91Ó°ÊÓ

The Kenosha Company has three product lines of beer mugs \(-A, B,\) and \(\mathrm{C}-\) with contribution margins of \(\$ 5, \$ 4,\) and \(\$ 3,\) respectively. The president foresees sales of 175,000 units in the coming period, consisting of 25,000 units of \(A, 100,000\) units of \(B,\) and 50,000 units of \(C .\) The company's fixed costs for the period are \(\$ 351,000\) 1\. What is the company's breakeven point in units, assuming that the given sales mix is maintained? 2\. If the sales mix is maintained, what is the total contribution margin when 175,000 units are sold? What is the operating income? 3\. What would operating income be if the company sold 25,000 units of \(A, 75,000\) units of \(B,\) and 75,000 units of \(C ?\) What is the new breakeven point in units if these relationships persist in the next period? 4\. Comparing the breakeven points in requirements 1 and 3 , is it always better for a company to choose the sales mix that yields the lower breakeven point? Explain.

Step by step solution

01

1. Calculate the breakeven point in units

To calculate the breakeven point, first, we need to find the weighted average contribution margin per unit (WACM). The sales mix is the percentage of each product in the total sales: - Product A: 25,000 / 175,000 = 0.14286 - Product B: 100,000 / 175,000 = 0.57143 - Product C: 50,000 / 175,000 = 0.28571 Next, we calculate the WACM by multiplying the sales mix of each product by its contribution margin and summing the results: WACM = (0.14286 * \(5) + (0.57143 * \)4) + (0.28571 * \(3) = \)3.85714 Now, we can calculate the breakeven point in units by dividing the fixed costs by WACM: Breakeven point(units) = \(351,000 / \)3.85714 = 90,945 units.

02

2. Calculate the total contribution margin and operating income

The total contribution margin is the sum of the contribution margin of each product: Total contribution margin = (25,000 * \(5) + (100,000 * \)4) + (50,000 * $3) Total contribution margin = \(125,000 + \)400,000 + \(150,000 = \)675,000 Now we can calculate the operating income by subtracting the fixed costs: Operating income = Total contribution margin - Fixed costs = \(675,000 - \)351,000 = $324,000

03

3. Calculate the operating income under different sales mix and new breakeven point

New sales scenario: 25,000 units of A, 75,000 units of B, and 75,000 units of C. Total contribution margin = (25,000 * \(5) + (75,000 * \)4) + (75,000 * $3) Total contribution margin = \(125,000 + \)300,000 + \(225,000 = \)650,000 New operating income = Total contribution margin - Fixed costs = \(650,000 - \)351,000 = $299,000 For the new breakeven point, first, find the new sales mix: - Product A: 25,000 / 175,000 = 0.14286 - Product B: 75,000 / 175,000 = 0.42857 - Product C: 75,000 / 175,000 = 0.42857 Calculate the new WACM: WACM = (0.14286 * \(5) + (0.42857 * \)4) + (0.42857 * \(3) = \)3.57143 New breakeven point(units) = \(351,000 / \)3.57143 = 98,267 units

04

4. Comparison of breakeven points and sales mix optimization

Comparing the breakeven points in requirements 1 and 3 (90,945 units vs. 98,267 units), we can see that the lower breakeven point corresponds to the initial sales mix. However, it's not always better for a company to choose the sales mix that yields the lower breakeven point, since the optimal sales mix depends not only on breakeven points but also on the operating income and market demands. A higher breakeven point might still result in a superior overall operating income. Therefore, the company should carefully evaluate the potential operating income generated by different sales mixes before making a decision.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Contribution Margin

Contribution margin is essentially the amount remaining after variable costs have been deducted from sales revenue. It is a crucial metric because it tells us how much revenue is available to cover fixed costs and generate profit. For example, in the context of Kenosha Company, each product line has its own contribution margin: $5 for Product A, $4 for Product B, and $3 for Product C. To calculate the total contribution margin, we multiply the contribution margin of each product by the units sold. This gives us:

• Product A: 25,000 units x $5 = $125,000
• Product B: 100,000 units x $4 = $400,000
• Product C: 50,000 units x $3 = $150,000

These figures are then summed to find the total contribution margin for all products, which is $675,000. This figure will be essential when calculating operating income, as it shows the total revenue available to cover fixed costs.

Sales Mix

Sales mix refers to the ratio of different products sold by a company. It is an essential factor in determining the overall profitability of the business, as different products may have varying contribution margins. The initial sales mix for Kenosha Company indicated 25,000 units of Product A, 100,000 units of Product B, and 50,000 units of Product C, which results in corresponding sales mix percentages. The calculation involved is typically expressed as the ratio of each product's sales to total sales. For instance:

• Product A's mix: 25,000 / 175,000 = 0.14286 (or 14.29%)
• Product B's mix: 100,000 / 175,000 = 0.57143 (or 57.14%)
• Product C's mix: 50,000 / 175,000 = 0.28571 (or 28.57%)

Understanding sales mix is crucial for calculating weighted average contribution margin (WACM) and breakeven point in units. Different sales mixes can significantly affect the financial outcome, as seen when Kenosha Company adjusted the product units sold.

Fixed Costs

Fixed costs are the expenses that do not change with the level of output produced by a company. They remain constant, regardless of how much the company produces or sells within a certain range. Kenosha Company's fixed costs for the period are $351,000. These costs typically include things like rent, salaries, and insurance. Knowing the total fixed costs is crucial for breakeven point analysis because it determines the total revenue needed to cover these expenses before generating profit. To find the breakeven point, we divide the total fixed costs by the weighted average contribution margin (WACM). This calculation helps businesses understand the number of units they must sell at a given sales mix to cover all costs.

Operating Income

Operating income is a measure of the profit earned from a company's core business operations. It is calculated by subtracting the total fixed costs from the total contribution margin. This figure provides insight into how efficiently a company is generating profit from its sales before interest and taxes are considered. In Kenosha Company's scenario, using the initial sales mix of 25,000 units of A, 100,000 units of B, and 50,000 units of C, the operating income is calculated as follows: Operating income = Total contribution margin - Fixed costs = $675,000 - $351,000 = $324,000. Changes in sales mix, such as shifting to sell 25,000 units of A, 75,000 units of B, and 75,000 units of C, result in a different total contribution margin and, subsequently, a different operating income of $299,000. It's important to note that the optimal sales mix may not always be the one with the highest operating income due to factors such as market demand and strategic focus.