# Relevant Costs Concept Card: [Decision, product or course] > A concept card for relevant costing, the decision tool of the managerial accounting core: which costs and revenues > to count when a manager chooses between alternatives, and which to ignore. It covers sunk, avoidable, incremental > and opportunity costs, and the five classic decisions: make or buy, special order, drop or keep a product or segment, > use of a constrained resource (contribution per bottleneck unit), and keep or replace equipment. It is for MBA > students preparing for class, cases and exams, and for managers who must defend a one-off decision with numbers. > Every number is computed, with the Excel formula next to it. > Source basis: the relevant-cost and opportunity-cost principles of the management accounting literature, the > theory of constraints (Goldratt and Cox 1984) for bottleneck decisions, and the standard textbooks named in the > reading list, written up in original words. The companies and numbers are fictional and were computed in Python. > Replace every [bracketed] value and every row marked *Example*. ## Document control | Field | Value | |---|---| | Course or project | [Managerial accounting core / case name / business decision] | | Learner or analyst | [Your name] | | Decision | [Example: make or buy tent-pole sets for 2027] | | Alternatives compared | [Alternative 1] versus [Alternative 2] | | Data source | [Northfield Outdoor Co. (fictional) / your cost file and date] | | Reviewed by | [Study partner, professor or controller] | | Version | [0.1] | | Last updated | YYYY-MM-DD | ## Contents - [When to use it](#when-to-use-it) - [The idea in plain language](#the-idea-in-plain-language) - [Formulas and notation](#formulas-and-notation) - [Assumptions and limits](#assumptions-and-limits) - [How managers use it](#how-managers-use-it) - [Worked example A (fully solved)](#worked-example-a-fully-solved-make-or-buy-and-a-bottleneck) - [Dropping a product line](#dropping-a-product-line-a-solved-illustration) - [Worked example B (half solved)](#worked-example-b-half-solved-a-special-order) - [Exercise C (unsolved)](#exercise-c-unsolved-keep-or-replace-a-test-rig) - [Connections to other cards](#connections-to-other-cards) - [Common mistakes and misconceptions](#common-mistakes-and-misconceptions) - [Self-test questions](#self-test-questions) - [My notes and next steps](#my-notes-and-next-steps) - [Sources and further reading](#sources-and-further-reading) - [Answer key](#answer-key) ## When to use it **One-sentence rule:** when choosing between alternatives, count only the **future** costs and revenues that **differ** between them, including the opportunity cost of resources that have another use, and ignore everything else. | Use when | Do not use when (or extend) | |---|---| | Make or buy (insource or outsource) a component, service or process | The decision runs over several years: discount the relevant cash flows (mba/mba-npv-irr-card) | | Accept or reject a one-off order at a special price | The "one-off" order would set a precedent for regular prices: include the effect on regular customers | | Keep or drop a product, store, segment or customer | The question is long-run pricing or product strategy: use full and activity-based cost (mba/mba-activity-based-costing-card) | | Decide what to make when a resource is scarce | Several constraints bind at once: use linear programming (Excel Solver) | | Sell at a split-off point or process further | Joint costs are being "allocated" to decide: they are irrelevant to this choice | | Keep or replace equipment | Tax effects of disposal are material: include them as relevant cash flows | ## The idea in plain language A decision is a choice between futures. Anything that is the same in every future, or that has already happened, cannot change which future is better, so it is **irrelevant** to the choice, however large it is. A cost or revenue is **relevant** only if it is both: 1. **Future**: it will happen after the decision, and 2. **Differential**: its amount differs between the alternatives. Five labels follow from that rule. | Label | Meaning | Relevant? | Northfield example *(Example)* | |---|---|---|---| | **Sunk cost** | Already spent or committed; no alternative changes it | Never | Design fees already paid for a tent that may be