Question

Calculating contribution margin ratio, preparing contribution margin income statements For its top managers, Worldwide Travel formats its income statement as follows:

Worldwide’s relevant range is between sales of \(253,000 and \)368,000. Requirements

1. Calculate the contribution margin ratio.

2. Prepare two contribution margin income statements: one at the \(253,000 sales level and one at the \)368,000 sales level. (Hint: The proportion of each sales dollar that goes toward variable costs is constant within the relevant range.)

Short answer

1. Contribution margin ratio is 57%
2. Contribution at $\mathbf{\$}\mathbf{253}\mathbf{,}\mathbf{000}\mathbf{}\mathbf{is}\mathbf{}\mathbf{\$}\mathbf{144}\mathbf{,}\mathbf{210}$ and $\mathbf{\$}\mathbf{209}\mathbf{,}\mathbf{760}\mathbf{}\mathbf{at}\mathbf{}\mathbf{\$}\mathbf{368}\mathbf{,}\mathbf{000}$

Step-by-step solution

Calculation of contribution margin ratio

$$\begin{gathered} \mathit{C}\mathit{o}\mathit{n}\mathit{t}\mathit{r}\mathit{i}\mathit{b}\mathit{u}\mathit{t}\mathit{i}\mathit{o}\mathit{n}\mathbf{}\mathit{m}\mathit{a}\mathit{r}\mathit{g}\mathit{i}\mathit{n}\mathbf{}\mathit{r}\mathit{a}\mathit{t}\mathit{i}\mathit{o}\mathbf{}\mathbf{=}\mathbf{}\frac{\mathbf{C}\mathbf{o}\mathbf{n}\mathbf{t}\mathbf{r}\mathbf{i}\mathbf{b}\mathbf{u}\mathbf{t}\mathbf{i}\mathbf{o}\mathbf{n}\mathbf{}\mathbf{m}\mathbf{a}\mathbf{r}\mathbf{g}\mathbf{i}\mathbf{n}}{\mathbf{N}\mathbf{e}\mathbf{t}\mathbf{}\mathbf{s}\mathbf{a}\mathbf{l}\mathbf{e}\mathbf{s}\mathbf{}\mathbf{r}\mathbf{e}\mathbf{v}\mathbf{e}\mathbf{n}\mathbf{u}\mathbf{e}} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\frac{\mathbf{\$}\mathbf{180}\mathbf{,}\mathbf{405}}{\mathbf{\$}\mathbf{316}\mathbf{,}\mathbf{500}} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{57}\mathbf{\%} \end{gathered}$$

Preparation of contribution margin income statements

Sales	$\mathbf{\$}\mathbf{253}\mathbf{,}\mathbf{000}$	$\mathbf{\$}\mathbf{368}\mathbf{,}\mathbf{000}$
Less: Variable cost	localid="1656155930651" $$\begin{gathered} \mathbf{\$}\mathbf{136}\mathbf{,}\mathbf{095}\mathbf{\times }\mathbf{\$}\mathbf{253}\mathbf{,}\mathbf{000}\mathbf{/}\mathbf{\$}\mathbf{316}\mathbf{,}\mathbf{500} \\ \mathbf{=}\mathbf{\$}\mathbf{108}\mathbf{,}\mathbf{790} \end{gathered}$$	$$\begin{gathered} \mathbf{\$}\mathbf{136}\mathbf{,}\mathbf{095}\mathbf{\times }\mathbf{\$}\mathbf{368}\mathbf{,}\mathbf{000}\mathbf{/}\mathbf{\$}\mathbf{316}\mathbf{,}\mathbf{500} \\ \mathbf{=}\mathbf{\$}\mathbf{158}\mathbf{,}\mathbf{240} \end{gathered}$$
Contribution margin	$\mathbf{\$}\mathbf{144}\mathbf{,}\mathbf{210}$	$\mathbf{\$}\mathbf{209}\mathbf{,}\mathbf{760}$
Less: Fixed cost	$\mathbf{\$}\mathbf{173}\mathbf{,}\mathbf{000}$	$\mathbf{\$}\mathbf{173}\mathbf{,}\mathbf{000}$
Operating income	$\left(\$28,790\right)$	$\mathbf{\$}\mathbf{36}\mathbf{,}\mathbf{760}$