Problem 9 - Accounting

Question

a. Spock Company budgets sales of \(840,000, fixed costs of \)378,000, and variable costs of \(378,000. What is the contribution margin ratio for Spock Company? b. If the contribution margin ratio for Kirk Company is 34%, sales were \)600,000, and fixed costs were $175,000, what was the income from operations?

Step-by-Step Solution

Answer

Spock's CM ratio is 55%. Kirk's income from operations is $29,000.

Step 1: Calculate Contribution Margin for Spock Company

The contribution margin (CM) is calculated by subtracting variable costs from sales. So, for Spock Company, the calculation is:\[ \text{CM} = \text{Sales} - \text{Variable Costs} = 840,000 - 378,000 = 462,000 \]

Step 2: Calculate Contribution Margin Ratio for Spock Company

The contribution margin ratio is found by dividing the contribution margin by the sales figure and is expressed as a percentage. For Spock Company, this is calculated as follows:\[ \text{CM Ratio} = \frac{\text{Contribution Margin}}{\text{Sales}} = \frac{462,000}{840,000} \approx 0.55 \text{ or } 55\% \]

Step 3: Calculate Contribution Margin for Kirk Company Using Ratio

Using Kirk Company's contribution margin ratio of 34%, calculate the contribution margin by multiplying this ratio by sales:\[ \text{CM} = \text{Sales} \times \text{CM Ratio} = 600,000 \times 0.34 = 204,000 \]

Step 4: Calculate Income from Operations for Kirk Company

To find the income from operations, subtract fixed costs from the contribution margin of Kirk Company:\[ \text{Income from Operations} = \text{Contribution Margin} - \text{Fixed Costs} = 204,000 - 175,000 = 29,000 \]

Key Concepts

Variable Costs

Variable costs refer to expenses that change in direct proportion to the level of production or sales activity. These costs fluctuate with the business's output, meaning the more you produce, the higher your variable costs will be. Key examples of variable costs include raw materials, direct labor, and manufacturing supplies. Understanding variable costs is essential for businesses as they impact the total cost of production and can influence pricing strategies. A business needs to manage these costs carefully to ensure profitability, particularly in industries with highly volatile markets. They are an integral part of calculating the contribution margin, which is the income remaining after covering these expenses. By subtracting variable costs from sales revenue, you can determine the contribution margin, which is crucial for understanding how much can be used to cover fixed costs and generate profit.

Fixed Costs

Unlike variable costs, fixed costs remain constant regardless of the level of production or sales activities. These costs do not fluctuate with the volume of goods or services a business produces. Examples of fixed costs include rent, salaries of permanent staff, and depreciation of equipment. Fixed costs represent the overhead expenses that a business incurs to keep operational, even when production is zero. While they remain unchanged in the short run, understanding fixed costs is crucial for long-term financial planning. Businesses aim to cover these costs through their contribution margin to achieve profitability. A solid grasp of fixed costs helps businesses in making informed decisions, like determining the break-even point and evaluating the impact of scaling production.

Income from Operations

Income from operations, also known as operating income, is a key measure of a company's financial performance. It indicates the profit a business makes from its primary activities, excluding any financial or investment incomes. Essentially, it is the income left after deducting both variable and fixed costs from gross sales. The equation for operating income is straightforward: \[ \text{Income from Operations} = \text{Contribution Margin} - \text{Fixed Costs} \]This metric provides insight into the efficiency with which a company generates profits from its ongoing operations. It is especially useful because it focuses solely on core business activities, offering a clearer picture of operational health without the noise of other financial elements. Accurate assessment of income from operations can help management make strategic decisions and investors evaluate the company's primary business functionality.