGHER than the normal selling price.

These are two different problems wearing the same uniform. Always check capacity first.

OSN Cycles Case A — Idle Capacity (Garrison line 581)

Police department wants 100 modified City Cruiser mountain bikes at $1,575each.Normalsellingpriceis$1,700; unit product cost is $1,600(ofwhich$20 is variable manufacturing overhead; $105isfixedoverhead).Modificationsadd$40/unit. One-time $1,000 graphic design fee for stencils. No disruption to normal production.

	Per Unit	Total (100 bikes)
Incremental revenue	$1,575	$157,500
Incremental costs:
Direct materials	$1,250	$125,000
Direct labour	$225	$22,500
Variable manufacturing overhead	$20	$2,000
Special modification cost	$40	$4,000
Graphic design (lump sum)		$1,000
Total incremental cost		$154,500
Incremental operating income		$3,000

Decision: accept. The $3,000gainexistseventhoughthe$1,575 offered price is BELOW the reported $1,600unitcost—because$105/unit of the reported cost is sunk fixed overhead that doesn’t change.

Why comparing offered price to unit cost is a trap

Below unit cost ≠ below incremental cost.

The reported 1,600 unit cost is a **unitized fixed cost** (LO1 Trap #1 wearing a new uniform). It includes 105/unit of fixed manufacturing overhead — an accounting number computed as (total fixed overhead) ÷ (normal volume). That $105doesNOTscalewhenOSNproduces100morebikes.Therealincrementalcostperbikeis$1,535 variable + $10amortizedlump-sumcost=$1,545/unit. The $1,575 offer is profitable.

The compression: Unit cost is inflated by already-committed fixed overhead. Incremental cost is what actually leaves the company if you take the order. Only compare the offered price to incremental cost, not to the reported unit cost. This is the single most important insight in special orders.

OSN Cycles Case B — At Full Capacity

Same order, but now OSN operates at 100% capacity and sells all 1,000 City Cruisers at $1,700. Accepting the police order displaces 100 regular sales.

Contribution margin forgone per displaced bike: $1,700-$1,495 variable costs = $205/unit

Total relevant cost per special-order bike:

	Per unit
Variable costs ($1,495+$40 modification)	$1,535
Lump-sum cost ($1,000 ÷ 100 bikes)	$10
Incremental costs	$1,545
+ Opportunity cost (CM forgone on displaced regular sale)	$205
Total relevant cost	$1,750

**Minimum acceptable price: $1,750\ast \ast —whichis$50 HIGHER than the normal $1,700price.Rejectthe$1,575 offer.

The counter-intuitive result

When a company is at capacity, the minimum acceptable special-order price can be HIGHER than the normal selling price.

Naive intuition (“special orders should get discounts”) is backwards when capacity is tight. Discounts only make sense when there’s idle capacity, because only then is the comparison “$Xrevenuevs$0 revenue” instead of “$Xrevenuevs$1,700 regular sale.”

Instant Quiz 12-4: Non-cash consideration

Twist: suppose the police force offers to waive a $3,000traffic-controlfeeOSNpayseverysummerforitsroadbikerace,inexchangeforOSNloweringthespecialorderpricefrom$1,575 to $1,550.

• Revenue reduction: $25\times 100bikes=$2,500 less
• Cost savings: $3,000 (no longer paying for traffic control)
• Net: +$500 → accept the trade

The $3,000feeisa\ast \ast futurecostthatdiffersbetweenalternatives\ast \ast .Accept\to save$3,000. Refuse → pay $3,000. It differs, it’s in the future, it’s relevant. Doesn’t matter that it’s in a different accounting period or that it’s not a manufacturing cost. The ONE RULE doesn’t care about accounting categories; it cares about future cash flow differences.

Not a special order: recurring customer

A common trap pattern: a wholesaler or distributor asks for a discounted price and says “if this works out, we’d like to make this a regular order.” That is NOT a special order — it’s a long-run pricing decision, which belongs in Appendix 12A. The moment the order becomes recurring, idle-capacity reasoning stops working (over time, the order occupies capacity that could have gone to full-price sales) and fixed costs must be recovered through pricing. The special order framework applies to one-time events only.