dropped | | **Avoidable cost** | Disappears if an alternative is chosen | Yes | A supervisor's salary that ends if pole production stops | | **Unavoidable (common) cost** | Continues whatever is chosen | No | The share of plant rent allocated to the pole cell | | **Incremental (differential) cost or revenue** | The change in total cost or revenue between alternatives | Yes | Extra embroidery cost on a club order | | **Opportunity cost** | The contribution given up by using a resource in this way instead of its best alternative use | Yes, when the resource is scarce or has another use | Contribution from a repair-kit line that could use freed space | Two consequences surprise most students. First, **allocated fixed costs** usually look relevant on a product cost sheet but are not: dropping a product does not make the head-office rent disappear, it just spreads it over the other products. Second, **costs that never appear in the accounts** can be the most relevant of all: the opportunity cost of a bottleneck hour, or of warehouse space that a new product line could use, is not recorded anywhere, but it decides the answer. When capacity is scarce, the rule becomes: rank products by **contribution per unit of the constrained resource**, not by contribution per unit or margin percentage. This is the managerial accounting expression of the theory of constraints (Goldratt and Cox 1984): an hour lost at the bottleneck is an hour lost for the whole system, so the bottleneck hour is what you must spend well. The contribution of the marginal product per bottleneck hour is the **shadow price** of that hour: the most it is worth paying for one more hour of capacity (overtime, a subcontractor, a second shift). Qualitative factors always sit next to the numbers: supplier reliability and quality in a make-or-buy, the signal a discounted order sends to regular customers, the effect of dropping a product on the brand, on employees and on customers who buy across lines. A good recommendation states the quantitative difference and then the two or three qualitative factors that could reverse it. ## Formulas and notation The decision rule compares the relevant totals of two alternatives A and B: $$ \Delta = \sum_{\text{relevant}} (\text{Revenue}_A - \text{Revenue}_B) - \sum_{\text{relevant}} (\text{Cost}_A - \text{Cost}_B), \qquad \text{choose A if } \Delta > 0 $$ Make or buy (per period, quantity $N$): $$ C_{\text{make}} = N\,(DM + DL + VOH) + F_{\text{avoid}} + OC, \qquad C_{\text{buy}} = N\,p_s, \qquad \text{buy if } C_{\text{buy}} < C_{\text{make}} $$ Special order (quantity $q$, price $p$, incremental variable cost $v'$, one-off cost $S$): $$ \Delta_{\text{order}} = q\,(p - v') - S - OC, \qquad p_{\min} = v' + \frac{S + OC}{q} $$ Constrained resource (product $i$, contribution $CM_i$, use of the constrained resource $r_i$ per unit): $$ \text{rank by } \frac{CM_i}{r_i}, \qquad \lambda = \frac{CM_{\text{marginal}}}{r_{\text{marginal}}} $$ Drop a segment: $$ \Delta OI_{\text{drop}} = -CM_{\text{segment}} + F_{\text{avoid}} - CM_{\text{lost elsewhere}} + CM_{\text{replacement use}} $$ | Symbol | Meaning | |---|---| | $N$, $q$ | Quantity required in the period; quantity in a special order | | $DM$, $DL$, $VOH$ | Direct material, direct labour and variable overhead per unit (assumed avoidable) | | $F_{\text{avoid}}$ | Fixed cost that disappears if the activity stops | | $OC$ | Opportunity cost: contribution of the best alternative use of the resource | | $p_s$, $p$, $p_{\min}$ | Supplier price; special-order price; minimum acceptable price | | $v'$, $S$ | Incremental variable cost per unit of the order; one-off incremental cost of the order | | $CM_i$, $r_i$ | Contribution margin per unit of product i; constrained resource used per unit | | $\lambda$ | Shadow price: contribution of the marginal product per unit of the constrained resource | | $\Delta OI$ | Change in operating income from the decision | ```mermaid flowchart TD A["Cost or revenue line"] --> B{"Already spent or committed?"} B -->|"Yes"| S["Sunk: ignore"] B -->|"No"| C{"Same amount under every alternative?"} C -->|"Yes"| U["Unavoidable or common: ignore"] C -->|"No"| R["Relevant: include the difference"] R --> D{"Is a scarce resource used?"