Problem 23 - Accounting

Question

a. If Fama Company, with a break-even point at \(\$ 360,000\) of sales, has actual sales of \(\$ 480,000\), what is the margin of safety expressed (1) in dollars and (2) as a percentage of sales? b. If the margin of safety for Watkins Company was \(25 \%\), fixed costs were \(\$ 1,200,000\), and variable costs were \(75 \%\) of sales, what was the amount of actual sales (dollars)?

Step-by-Step Solution

Answer

Fama Company's MoS is $120,000 and 25%. Watkins Company's actual sales are $4,800,000.

Step 1: Margin of Safety in Dollars for Fama Company

The Margin of Safety (MoS) in dollars is the difference between actual sales and the break-even sales. Calculate it using the formula:\[MoS_{dollars} = \text{Actual Sales} - \text{Break-even Sales} = 480,000 - 360,000 = 120,000\]

Step 2: Margin of Safety as a Percentage for Fama Company

The Margin of Safety as a percentage can be calculated by dividing the Margin of Safety in dollars by the actual sales and then multiplying by 100:\[MoS_{percentage} = \left(\frac{MoS_{dollars}}{\text{Actual Sales}}\right) \times 100 = \left(\frac{120,000}{480,000}\right) \times 100 = 25\%\]

Step 3: Understanding Watkins Company's Sales Structure

For Watkins Company, the margin of safety is given as 25%. Let \(S\) denote the actual sales. From the margin of safety formula, we have:\[MoS_{percentage} = \left(\frac{S - \text{Break-even Sales}}{S}\right) \times 100 = 25\]First calculate the break-even sales using the given cost structure:\[ \frac{S - \text{Fixed Costs}}{S} = \frac{\text{Variable Cost Ratio}}{1}\,. \] Given \( \text{Variable Cost Ratio} = 0.75 \) (or 75% of sales), we have:\[ 1 - \frac{1,200,000}{S} = 0.75 \right) \]

Step 4: Solve for Actual Sales in Watkins Company

From the break-even sales equation in step 3, solve for \(S\):\[ 1 - \frac{1,200,000}{S} = 0.75 \0.25 = \frac{1,200,000}{S} \S = \frac{1,200,000}{0.25} = 4,800,000\] Thus, the actual sales for Watkins Company is \( \$ 4,800,000 \).

Key Concepts

Break-even Point

Understanding the Break-even Point is crucial for any business. This is the point where total revenue equals total costs; no profit or loss is made. In simple terms, it's where a company breaks even. This helps businesses know the minimum income they need to avoid losses. For instance, if a company has a break-even point of $360,000, it must generate at least this amount in sales to cover expenses entirely.

• At the Break-even Point, total fixed costs are fully covered by the contribution margin (sales minus variable costs).
• Profit begins only after the break-even point.
• It's a fundamental tool in financial planning and analysis.

By calculating the break-even point, businesses can make informed decisions about pricing, budgeting, and sales strategies.

Variable Costs

Variable Costs change with the level of output - they go up with more production and sales increase and go down when sales decrease. For example, manufacturing more products requires more materials, making variable costs higher. The idea is that these costs vary directly with the volume of activity.

• Examples of variable costs include raw materials, direct labor, and sales commissions.
• A company with high variable costs is less risky in downturns since costs reduce with lowered sales.
• Businesses analyze variable costs to set competitive pricing and maximize profits.

To calculate total variable costs, multiply the variable cost per unit by the total number of units produced. Understanding these costs helps businesses estimate margins and adjust their strategies according to market demand.

Fixed Costs

Fixed Costs, unlike variable costs, remain constant regardless of production levels. They include expenses such as rent, salaries, and insurance that do not change with the level of goods or services a company produces. These costs are crucial in understanding financial stability and planning.

• Examples include property taxes, lease payments, and management salaries.
• Companies need to cover fixed costs to achieve the Break-even Point.
• Understanding fixed costs aids in pricing strategies and financial forecasting.

Even when production is zero, fixed costs must still be paid. This predictable nature allows firms to budget accurately. Firms often try to lower their fixed costs to reduce their break-even point and achieve profitability sooner.