Problem 17 - Accounting

Question

For the coming year, Paladin Inc. anticipates fixed costs of \(\$ 120,000\), a unit variable cost of \(\$ 60\), and a unit selling price of \(\$ 90\). The maximum sales within the relevant range are \(\$ 900,000\). a. Construct a cost-volume-profit chart. b. Estimate the break-even sales (dollars) by using the cost-volume-profit chart constructed in part (a). c. What is the main advantage of presenting the cost-volume-profit analysis in graphic form rather than equation form?

Step-by-Step Solution

Answer

The break-even sales are approximately \(\$ 360,000\). Using the graphical method visually shows cost and revenue intersections, aiding intuitive understanding.

Step 1: Define Key Terms and Variables

Identify the fixed costs, unit variable cost, and unit selling price. Fixed costs are given as \(\\( 120,000\), unit variable cost is \(\\) 60\), and unit selling price is \(\$ 90\). These are essential for constructing the cost-volume-profit (CVP) chart.

Step 2: Calculate Total Revenue and Total Cost

To construct the CVP chart, first calculate the total revenue line and total cost line. The total revenue is calculated by multiplying the unit selling price by the number of units sold, and the total cost is the sum of fixed costs and total variable costs (unit variable cost times the number of units sold).

Step 3: Plot the Cost-Volume-Profit Chart

Draw a graph with sales volume (number of units) on the x-axis and dollars on the y-axis. Plot the fixed cost line horizontally at \(\\( 120,000\). Plot the total revenue line, starting from the origin, with a slope of \(\\) 90\). Plot the total cost line starting from \(\\( 120,000\) with a slope of \(\\) 60\).

Step 4: Determine Break-even Point from Chart

The break-even point is where the total revenue line intersects the total cost line. This intersection can be estimated visually on the chart, which represents the point at which total revenue equals total costs.

Step 5: Calculate the Break-even Sales with a Formula

The break-even sales in dollars can also be calculated using the formula: \[ \text{Break-even Sales (units)} = \frac{\text{Fixed Costs}}{\text{Unit Selling Price} - \text{Unit Variable Cost}} \] Substituting the values: \[ \frac{\\( 120,000}{\\) 90 - \\( 60} = 4,000 \text{ units} \]. To find in dollars, multiply by unit selling price: \(4,000 \times \\) 90 = \$ 360,000\).

Step 6: Interpret the Graphic Presentation Advantage

The main advantage of the graphical form is its ability to visually demonstrate the relationship between costs, volume, and profit. It allows for easy identification of break-even points and the impact of varying sales volumes on profitability.

Key Concepts

Break-even Point

The break-even point is a critical concept in a cost-volume-profit (CVP) analysis. It represents the sales level where total revenues equal total costs, resulting in no profit or loss. Understanding this point is essential, as it helps businesses determine the minimum sales volume needed to avoid losses.

To find the break-even point in units for Paladin Inc., we use the formula:

• Break-even in units = \( \frac{\text{Fixed Costs}}{\text{Unit Selling Price} - \text{Unit Variable Cost}} \)

By plugging in Paladin Inc.'s numbers, we see:

• \( \frac{120,000}{90 - 60} = 4,000 \) units

This means Paladin must sell 4,000 units to cover all its costs.

To determine the break-even point in sales dollars, multiply the break-even units by the unit selling price:

• 4,000 units \( \times 90 = 360,000 \) dollars

Therefore, sales of \(360,000 \) dollars are needed for Paladin to break even.

Fixed Costs

Fixed costs remain unchanged regardless of the number of units produced or sold. For Paladin Inc., these costs are estimated at \(120,000 \) dollars. Such costs include salaries, rent, and depreciation, among other overhead expenses.

Understanding fixed costs is crucial for businesses as they represent the baseline costs that must be covered irrespective of sales levels. This means that even if no sales occur, Paladin Inc. still needs to cover its fixed costs. Therefore, these costs play a vital role in determining the break-even point and overall profitability.

Graphical Representation

A graphical representation, like the cost-volume-profit (CVP) chart, provides a valuable visual overview of cost and revenue relationships. This type of chart helps in quickly understanding complex information and making informed decisions.

When constructing the CVP chart for Paladin Inc., you start by plotting costs and revenues:

• Fixed Costs: A horizontal line at \(120,000 \) dollars since these costs remain constant regardless of sales volume.
• Total Revenue Line: Starts from the origin, with a slope determined by the unit selling price per unit (\(90 \) dollars).
• Total Cost Line: Starts at the fixed cost level, with a slope equal to the unit variable cost (\(60 \) dollars per unit).

The intersection of the total revenue and total cost lines illustrates the break-even point. This visual tool allows you to quickly estimate how changes in sales volume affect profitability, making it a powerful asset in strategic planning.

Unit Variable Cost

Unit variable cost is the cost associated with producing or selling one additional unit. For Paladin Inc., this cost is \(60 \) dollars. Variable costs change directly with the number of units produced or sold, encompassing materials, labor, and other costs directly tied to production.

Understanding unit variable costs is crucial for identifying the contribution margin per unit, calculated by subtracting the unit variable cost from the unit selling price. For Paladin, the contribution margin is:

• \(90 - 60 = 30 \) dollars per unit

This margin contributes towards covering fixed costs, and any remaining margin represents profit. Knowledge of the contribution margin enables businesses to make informed decisions about pricing, production levels, and sales strategies.