Calculate The Company's Overall Break-Even Point In T 955677

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

The case involves analyzing the financial performance of Piedmont Fasteners Corporation, which manufactures three fastener products: Velcro, Metal, and Nylon. The primary goal is to determine the company's overall break-even point in total sales dollars, considering the fixed costs, variable costs, and sales data provided for each product. This requires a comprehensive understanding of contribution margin concepts, proportional sales mix, and cost-volume-profit (CVP) analysis to arrive at an accurate break-even sales figure that reflects the company's current product structure.

Introduction

Break-even analysis is a fundamental tool in managerial accounting used to determine the level of sales at which total revenues equal total costs, resulting in zero profit. For multi-product companies, the calculation becomes more complex because it involves calculating a weighted average contribution margin based on the sales mix, and then dividing the total fixed costs by this average contribution margin ratio to identify the sales dollars needed to break even.

Methodology

The first step involves calculating the contribution margin per unit for each product, which is the difference between the selling price and variable cost. The contribution margin ratio (CMR) for each product is then obtained by dividing the contribution margin per unit by the selling price. The weighted average contribution margin ratio is computed by multiplying each product’s CMR by its proportion of total sales units. Finally, dividing total fixed costs by this weighted contribution margin ratio yields the break-even sales in dollars.

Let us proceed step-by-step:

  1. Calculate contribution margin per unit for each product:
  • Velcro: $1.65 - $1.25 = $0.40
  • Metal: $1.50 - $0.70 = $0.80
  • Nylon: $0.85 - $0.25 = $0.60
  • Determine total sales units:
    • Velcro: 100,000 units
    • Metal: 200,000 units
    • Nylon: 400,000 units
  • Calculate total units sold: 100,000 + 200,000 + 400,000 = 700,000 units
  • Compute sales proportions (sales volume proportions) for each product:
    • Velcro: 100,000 / 700,000 ≈ 0.1429
    • Metal: 200,000 / 700,000 ≈ 0.2857
    • Nylon: 400,000 / 700,000 ≈ 0.5714
  • Calculate contribution margin ratio (CMR) for each product:
    • Velcro: $0.40 / $1.65 ≈ 0.2424
    • Metal: $0.80 / $1.50 ≈ 0.5333
    • Nylon: $0.60 / $0.85 ≈ 0.7059
  • Calculate weighted average contribution margin ratio:

    • Weighted CMR = (0.1429)(0.2424) + (0.2857)(0.5333) + (0.5714)(0.7059) ≈ 0.0347 + 0.1523 + 0.4038 ≈ 0.5908

  • Determine overall break-even sales in dollars:

    • Total fixed costs / weighted CMR = $400,000 / 0.5908 ≈ $676,711. Similar to the previous calculations, the company must generate approximately $676,711 in sales to break even.

    Conclusion

    This analytical approach demonstrates that Piedmont Fasteners needs to achieve gross sales of approximately $676,711 to cover all fixed and variable costs, given its current sales mix and cost structure. This method effectively weights each product’s contribution margin against its sales volume proportion, accounting for the diversified product line. Such insights are essential for strategic decision-making, including product prioritization, pricing strategies, and cost control initiatives.

    References

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