Chapter 20, Problem 8AP

a.

To determine

Compute contribution margin ratio for each line of products.

Explanation of Solution

Contribution Margin Ratio: The contribution margin ratio shows the amount of difference in the actual sales value and the variable expenses in percentage. This margin indicates that percentage which is available for sale above the fixed costs and the profit.

Following formula is used to calculate contribution margin ratio:

$\begin{array}{c}\text{Contribution margin ratio = }\left[\frac{\begin{array}{l}\left(\text{Sales}-\text{Variable cost}\right)\\ \text{Contribution margin}\end{array}}{\text{Sales}}\right]\times 100\\ \end{array}$

Calculate the contribution margin ratio for each line of products:

Product shoes:

$\begin{array}{c}\text{Contribution margin ratio = }\left[\frac{\text{Contribution margin}}{\text{Sales}}\right]\times 100\\ =\left[\frac{\text{\$15}}{\text{\$50}}\right]\times 100\\ =30\%\end{array}$

Product shorts:

$\begin{array}{c}\text{Contribution margin ratio = }\left[\frac{\text{Contribution margin}}{\text{Sales}}\right]\times 100\\ =\left[\frac{\text{\$4}}{\text{\$5}}\right]\times 100\\ =80\%\end{array}$

Conclusion

Hence, the contribution margin ratio for product shoes is 30% and for product shorts is 80%.

b.

To determine

Compute the following assuming the current sales mix:

1. 1. Average contribution margin ratio of total monthly sales.
2. 2. Monthly operating income.
3. 3. Monthly break-even sales volume.

Explanation of Solution

Sales mix: Sales mix refers to the relative percentage of the total sales based on the provided number of products. In other words, it is expressed as a percentage of units sold for each product with respect to the total units sold for all the products.

1. 1. Calculate the average contribution margin ratio of total monthly sales:

Particulars	Contribution margin ratio
From shoes	24%
From shorts	16%
Average contribution margin ratio	40%

Table (1)

Working notes:

Calculate the average contribution margin ratio for product shoes:

$\begin{array}{c}\begin{array}{l}\text{Average contribution margin}\\ \text{ ratio for product shoes}\end{array}\}\text{ =}\left(\begin{array}{l}\text{Contribution margin ratio}\times \\ \text{ Sales mix from shoes}\end{array}\right)\\ =\left(30\%\times 80\%\right)\\ =24\%\end{array}$

Calculate the average contribution margin ratio for product shorts:

$\begin{array}{c}\begin{array}{l}\text{Average contribution margin}\\ \text{ ratio for product shorts}\end{array}\}\text{ =}\left(\begin{array}{l}\text{Contribution margin ratio}\times \\ \text{ Sales mix from shorts}\end{array}\right)\\ =\left(80\%\times 20\%\right)\\ =16\%\end{array}$

1. 2. Calculate the monthly operating income.

Step 1: Calculate total contribution margin.

$\begin{array}{c}\text{Total contribution margin =}\left(\begin{array}{l}\text{ Total sales}\times \text{Average}\\ \text{ contribution margin ratio}\end{array}\right)\\ =\left(\$1,000,000\times 40\%\right)\\ =\$400,000\end{array}$

Step 2: Calculate the monthly operating income.                       

$\begin{array}{c}\text{Operating income}=\left(\text{Contribution margin}-\text{Fixed cost}\right)\\ \text{=}\left(\text{\$40}0,000-\$378,000\right)\\ =\$22,000\end{array}$

1. 3. Calculate the monthly break-even sales volume in dollars:

$\begin{array}{c}\text{Break-even Sales volume in dollars}=\left(\frac{\text{Fixed Costs }}{\text{Contribution Margin Ratio}}\right)\\ =\left(\frac{\$378,000}{40\%}\right)\\ =\$945,000\end{array}$

c.

To determine

Compute the following assuming the new sales mix:

1. 1. Average contribution margin ratio of total monthly sales.
2. 2. Monthly operating income.
3. 3. Monthly break-even sales volume.

Explanation of Solution

Sales mix: Sales mix refers to the relative percentage of the total sales based on the provided number of products. In other words, it is expressed as a percentage of units sold for each product with respect to the total units sold for all the products.

1. 1. Calculate the average contribution margin ratio of total monthly sales:

Particulars	Contribution margin ratio
From shoes	21%
From shorts	24%
Average contribution margin ratio	45%

Table (1)

Working notes:

Calculate the average contribution margin ratio for product shoes:

$\begin{array}{c}\begin{array}{l}\text{Average contribution margin}\\ \text{ ratio for product shoes}\end{array}\}\text{ =}\left(\begin{array}{l}\text{Contribution margin ratio}\times \\ \text{ Sales mix from shoes}\end{array}\right)\\ =\left(30\%\times 70\%\right)\\ =21\%\end{array}$

Calculate the average contribution margin ratio for product shorts:

$\begin{array}{c}\begin{array}{l}\text{Average contribution margin}\\ \text{ ratio for product shorts}\end{array}\}\text{ =}\left(\begin{array}{l}\text{Contribution margin ratio}\times \\ \text{ Sales mix from shorts}\end{array}\right)\\ =\left(80\%\times 30\%\right)\\ =24\%\end{array}$

1. 2. Calculate the monthly operating income.

Step 1: Calculate total contribution margin.

$\begin{array}{c}\text{Total contribution margin =}\left(\begin{array}{l}\text{ Total sales}\times \text{Average}\\ \text{ contribution margin ratio}\end{array}\right)\\ =\left(\$1,000,000\times 45\%\right)\\ =\$450,000\end{array}$

Step 2: Calculate the monthly operating income.                       

$\begin{array}{c}\text{Operating income}=\left(\text{Contribution margin}-\text{Fixed cost}\right)\\ \text{=}\left(\text{\$45}0,000-\$378,000\right)\\ =\$72,000\end{array}$

1. 3. Calculate the monthly break-even sales volume in dollars:

$\begin{array}{c}\text{Break-even Sales volume in dollars}=\left(\frac{\text{Fixed Costs }}{\text{Contribution Margin Ratio}}\right)\\ =\left(\frac{\$378,000}{45\%}\right)\\ =\$840,000\end{array}$

d.

To determine

Explain the changes in the company’s financial position so significantly with the new sales mix.

Explanation of Solution

In the new sales mix, sales of shorts overcame some types of sales of shoes as shorts contribute a much higher margin than shoes. That says the sales of shorts in a particular sales volume contribute more than that of shoes, generate a good income and avoid break even by reducing the sales volume.