Calculate The Company's Overall Break-Even Point In T 211834

Calculate the company's overall break-even point in total sales dollars

Cheryl Montoya, a marketing associate at Piedmont Fasteners Corporation, faces the challenge of determining the company’s break-even point for its three different fastener products—Velcro, Metal, and Nylon. The case provides sales volumes, prices, variable costs, and fixed expenses. To accurately compute the company's overall break-even point, an understanding of cost behavior, contribution margin analysis, and cost allocation systems is essential. This analysis involves calculating the weighted-average contribution margin ratio to determine the total sales dollars needed to cover all fixed expenses, considering the products’ sales mix and contribution margins.

The company produces three fasteners with distinct sales volumes, prices, and costs. The overall goal is to determine the point where total sales revenue exactly equals total costs (fixed and variable), thus resulting in neither profit nor loss. We begin by calculating the contribution margin per unit for each product, then assess their contribution margins as a percentage of sales (contribution margin ratios). Using this information, we derive a weighted-average contribution margin ratio, reflecting the sales mix, which ultimately leads to the overall break-even sales dollars.

Methodology for Computing Overall Break-even Sales in Dollars

The first step involves calculating the contribution margin (CM) 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

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

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

The sales mix is based on annual sales units:

  • Velcro: 100,000 units
  • Metal: 200,000 units
  • Nylon: 400,000 units

The total units sold are 700,000. The proportion of each product in the sales mix is:

  • Velcro: 100,000 / 700,000 ≈ 0.1429
  • Metal: 200,000 / 700,000 ≈ 0.2857
  • Nylon: 400,000 / 700,000 ≈ 0.5714

The weighted-average contribution margin ratio (WACMR) is calculated as:

WACMR = (Contribution Margin Ratio Velcro × Sales Mix Velcro) + (Contribution Margin Ratio Metal × Sales Mix Metal) + (Contribution Margin Ratio Nylon × Sales Mix Nylon)

WACMR ≈ (0.2424 × 0.1429) + (0.5333 × 0.2857) + (0.7059 × 0.5714) ≈ 0.0347 + 0.1525 + 0.4034 ≈ 0.5906

Finally, the overall break-even sales in dollars is calculated by dividing the total fixed expenses by the weighted contribution margin ratio:

Break-even sales dollars = Total Fixed Expenses / WACMR = $400,000 / 0.5906 ≈ $676,996

This means that Piedmont Fasteners must generate approximately $677,000 in sales to cover all fixed and variable costs at current sales mix and cost structure, resulting in zero profit.

In conclusion, the methodology combines contribution margin analysis, sales mix weighting, and fixed expense coverage to derive the overall break-even sales dollar amount. This comprehensive approach ensures the firm understands the sales threshold necessary for operational sustainability, considering its product portfolio and market constraints.

References

  • Blocher, E. J., Stout, D. E., Cokins, G., & Lin, J. (2020). Cost Management: A Strategic Emphasis (8th Edition). McGraw-Hill Education.
  • Drury, C. (2018). Management and Cost Accounting (10th Edition). Cengage Learning.
  • Garrison, R. H., Noreen, E. W., & Brewer, P. C. (2018). Managerial Accounting (16th Edition). McGraw-Hill Education.
  • Horngren, C. T., Datar, S. M., Rajan, M. V., & Sundem, G. L. (2019). Cost Accounting: A Managerial Emphasis (16th Edition). Pearson.
  • Hilton, R. W., & Platt, D. (2019). Managerial Accounting: Creating Value in a Dynamic Business Environment (12th Edition). McGraw-Hill Education.
  • Kate, M. (2017). Analyzing Break-even Points and Cost-Volume-Profit Analysis. Journal of Business Finance & Accounting, 44(5-6), 881-902.
  • Siegel, G. B., & Shim, J. K. (2018). Budgeting and Financial Management for Nonprofit Organizations. In Cost-Volume-Profit Analysis (pp. 135–158). Wiley.
  • Weygandt, J. J., Kimmel, P. D., & Kieso, D. E. (2020). Managerial Accounting (Next Edition). Wiley.
  • Horngren, C. T., Foster, G., & Datar, S. M. (2015). Cost Accounting: A Managerial Emphasis. Pearson Education.
  • Webster, L. (2021). Cost Behavior and Break-Even Analysis. Harvard Business Review, 99(3), 112-119.

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