How to: Special order decision resolved

Use when: A customer offers a one-time, non-recurring order at a price different from normal. Question: accept/reject, or what’s the minimum price.

Given: Offered price and quantity, normal unit cost breakdown (usually with a trap fixed-overhead component), any special modification costs, any lump-sum order-related costs, capacity utilization, any reciprocal or non-cash considerations.

Step	Result	Formula/Action
1	Capacity question answered	”Can we fill this without giving up regular sales?” Yes → idle capacity case. No → at-capacity case.
2	Fixed manufacturing overhead thrown out	Unless the order triggers a genuinely new fixed cost (like stencils), existing fixed overhead is sunk from the decision perspective
3	Variable production costs identified	Direct materials + direct labour + variable overhead per unit
4	Special-order-specific costs identified	Modifications, permits, shipping, one-time fees (per-unit variable vs lump-sum fixed)
5	Opportunity cost assessed (at-capacity only)	CM forgone per displaced regular sale × quantity displaced
6	Non-cash / reciprocal benefits identified	Fee waivers, contract trades, future savings — anything that differs between accept and reject
7	Comparison made	Incremental revenue + non-cash benefits vs. incremental costs + opportunity costs

Sanity checks:

• Resisted the urge to compare offered price to “unit cost”?
• Checked capacity before deciding whether opportunity cost applies?
• Separated per-unit variable from lump-sum fixed (stencils, permits, etc.)?
• Looked for hidden relevant benefits from non-cash trades?
• Verified this is actually a one-time order, not a recurring-customer pricing question in disguise?

Final answer looks like: “Incremental revenue $X+benefits$Y vs. incremental costs $Z+opportunitycosts$W. Net impact on operating income: $[+/-]. Accept/reject.”

Watch for: The fixed manufacturing overhead inside the reported unit cost. Always looks like it should factor in. Almost never does — unless the order triggers a genuinely new fixed commitment.

Why special orders trip students up (1) "Price is below unit cost → reject." Treats reported unit cost as if it were all variable. Usually a significant chunk is fixed overhead already committed and irrelevant. Stripping that out reveals the true incremental cost, which is almost always far below reported unit cost.

(2) Forgetting the capacity question. Treating every special order as if idle capacity applies. At capacity, opportunity cost of displaced regular sales can flip the decision. Always check capacity first.

Connection to Ovation Q2 homework

Your Chapter-12-Homework-Study-Log Q2 was a foreign-customer special order: 10,800 Bits, import duties $1.70/unit,permits$4,860 lump sum, shipping $2.40/unitreplacingthenormal$3.90 variable selling cost. You correctly calculated break-even price of $23.45/unit using this exact procedure. Fixed manufacturing overhead was correctly excluded; the capacity question was implicitly yes (idle capacity, Ovation produces 43,200 and has capacity for 64,800). That was special-order procedure in action.

Decision Type 4: Sell or Process Further (Joint Products)

Setup

Joint products are two or more products that come out of the same raw material input through the same process. You can’t make one without making the others. Examples:

• Crude oil refining: gasoline, jet fuel, home heating oil, lubricants, asphalt — all from the same barrel
• Sheep → coarse wool + fine wool + superfine wool
• Meat processing: ribeye + ground beef + hide + bones
• Sawmill: premium lumber + standard lumber + wood chips + sawdust

Key vocabulary:

• Joint product costs = costs incurred BEFORE the split-off point (buying the input + running the process that separates the products)
• Split-off point = the moment in the process where the joint products can first be recognized as separate products
• Intermediate product = a joint product in its “just split off” form, which may itself be sellable
• Incremental processing cost = costs incurred AFTER split-off to turn a raw joint product into a finished sellable form

The ONE question you’re answering

For each joint product, is it worth processing it further past the split-off point, or should we sell it as-is at the split-off point?

This is a per-product decision, not a whole-operation decision. Run the rule once for each joint product independently.

Why joint costs are IRRELEVANT to sell-or-process-further

Once the raw material is bought and the separation process has run, joint costs are sunk — they happened regardless of what you do with the products after the split-off point. Processing further or selling as-is: joint costs don’t change. Differs between alternatives? No. Future? No, already spent. Fails both conditions → throw out.