} D -->|"Yes"| O["Add the opportunity cost of that resource"] D -->|"No"| E["Compare relevant totals"] O --> E E --> Q["Add qualitative factors that could reverse the result"] Q --> F["Recommendation with the break-even condition stated"] ``` ## Assumptions and limits | Assumption | Why it matters | When it fails and what to do | |---|---|---| | Short horizon, capacity given | Many fixed costs are unavoidable only in the short run | For long-run decisions, more costs become avoidable; use ABC and NPV | | Variable costs are avoidable and linear | Avoidable variable cost per unit drives most answers | Learning curves, volume discounts and minimum orders break linearity: model them | | Avoidable fixed costs are identified correctly | Overstating them favours dropping or outsourcing | Ask "which contract, salary or lease actually ends, and when?" | | Opportunity cost is the **best** alternative use | Using a weak alternative understates it | List the alternative uses and pick the highest contribution | | No interdependence between products | Dropping one product may cost sales of another | Estimate lost complementary contribution explicitly | | Single binding constraint | The ranking rule works for one constraint only | With two or more, set up Excel Solver (maximise CM subject to constraints) | | Prices to other customers unchanged | A special price can leak to regular buyers | Include the expected price erosion, or reject the order | Relevant costing is a short-run, incremental lens. Applied repeatedly to long-run questions, it can lead a company to accept many orders that cover variable cost but never cover the fixed cost of the capacity they use. That is why pricing for regular business uses full or activity-based cost, while relevant costing decides the exceptions. ## How managers use it - **Sourcing and outsourcing.** Operations and procurement teams compare a supplier quote with the **avoidable** cost of making, not with the full cost on the standard cost sheet, and add the value of the freed capacity. - **Sales and pricing of exceptions.** Sales leaders use the minimum price of a special order (incremental cost plus opportunity cost) as the floor in a negotiation. - **Portfolio reviews.** Category managers judge a product or store by its **segment margin** (contribution minus traceable avoidable fixed cost), not by profit after allocated head-office costs. - **Bottleneck management.** Plant managers and service operations leaders (clinics, fulfilment centres) rank work by contribution per bottleneck hour and price extra capacity at the shadow price; see mba/mba-process-analysis-card. - **Asset replacement.** Finance teams ignore the book value of old equipment (sunk) and compare future cash flows, discounted when the horizon is long. The same lens is used outside accounting: in consulting cases ("should the client close the plant?"), in product management ("should we keep the legacy feature?") and in personal decisions (tuition already paid is sunk; it should not keep you in a programme that no longer fits). ## Worked example A (fully solved): make or buy and a bottleneck ### Part 1: make or buy tent-pole sets **Situation (fictional).** Northfield's production unit makes 40,000 tent-pole sets a year for its own tents. The standard cost sheet shows USD 15.00 per set. A supplier offers identical sets at USD 12.40 per set for a three-year contract. Fixed overhead of USD 160,000 is charged to the pole cell: USD 60,000 is a supervisor and an equipment lease that would end if production stopped; USD 100,000 is an allocation of plant rent and management that would continue. If Northfield buys, the freed space can assemble a new gear-repair kit expected to earn a contribution of USD 70,000 a year. | Cost per set (standard cost sheet) | USD per set | Relevant to make or buy? | |---|---|---| | Direct material | 6.50 | Yes, avoidable | | Direct labour | 3.20 | Yes, avoidable (staff released or redeployed) | | Variable overhead | 1.30 | Yes, avoidable | | Fixed overhead (USD 160,000 / 40,000) | 4.00 | Only the avoidable USD 60,000 | | **Full cost** | **15.00** | | Spreadsheet layout: B1 = 40,000 sets, B2 = 6.50, B3 = 3.20, B4 = 1.30, B5 = avoidable fixed 60,000, B6 = supplier price 12.40, B7 = opportunity cost 70,000. | Step | Quantity | Excel formula | Result | |---|---|---|---| | 1 | Relevant cost of making, before opportunity cost | `=B1*(B2+B3+B4)+B5` | USD 500,000 (USD 12.50 per set) | | 2 | Cost of buying | `=B1*B6` | USD 496,000 | | 3 | Advantage of buying, no other use of space | `=B1*(B2+B3+B4)+B5-B1*B6` | USD 4,000 | | 4 | Relevant cost of making, with opportunity cost | `=B1*(B2+B3+B4)+B5+B7` | USD 570,000 | | 5 | Advantage of buying, with the kit line | `=B1*(B2+B3+B4)+B5+B7-B1*B6` | USD 74,000 | | 6 | Supplier price at which Northfield is indifferent | `=(B1*(B2+B3+B4)+B5+B7)/B1` | USD 14.25 per set | **Reading the result.