BA2: Costing

Answer: A. A direct cost can be traced in full to the cost object — here, the timber physically incorporated into each table. The other three are indirect production costs (overheads): the supervisor's salary, machine depreciation and factory rent all support production generally but cannot be traced to a single table without apportionment. This distinction underpins all later costing work, so it is worth being secure on it.

Answer: C. The cost is fixed within a range of activity but jumps to a new fixed level once capacity is exceeded — the defining pattern of a stepped fixed cost. A variable cost would change continuously with each unit stored. A semi-variable cost has both a fixed and a variable element that varies with every unit. A pure fixed cost would not change at all across the activity range described. Recognising stepped costs matters because treating them as ordinary fixed costs understates cost at higher activity.

Answer: D. Variable cost per unit = (£74,000 − £54,000) ÷ (10,000 − 6,000) = £20,000 ÷ 4,000 = £5.00. Fixed cost = £74,000 − (10,000 × £5.00) = £24,000. Total cost at 8,000 units = £24,000 + (8,000 × £5.00) = £64,000. The £40,000 figure is the variable element only, omitting fixed cost, while £54,000 and £74,000 simply repeat the low and high observed totals without flexing to 8,000 units.

Answer: B. A relevant cost is a future cash flow that arises as a direct consequence of the decision. Materials bought specifically for the order meet this test. Depreciation is a non-cash, committed cost that does not change with the decision. Apportioned general fixed overheads are not incremental — they would be incurred regardless. Design costs already spent are sunk and cannot be relevant. The common error is to include apportioned overheads or sunk costs simply because they appear on a cost statement.

Answer: A. Let S and M be the total costs after reciprocal servicing. S = 18,000 + 0.50M and M = 9,000 + 0.20S. Substituting: M = 9,000 + 0.20(18,000 + 0.50M) = 9,000 + 3,600 + 0.10M, so 0.90M = 12,600 and M = £14,000. The £12,600 figure is the single-pass result that ignores the cost returning from Stores; £9,000 is the primary allocation before any reapportionment; and £18,000 is the Stores primary figure.

Answer: A. Overhead absorption rate = £180,000 ÷ 12,000 = £15 per labour hour. Overhead absorbed = 12,400 × £15 = £186,000. Actual overhead incurred = £190,000. As absorbed (£186,000) is less than incurred (£190,000), overhead is under-absorbed by £4,000. The £10,000 figure compares actual to budgeted overhead, ignoring the hours worked; £6,000 compares absorbed to budgeted overhead rather than to actual; and £2,000 is unsupported by the figures.

Answer: D. Full absorption cost includes all production costs: £8 + £6 + £2 + £4 = £20. The £14 figure is prime cost only (materials plus labour); £16 is the marginal (variable) production cost, omitting fixed overhead; and £18 wrongly omits the variable production overhead. Absorption costing differs from marginal costing precisely by including the fixed production overhead per unit.

Answer: A. The marginal cost of production is the variable production cost: prime cost £22 + variable production overhead £5 = £27. Fixed production overhead is excluded because it does not vary with production, and variable selling cost is excluded because it is not a production cost. The £30 figure wrongly adds the variable selling cost, £34 wrongly adds the fixed production overhead, and £37 adds everything. 'Marginal cost of production' excludes both fixed and non-production costs.

Answer: D. Production exceeded sales by 1,000 units, so inventory increased by 1,000 units. Under absorption costing, £6 of fixed overhead is carried forward in each unit of closing inventory, deferring £1,000 × £6 = £6,000 of fixed overhead to the next period. Absorption profit therefore exceeds marginal profit by £6,000: £40,000 + £6,000 = £46,000. The £34,000 figure subtracts the difference — the adjustment is reversed only when inventory falls; £40,000 ignores the inventory change; and £6,000 is the difference alone.

Answer: D. A margin is expressed as a percentage of selling price, so cost represents the remaining 75%: selling price = £90 ÷ 0.75 = £120.00. The £112.50 figure is the classic margin/mark-up error — adding 25% to cost (£90 × 1.25) gives a 25% mark-up, not a 25% margin. The £72.00 figure deducts 25% from cost, and £108.00 adds 20%. 'Margin' is based on selling price while 'mark-up' is based on cost.

Answer: D. Rent and rates relate to the premises, so floor area occupied is the most appropriate and commonly used basis for apportioning them across departments. Number of employees suits costs such as canteen or personnel; machinery value suits insurance or depreciation of plant; and labour hours are an absorption basis for production overhead. The apportionment basis should reflect the way each department causes or benefits from the cost.

Answer: A. The overhead absorption rate = budgeted overheads ÷ budgeted activity = £240,000 ÷ 30,000 machine hours = £8.00 per machine hour. The figure £0.125 inverts the calculation (hours ÷ overheads). £12.50 inverts the ratio and multiplies by 100 (30,000 ÷ 240,000 × 100), and £80.00 misplaces the decimal point. Dividing budgeted overhead by the budgeted level of the chosen activity gives the rate at which overhead is charged to output.

