Problem 11 - Accounting

Question

For the current year ending March 31, Zing Company expects fixed costs of \(425,750, a unit variable cost of \)40, and a unit selling price of \(65. a. Compute the anticipated break-even sales (units). b. Compute the sales (units) required to realize income from operations of \)85,125.

Step-by-Step Solution

Answer

The break-even sales are 17,030 units, and 20,435 units are needed for an $85,125 income.

Step 1: Understand the Break-Even Point Formula

The break-even point in units is calculated by the formula: \( \text{Break-even units} = \frac{\text{Fixed Costs}}{\text{Selling Price per Unit} - \text{Variable Cost per Unit}} \). This means we're finding how many units need to be sold to cover all fixed and variable costs.

Step 2: Calculate Break-Even Units

Plug the given values into the formula: \( \text{Break-even units} = \frac{425,750}{65 - 40} \). Simplify to find \( \frac{425,750}{25} = 17,030 \). Thus, Zing Company must sell 17,030 units to break even.

Step 3: Set Up the Target Sales Formula

To find units required for a specific income, use the formula: \( \text{Units} = \frac{\text{Fixed Costs} + \text{Target Income}}{\text{Selling Price per Unit} - \text{Variable Cost per Unit}} \). We want to solve for a target income of $85,125.

Step 4: Calculate Units for Target Income

Plug in the values: \( \text{Units} = \frac{425,750 + 85,125}{65 - 40} = \frac{510,875}{25} = 20,435 \). Hence, Zing Company must sell 20,435 units to achieve an income of $85,125.

Key Concepts

Fixed Costs

Fixed costs are expenses that do not change with the level of goods or services produced by a business. They remain constant regardless of the company's activities or output levels. Typical examples include rent, salaries, and insurance. For Zing Company, the fixed costs are stated at $425,750.
These costs are crucial for break-even analysis as they need to be covered by initial revenue before a company can start making a profit.
Knowing fixed costs helps businesses plan their production and sales strategies properly. Identifying and understanding these costs can support better financial forecasting and decision-making.

Variable Costs

Variable costs change directly with the volume of production. As production increases, variable costs rise, and they decrease as production falls. These include costs of materials, labor, and other expenses that vary with the level of output. For Zing Company, the variable cost per unit is $40.
In break-even analysis, variable costs per unit are deducted from the unit selling price to determine the contribution margin for each unit sold. Understanding these dynamics is key to optimizing production and maximizing profitability.

Unit Selling Price

The unit selling price is the amount a company charges customers for a single unit of product. Zing Company has set their unit selling price at $65.
This price is vital because it determines how much revenue is generated per unit sold. In the context of break-even analysis, the unit selling price needs to exceed the variable cost per unit to contribute towards covering fixed costs and generating profit.

• A higher unit selling price increases the contribution margin, reducing the number of units needed to break even.
• Conversely, if the unit selling price is too low, it may not cover the variable costs, making it harder to reach profitability.

Consequently, businesses must carefully set their unit selling prices to balance competitiveness and profitability.

Income from Operations

Income from operations, also known as operating income, is the profit earned from a firm's core business activities. For Zing Company, achieving an income from operations of $85,125 requires precise sales targets.
Calculating the required sales units to achieve a specific operating income involves adding this target income to fixed costs and then dividing by the contribution margin (unit selling price minus variable cost per unit). This calculation ensures that both fixed costs and desired income are met through sales.
Understanding income from operations is essential for business planning as it reflects the company's efficiency in generating profits from its primary operations, without considering the effects of taxes or interest.