Problem 23 - Accounting

Question

a. If Larker Company, with a break-even point at \(450,000 of sales, has actual sales of \)500,000, what is the margin of safety expressed (1) in dollars and (2) as a percentage of sales? b. If the margin of safety for Porter Company was 20%, fixed costs were $600,000, and variable costs were 70% of sales, what was the amount of actual sales (dollars)? (Hint: Determine the break-even in sales dollars first.)

Step-by-Step Solution

Answer

a: $50,000 (10%); b: Actual sales are $2,000,000.

Step 1: Identify the Required Information for Part (a)

To calculate the margin of safety, we need to know both the actual sales and the break-even sales of Larker Company. The actual sales are $500,000 and the break-even sales are $450,000.

Step 2: Calculate the Margin of Safety in Dollars for Part (a)

The margin of safety in dollars is calculated by subtracting the break-even sales from the actual sales: \[\text{Margin of Safety (in dollars)} = \text{Actual Sales} - \text{Break-even Sales} = 500,000 - 450,000 = 50,000\]

Step 3: Calculate the Margin of Safety as a Percentage for Part (a)

To express the margin of safety as a percentage of sales, divide the margin of safety in dollars by the actual sales, then multiply by 100:\[\text{Margin of Safety (in percentage)} = \left(\frac{\text{Margin of Safety (in dollars)}}{\text{Actual Sales}}\right) \times 100 = \left(\frac{50,000}{500,000}\right) \times 100 = 10\%\]

Step 4: Identify the Required Information for Part (b)

For Porter Company, the margin of safety as a percentage is 20%, total fixed costs are $600,000, and variable costs are 70% of sales. We need to find the actual sales.

Step 5: Calculate the Break-even Sales for Part (b)

The break-even point is achieved when:\[\text{Break-even Sales} = \text{Fixed Costs} = 600,000\]

Step 6: Relationship Between Sales and Break-even for Part (b)

Since the margin of safety is 20%, the sales exceed the break-even sales by 20%. Let the actual sales be denoted by \( x \). Thus, \( x = 1.20 \times \text{Break-even Sales} \).

Step 7: Solve for the Break-even Sales Equation in Part (b)

Given that variable costs are 70% of sales, we have:\[0.70x + 600,000 = x\]This equation simplifies to:\[0.30x = 600,000 \]

Step 8: Solve for Actual Sales (\( x \)) in Part (b)

Divide both sides by 0.30 to find actual sales:\[x = \frac{600,000}{0.30} = 2,000,000\]

Step 9: Confirm the Margin of Safety in Part (b)

Calculate the break-even sales from \( x = 2,000,000 \):\[\text{Break-even Sales} = \frac{x}{1.20} = \frac{2,000,000}{1.20} = 1,666,667\]The margin of safety in percentage is:\[\left(\frac{2,000,000 - 1,666,667}{2,000,000}\right) \times 100 = 20\%\]This confirms our calculation.

Key Concepts

Break-even Analysis

Break-even analysis is an essential financial tool that helps businesses determine the point at which total revenues equal total costs. This means that the business is not making a profit or a loss, it's simply covering all its costs. This specific point is called the break-even point. To calculate it, companies consider both fixed and variable costs against their revenues.

• Fixed Costs: These are expenses that do not change with the level of production or sales, such as rent, salaries, and insurance.
• Variable Costs: These costs vary depending on the level of production or sales, like materials and direct labor.

Essentially, businesses use break-even analysis to evaluate different pricing strategies and determine the minimum sales volume needed to avoid losses. A deeper understanding of the break-even analysis aids management in making informed decisions about cost structures, resource allocations, and potential profit levels.

Variable Costs

Variable costs are those expenses that vary directly with the level of production or sales. For instance, if a business produces more units, the cost for raw materials and labor might increase directly with the increase in production volume. These costs are crucial in determining the total cost of production, and thus, significantly impact net profitability.

• Examples: Costs of raw materials, direct labor costs, and utility expenses linked to production.
• Impact on Profitability: As variable costs go up with increased production, they can diminish the profit margin if not managed properly.

Understanding variable costs is vital for pricing strategies, as it helps determine the base price required to cover costs. Businesses aim to keep variable costs low to increase the margin between sales prices and total costs, thereby enhancing profitability.

Fixed Costs

Fixed costs are expenses that remain constant regardless of the company’s level of production or sales. These costs do not fluctuate with the increase or decrease in the number of goods produced or sold. Knowing your fixed costs is crucial because it enables you to predict how much money is needed to sustain the business no matter the sales level.

• Characteristics: These costs are consistent and include expenses like office rent, salaries of permanent staff, and machinery leases.
• Management Importance: Understanding fixed costs aids in planning and budgeting, ensuring that these costs are covered even before profits can be considered.

By analyzing fixed costs, businesses can set realistic sales targets and make decisions about scaling operations. They can determine how changes in production levels affect total costs and understand how increasing sales can leverage these fixed expenses to increase overall profitability.