Chapter 3, Problem 17PSA

a.

To determine

Calculate the break-even points using the equation method.

Explanation of Solution

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

$\begin{array}{l}\text{Sales}-\text{Variable cost}-\text{Fixed cost}=\text{Profit}\\ \left(\text{Sales price}\times \text{N}\right)-\left(\text{Variable cost per unit}\times \text{N}\right)=\text{Fixed cost}+\text{Profit}\\ \left(\text{Contribution margin per unit}\times \text{N}\right)=\text{Fixed cost}+\text{Profit}\\ \text{N}=\frac{\text{Fixed cost}+\text{Profit}}{\text{Contribution margin per unit}}\end{array}$

$\begin{array}{c}\text{N}=\frac{\left(\left(\begin{array}{l}\text{Fixed cost (manufacturimg)}+\\ \text{Fixed cost (administrative)}\end{array}\right)+\text{profit}\right)}{\text{Contribution margin per unit}}\\ =\frac{\left(\left(\$240,000+\$165,000\right)+\$0\right)}{\text{36 }\left(\text{1}\right)}\\ =\frac{\$405,000}{\text{36 }}\\ =11,250\text{ units}\end{array}$

Hence, the break-even units is 11,250 units.

The calculation of break-even point in dollars is as follows:

$\begin{array}{c}\text{Break-even in dollars}=\text{Break-even units}\times \text{Sales price}\\ =11,250\times \$75\text{ per unit}\\ =\$843,750\end{array}$

Hence, the break-even in dollars is $843,750.

Note:

N denote number of units to break-even.

Working note:

The calculation of contribution margin is as follows:

$\begin{array}{c}\text{Contribution margin}=\left(\text{Sales price}-\left(\begin{array}{l}\text{Variable cost(manufacturimg)}\\ +\text{Variable cost(administrative)}\end{array}\right)\right)\\ =\$75-\left(\$30+\$9\right)\\ =\$36\end{array}$

Hence, the contribution margin is $36.

…… (1)

b.

To determine

Calculate the break-even point in dollars and units using contribution margin per unit approach.

Explanation of Solution

The calculation of sales in units is as follows:

$\begin{array}{c}\text{Number of units to break-even}=\frac{\text{Fixed cost (manufacturimg)}+\text{Fixed cost (administrative)}}{\text{Contribution margin per unit}}\\ =\frac{\$240,000+\$165,000}{\text{36 }\left(\text{1}\right)}\\ =\frac{\$405,000}{\text{36 }}\\ =11,250\text{ units}\end{array}$

Hence, the break-even units is 11,250 units.

The calculation of sales in dollars is as follows:

$\begin{array}{c}\text{Break-even in dollars}=\text{Break-even units}\times \text{Sales price}\\ =11,250\times \$75\text{ per unit}\\ =\$843,750\end{array}$

Hence, the sales in dollars is $843,750.

c.

To determine

Calculate the break-even points in dollars and units using contribution margin ratio approach.

Explanation of Solution

The calculation of break even in dollars is as follows:

$\begin{array}{c}\text{Break-even in dollars}=\frac{\text{Fixed cost (manufacturimg)}+\text{Fixed cost (administrative)}}{\text{Contribution margin ratio }}\\ =\frac{\$240,000+\$165,000}{\text{48\% }\left(\text{2}\right)}\\ =\frac{\$405,000}{\text{48\% }}\\ =\$843,750\end{array}$

Hence, the break-even in dollars is $843,750.

The calculation of break even in units is as follows:

$\begin{array}{c}\text{Break-even in units}=\frac{\text{Break-even in dollars}}{\text{Sales price}}\\ =\frac{\$843,750}{\$75}\\ =11,250\text{ units}\end{array}$

Hence, the break-even in units is 11,250 units.

Working note:

The calculation of break-even dollars is as follows:

        $\begin{array}{c}\text{Contribution margin ratio}=\frac{\text{Contribution margin per unit}}{\text{Sales price}}\\ =\frac{\$36\left(\text{1}\right)}{\$75}\\ =48\%\end{array}$

Hence, the contribution margin ratio is 48%.

…… (2)

d.

To determine

Calculate the contribution margin income statement for break-even sales volume to confirm the result.

Explanation of Solution

The calculation of contribution margin income statement is as follows:

Table (1)