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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

Juicy Beauty manufactures and sells a face cream to small specialty stores in the greater Los Angeles area. It presents the monthly operating income statement shown here to George Lopez, a potential investor in the business. Help Mr. Lopez understand Juicy Beauty's cost structure. 1. Recast the income statement to emphasize contribution margin. 2\. Calculate the contribution margin percentage and breakeven point in units and revenues for June 2017 3\. What is the margin of safety (in units) for June \(2017 ?\) 4\. If sales in June were only 16,000 units and Juicy Beauty's tax rate is \(30 \%\), calculate its net income.

The Deli-Sub Shop owns and operates six stores in and around Minneapolis. You are given the following corporate budget data for next year: $$\begin{array}{lr}\text { Revenues } & \$ 11,000,000 \\\\\text { Fixed costs } & \$ 3,000,000 \\\\\text { Variable costs } & \$ 7,500,000\end{array}$$ Variable costs change based on the number of subs sold. Compute the budgeted operating income for each of the following deviations from the original budget data. (Consider each case independently.) 1\. \(A 10 \%\) increase in contribution margin, holding revenues constant 2\. \(A\) 10 \(\%\) decrease in contribution margin, holding revenues constant 3\. \(A 5 \%\) increase in fixed costs 4\. \(A\) 5\% decrease in fixed costs 5\. A \(5 \%\) increase in units sold 6\. \(A 5 \%\) decrease in units sold 7\. \(A 10 \%\) increase in fixed costs and a \(10 \%\) increase in units sold 8\. \(A 5 \%\) increase in fixed costs and a \(5 \%\) decrease in variable costs 9\. Which of these alternatives yields the highest budgeted operating income? Explain why this is the case.

Describe three methods that managers can use to express CVP relationships

Corporate Printing Company currently leases its only copy machine for \(\$ 1,500\) a month. The company is considering replacing this leasing agreement with a new contract that is entirely commission based. Under the new agreement, Corporate would pay a commission for its printing at a rate of \(\$ 20\) for every 500 pages printed. The company currently charges \(\$ 0.20\) per page to its customers. The paper used in printing costs the company \(\$ 0.05\) per page and other variable costs, including hourly labor, amount to \(\$ 0.10\) per page. 1\. What is the company's breakeven point under the current leasing agreement? What is it under the new commission-based agreement? 2\. For what range of sales levels will Corporate prefer (a) the fixed lease agreement and (b) the commission agreement? 3\. Do this question only if you have covered the chapter appendix in your class. Corporate estimates that the company is equally likely to sell \(20,000,30,000,40,000,50,000,\) or 60,000 pages of print. Using information from the original problem, prepare a table that shows the expected profit at each sales level under the fixed leasing agreement and under the commission- based agreement. What is the expected value of each agreement? Which agreement should Corporate choose?

What is operating leverage? How is knowing the degree of operating leverage helpful to managers?
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