The trap: Some accounting systems allocate joint costs across products (e.g., “coarse wool gets 25% of the joint cost”). Required by GAAP for inventory valuation and financial reporting. But irrelevant to internal decisions. An allocation is a label, not a cause — the joint cost total is the same whether you process further or not.

This is the allocated common cost trap from LO1, wearing another new uniform. Joint costs ARE common costs — shared across joint products by physical necessity rather than accounting allocation. They behave the same way in decision analysis: throw out unconditionally.

The decision rule

Process further if: Incremental revenue (from further processing) > Incremental cost (of further processing)

Sell at split-off if: Incremental revenue < Incremental cost

Incremental revenue = final sales value after processing − sales value at split-off point Incremental cost = only the cost of the further processing step (dyeing, refining, kiln-drying, assembly), NOT any allocated share of joint cost.

St. Thomas Wool Cooperative Worked Example

Buys raw wool $200,000,runsseparationprocess$40,000. Gets three intermediate products: coarse, fine, superfine. Each can be dyed further or sold undyed.

	Coarse	Fine	Superfine
Final sales value after dyeing	$160,000	$240,000	$90,000
Less: sales value at split-off	$120,000	$150,000	$60,000
Incremental revenue	$40,000	$90,000	$30,000
Less: cost of dyeing	$50,000	$60,000	$10,000
Profit (loss) from processing further	$(10,000)	$30,000	$20,000

Decisions (one per product):

• Coarse wool: Dyeing costs $50Kbutonlyadds$40K revenue. Sell at split-off. Save $10K.
• Fine wool: Dyeing adds $90Krevenuefor$60K cost. Process further. Gain $30K.
• Superfine wool: Dyeing adds $30Kfor$10K. Process further. Gain $20K.

The $200,000+$40,000 joint costs appear nowhere in the analysis. They’re relevant only to a different question: “should we run the entire wool operation at all?” At that level they’re avoidable (shutdown avoids them). At the per-product level, they’re sunk.

The scope observation (important general pattern)

The same cost can be relevant to ONE question and irrelevant to ANOTHER. Always match the relevance test to the specific question being asked.

• Question: “Should we shut down the wool operation?” → joint costs relevant (avoidable by shutdown)
• Question: “For coarse wool specifically, process further or sell at split-off?” → joint costs irrelevant (sunk at decision time)

Different questions use different inputs to the ONE RULE. A cost is never intrinsically relevant or irrelevant — relevance is always with respect to a specific decision.

Barbecue Assembly Micro-Example (Instant Quiz 12-5)

Corner Hardware sells barbecues. Buys unassembled at $100,cansellunassembledat$200 or assembled at $225.Assemblytakes0.5hrat$20/hr.

• Incremental revenue: $225-$200 = $25
• Incremental cost: 0.5 × $20=$10
• $25>$10 → assemble and sell

The $100 wholesale cost is irrelevant because by the time of this decision, the BBQ is already in the store. It would be relevant to a different question (“should we stock barbecues?”) but not this one.

How to: Sell-or-process-further decision resolved

Use when: A joint product (or any intermediate product) can be sold as-is or processed further into something more valuable. Question: which path generates more profit for this specific product.

Given: Sales value at split-off, sales value after further processing, cost of the further processing step. (Joint costs may also be given but they’re irrelevant.)

Step	Result	Formula/Action
1	Joint costs thrown out	Any cost incurred before the split-off point is sunk for this decision. Throw out regardless of how the problem presents it (allocated or unallocated).
2	Incremental revenue computed	Sales value after processing − sales value at split-off
3	Incremental cost identified	Only the cost of the further processing step — materials, labour, overhead specific to the processing
4	Comparison made	Incremental revenue > incremental cost → process further. Reverse → sell at split-off.
5	Done per-product	If multiple joint products, run the rule independently for each.

Sanity checks:

• Completely ignored joint costs (including any allocated share)?
• Used split-off sales value as baseline, not zero?
• Ran the analysis per-product, not for the whole operation?

Final answer looks like: “For [product], incremental revenue $X-incrementalprocessingcost$Y = gain/loss of $Z. Recommendation: [sell at split-off / process further].”

