Chapter 20, Problem 8BP

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 Hats:

$\begin{array}{c}\text{Contribution margin ratio = }\left[\frac{\text{Contribution margin}}{\text{Sales}}\right]\times 100\\ =\left[\frac{\text{\$6}}{\text{\$20}}\right]\times 100\\ =30\%\end{array}$

Product Shirts:

$\begin{array}{c}\text{Contribution margin ratio = }\left[\frac{\text{Contribution margin}}{\text{Sales}}\right]\times 100\\ =\left[\frac{\text{\$21}}{\text{\$28}}\right]\times 100\\ =75\%\end{array}$

Conclusion

Hence, the contribution margin ratio for product Hats is 30% and for product Shirts is 75%.

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 Hats	12%
From Shirts	45%
Average contribution margin ratio	57%

Table (1)

Working notes:

Calculate the average contribution margin ratio for product Hats:

$\begin{array}{c}\begin{array}{l}\text{Average contribution margin}\\ \text{ ratio for product hats}\end{array}\}\text{ =}\left(\begin{array}{l}\text{Contribution margin ratio}\times \\ \text{ Sales mix from shoes}\end{array}\right)\\ =\left(30\%\times 40\%\right)\\ =12\%\end{array}$

Calculate the average contribution margin ratio for product Shirts:

$\begin{array}{c}\begin{array}{l}\text{Average contribution margin}\\ \text{ ratio for product shirts}\end{array}\}\text{ =}\left(\begin{array}{l}\text{Contribution margin ratio}\times \\ \text{ Sales mix from shorts}\end{array}\right)\\ =\left(75\%\times 60\%\right)\\ =45\%\end{array}$

1. 2. Calculate the monthly operating income.

Step 1: Calculate total contribution margin.

$\begin{array}{c}\text{Total contribution margin =}\left(\begin{array}{l}\text{ Total sales}\times \text{Average}\\ \text{ contribution margin ratio}\end{array}\right)\\ =\left(\$1,500,000\times 57\%\right)\\ =\$855,000\end{array}$

Step 2: Calculate the monthly operating income.                       

$\begin{array}{c}\text{Operating income}=\left(\text{Contribution margin}-\text{Fixed cost}\right)\\ \text{=}\left(\text{\$}855,000-\$684,000\right)\\ =\$171,000\end{array}$

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

$\begin{array}{c}\text{Break-even Sales volume in dollars}=\left(\frac{\text{Fixed Costs }}{\text{Contribution Margin Ratio}}\right)\\ =\left(\frac{\$684,000}{57\%}\right)\\ =\$1,200,000\end{array}$

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 Hats	18%
From Shirts	30%
Average contribution margin ratio	48%

Table (1)

Working notes:

Calculate the average contribution margin ratio for product Hats:

$\begin{array}{c}\begin{array}{l}\text{Average contribution margin}\\ \text{ ratio for product hats}\end{array}\}\text{ =}\left(\begin{array}{l}\text{Contribution margin ratio}\times \\ \text{ Sales mix from shoes}\end{array}\right)\\ =\left(30\%\times 60\%\right)\\ =18\%\end{array}$

Calculate the average contribution margin ratio for product Shirts:

$\begin{array}{c}\begin{array}{l}\text{Average contribution margin}\\ \text{ ratio for product shirts}\end{array}\}\text{ =}\left(\begin{array}{l}\text{Contribution margin ratio}\times \\ \text{ Sales mix from shorts}\end{array}\right)\\ =\left(75\%\times 40\%\right)\\ =30\%\end{array}$

1. 2. Calculate the monthly operating income.

Step 1: Calculate total contribution margin.

$\begin{array}{c}\text{Total contribution margin =}\left(\begin{array}{l}\text{ Total sales}\times \text{Average}\\ \text{ contribution margin ratio}\end{array}\right)\\ =\left(\$1,500,000\times 48\%\right)\\ =\$720,000\end{array}$

Step 2: Calculate the monthly operating income.                       

$\begin{array}{c}\text{Operating income}=\left(\text{Contribution margin}-\text{Fixed cost}\right)\\ \text{=}\left(\text{\$72}0,000-\$684,000\right)\\ =\$36,000\end{array}$

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

$\begin{array}{c}\text{Break-even Sales volume in dollars}=\left(\frac{\text{Fixed Costs }}{\text{Contribution Margin Ratio}}\right)\\ =\left(\frac{\$684,000}{48\%}\right)\\ =\$1,425,000\end{array}$

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 shirts overcame some types of sales of hats as shirts contribute a much higher margin than hats. That says the sales of shirts in a particular sales volume contribute less than that of hats, generate a good income and avoid break even by reducing the sales volume.