Chapter 3, Problem 24PSB

a.

To determine

Calculate the sales volume in units and dollars that is required to earn profit and prepare income statement.

Explanation of Solution

The calculation of sales volume in units is as follows:

$\begin{array}{c}\text{Sales volume in units}=\frac{\text{Fixed cost}+\text{Target profit}}{\text{Contribution margin per unit}}\\ =\frac{\$540,000+\$270,000}{\$90\left(\text{1}\right)}\\ =\frac{\$810,000}{\$90}\\ =9,000\text{ units}\end{array}$

Hence, the sales volume in units is 9,000 units.

The calculation of sales volume in dollars is as follows:

$\begin{array}{c}\text{Sales volume in dollars}=\text{Sales volume in units}\times \text{Sales price}\\ =9,000\text{ units}\times \$135\text{ per unit}\\ =\$1,215,000\end{array}$

Hence, the sales volume in dollars is $1,215,000.

The calculation of income statement is as follows:

(Table 1)

Working note:

The calculation of contribution margin per unit is as follows:

$\begin{array}{c}\text{Contribution margin per unit}=\text{Sales price}-\text{Variable cost}\\ =\$135-\$45\\ =\$90\end{array}$

Hence, the contribution margin per unit is $90.

(1)

The calculation of variable cost is as follows:

$\begin{array}{c}\text{Variable cost}=\text{Number of units}\times \text{Variable cost per unit}\\ =9,000\text{ units}\times \text{\$45}\\ =\$405,000\end{array}$

Hence, the variable cost is $405,000.

(2)

b.

To determine

Calculate the income statement and comment whether Company C should whether proceed with the plan.

Explanation of Solution

The calculation of income statement is as follows:

(Table 2)

Company M should continue with the plan to improve the quality of the product. As specified the project should add $90,000 to net income $(\$360,000-\$270,000)$.

Note:

The total number of units is 14,000 units $(9,000+5,000)$.

The variable cost is $60$(\$45+\$15)$

Working note:

The calculation of sales volume in dollars is as follows:

$\begin{array}{c}\text{Sales volume in dollars}=\text{Change in sales volume units}\times \text{Sales price}\\ =14,000\text{ units}\times \$135\text{ per unit}\\ =\$1,890,000\end{array}$

Hence, the sales volume in dollars is $1,890,000.

(3)

The calculation of variable cost is as follows:

$\begin{array}{c}\text{Variable cost}=\text{Number of units}\times \text{Variable cost per unit}\\ =14,000\text{ units}\times \text{\$60}\\ =\$840,000\end{array}$

Hence, the variable cost is $840,000.

(4)

The calculation of fixed cost is as follows:

$\begin{array}{c}\text{Total fixed cost}=\text{Fixed cost}+\text{Additional spending}\text{}\text{ (advertising)}\\ =\$540,000+\$150,000\\ =\$690,000\end{array}$

Hence, the total fixed cost is $690,000.

(5)

c.

To determine

Calculate the margin of safety in dollars, units and as a percentage.

Explanation of Solution

The calculation of break-even points in units is as follows:

$\begin{array}{c}\text{Break-even point in units}=\frac{\text{Fixed cost}}{\text{Contribution margin per unit}}\\ =\frac{\$690,000\left(\text{5}\right)}{\$75\left(6\right)}\\ =9,200\text{ units}\end{array}$

Hence, the break-even units is 9,200 units.

The calculation of sales volume in dollars is as follows:

$\begin{array}{c}\text{Break-even in dollars}=\text{Break-even in units}\times \text{Sales price}\\ =9,200\text{ units}\times \$135\text{ per unit}\\ =\$1,242,000\end{array}$

Hence, the sales volume in dollars is $1,242,000.

The calculation of margin of safety in dollars and units is as follows:

(Table 3)

The calculation of margin of safety in percentage is as follows:

$\begin{array}{c}\text{Margin of safety in percentage}=\frac{\text{Margin of safety in dollars}}{\text{Budgeted sales}}\\ =\frac{\$648,000}{\$1,890,000}\\ =0.3429\\ =34.29\%\end{array}$

Hence, the margin of safety in percentage is 34.29%

Working note:

The calculation of contribution margin per unit is as follows:

$\begin{array}{c}\text{Contribution margin per unit}=\text{Sales price}-\text{Variable cost}\\ =\$135-\left(\$45+\$15\right)\\ =\$135-\$60\\ =\$75\end{array}$

Hence, the contribution margin per unit is $75.

(6)

d.

To determine

Draw a break-even graph using the data in requirement (c).

Explanation of Solution

The break-even graph is as follows:

Figure 1