Problem 11 - Accounting

Question

For the current year ending March 31 , Jwork Company expects fixed costs of \(\$ 440,000\), a unit variable cost of \(\$ 50\), and a unit selling price of \(\$ 75\). a. Compute the anticipated break-even sales (units). b. Compute the sales (units) required to realize income from operations of \(\$ 90,000\).

Step-by-Step Solution

Answer

a. 17,600 units; b. 21,200 units.

Step 1: Understanding the Break-Even Point

The break-even point in units is the level of sales at which the total revenue equals the total costs (both fixed and variable), meaning the company makes neither a profit nor a loss. The formula for break-even sales in units is \( \frac{\text{Total Fixed Costs}}{\text{Selling Price per Unit} - \text{Variable Cost per Unit}} \).

Step 2: Calculate the Contribution Margin

The contribution margin per unit is calculated by subtracting the variable cost per unit from the selling price per unit. This contribution covers the fixed costs and any remaining contributes to profit. \[ \text{Contribution Margin per Unit} = 75 - 50 = 25 \]

Step 3: Compute the Break-Even Units

Using the contribution margin calculated previously, compute the break-even point in units as follows: \[ \frac{\text{Fixed Costs}}{\text{Contribution Margin per Unit}} = \frac{440,000}{25} = 17,600 \]Jwork Company needs to sell 17,600 units to break even.

Step 4: Understand the Target Profit Concept

To find out how many units must be sold to achieve a specific profit, modify the break-even formula by including the desired profit in the total fixed costs. The modified formula is: \( \frac{\text{Fixed Costs} + \text{Target Profit}}{\text{Contribution Margin per Unit}} \).

Step 5: Compute the Required Sales for Target Profit

Substitute the fixed costs and target profit into the modified break-even formula:\[ \frac{440,000 + 90,000}{25} = \frac{530,000}{25} = 21,200 \]Jwork Company must sell 21,200 units to achieve an income from operations of \$ 90,000.

Key Concepts

Fixed Costs

Fixed costs are expenses that do not change with the level of goods or services produced by a company. They remain constant even when the production or sales volume increases or decreases. Examples of fixed costs include rent, salaries, and insurance. For Jwork Company, the fixed costs amount to $440,000.
These costs are crucial when calculating the break-even point. Unlike variable costs, which fluctuate with production or sales volume, fixed costs remain the same, providing stability in budgeting and financial planning.
To determine the break-even point, fixed costs are divided by the contribution margin per unit. This helps to understand how many units must be sold before the company can begin to make a profit.

Contribution Margin

The contribution margin is a key financial metric that represents the amount per unit sold that contributes to covering the fixed costs of a business, with any surplus contributing to profit. It is calculated as the selling price per unit minus the variable cost per unit.
For Jwork Company, the selling price is $75 per unit, and the variable cost is $50 per unit. Therefore, the contribution margin is $75 - $50 = $25 per unit. This means that every unit sold generates $25 to cover fixed costs and eventually contribute to profit.
To find the break-even point, you need the contribution margin because it tells you how much from each unit sale is available to cover fixed costs. Once fixed costs are covered, any extra unit sold boosts profit.

Variable Costs

Variable costs are expenses that vary directly with the volume of production or sales. Unlike fixed costs, they increase as production increases and decrease as production decreases.
In the case of Jwork Company, the variable cost per unit is $50. This cost includes materials, labor, or any other cost directly associated with producing each unit. When planning financial strategies, companies must consider how variable costs can affect their pricing and production decisions.
By understanding variable costs, businesses can more accurately calculate their contribution margin and break-even point. Keeping variable costs low increases the contribution margin, allowing businesses to reach profitability faster as they cover fixed costs.