Calculate The Company's Overall Break-Even Point In Total Sa

Calculate the company's overall break-even point in total sales dollars and explained your methodology

Cheryl Montoya contacted her boss, Wes Chan, to seek clarification on calculating the break-even point for Piedmont Fasteners Corporation's products, highlighting a common challenge in managerial accounting: accurately determining the break-even point for multiple products within a firm. The company produces three fasteners—Velcro, Metal, and Nylon—each with distinct sales volumes, prices, and costs, and the company faces fixed costs totaling $400,000 annually. To undertake this analysis, it is essential to understand the principles of break-even analysis, especially within a multi-product context, and apply relevant costing and contribution margin concepts.

The overall break-even point in total sales dollars is calculated by identifying the contribution margins for each product and proportionally weighting these margins based on sales volume. The contribution margin per unit—selling price minus variable cost—is the starting point. For each product:

• Velcro: $1.65 - $1.25 = $0.40
• Metal: $1.50 - $0.70 = $0.80
• Nylon: $0.85 - $0.25 = $0.60

Next, we calculate the contribution margin ratio for each product:

• Velcro: $0.40 / $1.65 ≈ 0.2424
• Metal: $0.80 / $1.50 ≈ 0.5333
• Nylon: $0.60 / $0.85 ≈ 0.7059

The total sales volume is 100,000 units for Velcro, 200,000 for Metal, and 400,000 for Nylon, summing up to 700,000 units annually. To find the weighted average contribution margin ratio, multiply each product's ratio by its proportion of total units:

Velcro: (100,000 / 700,000) × 0.2424 ≈ 0.0347

Metal: (200,000 / 700,000) × 0.5333 ≈ 0.1521

Nylon: (400,000 / 700,000) × 0.7059 ≈ 0.4034

Sum of weighted ratios: 0.0347 + 0.1521 + 0.4034 ≈ 0.5902

The overall break-even sales in dollars are calculated using the formula:

Break-even sales = Fixed costs / Weighted average contribution margin ratio

= $400,000 / 0.5902 ≈ $677,393

Thus, the company's overall break-even point in total sales dollars is approximately $677,393. This methodology considers the contribution margins of each product, weighted by their sales proportions, providing a realistic assessment necessary for managerial decision-making and profitability analysis.

Paper For Above instruction

The calculation of the overall break-even point in total sales dollars requires an understanding of contribution margins, sales mix, and fixed costs within a multi-product environment. Piedmont Fasteners produces three distinct products with differing sales prices, variable costs, and sales volumes. To accurately assess the break-even point, it is essential to analyze each product's contribution margin per unit and determine their contribution margin ratios, which express the contribution margin as a percentage of sales revenue.

The contribution margin per unit for each product is calculated straightforwardly:

• Velcro: $1.65 - $1.25 = $0.40
• Metal: $1.50 - $0.70 = $0.80
• Nylon: $0.85 - $0.25 = $0.60

Next, the contribution margin ratio for each product is derived by dividing the contribution margin per unit by the selling price:

• Velcro: $0.40 / $1.65 ≈ 0.2424 (or 24.24%)
• Metal: $0.80 / $1.50 ≈ 0.5333 (or 53.33%)
• Nylon: $0.60 / $0.85 ≈ 0.7059 (or 70.59%)

Given the sales volumes, the total units sold are 100,000 Velcro units, 200,000 Metal units, and 400,000 Nylon units, totaling 700,000 units annually. To compute the overall contribution margin ratio, the weighted average is calculated based on the sales mix:

(Units of each product / Total units) × Contribution margin ratio of each:

• Velcro: (100,000 / 700,000) × 0.2424 ≈ 0.0347
• Metal: (200,000 / 700,000) × 0.5333 ≈ 0.1521
• Nylon: (400,000 / 700,000) × 0.7059 ≈ 0.4034

Summing these weighted ratios yields an overall contribution margin ratio of approximately 0.5902. The total fixed costs are $400,000, so dividing fixed costs by the contribution margin ratio produces the break-even sales in dollars:

$400,000 / 0.5902 ≈ $677,393

This analysis indicates that Piedmont Fasteners must generate approximately $677,393 in sales annually to cover all fixed costs and achieve a break-even point. Such an approach ensures that managers can understand the sales level necessary to avoid losses, considering the different contribution margins of each product and the sales mix proportion.

Calculations for Fixed Costs and Costing System Recommendations

The fixed costs are categorized into avoidable and unavoidable costs. The total fixed costs are $400,000, with specific fixed costs that can be avoided if certain products are dropped: $20,000 for Velcro, $80,000 for Metal, and $60,000 for Nylon. The remaining $240,000 represent common fixed costs that can only be eliminated by closing the entire operation, such as administrative salaries and rent.

The fixed costs specifically associated with each product reveal how the profitability of discontinuing a product impacts overall fixed costs and profit margins. For decision-making, the company must focus on contribution margins and avoidable fixed costs to determine if product discontinuation is advantageous.

Break-even point in units for each product

• Velcro: Fixed costs attributable to Velcro / contribution margin per unit = $20,000 / $0.40 = 50,000 units
• Metal: $80,000 / $0.80 = 100,000 units
• Nylon: $60,000 / $0.60 = 100,000 units

The break-even quantities indicate the number of units each product must sell to cover the fixed costs specifically allocated to each. The calculation demonstrates the importance of contribution margin per unit and fixed cost attribution, particularly in multi-product environments with mixed fixed cost types.

Overall profit at break-even quantity

If Piedmont Fasteners sells exactly the break-even quantity for each product, total revenues exactly cover the fixed costs (both avoidable and common) and variable costs, resulting in zero profit. Therefore, total profit at this point is zero. It implies that any sales beyond this level contribute toward profit, emphasizing the need for continuous sales growth or cost improvement to enhance profitability.

Costing System Evaluation for Piedmont Fasteners

Regarding the appropriate costing system, Piedmont Fasteners should utilize process costing rather than job-order costing. Given its high-volume production of standardized fasteners with similar processes, a process-costing system is more appropriate. Process costing accumulates costs across processes for large quantities of homogeneous products, providing efficiency in cost measurement and control. This system simplifies cost accumulation, especially under lean manufacturing, where work-in-process inventory is minimal, and continuous flow production is typical.

Job-order costing, while effective in environments producing customized or diverse products, introduces unnecessary complexity and overhead in this scenario. Instead, process costing facilitates accurate, timely, and consistent cost allocation, allowing management to monitor production costs, analyze cost variances, and implement cost-saving initiatives effectively.

In summary, Piedmont Fasteners should adopt a process-costing approach to improve cost accuracy and operational efficiency, supporting strategic decisions such as pricing, product discontinuation, and cost control.

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