Cost Accounting Problems and Solutions (With Answers)
Eight worked problems with step-by-step solutions: cost classification, cost of goods sold, overhead absorption, absorption vs marginal costing, break-even and variances.
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Try each problem on paper first, then open the solution to check your method as well as your answer. Problems run from easy to hard. New to the topic? Start with the Cost Accounting learning path and the glossary.
- 1. Classify costs
- 2. Prime cost
- 3. Cost of goods sold
- 4. Overhead absorption
- 5. Job costing
- 6. Absorption vs marginal
- 7. Break-even
- 8. Variances
Problem 1: Classify the costs of a furniture workshop
A workshop makes wooden tables. Classify each cost as direct or indirect and as fixed or variable: (a) timber used in the tables, (b) workshop rent, (c) wages of carpenters who build the tables, (d) salary of the workshop supervisor, (e) electricity used to run the machines.
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| Cost | Direct or indirect | Fixed or variable |
|---|---|---|
| (a) Timber | Direct material | Variable: rises with output |
| (b) Workshop rent | Indirect (overhead) | Fixed |
| (c) Carpenters’ wages | Direct labour | Variable if paid per table or per hour worked |
| (d) Supervisor’s salary | Indirect labour (overhead) | Fixed |
| (e) Electricity for machines | Indirect (overhead) | Semi-variable: a standing charge plus usage |
Key takeaway: “direct or indirect” asks whether you can trace the cost to a product. “Fixed or variable” asks how it behaves when output changes. They are separate questions. See direct cost, fixed cost and variable cost.
Problem 2: Prime cost and total production cost
A factory reports: direct materials 12,000; direct labour 8,000; direct expenses 1,500; factory overhead 6,000. Calculate (a) the prime cost and (b) the total production cost.
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- Prime cost = direct materials + direct labour + direct expenses.
- Prime cost = 12,000 + 8,000 + 1,500 = 21,500.
- Total production cost = prime cost + factory overhead = 21,500 + 6,000 = 27,500.
Key takeaway: prime cost contains only direct costs. Adding overhead gives the full cost of production.
Problem 3: Calculate cost of goods sold and gross profit
Opening inventory 4,000; purchases 28,000; carriage inwards 1,000; closing inventory 5,500; sales 40,000. Find the cost of goods sold and the gross profit.
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| Opening inventory | 4,000 |
| Add: purchases | 28,000 |
| Add: carriage inwards | 1,000 |
| Goods available for sale | 33,000 |
| Less: closing inventory | (5,500) |
| Cost of goods sold | 27,500 |
|---|
Gross profit = sales − cost of goods sold = 40,000 − 27,500 = 12,500.
Key takeaway: carriage inwards is part of the cost of getting goods ready for sale, so it is added to purchases. See cost of goods sold.
Problem 4: Under- or over-absorbed overhead
Budgeted overhead is 120,000 and budgeted machine hours are 40,000. Actual overhead was 126,000 and actual machine hours were 41,000. Calculate the absorption rate, the overhead absorbed, and the under- or over-absorption.
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- Absorption rate = budgeted overhead ÷ budgeted hours = 120,000 ÷ 40,000 = 3 per machine hour.
- Overhead absorbed = actual hours × rate = 41,000 × 3 = 123,000.
- Actual overhead = 126,000. Absorbed 123,000, so overhead is under-absorbed by 3,000.
Key takeaway: under-absorption means too little overhead was charged to products. The 3,000 shortfall is normally written off against profit for the period. See overhead.
Problem 5: Cost and price a job
Job 101 uses materials costing 2,400 and 30 labour hours at 12 per hour. Overhead is absorbed at 5 per labour hour. The firm prices jobs at cost plus a 25% mark-up. Find the total cost and the selling price.