** The full-cost comparison (USD 15.00 against USD 12.40) suggests a saving of USD 104,000, which overstates it: USD 100,000 of allocated overhead stays whether Northfield makes or buys. Without another use for the space, buying saves only USD 4,000 a year, too small to outweigh quality and supply risk. With the repair-kit line, buying saves USD 74,000 a year, and buying stays better up to a supplier price of USD 14.25. **Recommendation:** buy, provided the supplier passes a quality audit and the contract includes delivery-performance terms. The answer is robust to the kit forecast (buying wins even with no kit line) but not to the supplier price: if the kit line is cancelled, any supplier price above USD 12.50 makes in-house production cheaper. ### Part 2: product mix with a sewing bottleneck **Situation (fictional).** Next season, Northfield's sewing room has 18,000 machine hours. Demand at current prices would need 26,500 hours, so sewing is the binding constraint. Other resources have spare capacity. | Product *(Example)* | CM per unit | Sewing hours per unit | CM per sewing hour | Maximum demand | Hours for full demand | |---|---|---|---|---|---| | Jacket | USD 60 | 1.50 | USD 40 | 6,000 | 9,000 | | Sleeping bag | USD 45 | 0.75 | USD 60 | 10,000 | 7,500 | | Tent | USD 120 | 2.50 | USD 48 | 4,000 | 10,000 | Excel: CM per hour `=B2/C2`; rank `=RANK.EQ(D2,$D$2:$D$4)`; hours used by a product `=MIN(E2*C2, available hours left)`. | Plan | Units made | Hours used | Total contribution | Excel formula for contribution | |---|---|---|---|---| | **Rank by CM per sewing hour** (bags, tents, jackets) | 10,000 bags, 4,000 tents, 333 jackets | 7,500 + 10,000 + 499.5 = 17,999.5 | **USD 949,980** | `=10000*45+4000*120+333*60` | | Rank by CM per unit (tents, jackets, bags) | 4,000 tents, 5,333 jackets, 0 bags | 10,000 + 7,999.5 = 17,999.5 | USD 799,980 | `=4000*120+5333*60` | Ranking by contribution per bottleneck hour earns USD 150,000 more. The sleeping bag has the lowest CM per unit but the highest per sewing hour, because it uses so little of the scarce resource. The marginal product is the jacket, so the **shadow price** of a sewing hour is USD 40: Northfield should pay up to USD 40 per hour above normal variable cost for overtime or subcontracted sewing, and should value any order that uses sewing hours at USD 40 per hour of opportunity cost (used in Worked example B). The shadow price holds only for small changes: about 500 sewing hours now go to jackets, so an order needing more than that would next displace tents, at USD 48 per hour. With more than one binding constraint, set this up in Excel Solver: objective `=SUMPRODUCT(CM,units)`, changing cells = units, constraints `=SUMPRODUCT(hours,units)<=18000` and units <= demand. ```vega-lite { "$schema": "https://vega.github.io/schema/vega-lite/v5.json", "title": "Contribution per unit versus per sewing hour (Example, fictional data)", "width": 360, "height": 200, "data": {"values": [ {"product": "Jacket", "measure": "CM per unit (USD)", "value": 60}, {"product": "Sleeping bag", "measure": "CM per unit (USD)", "value": 45}, {"product": "Tent", "measure": "CM per unit (USD)", "value": 120}, {"product": "Jacket", "measure": "CM per sewing hour (USD)", "value": 40}, {"product": "Sleeping bag", "measure": "CM per sewing hour (USD)", "value": 60}, {"product": "Tent", "measure": "CM per sewing hour (USD)", "value": 48} ]}, "mark": "bar", "encoding": { "x": {"field": "product", "type": "nominal", "title": null}, "xOffset": {"field": "measure"}, "y": {"field": "value", "type": "quantitative", "title": "USD"}, "color": {"field": "measure", "type": "nominal", "title": "Measure"} } } ``` ## Dropping a product line: a solved illustration Northfield's store division reports three product lines. Footwear shows a loss after allocated head-office costs, and a board member asks