Problem 1: The Peace Company Has The Following Functional Is

Problem 1the Peace Company Has The Following Functional Income Statem

Problem 1: The Peace Company has the following functional income statement for the prior month. Sales ($50 * 100,000 units) $5,000,000 Cost of goods sold: Direct materials $1,200,000; Direct labor $950,000; Variable factory overhead $600,000; Fixed factory overhead $850,000. Total cost of goods sold amounts to $3,600,000. Gross profit is $1,400,000. Selling and administrative expenses include variable costs (unspecified) and fixed costs (unspecified), resulting in operating income. There were no beginning or ending inventories.

Paper For Above instruction

This analysis aims to assess the profitability and cost management of The Peace Company by calculating various financial metrics based on the provided income statement. The primary focus is on understanding contribution margins, break-even points, and sales targets necessary for desired profits. Additionally, the analysis explores implications of fixed and variable costs in decision-making processes, offering insights into the company's cost structure and operational efficiency.

Introduction

Understanding a company's cost behavior and profitability metrics is vital for strategic decision-making and financial planning. In this context, the income statement provides essential data to compute contribution margins, break-even sales, and profit targets. This report systematically calculates these figures based on The Peace Company's prior month's income statement, facilitating a comprehensive understanding of its financial performance.

Calculation of Contribution Margin Per Unit

The contribution margin per unit is calculated as the difference between the selling price per unit and the variable cost per unit. The total sales revenue is $5,000,000 for 100,000 units, resulting in a selling price per unit of $50 ($5,000,000 / 100,000). The total variable costs include direct materials ($1,200,000), direct labor ($950,000), and variable factory overhead ($600,000), summing to $2,750,000. Dividing this by the number of units (100,000), the variable cost per unit is $27.50. Therefore, the contribution margin per unit is $50 - $27.50 = $22.50.

Calculation of Contribution Margin Ratio

The contribution margin ratio is computed by dividing the contribution margin per unit by the selling price per unit. Using the previous calculations, $22.50 / $50 = 0.45 or 45%. This ratio indicates that 45% of each sales dollar contributes to covering fixed costs and generating profit.

Calculation of Break-Even Point in Units

The break-even point in units is determined by dividing total fixed costs by the contribution margin per unit. The fixed costs include fixed factory overhead ($850,000) and fixed selling and administrative expenses (unspecified), but since only fixed factory overhead is specified, we assume total fixed costs are $850,000. Therefore, break-even units = $850,000 / $22.50 ≈ 37,778 units. This means the company must sell approximately 37,778 units to cover all fixed costs.

Sales in Dollars for Target Before-Tax Profit

To achieve a before-tax profit of $40,000, the required contribution margin must cover fixed costs plus profit. The total fixed costs are $850,000 (fixed factory overhead). Therefore, the required contribution margin = fixed costs + profit = $850,000 + $40,000 = $890,000. Dividing this by the contribution margin ratio (45%), the required sales in dollars = $890,000 / 0.45 ≈ $1,977,778. This amount represents the sales revenue needed to attain the targeted profit.

Conclusion

This financial analysis of The Peace Company demonstrates the importance of understanding contribution margins and cost structure for effective decision-making. By identifying the contribution margin per unit and the break-even sales volume, management can set realistic sales targets and assess profitability under different scenarios. The calculated sales needed for a specific profit margin aids in strategic planning and resource allocation.

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