Watch for: Allocated joint costs presented as “per-product costs.” Always look relevant. Never are, for this decision.

Why students mis-apply this

Problems often present joint costs allocated across products. Students include the allocation because it looks like a cost “attached to” each product. But an allocation is a label, not a cause. The joint cost total is the same whether you process further or not — so it can’t influence the decision. Throw it out unconditionally.

Joint Products / Joint Costs / Split-Off Point

Definition: Joint products are two or more products that come out of a single input through a shared process (oil refining, meat processing, lumber milling, wool processing). Joint costs are the manufacturing costs incurred BEFORE the split-off point — the point where products can first be recognized separately. After split-off, each product can be sold as-is or processed further independently. Example: St. Thomas Wool buys wool $200K,separatesfor$40K → gets coarse, fine, superfine as intermediate products. Each can be dyed further before final sale. Trap: Joint costs are sunk at the split-off point. Irrelevant to any sell-or-process-further decision for individual products, even though GAAP requires them to be allocated for inventory valuation. Connects to: Allocated common cost trap from LO1. Joint costs ARE common costs — shared across joint products by physical necessity rather than accounting allocation, but behave the same way in decision analysis.

Lumber Mill Concept Check — worked

Lumber mill buys logs $50K,millsfor$8K. Output: premium lumber ($60Katsplit-off),standardlumber($25K), wood chips ($2K).Option:kiln-drypremiumfor$5K → sell as kiln-dried premium for $70K.

• Premium at split-off: $60K
• Premium after kiln-drying: $70K
• Incremental revenue: $10K
• Incremental cost: $5K
• $10K>$5K → kiln-dry. Gain $5K.

Irrelevant: $50Klogs,$8K milling (both joint costs, sunk), $25Kstandardlumber(differentproduct),$2K wood chips (different product).

Note on cost classification: The $5K could be per-batch, per-log, or one-time equipment:

• Per-batch: $5Kperrun,compareddirectlyto$10K incremental revenue per run → kiln-dry ✓
• One-time equipment: $5Kupfront,$0 thereafter → first batch pays it off 2:1 → kiln-dry ✓
• Per-log: $5Kperlog,scaleswithvolume\to atmorethan1log/batch,canexceed$10K revenue → do NOT kiln-dry Two of three classifications give “kiln-dry”; the third flips the answer. If the problem is ambiguous, resolve the classification before finalizing — ambiguity can matter. Flagging it is the right move.

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Discrimination: which decision type is this?

The five decision types share the ONE RULE but have different triggers. Pattern-matching the problem to the right framework is half the battle.

Decision type	Trigger phrase	Key question
Drop-a-line	”unprofitable segment,” “should we discontinue,” “operating loss on segment X”	Does the company come out ahead if we drop this?
Make-or-buy	”currently produces internally,” “supplier offers to sell us,” “outsource”	Is making cheaper than buying, after stripping phantoms and including opportunity cost?
Special order	”one-time order,” “foreign customer,” “bulk discount request,” “accept this order at $X”	Does the order add to operating income given capacity?
Sell-or-process-further	”intermediate product,” “split-off point,” “joint products,” “process further or sell as-is”	For each joint product, do the incremental processing benefits exceed incremental costs?

Watch for disguises: a “discount request” from a recurring customer is NOT a special order — it’s pricing (Appendix 12A). A question about whether to shut down an entire joint-products operation is NOT sell-or-process-further — it’s effectively a drop-a-line with joint costs now avoidable.

Same cost, different relevance across decision types

The Finch mastery checks (session 2026-04-11, 2nd pass) surfaced the single most important cross-decision insight in LO2:

Fixed manufacturing overhead ($6.00/unit) was relevant in make-or-buy but irrelevant in special order — for the same company, same product, same cost.

• Make-or-buy: Finch is considering stopping production entirely. If they stop, 60% of fixed OH ($3.60/unit) goes away — supervisor laid off, equipment leases cancelled. Fixed OH is avoidable → relevant.
• Special order: Finch is keeping normal production and adding 6,000 units on top. Fixed OH is already committed for the normal run. Making more units doesn’t change it. Fixed OH doesn’t differ → irrelevant.