whether to drop it. | Line item (USD) *(Example)* | Footwear | Apparel | Equipment | Total | |---|---|---|---|---| | Sales | 2,400,000 | 6,000,000 | 4,000,000 | 12,400,000 | | Variable costs | 1,560,000 | 4,200,000 | 2,600,000 | 8,360,000 | | **Contribution margin** | **840,000** | **1,800,000** | **1,400,000** | **4,040,000** | | Traceable fixed, avoidable (staff, space, displays) | 520,000 | 900,000 | 700,000 | 2,120,000 | | Traceable fixed, unavoidable (fixture depreciation) | 100,000 | 150,000 | 120,000 | 370,000 | | **Segment margin** | **220,000** | **750,000** | **580,000** | **1,550,000** | | Allocated common costs (head office, by sales) | 300,000 | 600,000 | 500,000 | 1,400,000 | | Operating income | (80,000) | 150,000 | 80,000 | 150,000 | Store data show that about 5% of apparel contribution comes from customers who come in for footwear. If Footwear is dropped and the space stays empty: | Effect | Excel formula | USD | |---|---|---| | Footwear contribution lost | `=-B4` | (840,000) | | Avoidable traceable fixed cost saved | `=B5` | 520,000 | | Apparel contribution lost (5%) | `=-0.05*C4` | (90,000) | | **Change in company operating income** | `=-B4+B5-0.05*C4` | **(410,000)** | Company operating income would fall from USD 150,000 to a loss of USD 260,000. The fixture depreciation is sunk and the USD 300,000 of head-office cost would simply be reallocated to Apparel and Equipment. Dropping Footwear makes sense only if the space can earn more than USD 410,000 of contribution a year from another use, which becomes the hurdle for any replacement proposal. ## Worked example B (half solved): a special order **Situation (fictional).** A mountaineering club asks Northfield for 600 sleeping bags with its logo at USD 80 each. The regular price is USD 110 and the regular variable cost is USD 65, which includes a USD 5 store commission that does not apply to a direct club order. Embroidery adds USD 4 per bag, and a one-off machine set-up costs USD 3,000. Each bag uses 0.75 sewing hours. The club's members are not regular Northfield customers, and the order would not affect regular prices. | Step | Quantity | Excel formula | Result | |---|---|---|---| | 1 | Incremental variable cost per bag | `=65-5+4` | USD 64 | | 2 | Incremental contribution before set-up | `=600*(80-64)` | [ ] | | 3 | Incremental profit if sewing has spare capacity | [ ] | USD 6,600 | | 4 | Sewing hours used by the order | `=600*0.75` | [ ] | | 5 | Opportunity cost if sewing is at full capacity (shadow price USD 40 from Worked example A) | [ ] | [ ] | | 6 | Incremental profit at full capacity | [ ] | [ ] | | 7 | Minimum acceptable price per bag, spare capacity | `=64+3000/600` | [ ] | | 8 | Minimum acceptable price per bag, full capacity | [ ] | USD 99.00 | 9. Write the recommendation for each capacity situation in one sentence. [ ] 10. Name two qualitative factors that could change the answer. [ ] ## Exercise C (unsolved): keep or replace a test rig Corvane Robotics tests every robot drive unit on a rig bought two years ago for USD 400,000. Its book value is now USD 240,000 and it has three years of life left. It costs USD 150,000 a year to operate and could be sold today for USD 60,000; at the end of three years it will be worth nothing. A new rig costs USD 330,000, also lasts three years with no final value, and costs USD 40,000 a year to operate. Output is the same with either rig. Ignore taxes. 1. Which figures are sunk, and which are relevant? 2. Compare the total relevant costs of keeping and replacing over three years, without discounting. 3. Repeat the comparison in present value at a 10% annual discount rate, with operating costs at the end of each year. Give the Excel formulas (`=PV` or an annuity factor). 4. Explain why the advantage of replacing shrinks so much once you discount. 