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Chapter 20: Problem 25

Abdel Inc. and Hui Inc. have the following operating data: Abdel Hui Sales \(150,000 \)200,000 Variable costs 90,000 125,000 Contribution margin \( 60,000 \) 75,000 Fixed costs 10,000 60,000 Income from operations \( 50,000 \) 15,000 a. Compute the operating leverage for Abdel Inc. and Hui 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.

Short Answer

Expert verified
a. Abdel Inc. leverage is 1.2; Hui Inc. is 5.0. b. Abdel's income increases by $12,000; Hui's by $15,000. c. Hui Inc.'s higher operating leverage results in a larger income increase.

Step by step solution

01

Understand Operating Leverage

Operating leverage measures how much a company can increase its income from operations from a given change in sales. It is calculated using the formula: \( \text{Operating Leverage} = \frac{\text{Contribution Margin}}{\text{Income from Operations}} \).
02

Calculate Operating Leverage for Abdel Inc.

Use the formula with Abdel Inc.'s data: \( \text{Operating Leverage} = \frac{60,000}{50,000} = 1.2 \). This means Abdel Inc. has an operating leverage of 1.2.
03

Calculate Operating Leverage for Hui Inc.

Apply the formula to Hui Inc.: \( \text{Operating Leverage} = \frac{75,000}{15,000} = 5.0 \). Hui Inc. has an operating leverage of 5.0.
04

Calculate Income Increase for Abdel Inc.

With a 20% increase in sales, Abdel Inc.'s contribution margin will also increase by the same percentage. New sales = \( 150,000 \times 1.2 = 180,000 \), and the income increase = Operating Leverage \( \times \%\text{Increase in Sales} = 1.2 \times 0.20 \times 50,000 = 12,000 \).
05

Calculate Income Increase for Hui Inc.

Similarly, for Hui Inc., New sales = \( 200,000 \times 1.2 = 240,000 \), and the increase in income from operations = \( 5.0 \times 0.20 \times 15,000 = 15,000 \).
06

Explain the Difference in Income Increase

The difference in operating leverage causes different increases in income from operations. Hui Inc.'s higher operating leverage of 5.0 means its fixed cost structure is more sensitive to changes in sales, leading to a larger income increase compared to Abdel Inc.'s lower leverage of 1.2.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Contribution Margin
The contribution margin is a crucial concept in accounting that helps businesses understand how much sales revenue is exceeding variable costs. This amount contributes to covering the company's fixed costs and ultimately impacts the income from operations.
To calculate the contribution margin, subtract the total variable costs from the total sales revenue:
  • For Abdel Inc., the contribution margin is calculated as follows: \[\text{Contribution Margin for Abdel Inc.} = 150,000 - 90,000 = 60,000\]
  • For Hui Inc., it is:\[\text{Contribution Margin for Hui Inc.} = 200,000 - 125,000 = 75,000\]
These figures indicate the portion of sales that helps cover fixed costs and generate profit. A higher contribution margin means more funds are available after variable costs are paid.
Fixed Costs
Fixed costs remain constant regardless of the sales volume a company experiences. These are expenses that do not fluctuate in the short term, such as rent, salaries, and utilities. Understanding fixed costs is vital, as they affect profitability and operational decisions.
  • Abdel Inc. has fixed costs amounting to 10,000. This implies lower risk exposure from sales fluctuations, as their fixed expenses are relatively small.
  • On the other hand, Hui Inc. has fixed costs of 60,000. Higher fixed costs mean Hui Inc. has more expenses that need to be covered before it can achieve profitability.
Due to its high fixed costs, Hui Inc. exhibits greater sensitivity to sales changes, which is evident through its higher operating leverage.
Income from Operations
Income from operations, sometimes referred to as operating income, is the profit a company makes from its core business activities, excluding other income such as interest and taxes. It represents the efficiency of a company's management in operating its business model.
To find income from operations:
  • Abdel Inc. derives its income from operations by taking the contribution margin and subtracting the fixed costs:\[\text{Income for Abdel Inc.} = 60,000 - 10,000 = 50,000\]
  • Hui Inc., similarly:\[\text{Income for Hui Inc.} = 75,000 - 60,000 = 15,000\]
A higher income from operations suggests better performance from regular business operations. It is crucial for gauging a company's profitability and operational fitness without external financial factors.
Variable Costs
Variable costs are expenses directly tied to the production or sales volume of a company. These costs rise or fall in proportion with the business activity levels.
Examples include costs of raw materials, direct labor, and utilities used in production.
  • Abdel Inc.'s variable costs were tabulated at 90,000, indicating the costs are directly associated with their sales volume.
  • Hui Inc.鈥檚 was higher, at 125,000, possibly due to a greater sales volume or higher costs per unit.
Understanding variable costs is key to setting pricing strategies and managing operations efficiently, as this affects the contribution margin and overall profitability of the company.

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Most popular questions from this chapter

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