Management Accounting Problems and Solutions (With Answers)
Eight worked problems with step-by-step solutions: budgeting, flexed budgets, relevant costs, limiting factors, ROI, residual income, payback and NPV.
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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 Management Accounting learning path and the glossary.
- 1. Production budget
- 2. Cash budget
- 3. Flexed budget
- 4. Special order
- 5. Make or buy
- 6. Limiting factor
- 7. ROI and RI
- 8. Payback and NPV
Problem 1: Production and purchases budget
Expected sales are 5,000 units. Opening finished goods inventory is 400 units and the desired closing inventory is 600 units. Each unit needs 2 kg of material costing 3 per kg. Opening material inventory is 500 kg and desired closing material inventory is 700 kg. Find (a) the units to produce, (b) the material needed for production, and (c) the material to purchase, in kg and in cost.
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- (a) Production = sales + closing inventory − opening inventory = 5,000 + 600 − 400 = 5,200 units.
- (b) Material needed = 5,200 × 2 = 10,400 kg.
- (c) Purchases = needed + closing material − opening material = 10,400 + 700 − 500 = 10,600 kg. Cost = 10,600 × 3 = 31,800.
Key takeaway: the same “needed + closing − opening” pattern works for both finished goods and materials. See budget.
Problem 2: One-month cash budget
A business starts the month with 5,000 cash. During the month it expects receipts from customers of 20,000. It expects to pay suppliers 12,000, wages 4,000 and rent 1,500, and to buy equipment for 6,000. The business wants to keep at least 3,000 in cash. Calculate the closing cash balance and any funding needed.
Show solution
| Opening cash | 5,000 |
| Receipts from customers | 20,000 |
| Total available | 25,000 |
| Payments: suppliers 12,000 + wages 4,000 + rent 1,500 + equipment 6,000 | (23,500) |
| Closing cash | 1,500 |
|---|
The minimum balance is 3,000, so there is a shortfall of 3,000 − 1,500 = 1,500. The business needs at least 1,500 of extra funding, such as an overdraft or short-term loan.
Key takeaway: a cash budget tracks cash, not profit. The equipment purchase affects cash now even though it is not an expense. See cash flow.
Problem 3: Flex the budget and explain the variances
The original budget was for 10,000 units: sales 100,000, variable costs 60,000, fixed costs 20,000, profit 20,000. Actual results for 12,000 units were: sales 117,000, variable costs 73,000, fixed costs 21,000. Prepare a flexed budget and explain the profit variances.
Show solution
Budget per unit: selling price 10, variable cost 6. Fixed costs do not flex.
| Original (10,000) | Flexed (12,000) | Actual (12,000) | Variance vs flexed | |
|---|---|---|---|---|
| Sales | 100,000 | 120,000 | 117,000 | 3,000 adverse |
| Variable costs | (60,000) | (72,000) | (73,000) | 1,000 adverse |
| Fixed costs | (20,000) | (20,000) | (21,000) | 1,000 adverse |
| Profit | 20,000 | 28,000 | 23,000 | 5,000 adverse |
Volume effect: flexed profit 28,000 − original 20,000 = 8,000 favourable, because 2,000 more units were sold.
Efficiency and price effects: actual 23,000 − flexed 28,000 = 5,000 adverse (3,000 + 1,000 + 1,000).
Net effect on the original budget: 8,000 − 5,000 = 3,000 favourable (23,000 − 20,000).
Key takeaway: compare actual with the flexed budget to judge performance fairly, because the original budget was set for a different volume. See variance analysis.
Problem 4: Should the firm accept a special order?
A firm has spare capacity. A customer offers to buy 2,000 units at 18 each. The normal cost per unit is: materials 6, labour 4, variable overhead 2, and fixed overhead absorbed 5, a total of 17. Total fixed costs will not change if the order is accepted, and normal sales will not be affected. Should the firm accept?
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- Relevant costs are future costs that change because of the decision. Fixed overhead stays the same either way, so it is not relevant.
- Relevant cost per unit = 6 + 4 + 2 = 12.
- Contribution per unit = 18 − 12 = 6.
- Total extra profit = 2,000 × 6 = 12,000.
Decision: accept the order. Using the full cost of 17 would make the order look like it earns only 1 per unit, which is misleading.
Key takeaway: ignore fixed costs that do not change. See contribution margin and sunk cost.