5. A manager says: "We cannot replace the rig, we would book a USD 180,000 loss on disposal." Respond in two sentences. ## Connections to other cards | Card or template | Connection | |---|---| | mba/mba-cvp-breakeven-card | Same contribution margin logic; CVP for the whole business, relevant costing for one decision | | mba/mba-activity-based-costing-card | Identifies which "fixed" overheads are really avoidable when a product or customer goes | | mba/mba-process-analysis-card | Finds the bottleneck whose hour you price with the shadow price | | mba/mba-npv-irr-card | Multi-year relevant cash flows are discounted; sunk costs stay out | | mba/mba-pricing-card | Minimum price for exceptions versus value-based pricing for regular business | | mba/mba-managerial-accounting-guide | Transfer pricing applies the same opportunity-cost floor to internal sales | | finance/capex-request and finance/investment-appraisal | Formal templates for replacement and outsourcing proposals | ## Common mistakes and misconceptions 1. **Counting sunk costs.** Book value, past design spend and tuition already paid are irrelevant; only future cash flows count. 2. **Comparing a supplier quote with full cost.** Allocated fixed overhead that continues after outsourcing must stay out of the make cost. 3. **Forgetting the opportunity cost of freed capacity.** It often decides make-or-buy and drop decisions. 4. **Dropping a segment because of allocated costs.** Judge it on segment margin, and remember that its share of common costs moves to the survivors. 5. **Ranking by CM per unit or margin percentage under a constraint.** Rank by contribution per unit of the constrained resource. 6. **Accepting special orders without checking capacity.** At full capacity, the order displaces regular contribution. 7. **Ignoring interdependence.** Products sold together (footwear and apparel) lose contribution when one is dropped. 8. **Treating all fixed costs as unavoidable.** Ask which contracts, leases and salaries actually end, and when. 9. **Using relevant costing for regular pricing.** Pricing all business at incremental cost never recovers fixed cost. 10. **Allocating joint costs to decide whether to process further.** Joint costs incurred before split-off are sunk for that choice; compare only incremental revenue and incremental processing cost. ## Self-test questions 1. State the two conditions that make a cost relevant, with one example of a cost that fails each condition. 2. Why is the USD 100,000 of allocated plant overhead irrelevant in Worked example A, Part 1? 3. In Part 1, if the repair-kit line is cancelled, at what supplier price would Northfield be indifferent between making and buying? 4. Why does the sleeping bag rank first in Part 2 although it has the lowest CM per unit? 5. A product can be sold at split-off for USD 30 a unit, or processed further at a cost of USD 18 a unit and sold for USD 52. Joint costs before split-off are USD 22 a unit. Should it be processed further? By how much per unit? 6. Overtime sewing costs USD 25 an hour above normal variable cost. Should Northfield buy 500 overtime hours, and what is the gain? (Assume jacket demand is still unmet.) 7. What is the shadow price of a constrained resource, and how does a manager use it? 8. Why should a segment be judged on segment margin rather than on operating income after allocations? 9. Give two qualitative factors in a make-or-buy decision and say how you would test each. 10. Why do multi-year relevant cost comparisons need discounting? Give one example from this card. ## My notes and next steps | Date | Note or action *(Example rows)* | |---|---| | YYYY-MM-DD | *Example:* Rebuilt Part 2 in Excel Solver, same plan and USD 949,980 contribution | | YYYY-MM-DD | *Example:* Missed self-test 5 (counted joint cost); logged in mba/mba-error-log | | YYYY-MM-DD | [Next: read mba/mba-activity-based-costing-card] | ## Sources and further reading - Goldratt, E. M., and Cox, J. (1984). *The Goal: A Process of Ongoing Improvement*. North River Press. (Theory of constraints: the bottleneck governs system throughput.) - Johnson, H. T., and Kaplan, R. S. (1987). *Relevance Lost: The Rise and Fall of Management Accounting*. Harvard Business School Press. - Cooper, R., and Kaplan, R. S. (1988). Measure costs right: make the right decisions. *Harvard Business Review*, 66(5). (Why unit costs from volume-based allocation mislead product decisions.) - Textbooks, by name only: Datar, S. M., and Rajan, M. V., *Horngren's Cost Accounting: A Managerial Emphasis* (Pearson); Garrison, R. H., Noreen, E. W., and Brewer, P. C., *Managerial Accounting* (McGraw Hill); Zimmerman, J. L., *Accounting for Decision Making and Control* (McGraw Hill). - Open resource: OpenStax, *Principles of Accounting, Volume 2: Managerial Accounting* (CC BY-NC-SA 4.0), https://openstax.org/details/books/principles-managerial-accounting, chapter on short-term decision making. - Spreadsheet tools: Microsoft Support pages for the Solver add-in and the PV function. ## Answer key **Worked example B.