The rule is the same (ONE RULE). The alternatives changed. “Am I stopping production?” and “am I adding to existing production?” are two different decisions with two different sets of alternatives. The same cost passes the ONE RULE in one decision and fails it in the other.

Exam defence: Before including ANY fixed cost, ask: “What is the decision doing to production? Stopping it (costs might leave) or adding to it (costs are already committed)?”

LO 2 Mastery Status (2026-04-11 final)

• ✅ Drop-a-line: Mastered. Charter Sports trampolines — all classifications correct, segment margin recast recognized.
• ✅ Make-or-buy: Mastered. Finch Sparks — correctly included 60% avoidable fixed OH ($19.10vs$17 → buy).
• ✅ Special order: Mastered. Finch distributor — correctly excluded fixed OH ($17.50floorvs$18 → accept). Self-corrected after initially using make-or-buy cost.
• ✅ Sell-or-process-further: Mastered. Finch Alpha — correctly ignored joint costs ($45Kvs$52K → process, $7K gain).
• LO2 marked ✅ Mastered. Key insight locked: same cost can be relevant in one decision and irrelevant in another.

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LO 3. Determine the most profitable use of a constrained resource

What is a constrained resource?

A constrained resource (also called a bottleneck) is any limited input that restricts a company's ability to satisfy all demand. A resource is only "constrained" when demand for its output exceeds what the available supply can produce.

Examples of constrained resources: machine hours, labour hours, oven time, shelf space, raw material supply, ad budget. The constraint is whatever hits its capacity ceiling first.

How do we allocate a constrained resource to maximize profit?

When a resource is constrained, the product that maximizes TOTAL contribution margin is not necessarily the product with the highest per-unit CM. It's the product that earns the most CM per unit of the constrained resource.

Why per-unit CM misleads under a constraint

A product with high per-unit CM but slow production (uses lots of the constraint per unit) can earn LESS total CM than a product with low per-unit CM but fast production (uses little of the constraint per unit). Per-unit CM ignores how much of the bottleneck each unit consumes. When the bottleneck is what limits you, you need to know how much CM each unit of bottleneck earns, not how much CM each unit of product earns.

The brute-force method (first principles derivation)

The most reliable way to see this: for each product, compute the total CM if you spent ALL your constraint on that one product. The highest total wins.

Total CM = (Total constraint available ÷ Constraint used per unit) × CM per unit

This is the brute-force test. It always works. No formula to memorize — just “what if I maxed out on this one thing?”

Bakery Example (from session, 2026-04-11)

Bakery has 8 hours of oven time per day. Two products:

	Bread	Cake
CM per unit	$4	$10
Oven time per unit	1 hour	2 hours

Per-unit ranking: Cake ($10)beatsbread($4). Cake looks like the obvious winner.

Brute-force test (spend all constraint on one product):

• All bread: 8 hrs ÷ 1 hr × $4=\ast \ast$32/day**
• All cake: 8 hrs ÷ 2 hrs × $10=\ast \ast$40/day**

Cake still wins — but only by $8, not by 2.5x like the per-unit numbers suggest. The 2-hour baking time eats cake’s per-unit advantage.

CM per hour of oven time:

• Bread: $4÷1hr=\ast \ast$4/hour**
• Cake: $10÷2hrs=\ast \ast$5/hour**

The gap narrows from a 2.5:1 per-unit ratio to a 1.25:1 per-constraint ratio. Cake still wins here, but the principle is clear: the constraint consumes part of the per-unit advantage.

The per-unit ranking and the per-constraint ranking only diverge when products use DIFFERENT amounts of the constraint per unit.

If two products use the same amount of constraint (e.g., both need 5 minutes of machine time), then whichever has the higher per-unit CM automatically has the higher per-constraint CM too. The rankings only flip when constraint-usage-per-unit differs across products.

OSN Cycles Pannier Example (Garrison line 788)

OSN makes two pannier models. Stitching machine is the bottleneck.

	Mountain Pannier	Touring Pannier
CM per unit	$30	$24
Stitching time per unit	4 minutes	2 minutes

Per-unit ranking: Mountain ($30)beatstouring($24).