Problem 5: Make or buy a component
A company needs 5,000 components a year. It can make them at a variable cost of 14 each. Making them also carries fixed costs of 30,000, of which 10,000 would be avoided if it stopped making them. A supplier offers the component at 17 each. Should the company make or buy?
Show solution
| Make | Buy | |
|---|---|---|
| Variable cost (5,000 × 14) | 70,000 | |
| Avoidable fixed costs | 10,000 | |
| Purchase cost (5,000 × 17) | 85,000 | |
| Relevant cost | 80,000 | 85,000 |
The other 20,000 of fixed cost is incurred whichever option is chosen, so it is ignored.
Decision: make the component. It is cheaper by 85,000 − 80,000 = 5,000.
Key takeaway: only avoidable fixed costs are relevant. Compare the relevant cost of each option.
Problem 6: Best product mix with limited machine hours
Product A earns a contribution of 12 per unit and uses 4 machine hours. Product B earns 10 per unit and uses 2 machine hours. Only 6,000 machine hours are available. Maximum demand is 1,500 units of A and 2,000 units of B. Find the plan that maximises contribution.
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- Contribution per machine hour: A = 12 ÷ 4 = 3. B = 10 ÷ 2 = 5.
- Rank by contribution per hour: B first, then A.
- Make B up to demand: 2,000 units × 2 hours = 4,000 hours.
- Hours left = 6,000 − 4,000 = 2,000. Make A with the remainder: 2,000 ÷ 4 = 500 units (below the demand of 1,500).
- Total contribution = (2,000 × 10) + (500 × 12) = 20,000 + 6,000 = 26,000.
Key takeaway: when one resource is limited, rank products by contribution per unit of that resource, not by contribution per unit of product. Product A has the higher contribution per unit, but B is the better use of scarce hours.
Problem 7: ROI versus residual income
A division earns a profit of 90,000 on capital employed of 600,000. The company’s required return is 12%. The manager can invest a further 100,000 in a project that would earn 13,000 a year. Calculate the division’s ROI and residual income now, then say how each measure changes if the project goes ahead.
Show solution
Now:
- ROI = 90,000 ÷ 600,000 = 15%.
- Residual income = profit − (required return × capital employed) = 90,000 − (12% × 600,000) = 90,000 − 72,000 = 18,000.
With the project: profit = 103,000 and capital employed = 700,000.
- ROI = 103,000 ÷ 700,000 = 14.7%, which is lower than 15%.
- Residual income = 103,000 − (12% × 700,000) = 103,000 − 84,000 = 19,000, which is higher by 1,000.
The project itself earns 13% (13,000 ÷ 100,000), which beats the 12% required return.
Key takeaway: a manager judged on ROI might reject a project that is good for the company, because it lowers the divisional average. Residual income encourages accepting any project that earns more than the required return. See return on investment.
Problem 8: Payback period and net present value
A project costs 50,000 now and will return cash inflows of 20,000 at the end of each of the next three years. The cost of capital is 10%. Calculate the payback period and the net present value (NPV), and comment.
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Payback. After two years the business has recovered 40,000. It needs another 10,000 in year 3, which takes 10,000 ÷ 20,000 = 0.5 of the year. Payback = 2.5 years.
NPV at 10%.
| Year | Cash flow | Discount factor (10%) | Present value |
|---|---|---|---|
| 0 | (50,000) | 1.0000 | (50,000) |
| 1 | 20,000 | 0.9091 | 18,182 |
| 2 | 20,000 | 0.8264 | 16,528 |
| 3 | 20,000 | 0.7513 | 15,026 |
| Net present value | (264) | ||
Rounded discount factors give an NPV of about −260 (using the combined factor of 2.4869, the NPV is −262). The exact figure depends on rounding, but it is slightly negative either way.
Comment: payback of 2.5 years may look attractive, but the NPV is slightly negative, so the project does not quite earn the 10% required return. Payback ignores the time value of money. NPV does not.
Frequently asked questions
What is a flexed budget?
A budget adjusted to the actual level of activity. It lets you compare actual results with what costs and revenues should have been at the volume actually achieved.
Which costs are relevant for a decision?
Future costs and revenues that differ between the options. Sunk costs and fixed costs that do not change are irrelevant.
What is residual income?
Profit minus a charge for the capital used, calculated as required return multiplied by capital employed. A positive figure means the division earns more than the required return.
Keep learning
These problems are for general learning. Methods and terminology vary by syllabus and country, so follow your own course materials for exams.