Problem 13 - Accounting

Question

Currently, the unit selling price of a product is \(\$ 280\), the unit variable cost is \(\$ 230\), and the total fixed costs are \(\$ 525,000\). A proposal is being evaluated to increase the unit selling price to \(\$ 300\). a. Compute the current break-even sales (units). b. Compute the anticipated break-even sales (units), assuming that the unit selling price is increased and all costs remain constant.

Step-by-Step Solution

Answer

Current break-even is 10,500 units; anticipated break-even is 7,500 units.

Step 1: Understand Break-even Sales Formula

The break-even point in units can be calculated using the formula: \[ \text{Break-even units} = \frac{\text{Total fixed costs}}{\text{Unit selling price} - \text{Unit variable cost}} \] It represents the number of units that need to be sold to cover all fixed and variable costs.

Step 2: Calculate Current Break-even Sales

First, insert the current values into the break-even formula: the unit selling price is \(\\(280\), the unit variable cost is \(\\)230\), and the total fixed costs are \(\\(525,000\). \[ \text{Break-even units} = \frac{\\)525,000}{\\(280 - \\)230} = \frac{\\(525,000}{\\)50} = 10,500 \] The current break-even sales are 10,500 units.

Step 3: Calculate Anticipated Break-even Sales with New Selling Price

Next, use the anticipated selling price. The new selling price is \(\\(300\), while the unit variable cost and total fixed costs remain the same. Use these in the break-even formula: \[ \text{Break-even units} = \frac{\\)525,000}{\\(300 - \\)230} = \frac{\\(525,000}{\\)70} = 7,500 \] The anticipated break-even sales, with the increased selling price, are 7,500 units.

Key Concepts

Unit Selling Price

The unit selling price is simply the amount of money a customer pays to buy one unit of a product. In our example, this value was initially set at $280 per unit. That's the price customers are willing to pay for one item. It plays a critical role in determining how attractive the product is in the market, and it directly influences the revenue generated by each unit sold. The unit selling price is important because:

• It affects the break-even point; a higher selling price typically lowers the number of units needed to cover costs.
• If set too high, it might reduce demand, and if too low, it might not cover costs.
• It helps balance between competitive pricing and profit margins.

In the break-even analysis, any changes in the unit selling price affect how many units need to be sold to cover expenses. For instance, increasing the unit selling price from $280 to $300 decreased the break-even units from 10,500 to 7,500.

Fixed Costs

Fixed costs are those costs that do not change with the level of production or sales volume. They remain constant irrespective of the number of units a company produces or sells. In our case, the total fixed costs were $525,000. This means that no matter how many units are sold, these costs need to be covered. Key aspects of fixed costs include:

• Rental expenses for facilities and equipment.
• Salaries of permanent staff.
• Insurance and utility charges that are constant month to month.

Understanding fixed costs is crucial because they dictate the amount of revenue needed before a company can start making a profit. In break-even analysis, fixed costs are the overseer of the minimum financial requirement to succeed, regardless of production volume.

Variable Cost

Variable costs fluctuate with the production volume. Each product sold incurs certain costs, which make up the variable cost component. In our current scenario, each unit had a variable cost of $230. These costs typically include:

• Materials used in manufacturing.
• Labor directly used in the production process.
• Commission for sales personnel if paid per unit sold.

Variable costs are critical in determining the portion of revenue that is not absorbed by other factors and remains to cover fixed costs and profit margins. In our calculations, we witnessed that the variable cost influenced how much revenue remains from each sale to address total fixed costs, which then defines the break-even point.

Cost-Volume-Profit Analysis

Cost-Volume-Profit (CVP) analysis is a management accounting tool that helps companies understand the interplay between costs (both fixed and variable), sales volume, and profit. Essentially, it is used to assess how these variables will affect a company's financial performance. The CVP analysis considers:

• How changes in unit selling prices impact profitability.
• The effect of varying levels of sales and production on total fixed costs and variable costs.
• Determining the necessary sales volume to achieve a targeted profit.

In the exercise, CVP analysis was used to determine the break-even point, showing how many units must be sold at a given price to cover all costs. By manipulating the unit selling price, we've seen how CVP analysis gives valuable insight into the financial impacts of pricing strategies.