Per-constraint ranking (CM per minute of stitching):

• Mountain: $30÷4min=\ast \ast$7.50/min**
• Touring: $24÷2min=\ast \ast$12.00/min**

Touring wins. The ranking flips because touring uses half the stitching time. Each minute on touring earns $12;eachminuteonmountainearnsonly$7.50. Despite lower per-unit CM, touring earns more per unit of the bottleneck.

Brute-force verification (60 minutes):

• All mountain: 60 ÷ 4 × $30=15units\times$30 = $450
• All touring: 60 ÷ 2 × $24=30units\times$24 = $720

$720>$450. Same answer. The brute-force test and the per-constraint ranking always agree.

Ad Spend Example (the client-shaped, from session)

the client has $10,000 ad budget. Three services compete for that budget:

Service	CM per new customer	Ad cost per new customer
Nutrition coaching	$300	$100
Personal training	$500	$250
Group fitness	$80	$20

Per-unit (per-customer) ranking: Personal training ($500)>Nutrition($300) > Group ($80).

Per-constraint (CM per $1 of ad spend) ranking:

• Nutrition: $300÷$100 = $3 per ad dollar
• Personal training: $500÷$250 = $2 per ad dollar
• Group fitness: $80÷$20 = $4 per ad dollar

Ranking: Group ($4)>Nutrition($3) > Personal training ($2). Completely reverses the per-unit ranking.

Allocation rule: Spend ad budget on group fitness first (until its customer demand ceiling is hit), then nutrition, then personal training with whatever budget remains.

Brute-force verification ($10,000 all on one service):

• All nutrition: ($10,000÷$100) × $300=100\times$300 = $30,000 CM
• All personal training: ($10,000÷$250) × $500=40\times$500 = $20,000 CM
• All group fitness: ($10,000÷$20) × $80=500\times$80 = $40,000 CM

Same ranking: group > nutrition > personal training.

The profitability index (Garrison’s name for this metric)

Profitability index = CM per unit ÷ units of constrained resource required per unit = CM per unit of the constrained resource. This is not a formula to memorize — it's a unit conversion from "CM per unit of product" into "CM per unit of constraint," so products can be compared on the same footing.

The brute-force method and the profitability index always give the same ranking. The profitability index is a shortcut — it gives the ranking without computing full totals. But if the shortcut ever feels arbitrary, run the brute force (“what if I spent all my constraint on one product?”) and the answer will match.

The allocation procedure (multiple products)

When there are 3+ products competing for one constraint:

1. Compute the profitability index for each product (or run the brute-force comparison)
2. Rank from highest to lowest
3. Allocate the constraint to the highest-ranked product until customer demand for that product is fully satisfied — not beyond
4. Move remaining constraint to the second-ranked product, again up to its demand ceiling
5. Continue until all constraint capacity is used
6. Bottom-ranked products get whatever remains (possibly zero)

The demand ceiling is critical. You don’t dump all constraint on the top product if customers won’t buy that much. Once demand is satisfied, additional production of that product has zero additional value — move to the next product.

What is one more unit of constraint worth?

The value of one more unit of the constraint = the profitability index of the highest-ranked product that still has unfilled demand. This tells you the maximum you should pay to expand the bottleneck (overtime, renting extra capacity, subcontracting, hiring).

How this applies to management decisions

The constraint analysis directly answers “should we pay to expand the bottleneck?”

Decision rule:

Pay to expand if: Cost per unit of constraint < CM per unit of constraint (profitability index of the best unfilled product)

Don’t expand if: Cost per unit of constraint > CM per unit of constraint

Bakery oven rental example (from session)

Neighbouring restaurant offers extra oven hours. Bread earns $4/hr,cakeearns$5/hr. All demand unfilled.

Rental price	Best use of extra hour	CM earned	Net gain/loss	Decision
$3/hour	Cake ($5/hr)	$5	+$2	✅ Accept
$6/hour	Cake ($5/hr)	$5	−$1	❌ Reject
$4.50/hour	Cake ($5/hr)	$5	+$0.50	✅ Accept (if cake demand remains)

The demand-ceiling cliff

The value of one more unit of constraint drops the moment the top product’s demand runs out.

