Problem 25 - Accounting

Question

Varner Inc. and King Inc. have the following operating data: \begin{tabular}{lcc} & Varner & King \\ \hline Sales & \(\$ 300,000\) & \(\$ 600,000\) \\ Variable costs & \(\frac{120,000}{\underline{\phantom{xx}}}\) & \(\underline{360,000}\) \\ Contribution margin & \(\$ 180,000\) & \(\$ 240,000\) \\ Fixed costs & \(\underline{120,000}\) & 80,000 \\ Income from operations & \(\$ 60,000\) & \(\$ 160,000\) \\ \hline \end{tabular} a. Compute the operating leverage for Varner Inc. and King Inc. b. How much would income from operations increase for each company if the sales of each increased by \(20 \%\) ? c. Why is there a difference in the increase in income from operations for the two companies? Explain.

Step-by-Step Solution

Answer

a. Varner: 3, King: 1.5. b. Varner increase: $36,000, King increase: $48,000. c. Varner's higher operating leverage and contribution margin ratio cause a larger income sensitivity.

Step 1: Calculate Operating Leverage for Varner Inc.

The formula for operating leverage is: \[ \text{Operating Leverage} = \frac{\text{Contribution Margin}}{\text{Income from Operations}} \] For Varner Inc., the contribution margin is \\(180,000 and income from operations is \\)60,000. Substitute these values into the formula: \[ \text{Operating Leverage (Varner)} = \frac{180,000}{60,000} = 3 \]

Step 2: Calculate Operating Leverage for King Inc.

Using the same formula for operating leverage for King Inc.: Contribution margin is \\(240,000 and income from operations is \\)160,000:\[ \text{Operating Leverage (King)} = \frac{240,000}{160,000} = 1.5 \]

Step 3: Calculate Increased Sales

Next, we calculate the increase in sales revenue for a 20% increase: For Varner Inc., increase in sales: \[ \text{Increased Sales (Varner)} = 300,000 \times 0.20 = 60,000 \text{ dollars} \] For King Inc., increase in sales: \[ \text{Increased Sales (King)} = 600,000 \times 0.20 = 120,000 \text{ dollars} \]

Step 4: Calculate Increase in Income from Operations (Varner Inc.)

We use the operating leverage to find the increase in income from operations. The increase in income for Varner is the percentage change in sales times the operating leverage.For Varner Inc., \[ \text{Income Increase (Varner)} = 60,000 \times 3 = 180,000 \text{ dollars} \]

Step 5: Calculate Increase in Income from Operations (King Inc.)

For King Inc., use the same methodology: \( \text{Income Increase (King)} = 120,000 \times 1.5 = 180,000 \text{ dollars} \). However, this does not take into account variable costs changes. So, find the actual increase using contribution. Contribution from added sales: \[ \text{Varner Contribution (per dollar)} = \frac{180,000}{300,000} = 0.60 \text{ and King Contribution (per dollar)} = \frac{240,000}{600,000} = 0.40 \] Actual income increase (Varner) = \( 60,000 \times 0.60 = 36,000 \text{ dollars} \) Actual income increase (King) = \( 120,000 \times 0.40 = 48,000 \text{ dollars} \)

Step 6: Explain the Difference in Increase of Income from Operations

The difference in income from operations between the two companies arises from their different operating leverages. Varner Inc. has a higher operating leverage (3) compared to King Inc. (1.5), meaning Varner's income is more sensitive to changes in sales volume. Also, the contribution margin ratio shows how much each dollar of sales increases income after variable costs, and it's higher for Varner Inc., leading to a higher increase in income for each additional dollar of sales.

Key Concepts

Contribution Margin

The contribution margin is a vital concept in understanding how much sales revenue remains to cover fixed costs and generate profit after variable costs have been deducted.
Essentially, it's the part of each sales dollar that contributes to covering fixed expenses. The formula for the contribution margin is: - Contribution Margin = Sales - Variable Costs - It can also be expressed as a percentage of sales, called the contribution margin ratio. In the example given:

• Varner Inc. had sales of $300,000 and variable costs of $120,000, resulting in a contribution margin of $180,000.
• King Inc. had sales of $600,000 and variable costs of $360,000, resulting in a contribution margin of $240,000.

For Varner Inc., the contribution margin ratio is 0.60 (or 60%), meaning $0.60 of every $1.00 in sales contributes to fixed costs and profits. Similarly, for King Inc., it is 0.40 (or 40%), which signifies a lower contribution available for covering fixed costs compared to Varner Inc.

Income from Operations

Income from operations is a critical number in a company's financial reporting. It reflects the profit earned from the core business operations and excludes any extraneous income or expenses.
Thus, it shows how efficiently a company runs its everyday business. To calculate income from operations: 1. Subtract all operating expenses (including variable and fixed costs) from gross sales. In the given scenario:

• Varner Inc.'s income from operations is calculated as $60,000, which is derived after deducting all applicable costs from the contribution margin.
• King Inc. has a higher income from operations, at $160,000, resulting from its sizable contribution margin.

This value serves as an indicator of operational efficiency and sustainability, guiding business decisions and strategy formulation. A higher income from operations suggests better efficiency and profitability in core operations.

Variable Costs

Variable costs are expenses that change in direct proportion to the level of production or sales volume. Common examples include: - Raw materials - Direct labor costs - Commissions In the exercise:

• Varner Inc. has variable costs of $120,000, accounting for the costs that fluctuate with sales volume.
• King Inc.'s variable costs are $360,000, which indicates a scalable nature of production expenses.

Understanding variable costs helps companies price their products effectively to ensure they cover these costs before achieving profitability. Variable costs directly impact the contribution margin, and thus the profitability, making it crucial to manage them effectively within operations. By minimizing variable costs, a company can enhance its contribution margin and, consequently, its profitability.

Fixed Costs

Fixed costs are those expenditures that do not vary with the level of production or sales. These are the costs that a company needs to incur even if it doesn’t produce any goods or services: - Examples include rent, salaries, insurance, and utilities. In the case study:

• Varner Inc. incurs $120,000 in fixed costs.
• King Inc. incurs comparatively lower fixed costs of $80,000.

Fixed costs are crucial because they represent the financial hurdle a company must overcome to achieve profitability. Lower fixed costs can reduce the break-even point, making it easier for companies to become profitable quicker. Raising fixed costs increases the risk if sales do not meet expectations, as these costs remain constant regardless of revenue levels. Therefore, understanding and managing fixed costs is fundamental for strategic business decision-making, particularly in planning for growth or assessing profitability.