The Cost Allocation Conundrum
A company has two production departments (Machining and Assembly) and two service departments (Maintenance and Personnel). The following costs and usage data are available for the month:
| Department | Overhead costs (£) | Labour hours | Machine hours | Number of employees | Maintenance hours |
|---|---|---|---|---|---|
| Machining | 100,000 | 5,000 | 10,000 | 50 | 2,000 |
| Assembly | 80,000 | 8,000 | 2,000 | 80 | 1,000 |
| Maintenance | 40,000 | 2,000 | 1,000 | 20 | - |
| Personnel | 30,000 | 1,000 | 500 | - | 500 |
Maintenance costs are allocated based on maintenance hours, and Personnel costs are allocated based on number of employees. The company uses the step-down method, allocating Maintenance first, then Personnel. The company is considering switching to the reciprocal method but is unsure of the benefits. The production manager is concerned that the current method may not reflect the true cost of each department and is affecting pricing decisions.
1. Allocate the service department costs to the production departments using the step-down method (Maintenance first, then Personnel). Show the allocation calculations and the final overhead costs for Machining and Assembly.
Read the worked answer
Step 1: Allocate Maintenance costs based on maintenance hours. Total maintenance hours = 2,000 (Machining) + 1,000 (Assembly) + 500 (Personnel) = 3,500 hours. (Maintenance department does not use its own services.) Allocation rates:
- Machining: 2,000/3,500 = 4/7 ≈ 0.5714
- Assembly: 1,000/3,500 = 2/7 ≈ 0.2857
- Personnel: 500/3,500 = 1/7 ≈ 0.1429 Maintenance cost = £40,000. Allocations:
- Machining: £40,000 * 4/7 = £22,857.14
- Assembly: £40,000 * 2/7 = £11,428.57
- Personnel: £40,000 * 1/7 = £5,714.29 After this, Personnel department now has its original cost £30,000 plus £5,714.29 = £35,714.29.
Step 2: Allocate Personnel costs based on number of employees. Total employees in production departments = 50 (Machining) + 80 (Assembly) = 130. (Personnel department has no employees? The table shows '-' for Personnel employees, so we assume no employees in Personnel? Actually, the table shows Personnel department has '-' for number of employees, meaning it has no employees? That seems odd. Typically, Personnel would have employees, but the data shows '-' meaning not applicable or zero. We'll assume Personnel department does not use its own services, so we allocate only to production departments. So total employees = 130. Allocation rates:
- Machining: 50/130 = 5/13 ≈ 0.3846
- Assembly: 80/130 = 8/13 ≈ 0.6154 Personnel cost to allocate = £35,714.29. Allocations:
- Machining: £35,714.29 * 5/13 = £13,736.26
- Assembly: £35,714.29 * 8/13 = £21,978.02
Final overhead costs:
- Machining: original £100,000 + £22,857.14 + £13,736.26 = £136,593.40
- Assembly: original £80,000 + £11,428.57 + £21,978.02 = £113,406.59 (Minor rounding differences may occur.)
2. Explain why the reciprocal method might provide a more accurate allocation than the step-down method, and discuss the potential impact on pricing decisions if the company switches to the reciprocal method.
Read the worked answer
The reciprocal method recognises mutual services provided between service departments. In the step-down method, once a service department's costs are allocated, they are not reallocated back even if that department receives services from other service departments. In this case, Maintenance provides services to Personnel, but Personnel also provides services to Maintenance (as shown by the 500 maintenance hours used by Personnel and the fact that Personnel likely has employees? Actually, the data shows Personnel department has '-' for employees, but it does receive maintenance hours. Also, Maintenance department has 20 employees, so it uses Personnel services. The step-down method ignores the services provided by Personnel to Maintenance because Personnel is allocated after Maintenance, and thus Maintenance's share of Personnel costs is not allocated. The reciprocal method solves simultaneous equations to allocate costs considering all interdepartmental services. This would result in a more accurate reflection of the true cost of each production department because it accounts for the full cost of support services. For pricing decisions, more accurate cost information leads to better pricing. If the step-down method understates the cost of one production department and overstates another, prices may be set too low for some products and too high for others, potentially leading to lost sales or reduced profitability. The reciprocal method, while more complex, provides a fairer allocation, which can improve decision-making. However, the company should consider the cost-benefit of implementing the reciprocal method; if the mutual services are small, the difference may not be material. In this case, the mutual services are not negligible: Personnel uses 500 maintenance hours (about 14% of maintenance hours) and Maintenance has 20 employees (about 13% of total employees? Actually, total employees = 50+80+20 = 150, so Maintenance is 13.3%). So the reciprocal method could change allocations by a few thousand pounds. The impact on pricing depends on the significance of overhead in total product cost. If overhead is a large proportion, the pricing effect could be significant.