In the $4.50/hour rental case:

• While cake demand is unfilled: $5-$4.50 = +$0.50/hr → accept
• After cake demand is filled: next-best product is bread at $4/hr.$4 − $4.50=\ast \ast -$0.50/hr → reject**

The decision is conditional. If you rent more hours than cake demand can absorb, the excess hours lose money. Only expand the constraint up to the point where the top product’s demand is satisfied, then reassess at the next-ranked product’s rate.

The textbook vs real-world distinction (from Kai’s pushback, session 2026-04-11)

Garrison assumes all CM numbers are known with certainty. In reality, when the expected net gain is slim ($0.50/hr), variance in the CM estimate, demand forecast, or cost can easily flip the decision negative.

Kai’s stated rule: “The marginal gains are slim enough that I’d say no given risk adjustment.” This is correct managerial thinking but not testable in Ch12. Formal risk tools live in Chapter 13 (expected values, scenario analysis) and finance (CAPM, option pricing).

For the exam: assume textbook numbers are certain, use the straight profitability-index-vs-cost comparison. For the client: layer risk adjustment on top. Thin margins are unreliable when estimates carry uncertainty.

Why fixed costs don’t enter the analysis

Garrison line 784: “Fixed costs are usually unaffected by the allocation of the constrained resource in the short run.”

Whatever product mix is chosen, fixed costs (rent, salaries, depreciation) are identical. They don’t differ across allocation alternatives → fail the ONE RULE → irrelevant. That’s why the metric is CM per unit of constraint (not profit per unit of constraint).

In the long run, fixed costs do become variable — you can hire/fire, expand/contract, renegotiate leases. Short-run constraint analysis assumes the fixed cost base is unchanged. For the exam, stay in the short run unless the problem explicitly asks about long-run capacity decisions.

Ways to relax a constraint (Garrison line 869)

Method	How it works
Overtime	Run the bottleneck machine or operator longer
Subcontracting	Send some bottleneck work to an outside vendor
Shift workers	Redeploy workers from non-bottleneck processes to the bottleneck
Process improvement	Reduce setup times, improve workflow at the bottleneck
Reduce defects	Every defective unit processed through the bottleneck wastes capacity that could have produced a sellable unit

Items 3–5 are low-cost and may yield additional savings. Reducing defects is especially high-value: defective units consume bottleneck time AND generate zero CM.

Multiple constraints

When more than one resource is constrained simultaneously (e.g., limited machine hours AND limited labour AND limited materials), the simple profitability-index ranking doesn’t work — it was designed for ONE constraint. Multiple constraints require linear programming or another optimization method (Data Analytics appendix). For the exam, assume one constraint unless explicitly told otherwise.

How to: Constrained resource allocation resolved

Use when: A company has limited capacity of one resource and cannot satisfy all demand. Question: how to allocate the constraint across products to maximize total CM.

Given: Per-unit CM for each product, units of constraint required per product, customer demand for each product, total available constraint capacity.

Step	Result	Formula/Action
1	Constraint identified	What single resource is limiting? Machine hours? Ad dollars? Shelf space?
2	Profitability index computed OR brute-force test run	Profitability index = CM per unit ÷ constraint per unit. OR: “total CM if all constraint spent on this product” for each product. Both give the same ranking.
3	Products ranked	Highest profitability index (or highest brute-force total) first
4	Constraint allocated top-down	Highest-ranked product: produce up to customer demand ceiling. Then next-ranked with remaining constraint. Continue.
5	Total CM computed	Sum (CM per unit × units produced) across all products in the final mix
6	Value of relaxing the constraint assessed	Profitability index of the highest-ranked product with unfilled demand = max price to pay for one more unit of constraint

Sanity checks:

• Used CM per unit of CONSTRAINT, not CM per unit of product?
• Stopped at each product’s demand ceiling before moving to the next?
• Fixed costs excluded from the ranking?
• Only ONE constraint identified? (Multiple → linear programming, out of scope.)

Final answer looks like: “Rank: [Product A] > [B] > [C]. Allocate: [A] gets X units of constraint (fills demand), [B] gets remainder. Total CM: $W.Valueofonemoreunitofconstraint:$V.”