Answer: B. Overhead absorbed = 31,000 × £8 = £248,000. Actual overhead incurred = £242,000. As more was absorbed (£248,000) than was incurred (£242,000), overhead is over-absorbed by £6,000. Over-absorption arises here because actual hours exceeded the level implied by spending. The £2,000 figures compare the wrong amounts. Over-absorbed overhead is credited to the income statement, increasing profit.

Answer: C. Sales exceeded production by 1,000 units, so inventory fell by 1,000 units. When inventory falls, absorption costing releases fixed overhead held in opening inventory, so absorption profit is lower than marginal profit by 1,000 × £5 = £5,000. Marginal profit = £60,000 + £5,000 = £65,000. The £55,000 figure adjusts in the wrong direction. When inventory falls, marginal profit exceeds absorption profit.

Answer: D. Variable cost per unit = (£88,000 − £60,000) ÷ (9,000 − 5,000) = £28,000 ÷ 4,000 = £7.00. Fixed cost = total cost − variable cost = £60,000 − (5,000 × £7.00) = £60,000 − £35,000 = £25,000 (confirmed at the high point: £88,000 − 9,000 × £7 = £25,000). The £7.00 figure is the variable cost per unit, not the fixed cost; £28,000 is the cost difference; and £60,000 is a total cost, not the fixed element.

Answer: A. A mark-up is added to cost, so selling price = £60 × (1 + 0.40) = £60 × 1.40 = £84. A mark-up of 40% on cost is not the same as a 40% margin on selling price (which would give £100). The £42 and £36 figures reduce rather than increase the cost. Mark-up is always based on cost, whereas margin is based on selling price — a frequent source of error.

Answer: A. Variable cost per unit = (£5,400 − £4,200) ÷ (900 − 600) = £1,200 ÷ 300 = £4.00. A semi-variable cost has a fixed element plus a variable element, and the high-low method isolates the variable element from the change in cost over the change in activity. The £7.00 and £6.00 figures result from dividing a total cost by units rather than using the differences, and £1.33 inverts part of the calculation.

Answer: B. P2 receives 40% of the service department overhead: £30,000 × 40% = £12,000 (and P1 receives the remaining £18,000). The £18,000 figure is P1's share, not P2's. The £15,000 figure would be an even split, which does not match the 60:40 ratio. Service department costs are reapportioned to production departments so that all overhead is ultimately recovered through production cost units.

Answer: C. Marginal cost is the variable cost of producing one more unit, comprising direct materials, direct labour and variable production overhead. Fixed factory rent, the managing director's salary and building depreciation are all fixed costs that do not change with the level of output and so are excluded from marginal cost. The defining test is whether the cost varies with the volume of production.

Answer: D. The profit difference = change in inventory units × fixed overhead per unit. Here the difference is £92,000 − £80,000 = £12,000, so the change in inventory = £12,000 ÷ £4 = 3,000 units. Because absorption profit is higher than marginal profit, inventory must have increased (fixed overhead was carried forward in closing inventory). The 12,000-unit figures forget to divide by the £4 rate, and a decrease would make absorption profit the lower of the two.

Answer: A. With a 20% margin on selling price, cost represents 80% of the selling price: selling price = £48 ÷ 0.80 = £60.00. The £57.60 figure adds 20% to cost (£48 × 1.20), which is a 20% mark-up, not a 20% margin. The £40.00 figure deducts 20% from cost. The distinction is that a margin is based on selling price (divide by 1 − margin) while a mark-up is based on cost (multiply by 1 + mark-up). £58.00 does not follow from either a margin or a mark-up calculation.

Answer: B. The £5,000 has already been spent and cannot be recovered, so it is a sunk cost and is irrelevant to the launch decision. A relevant cost is a future cash flow affected by the decision, and an opportunity cost is the benefit forgone from the next best alternative — neither describes money already committed. Sunk costs should be ignored in decision making because they do not change with the choice made.

Answer: C. Overhead absorbed = 150% × £8 direct labour = £12. Full production cost = direct materials £12 + direct labour £8 + overhead £12 = £32. The £20 figure is prime cost only (materials plus labour), omitting overhead. The £30 figure applies the 150% rate to materials rather than labour. When overhead is absorbed as a percentage of labour cost, the percentage is applied to the direct labour figure. £44 counts the £12 overhead twice.

Answer: D. A predetermined rate is set in advance using budgeted overheads and activity, so that product costs and prices can be determined during the period without waiting for actual figures, which are not known until the period has ended. It does not equal actual overhead exactly — hence over- or under-absorption arises — and it requires, rather than avoids, budgeting. Tax rules are not the reason. Timeliness of costing is the main motivation.

