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Every business has expenses that do not change, no matter how many units of a product or service they produce or sell. These are called fixed costs. These costs remain the same, regardless of the level of output or sales volume. They can include expenses like rent, salaried wages, insurance, and other overhead costs.
In the case of the companies in our exercise, fixed costs do not depend on sales levels, and their main role is to cover ongoing business expenses. For instance, Collier Company in the example has fixed costs of \( \$ 125,000 \). Understanding fixed costs is crucial for long-term planning as they contribute significantly to the overall cost structure of a business.

Unlike fixed costs, variable costs change in direct proportion to the number of products or services produced. These costs fluctuate depending on the business's activity levels. Common examples include raw materials, direct labor, and commissions.
For Collier Company, the variable costs are \( \$ 364,000 \). This figure is significant because it directly impacts the company's contribution margin. By understanding and managing these costs, a company can better control its profitability. Managing variable costs effectively can often lead to significant improvements in overall business efficiency.

Income from operations, also referred to as operating income, is a measure of a company's profitability from its core business activities. It is calculated by subtracting operating expenses, such as fixed and variable costs, from the gross profit.
For Morris Company, to find the income from operations, we use the contribution margin and subtract the fixed costs. In this instance, Morris Company's contribution margin is \( \\( 110,880 \). When we take away the fixed costs of \( \\) 100,000 \), we are left with an income from operations of \( \$ 10,880 \). This figure helps businesses and investors evaluate how efficiently a company is running its core operations.

The contribution margin ratio represents the percentage of each sales dollar that contributes to fixed costs and profit after variable costs have been covered. It is a vital tool in budgeting, cost control, and decision-making.
To find the contribution margin ratio, divide the contribution margin by sales. For instance, Collier Company has a contribution margin of \( \\( 196,000 \) and sales of \( \\) 560,000 \), which results in a contribution margin ratio of 35% \( \left( \frac{196,000}{560,000} = 0.35 \text{ or } 35\% \right) \). A higher contribution margin ratio indicates a greater ability to cover fixed costs and produce profit from sales. Understanding this ratio helps in analyzing potential pricing changes, sales promotions, or cost-cutting measures.