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:

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

$\begin{array}{c}\text{N}=\frac{\left(\left(\begin{array}{l}\text{Fixed cost (manufacturimg)}+\\ \text{Fixed cost (administrative)}\end{array}\right)+\text{profit}\right)}{\text{Contribution margin per unit}}\\ =\frac{\left(\left(\$480,000+\$240,000\right)+\$0\right)}{72\left(\text{1}\right)}\\ =\frac{\$720,000}{72}\\ =10,000\text{ units}\end{array}$

Hence, the break-even units is 10,000 units.

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

$\begin{array}{c}\text{Break-even in dollars}=\text{Break-even units}\times \text{Sales price}\\ =10,000\times \$150\text{ per unit}\\ =\$1,500,000\end{array}$

Hence, the break-even in dollars is $1,500,000.

Note:

N denote number of units to break-even.

Working note:

The calculation of contribution margin is as follows:

$\begin{array}{c}\text{Contribution margin}=\left(\text{Sales price}-\left(\begin{array}{l}\text{Variable cost(manufacturimg)}\\ +\text{Variable cost(administrative)}\end{array}\right)\right)\\ =\$150-\left(\$60+\$18\right)\\ =\$72\end{array}$

Hence, the contribution margin is $72.

(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:

$\begin{array}{c}\text{Number of units to break-even}=\frac{\text{Fixed cost (manufacturimg)}+\text{Fixed cost (administrative)}}{\text{Contribution margin per unit}}\\ =\frac{\$480,000+\$240,000}{\text{\$72 }(1)}\\ =10,000\text{ units}\end{array}$

Hence, the break-even units is 18,000 units.

The calculation of sales in dollars is as follows:

$\begin{array}{c}\text{Break-even in dollars}=\text{Break-even units}\times \text{Sales price}\\ =18,000\times \$72\text{ per unit}\\ =\$1,296,000\end{array}$

Hence, the sales in dollars is $1,300,000.

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:

$\begin{array}{c}\text{Break-even in dollars}=\frac{\text{Fixed cost (manufacturimg)}+\text{Fixed cost (administrative)}}{\text{Contribution margin ratio }}\\ =\frac{\$480,000+\$240,000}{\text{48\% }\left(\text{2}\right)}\\ =\frac{\$720,000}{\text{48\% }}\\ =\$1,500,000\end{array}$

Hence, the break-even in dollars is $1,500,000.

The calculation of break even in units is as follows:

$\begin{array}{c}\text{Break-even in units}=\frac{\text{Break-even in dollars}}{\text{Sales price}}\\ =\frac{\$1,500,000}{\$150}\\ =10,000\text{ units}\end{array}$

Hence, the break-even in units is 10,000 units.

Working note:

The calculation of break-even dollars is as follows:

        $\begin{array}{c}\text{Contribution margin ratio}=\frac{\text{Contribution margin per unit}}{\text{Sales price}}\\ =\frac{\$72\left(\text{1}\right)}{\$150}\\ =48\%\end{array}$

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)