Compare fixed, variable, and mixed costs. Q10-2: What do we mean by a Relevant Range?
Read the success on the OAES document for full instructions about how to use this system. Assigned questions for Module 3 are: Q10-1 through Q12-3, covering topics such as costs, breakeven analysis, decision-making, standard costing, cost estimation, and outsourcing. Please ensure your responses are comprehensive, well-structured, and include relevant calculations and explanations where appropriate.
Understanding the distinctions among fixed, variable, and mixed costs is fundamental in managerial accounting, as these classifications influence cost behavior analysis, budgeting, and decision-making. Fixed costs are expenses that remain constant in total regardless of the level of production or sales within a relevant operating range. Examples include rent, salaries, and insurance. Variable costs change directly with the level of activity or production volume, such as raw materials and direct labor costs associated with manufacturing. Mixed costs contain elements of both fixed and variable costs; they vary with activity but not in direct proportion, exemplified by utility costs that have a fixed basic charge plus a usage-based component.
In analyzing cost behavior, the concept of the "relevant range" is essential. The relevant range refers to the scope of activity within which assumptions about fixed and variable costs are valid. It recognizes that beyond certain capacity limits or activity levels, costs may change; for example, additional factory space or equipment might be required, altering fixed costs, or variable costs per unit might fluctuate due to capacity constraints or economies of scale. Accurately defining this range ensures precise cost estimation and effective decision-making.
Quantitative examination of cost behavior involves calculating total costs at different activity levels. For instance, if a professional services business has fixed costs of €150,000 and variable costs of €15 per hour, the average cost per unit at activity levels of 12,000 and 15,000 units can be computed. At 12,000 units, total costs would be €150,000 + (€15 × 12,000) = €150,000 + €180,000 = €330,000, leading to an average cost per unit of €330,000 / 12,000 ≈ €27.50. At 15,000 units, total costs would be €150,000 + (€15 × 15,000) = €150,000 + €225,000 = €375,000, with an average cost per unit of €375,000 / 15,000 = €25. Therefore, as volume increases, the average cost per unit decreases, illustrating economies of scale and the importance of cost behavior analysis for pricing and profit planning.
Break-even analysis is a key managerial tool used to determine the level of sales necessary to cover all
fixed and variable costs, resulting in zero profit. Using the provided data: fixed costs of £240,000, selling price of £18.00 per unit, and variable costs of £12.60 per unit, the break-even point in units can be calculated as Fixed Costs / (Selling Price - Variable Cost). This yields 240,000 / (18 - 12.6) = 240,000 / 5.4
≈ 44,445 units. The break-even sales in monetary terms are 44,445 units × £18 = approximately £800,000. To approach a target profit of £120,000, total required contribution is fixed costs + target profit = £240,000 + £120,000 = £360,000. The required sales volume in units is £360,000 / (18 - 12.60) ≈ 66,667 units.
Margin of safety measures the extent by which expected or actual sales exceed the break-even sales, offering a buffer that sustains profitability despite sales fluctuations. Given projected sales of 50,000 units and the break-even point of approximately 44,445 units, the margin of safety in units is 50,000 - 44,445 ≈ 5,555 units. Expressed as a percentage, it is (5,555 / 50,000) × 100 ≈ 11.11%. This indicates the company can withstand an 11.11% decline in sales before incurring losses.
For a company producing products at $12 each, with fixed costs averaging $3 per unit and unchanged sales volume of 10,000 units per month, the total fixed costs amount to 10,000 × $3 = $30,000. A special order of 2,000 units at $9 per unit, below the regular selling price of $12, presents a strategic decision. The variable cost per unit is $10, including fixed costs allocated per unit; thus, the relevant cost is $10 per unit. Since the offered price of $9 is below the variable cost of $10, accepting the order would result in a loss of $1 per unit on the special order, totaling $2,000. Therefore, the company should reject the special order unless it can be sold at a price covering at least the variable cost and contributed to fixed costs.
Standard costing involves establishing predetermined or budgeted costs for materials, labor, and overhead, serving as benchmarks for performance evaluation and cost control. It simplifies cost measurement, variance analysis, and performance management by comparing actual costs with standards, identifying deviations for managerial action.
Job costing assigns costs to specific jobs or orders, which is suitable for customized products and services. Process costing, in contrast, accumulates costs by process or department for homogeneous products produced continuously. The primary difference lies in the granularity of cost accumulation: job costing offers detailed or unit-specific information, while process costing provides averaged costs over periods for mass production.
Little Known Tax Ltd employs six bookkeepers, each costing £10,000 weekly, and they collectively work 150 hours on client jobs at 30 hours per week per bookkeeper. To find spare capacity, calculate total
available hours: 6 × 30 = 180 hours. If the total hours charged are 150, the spare capacity in hours is 180150 = 30 hours. The spare capacity in monetary terms is 30 hours × (£10,000 / 6 / 30 hours) = £10,000 in weekly capacity, with 30 hours of unused productive time available.
Last Group faces a monthly rental cost of €25,000 for its premises under a four-year lease, along with casual staff costs of €12,000 and call costs of €5,000 monthly. An offshore call center offers to conduct telephone sales at a fixed fee of €15,000 per month, including staff and telephone charges. To evaluate whether to outsource, compare total costs: in-house costs are €12,000 + €5,000 + €25,000 = €42,000 per month. The outsourcing cost is €15,000 fixed, representing a substantial cost saving of €27,000 per month. Accepting the outsourcing proposal reduces costs and improves profitability, assuming quality and control are maintained.
The daily cost rate of an employee with an annual salary of £80,000, with employer contributions up to 18% for insurance and 8% for retirement, can be calculated by first determining total annual employment costs: £80,000 + (0.18 × £80,000) + (0.08 × £80,000) = £80,000 + £14,400 + £6,400 = £100,800. The employee works 250 days annually, and productivity is 81%, so the actual productive days are 250 × 0.81
≈ 203 days. The daily cost rate is £100,800 / 203 ≈ £496. The calculation ensures comprehensive coverage of employment costs per productive day.
For the UCC market research project, various cost components include in-house and outsourced labor, data purchase, report updates, printing, internal processing, software, training, management oversight, and supervision. Using absorption costing principles, all direct and allocated indirect costs are assigned to the project. Internal hours from existing staff cost £22 per hour, while contracted hours from an agency cost £16 per hour. Data purchase costs, report updates, printing, and internal processing fees are direct costs. The software and training costs are variable, depending on the project, while management time including overtime is a fixed cost allocation. The total project cost is derived by summing all these components, ensuring all relevant costs are included.
The relevant costs for decision-making are those that differ between options—in this case, the costs directly impacted by choosing or rejecting the project. These include the incremental expenses such as agency labor, additional report costs, processing fees, and software/training costs. Fixed costs that do not change with the decision (e.g., existing staff salaries, data purchase from previous months) are considered sunk costs and are not relevant for the incremental analysis. Calculating these relevant costs enables the
company to assess the economic feasibility of the research project and make informed managerial decisions.
References
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Kaplan, R. S., & Atkinson, A. A. (2015). Advanced Management Accounting. Pearson.
Salazar, J. (2017). Cost Behavior and Relevant Range. Journal of Business & Economics Research, 15(3), 105-114.
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