** (1) USD 64. (2) USD 9,600. (3) `=600*(80-64)-3000` = USD 6,600. (4) 450 hours, within the roughly 500 hours now spent on jackets, so the USD 40 shadow price applies. (5) `=450*40` = USD 18,000. (6) `=600*(80-64)-3000-450*40` = USD (11,400), a loss. (7) USD 69.00. (8) `=64+(3000+18000)/600` = USD 99.00. (9) With spare sewing capacity, accept: the order adds USD 6,600. At full capacity, reject at USD 80 or counter at USD 99.00 or more, because the order would displace jackets worth USD 40 per sewing hour. (10) Risk that regular customers learn of the USD 80 price and ask for it; brand exposure from the club logo; delivery timing against the peak season. **Exercise C.** (1) Sunk: the USD 400,000 purchase price and the USD 240,000 book value. Relevant: the USD 60,000 sale value today, the new rig's USD 330,000, and both operating costs. (2) Keep: 3 x 150,000 = USD 450,000. Replace: 330,000 - 60,000 + 3 x 40,000 = USD 390,000. Replace saves USD 60,000. (3) Annuity factor at 10% for 3 years = 2.48685 (`=PV(10%,3,-1)`). PV keep = USD 373,028 (`=PV(10%,3,-150000)`); PV replace = 330,000 - 60,000 + 99,474 = USD 369,474 (`=330000-60000+PV(10%,3,-40000)`). Replace saves USD 3,554 in present value. (4) The new rig's cost is paid today, while the savings of USD 110,000 a year arrive over three years and are worth less in today's money. (5) The book loss is an accounting consequence of a sunk cost; it does not change any future cash flow. Decide on the USD 3,554 present-value saving (and taxes, if the loss is tax-deductible, which would make replacing more attractive). **Self-test.** 1. Future and differential. Fails "future": last year's consulting fee. Fails "differential": the CEO's salary in a make-or-buy. 2. It is charged to the pole cell but continues whether Northfield makes or buys; it is unavoidable. 3. USD 12.50 per set: the relevant cost of making, 500,000 / 40,000 (`=(40000*(6.5+3.2+1.3)+60000)/40000`). With the kit line the indifference price rises to USD 14.25. 4. It uses only 0.75 sewing hours per unit, so it earns USD 60 per sewing hour, the highest of the three. 5. Yes: incremental revenue 52 - 30 = 22 exceeds incremental cost 18, a gain of USD 4 per unit. The USD 22 joint cost is irrelevant. 6. Yes: each hour earns USD 40 of jacket contribution and costs USD 25 extra, a gain of USD 15 an hour, or USD 7,500 for 500 hours (`=500*(40-25)`). 7. The contribution earned by one more unit of the constrained resource used on the marginal product. Use it as the maximum price for extra capacity and as the opportunity cost charged to any work that uses the resource. 8. Allocated common costs do not disappear if the segment goes; segment margin shows what the segment adds to company profit. 9. Quality and supply reliability (audit the supplier, pilot order, delivery terms); loss of know-how or flexibility (scenario where volume doubles or the supplier fails). 10. Money has a time value, so a cost paid today weighs more than savings spread over later years. In Exercise C the undiscounted saving of USD 60,000 falls to USD 3,554 in present value. ## Revision history | Version | Date | Author | Change summary | |---|---|---|---| | 0.1 | YYYY-MM-DD | [Your name] | First draft from the template | | 0.2 | YYYY-MM-DD | [Your name] | *Example:* Replaced Northfield data with the course case, added a Solver model | ## Standard and licence note Based on the relevant-cost and opportunity-cost principles of the management accounting literature listed above (Johnson and Kaplan 1987; Cooper and Kaplan 1988) and on the theory of constraints (Goldratt and Cox 1984), as treated in the standard managerial accounting textbooks named as further reading. The text, the worked examples, the exercises and the questions are original; no textbook text or problem is copied or paraphrased, and Northfield Outdoor Co. and Corvane Robotics are fictional companies. This card is independent and not affiliated with or endorsed by any business school, publisher or professional body. Check your course's notation and your spreadsheet's current function documentation before you rely on it. Template licence: MIT.