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| Direct materials | 2,400.00 |
| Direct labour (30 × 12) | 360.00 |
| Overhead (30 × 5) | 150.00 |
| Total cost | 2,910.00 |
|---|---|
| Mark-up 25% (2,910 × 0.25) | 727.50 |
| Selling price | 3,637.50 |
Key takeaway: a mark-up is a percentage of cost. A margin is a percentage of selling price. Here the profit is 727.50 on a price of 3,637.50, which is a 20% margin.
Problem 6: Profit under absorption and marginal costing
A company produced 10,000 units and sold 8,000 at 30 each. The variable production cost is 14 per unit. Fixed production overhead is 50,000, absorbed at 5 per unit. There was no opening inventory and there are no other costs. Calculate the profit under (a) absorption costing and (b) marginal costing, and explain the difference.
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(a) Absorption costing. Unit cost = 14 + 5 = 19.
| Sales (8,000 × 30) | 240,000 |
| Cost of goods sold (8,000 × 19) | (152,000) |
| Profit | 88,000 |
|---|
(b) Marginal costing.
| Sales | 240,000 |
| Variable cost (8,000 × 14) | (112,000) |
| Contribution | 128,000 |
| Fixed production overhead | (50,000) |
| Profit | 78,000 |
|---|
Difference = 88,000 − 78,000 = 10,000. Closing inventory is 2,000 units (10,000 − 8,000). Under absorption costing each carries 5 of fixed overhead, so 2,000 × 5 = 10,000 of fixed cost is deferred in inventory instead of charged to this period.
Key takeaway: when production exceeds sales, absorption costing shows the higher profit. See absorption costing and marginal costing.
Problem 7: Break-even, target profit and margin of safety
A product sells for 60 and has a variable cost of 35 per unit. Fixed costs are 50,000. Calculate (a) the break-even point in units and in sales value, (b) the units needed to earn a profit of 20,000, and (c) the margin of safety if the firm sells 3,200 units.
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- Contribution per unit = 60 − 35 = 25.
- (a) Break-even units = 50,000 ÷ 25 = 2,000 units. In sales value: 2,000 × 60 = 120,000.
- (b) Units for target profit = (fixed costs + target profit) ÷ contribution per unit = (50,000 + 20,000) ÷ 25 = 2,800 units.
- (c) Margin of safety = 3,200 − 2,000 = 1,200 units, or 1,200 ÷ 3,200 = 37.5% of sales.
Key takeaway: every break-even question starts with contribution per unit. See break-even point and margin of safety.
Problem 8: Material price and usage variances
The standard material cost is 3 kg per unit at 4 per kg. The company made 1,000 units. It bought and used 3,200 kg at 4.25 per kg. Calculate the material price variance, the material usage variance, and the total material variance.
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- Standard quantity for 1,000 units = 1,000 × 3 = 3,000 kg. Standard cost = 3,000 × 4 = 12,000.
- Actual cost = 3,200 × 4.25 = 13,600.
- Price variance = (standard price − actual price) × actual quantity = (4.00 − 4.25) × 3,200 = 800 adverse.
- Usage variance = (standard quantity − actual quantity) × standard price = (3,000 − 3,200) × 4 = 800 adverse.
- Total variance = 800 + 800 = 1,600 adverse. Check: 13,600 − 12,000 = 1,600.
Key takeaway: price variance explains the cost per kg. Usage variance explains the quantity used. Together they reconcile standard cost to actual cost. See standard costing and variance analysis.
Frequently asked questions
How do I solve an overhead absorption problem?
Divide budgeted overhead by the budgeted activity (such as machine hours) to get the rate. Multiply the rate by actual activity to find the overhead absorbed. Compare it with actual overhead to find under- or over-absorption.
Why do absorption and marginal costing give different profits?
They treat fixed production overhead differently. Absorption costing includes it in unit cost, so some is held in closing inventory. Marginal costing charges all of it to the period. The profits differ only when inventory levels change.
How do you calculate break-even units?
Divide fixed costs by contribution per unit, where contribution is selling price minus variable cost per unit.
Keep learning
These problems are for general learning. Methods and terminology vary by syllabus and country, so follow your own course materials for exams.