Answer: A. The only difference between absorption and marginal costing profit comes from the fixed overhead carried in changes to inventory. When production equals sales there is no inventory change, so no fixed overhead is deferred or released, and the two methods give the same profit. A difference arises only when inventory rises (absorption higher) or falls (marginal higher). With no inventory movement, the profits are equal.

Answer: B. Required annual profit = 20% × £500,000 = £100,000. Required profit per unit = £100,000 ÷ 10,000 units = £10. Selling price = unit cost £40 + required profit £10 = £50. £48 adds a 20% mark-up to cost (£40 × 1.20), confusing return on investment with a mark-up on cost. £44 adds only 10% to cost, and £60 adds £20 a unit, double the profit required. Return-on-investment pricing adds the profit required to earn the target return on the investment to the unit cost.

Answer: C. Supervisory cost stays constant over a band of activity (up to 20 workers) and then jumps to a new fixed level when another supervisor is required — the pattern of a stepped fixed cost. A purely variable cost would change continuously with each unit, and a semi-variable cost has a fixed plus a continuously variable element. The cost is an indirect overhead, not a direct cost of each unit. The step pattern is the key feature.

Answer: D. The overhead absorption rate = budgeted overhead ÷ budgeted activity = £150,000 ÷ 25,000 labour hours = £6.00 per labour hour. The £0.17 figure inverts the calculation (hours ÷ overhead). Dividing budgeted overhead by the budgeted level of the chosen activity gives the rate at which overhead is charged to each unit of that activity — here, each labour hour. £60.00 misplaces the decimal point, and £3.75 does not follow from the figures.

Answer: A. Variable cost per unit = (£116,000 − £92,000) ÷ (11,000 − 7,000) = £24,000 ÷ 4,000 = £6.00. The high-low method isolates the variable element from the change in total cost over the change in activity between the highest and lowest points. The £10.50 and £8.00 figures come from dividing a total cost by units rather than using the differences. Only the change in cost over the change in volume gives the variable rate. £4.00 does not follow from the cost and volume differences.

Answer: B. Inventory rose by 2,000 units (production exceeded sales). Under absorption costing, £3 of fixed overhead is carried forward in each unit of closing inventory, deferring 2,000 × £3 = £6,000 to the next period, so absorption profit exceeds marginal profit by £6,000: £50,000 + £6,000 = £56,000. The £44,000 figure subtracts the difference, which would apply only if inventory had fallen. When inventory rises, absorption profit is the higher of the two.

Answer: C. The minimum price is the relevant (incremental) cost — the additional cash outflows caused by taking the contract — because any price above this leaves the business better off. Including a share of fixed overhead that would be incurred anyway overstates the minimum, and adding the normal profit margin gives a target price rather than the floor. The minimum acceptable price covers only the incremental cost; profit is what is earned above it.

Answer: D. P1 receives three of the four parts: £40,000 × 3/4 = £30,000 (and P2 receives the remaining £10,000). The £10,000 figure is P2's share, and £20,000 would be an even split, which does not match the 3:1 ratio. Service department overheads are reapportioned to production departments in proportion to the agreed basis so that all overhead is ultimately recovered through production.

Answer: A. A variable cost increases in total in direct proportion to activity, but the cost per unit stays constant. This contrasts with a fixed cost, whose total stays constant while the cost per unit falls as volume rises. A variable cost does not stay constant in total, decrease in total, or rise per unit as output increases. Understanding this behaviour is essential for flexing budgets and for marginal costing.

Answer: B. Overhead absorbed = 9,000 × £5 = £45,000. Actual overhead incurred = £48,000. As less was absorbed (£45,000) than was incurred (£48,000), overhead is under-absorbed by £3,000. Under-absorption arises because the hours worked recovered less overhead than was actually spent. Under-absorbed overhead is debited to the income statement, reducing profit; over-absorption would be the reverse.

Answer: C. Contribution per unit = selling price − total variable cost = £45 − (£12 + £8 + £5) = £45 − £25 = £20. The £25 figure is the total variable cost, not the contribution; £45 is the selling price; and £12 is just the materials. Contribution is what each unit provides towards covering fixed costs and then profit, and it is central to marginal costing and breakeven analysis.

Answer: D. Selling price = £80 × 1.25 = £100, so gross profit = £20. Margin = profit ÷ selling price = £20 ÷ £100 = 20%. The 25% figure is the mark-up on cost, not the margin on selling price — the two differ because they use different bases. A 25% mark-up on cost always equals a 20% margin on selling price. Mark-up is based on cost; margin is based on selling price. 16% does not follow from the figures; 80% is cost as a percentage of selling price.

Answer: A. Opportunity cost is the benefit forgone from the next best alternative use of a resource. Using the machine for the order means giving up the hire income it would otherwise earn, so that lost income is the relevant opportunity cost. The original purchase cost is sunk, depreciation is a non-cash accounting allocation, and the cost is not zero just because the machine is owned — the forgone hire income is a real economic cost.