Problem 21 - Accounting

Question

New Wave Technology Inc. manufactures and sells two products, MP3 players and satellite radios. The fixed costs are \(\$ 300,000\), and the sales mix is \(40 \%\) MP3 players and \(60 \%\) satellite radios. The unit selling price and the unit variable cost for each product are as follows: \begin{tabular}{lrc} Products & Unit Selling Price & Unit Variable Cost \\ \hline MP3 players & \(\$ 60.00\) & \(\$ 45.00\) \\ Satellite radios & \(100.00\) & \(60.00\) \end{tabular} a. Compute the break-even sales (units) for the overall product, E. b. How many units of each product, MP3 players and satellite radios, would be sold at the break-even point?

Step-by-Step Solution

Answer

The break-even point is 10,000 units, with 4,000 MP3 players and 6,000 satellite radios sold.

Step 1: Calculate the Contribution Margin per Unit for Each Product

The contribution margin per unit is calculated as the unit selling price minus the unit variable cost. For MP3 players:\[ CM_{ ext{MP3}} = 60 - 45 = 15 \]For satellite radios:\[ CM_{ ext{Sat}} = 100 - 60 = 40 \]

Step 2: Determine the Weighted Average Contribution Margin

To find the weighted average contribution margin per unit, multiply each individual contribution margin by its respective sales mix percentage, and then sum the results.\[ CM_{ ext{weighted}} = (15 \times 0.4) + (40 \times 0.6) = 6 + 24 = 30 \]

Step 3: Compute the Break-even Point in Total Units

The break-even point in total units is the fixed costs divided by the weighted average contribution margin.\[ E = \frac{300,000}{30} = 10,000 \text{ units} \]

Step 4: Calculate Units Sold for Each Product at Break-even

At break-even, the sales mix proportion dictates the number of units sold for each product:For MP3 players (40% of total units):\[ X_{ ext{MP3}} = 10,000 \times 0.4 = 4,000 \text{ units} \]For satellite radios (60% of total units):\[ X_{ ext{Sat}} = 10,000 \times 0.6 = 6,000 \text{ units} \]

Key Concepts

Contribution Margin

The contribution margin is a vital concept in understanding break-even analysis. It tells us how much revenue from each product sale is available to cover fixed costs. To find it, subtract the variable cost per unit from the selling price per unit. This gives you the contribution margin per unit, which is crucial for determining profitability. For example, if you sell an MP3 player for $60 and it costs $45 to make, then the contribution margin is $15. Similarly, for a satellite radio sold at $100 with a variable cost of $60, the contribution margin is $40.

• Formula: Contribution Margin = Selling Price - Variable Cost
• Purpose: It helps businesses understand which products are most profitable and better manage their pricing strategies to maximize income.

Understanding contribution margin is key to making informed production and sales decisions.

Sales Mix

Sales mix refers to the proportion of each different product a company sells, compared to its total sales. It is crucial because different products have different profitability levels, and the sales mix can impact the overall average contribution margin of all products combined. In the case of New Wave Technology Inc., the sales mix is 40% MP3 players and 60% satellite radios. This means that for every 100 units sold, 40 are MP3 players and 60 are satellite radios.

• Impact: The sales mix affects the weighted contribution margin and, consequently, the break-even point.
• Importance: A balanced sales mix can optimize profits, particularly if a more profitable product is sold in higher proportion.

By optimizing the sales mix, businesses can ensure a more stable and predictable path to reaching their financial goals.

Fixed Costs

Fixed costs are expenses that remain consistent, regardless of the number of units sold or produced. They include costs such as rent, salaries, and insurance. For New Wave Technology Inc., fixed costs are $300,000. These costs must be covered entirely by the contribution margin achieved from sales before a business can make a profit.

• Characteristics: Fixed costs do not change with business activity levels, making them predictable but sometimes harder to reduce without changes to operations.
• Role in Break-even Analysis: The break-even point is achieved when the total contribution margin equals total fixed costs. Hence, reducing fixed costs can lower the break-even point.

Managing fixed costs efficiently can improve a company's financial stability and lower its risk during periods of fluctuating demand.

Variable Costs

Variable costs fluctuate with the level of production. For each additional unit produced, these costs increase correspondingly. They include costs like materials and direct labor. In New Wave Technology Inc.'s scenario, the variable cost is $45 for each MP3 player and $60 for each satellite radio. Understanding variable costs is crucial for price setting and maintaining profitability.

• Calculation: Variable costs are calculated on a per-unit basis, making accurate record-keeping important to ensure cost control.
• Impact on Pricing: Since these costs change with production levels, setting a price above the sum of the variable cost and desired profit margin is essential for covering fixed costs and ensuring profitability.

Effectively managing variable costs can lead to better pricing strategies and ultimately higher profitability.