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Chapter 3: Problem 20

Once a company exceeds its breakeven level, operating income can be calculated by multiplying: a. The sales price by unit sales in excess of breakeven units. b. Unit sales by the difference between the sales price and fixed cost per unit. c. The contribution margin ratio by the difference between unit sales and breakeven sales. d. The contribution margin per unit by the difference between unit sales and breakeven sales.

Short Answer

Expert verified
The correct way to calculate operating income once a company exceeds its breakeven level is by multiplying the contribution margin per unit by the difference between unit sales and breakeven sales. So the answer is (d).

Step by step solution

01

Go through each option and evaluate its accuracy

a. The sales price by unit sales in excess of breakeven units: This option suggests that operating income can be calculated by simply multiplying the sales price by unit sales exceeding the breakeven units. However, this calculation only takes into account the revenue and doesn't subtract the variable costs associated with those additional unit sales. b. Unit sales by the difference between the sales price and fixed cost per unit: This option doesn't take variable costs into consideration; the difference between the sales price and fixed cost per unit doesn't accurately represent the contribution margin per unit. The correct measure should include variable costs and not fixed costs. c. The contribution margin ratio by the difference between unit sales and breakeven sales: The contribution margin ratio is calculated by dividing the contribution margin per unit by the sales price per unit. By multiplying the contribution margin ratio (which is a percentage) by the difference between the actual unit sales and the breakeven sales, we would get the operating income for the units sold beyond the breakeven point. d. The contribution margin per unit by the difference between unit sales and breakeven sales: This option calculates the operating income by multiplying the contribution margin per unit (which includes variable costs) by the difference between unit sales and breakeven sales. This way, we get the total profit value for the units sold beyond the breakeven point.
02

Compare and choose the correct option

Option c and d both seem appropriate for calculating operating income for units sold beyond the breakeven point as they take into consideration the variable costs associated with additional sales. However, option d is more precise, as it calculates the operating income in terms of the total profit value, whereas option c calculates it as a percentage-based value.
03

Conclusion

The correct answer is: d. The contribution margin per unit by the difference between unit sales and breakeven sales.

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Key Concepts

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

Operating Income Calculation
Understanding how to calculate operating income after reaching the breakeven point is essential for businesses to evaluate their profitability. Operating income, also known as operating profit, represents the amount of revenue left after deducting all the variable and fixed costs directly associated with the business operations.

The correct way to calculate operating income once the breakeven point has been exceeded is to use the contribution margin per unit. This approach, as outlined in option d, factors in the essential elements of cost and revenue. The formula involves multiplying the contribution margin per unit鈥攚hich is the sales price minus the variable cost per unit鈥攂y the total unit sales minus the breakeven unit sales. Mathematically, it can be expressed as: \[\text{Operating Income} = (\text{Sales Price} - \text{Variable Cost per Unit}) \times (\text{Unit Sales} - \text{Breakeven Unit Sales})\]

This calculation gives us the operating income derived from the sales in excess of breakeven units, providing a clear picture of the actual income generated from additional sales.
Contribution Margin Ratio
The contribution margin ratio is a powerful metric that reflects the percentage of each sales dollar that contributes to covering fixed costs and generating profit. It is calculated by dividing the contribution margin per unit by the sales price per unit.

Expressed as a formula: \[ \text{Contribution Margin Ratio} = \frac{\text{Contribution Margin per Unit}}{\text{Sales Price per Unit}} \]

For example, if a product's sale price is \$10 and the variable cost to produce it is \$6, the contribution margin per unit would be \$4. Thus, the contribution margin ratio would be \$4 / \$10 or 0.4 (which can also be expressed as 40%). This ratio is critical in decision-making processes, such as determining the pricing strategy, analyzing the impact of cost changes, and understanding the profit potential of additional sales.
Fixed and Variable Costs
In breakeven analysis, distinguishing between fixed and variable costs is a foundational concept. Fixed costs are those that do not change with the level of production or sales. Examples include rent, salaries, and insurance鈥攃osts that remain consistent regardless of how many units are produced or sold.

Variable costs, on the other hand, fluctuate with production volume. These could include materials, labor, and utilities directly tied to the manufacturing process. As production increases, variable costs rise proportionately. Conversely, these costs will decrease when production volume goes down.

Knowing the differences between these costs allows a business to compute the breakeven point accurately. The breakeven point occurs when the total revenue equals the sum of the fixed and variable costs, meaning the business neither profits nor loses money. It's pivotal for managers to understand these cost behaviors to make informed decisions about pricing, budgeting, and financial projections.

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Most popular questions from this chapter

"In CVP analysis, gross margin is a less-useful concept than contribution margin." Do you agree? Explain briefly.

Distinguish between operating income and net income.

A company needs to sell 10,000 units of its only product in order to break even. Fixed costs are \(\$ 110,000,\) and the per unit selling price and variable costs are \(\$ 20\) and \(\$ 9,\) respectively. If total sales are \(\$ 220,000,\) the company's margin of safety will be equal to: a. \(\$ 0\) b. \(\$ 20,000\) c. \(\$ 110,000\) d. \(\$ 200,000\)

Cover Rugs is holding a 2 -week carpet sale at Josh's Club, a local warehouse store. Cover Rugs plans to sell carpets for 950 each. The company will purchase the carpets from a local distributor for 760each, with the privilege of returning any unsold units for a full refund. Josh's Club has offered Cover Rugs two payment alternatives for the use of space. Option 1: A fixed payment of \$7,410 for the sale period Option 2: 10 \% of total revenues earned during the sale period Assume Cover Rugs will incur no other costs. 1\. Calculate the breakeven point in units for (a) Option 1 and (b) Option 2 . 2\. At what level of revenues will Cover Rugs earn the same operating income under either option? a. For what range of unit sales will Cover Rugs prefer Option 1? b. For what range of unit sales will Cover Rugs prefer Option 2 ? 3\. Calculate the degree of operating leverage at sales of 65 units for the two rental options. 4\. Briefly explain and interpret your answer to requirement 3 .

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.
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