Chapter 20, Problem 5BP

a.

To determine

Determine the unit contribution margin and break-even point in units and break-even point in dollar sales.

Explanation of Solution

Contribution Margin:

The process or theory which is used to judge the benefit given by each unit of the goods produced is called as contribution margin.

The contribution margin is the difference between the selling price and the cost of the product.

Formula to compute the unit contribution margin:

$\text{Unit Contribution Margin}=\text{Unit Sales Price}-\text{Per Unit Variable Cost}$

Calculate the contribution margin per unit:

Step 1: Calculate the variable cost per unit.

$\begin{array}{c}\text{Variable cost per unit = }\left(\begin{array}{l}\text{Cost of merchandise + }\\ \text{Amount of rental commission}\end{array}\right)\\ =\left(\$1.10+\$.10\right)\\ =\$1.20\end{array}$

Step 2: Calculate the contribution margin per unit.

$\begin{array}{c}\text{Unit Contribution Margin}=\left(\begin{array}{l}\text{Sales price per unit}-\\ \text{Variable cost per unit}\end{array}\right)\\ \text{=}\left(\text{\$3}\text{.20}-\$1.20\right)\\ =\$\mathrm{.2.00}\end{array}$

Calculate the break-even volume in units:

Step 1: Calculate the total monthly fixed costs.

$\begin{array}{c}\text{Total monthly fixed costs = }\left(\begin{array}{c}\text{Depreciation + Wages}\\ \text{ + Others}\end{array}\right)\\ =\left(\$1,000+\$1,800+\$200\right)\\ =\$3,000\end{array}$

Step 2: Calculate the break-even volume in units.

$\begin{array}{c}\text{Break-even volume in units = }\left(\frac{\text{Total monthly fixed costs}}{\text{Unit contribution margin}}\right)\\ =\left(\frac{\$3,000}{\$2}\right)\\ =1,500\end{array}$

Working note:

Calculate the amount of depreciation:

$\begin{array}{c}\text{Depreciation = }\left(\begin{array}{l}\text{Cost of machine}\times \text{.20}\times \\ \text{Depreciation for one month}\end{array}\right)\\ =\left(\$60,000\times \text{.20}\times \frac{\text{1}}{12}\right)\\ =\$1,000\end{array}$

Calculate the break-even volume in dollars:

$\begin{array}{c}\text{Break-even volume in dollars =}\left(\begin{array}{l}\text{ Break-even volume in units}\\ \times \text{Unit sales price}\end{array}\right)\\ =\left(1,500\times \$3.20\right)\\ =\$4,800\end{array}$

b.

To determine

Draw a monthly cost-volume-profit graph for the sales volume up to 800 units per machine per month.

Explanation of Solution

Cost-Volume- Profit Analysis (CVP Analysis): This analysis is helpful in determining that how any type of change in cost determines company’s income.

c.

To determine

Compute the sales volume in units and in dollars per month.

Explanation of Solution

Compute the sales volume in units:

Step 1: Calculate the total desired contribution margin.

$\begin{array}{c}\text{Total desired contribution margin = }\left(\begin{array}{l}\text{Total monthly fixed costs + }\\ \text{Desired operating income}\end{array}\right)\\ =\left(\$3,000+\$700\right)\\ =\$3,700\end{array}$

Step 2: Calculate the sales volume in units.

$\begin{array}{c}\text{Sales volume in units = }\left(\frac{\text{Total desired contribution margin}}{\text{Contribution margin per unit}}\right)\\ =\left(\frac{\$3,700}{\$2.00}\right)\\ =1,850\end{array}$

Working note:

Calculate the amount of desired operating income:

$\begin{array}{c}\text{Desired operating income = }\left(\begin{array}{l}\text{Cost of investment}\times \\ \text{Annual return percentage}\times \\ \text{Operating income for one month}\end{array}\right)\\ =\left(\$70,000\times \text{.12}\times \frac{\text{1}}{12}\right)\\ =\$700\end{array}$

Compute the sales volume in dollars:

$\begin{array}{c}\text{Sales volume in dollars = }\left(\begin{array}{l}\text{Sales volume in units }\\ \times \text{ Unit sales price}\end{array}\right)\\ =\left(1,850\times \$3.20\right)\\ =\$5,920\end{array}$

d.

To determine

Determine the changes in break-even volume in units.

Explanation of Solution

Calculate the changes in break-even volume in units:

$\begin{array}{c}\text{Changes in break-even volume in units = }\left(\frac{\text{New monthly fixed costs}}{\text{New contirbution margin per unit}}\right)\\ =\left(\frac{\$5,250}{\$\mathrm{.2.10}}\right)\\ =2,500\end{array}$

Working notes:

Calculate the amount of new monthly fixed costs:

$\begin{array}{c}\text{New monthly fixed costs = }\left\{\begin{array}{l}\text{Total monthly fixed costs +}\\ \left(\begin{array}{l}\text{Number of machines}\times \\ \text{Rental cost per machine per month}\end{array}\right)\end{array}\right\}\\ =\left\{\text{\$3,000 +}\left(50\times \text{\$45}\right)\right\}\\ =\left(\text{\$3,000 +\$}2,250\right)\\ =\$5,250\end{array}$

Calculate the new contribution margin per unit:

$\begin{array}{c}\text{New contribution margin per unit =}\left(\begin{array}{l}\text{ Unit sales price}-\\ \text{Varaible cost per unit}\\ \text{ of merchandise}\end{array}\right)\\ =\left(\$3.20-\$1.10\right)\\ =\$2.10\end{array}$