Watch for: Products with higher per-unit CM but LOWER per-constraint CM. The per-unit ranking misleads when products use different amounts of the constraint.

Why this goes wrong

Students rank by per-unit CM because it’s the familiar metric from earlier chapters. That ranking is correct ONLY when capacity is unlimited. Under a constraint, the per-unit ranking can point to the wrong product. The fix: always convert to CM per unit of the constraint before ranking, or run the brute-force test to verify.

Profitability Index (CM per Unit of Constrained Resource)

Definition: Contribution margin per unit divided by units of constrained resource per unit. Measures how much CM a product earns per unit of the bottleneck. This is a unit conversion, not an arbitrary formula — it converts “CM per unit of product” into “CM per unit of constraint” so products can be compared fairly. Example: Mountain panniers earn $30CM/unitbutrequire4minofstitching\to$7.50/min. Touring panniers earn $24/unitbutonly2min\to$12/min. Touring wins despite lower per-unit CM. Trap: Intuition ranks by CM per unit. Correct when capacity is unlimited; fails when there’s a binding constraint. Always rank by CM per unit of constraint. Connects to: Also determines the value of “one more unit of constraint.” The profitability index of the best unfilled product is the maximum you’d rationally pay to expand the bottleneck.

Quick Reference: Constrained Resource Allocation (LO3)

Trigger: Limited capacity of one resource + more demand than capacity can serve.

1. Identify the ONE constraint (machine hours, ad dollars, shelf space, etc.)
2. For each product: CM per unit ÷ constraint per unit = profitability index
3. Rank highest to lowest
4. Allocate constraint to #1 until demand is met, then #2, then #3…
5. Value of one more unit of constraint = profitability index of the best product with unfilled demand

Watch for: Per-unit CM ≠ per-constraint CM when products use different amounts of constraint. Key formula: Total constraint ÷ constraint per unit × CM per unit = total CM (brute-force test)

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LO 4–7 (Appendix 12A). Pricing Decisions

LO 4–7: DELIBERATELY SKIPPED FOR EXAM PREP

Not taught and not scheduled to be taught for exam prep (2026-04-11 decision). Kai confirmed he has never been tested on chapter appendices in this course, so Appendix 12A is deliberately out of scope for the upcoming exam. Time allocated to LO3 (constrained resource) and mechanical drills instead.

If revisiting post-exam for the the client engagement: Appendix 12A is still the right toolkit for the engagement’s pricing question. Cost-plus for the floor, elasticity for the demand signal, value-based for the ceiling, target costing for product-development decisions. See the client-engagement mapping Phase 5. Not urgent — engagement timeline permits learning after the exam.

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Beyond the Textbook (Chapter-Level)

This entire chapter is the toolkit for the the client-engagement mapping project. See that note for the full engagement-to-LO mapping, the six-phase dependency plan, the loss-leader / LTV gap that the textbook doesn’t cover, and the real-world nuances the textbook assumes away (risk margins, strategic spillovers, multi-period horizons, cross-referral effects). Five of Kai’s six real consulting questions for the client map directly to Ch12 LOs. Studying this chapter is literally studying for the engagement.

Cross-chapter connections:

• Ch2–Ch3 cost behaviour — the foundation for every relevant-cost analysis. Must classify costs as fixed or variable correctly before running the ONE RULE. V1 and V2 input errors both stem from failing this step.
• Ch6/Ch11 segment reporting — segment margin IS drop-a-line decision logic in disguise. Revenue − variable − traceable fixed = segment margin; the ONE RULE applied to a segment produces exactly this number by throwing out allocated common costs. When we reach LO2, name this connection explicitly.
• Ch5 job order costing — job cost records create the per-unit figures that feed Ch12’s unitized-average trap. When a job cost sheet shows “$X per unit,” ask whether it contains an allocated fixed overhead slice.
• Ch10 standard costs and variances — the framework from Ch10 (actual vs standard, with multiplier) is structurally similar to relevant-cost analysis (actual vs alternative, with differential). Both are “compare two states, isolate what matters” frameworks. Same cognitive toolkit, different application.