Chapter 7, Problem 51P

1.

To determine

Calculate the contribution margin ratio of touring model for A T S Company.

Explanation of Solution

Contribution Margin: It is defined as the difference between the sales and the variable cost. In other words, contribution margin is the excess amount of sales revenue after deducting variable expenses.

The formula to calculate contribution margin is as follows:

$\text{Contribution}\text{Margin}\text{=}\text{ Sales }-\text{Variable}\text{costs}$

Contribution Margin ratio: It is a ratio that measures the contribution margin generated by the company from the sales to make it avialable for paying the fixed cost and generate a profit. It is expressed as percentage of margin available from each dollar sales to pay fixed expenses and to provide profit.

The formula to calculate the contribution margin ratio is as follows:

$\text{Contribution}\text{Margin}\text{Ratio }=\frac{\text{Contribution}\text{Margin}}{\text{Sales}}\times 100$

Calculate the contribution margin ratio.

$\begin{array}{c}\text{Contribution margin ratio = }\frac{\text{Contribution margin}}{\text{Sales}}\times 100\\ =\frac{\$27.2}{\$80}\\ =0.34\end{array}$

Working note:

Calculate the contribution margin.

$\begin{array}{c}\text{Contribution margin = Sales}-\text{Variable cost}\\ =\$80-\$52.80\\ =\$27.2\end{array}$

2.

To determine

Calculate the sales volume (in units) to attain after- tax net income of $22,080.

Explanation of Solution

Target Profit: It refers to the desired amount of profit that a company expects to achieve by the end of an accounting period after it reaches its break-even point. Thus, the company needs to compute the required sales to earn the target profit.

Calculate the sales volume (in units).

$\begin{array}{c}\begin{array}{l}\text{Number of units of sales required}\\ \text{to earn target after-tax net-income}\end{array})=\frac{\text{Fixed expenses+}\frac{\text{Target after-tax net income}}{\left(1-\text{Tax}\text{rate}\right)}}{\text{Unit contribution margin}}\\ =\frac{\$316,800+\frac{\$22,080}{\left(1-.40\right)}}{\$80-\$52.80}\\ =\frac{\$316,800+\frac{\$22,080}{0.60}}{\$27.20}\\ =\frac{\$316,800+\$36,800}{\$27.20}\end{array}$

$\begin{array}{c}\begin{array}{l}\text{Number of units of sales required}\\ \text{to earn target after-tax net-income}\end{array})=\frac{\$353,600}{\$27.20}\\ =13,000\text{ units}\end{array}$

3.

To determine

Calculate the variable cost per unit of the touring model to change that have the same break-even point as mountaineering model.

Explanation of Solution

Break-even Point: It refers to a point in the level of operations at which a company experiences its revenues generated is equal to its costs incurred. Thus, when a company reaches at its break-even point, it reports neither an income nor a loss from operations.

The formula to calculate the break-even point in sales units is as follows:

$\text{Break-even}\text{point}\text{in}\text{units }=\frac{\text{Fixed}\text{Costs}}{\text{Contribution}\text{Margin}\text{per}\text{unit}}$

Variable cost: A variable cost is the cost that proportionately changes with the changes in the activity base such as units of production.

Calculate the break-even point (in units) for mountaineering model.

$\begin{array}{c}\text{Break-even point }\left(\text{in units }\right)=\frac{\text{Fixed Costs}}{\text{Contribution Margin per unit}}\\ =\frac{\$369,600}{\$35.2}\\ =10,500\text{ units}\end{array}$

Working note:

Calculate the contribution per unit.

$\begin{array}{c}\text{Contribution margin per unit =}\left(\begin{array}{l}\text{Selling price per unit}\\ -\text{Variable cost per unit}\end{array}\right)\\ \text{=\$88}-\$52.80\\ =\$35.2\end{array}$

Let assume Y denotes the variable cost of the touring model and break-even point for the touring model is 10,500 units.

$\begin{array}{c}\text{Break-even point }\left(\text{in units }\right)=\frac{\text{Fixed Costs}}{\text{Selling price}-\text{Variable cost}}\\ 10,500=\frac{\$316,800}{\$80-\text{Y}}\\ \text{(10,500)}\times \text{(\$80}-\text{Y})=\text{ \$316,800}\\ \text{\$840,000}-\text{10,500Y }=\text{ \$316,800}\end{array}$$\begin{array}{c}\text{\$840,000}-\$316,800=10,500\text{Y}\\ \text{10,500Y }=\text{ \$523,200}\\ \text{Y=}\frac{\text{\$523,200}}{10,500}\\ \text{Y }=\text{ \$49}\text{.83 (rounded)}\end{array}$

Therefore, the variable cost per unit will decrease by $2.97$\left(\$52.80-\$49.83\right)$ .

4.

To determine

Calculate the new break-even point in units, if variable cost decreases by 10 percent and fixed cost increases by 10 percent.

Explanation of Solution

$\begin{array}{c}\text{Break-even point }\left(\text{in units }\right)=\frac{\text{Fixed Costs}}{\text{Contribution Margin per unit}}\\ =\frac{\$316,800\times 110\%}{\$32.48}\\ =\frac{\$348,480}{\$32.48}\\ =10,729\text{ units}\left(\text{rounded}\right)\end{array}$

Working note:

Calculate the contribution margin.

$\begin{array}{c}\text{Contribution margin = Sales}-\text{Variable cost}\\ =\$80-\$47.52\\ =\$32.48\end{array}$

Calculate the variable cost.

$\begin{array}{c}\text{Variable cost = Variable cost}\times \text{Percentage change in variable cost}\\ =\$52.80\times 90\%\\ =\$47.52\end{array}$

5.

To determine

Calculate the break-even point (in units), if the management decided to produce both the products in equal proportions.

Explanation of Solution

Break-even Point: It refers to a point in the level of operations at which a company experiences its revenues generated is equal to its costs incurred. Thus, when a company reaches at its break-even point, it reports neither an income nor a loss from operations.

The formula to calculate the break-even point in sales units for multiple products is as follows:

$\text{Break-even}\text{point}\text{in}\text{units }=\frac{\text{Fixed}\text{Costs}}{\text{Weighted average contribution}\text{Margin}\text{per}\text{unit}}$

Calculate the break-even point (in units).

$\begin{array}{c}\text{Break-even point in units }=\frac{\text{Fixed Costs}}{\text{Weighted average contribution Margin per unit}}\\ =\frac{\$343,200}{\$31.20}\\ =11,000\text{ units}\end{array}$

Working note:

Calculate the weighted-average unit contribution margin.

$\begin{array}{c}\begin{array}{l}\text{Weighted average unit}\\ \text{contribution margin}\end{array})=\left[\begin{array}{l}\left(\begin{array}{l}\text{Percentage of sale proportions}\times \\ \text{Unit contribution margin of mountaineering model}\end{array}\right)\\ +\left(\begin{array}{l}\text{Percentage of sale proportions}\times \\ \text{Unit contribution margin of touring model}\end{array}\right)\end{array}\right]\\ =\left[\left(50\%\times \$35.20\right)+\left(50\%\times \$27.20\right)\right]\\ =\$17.6+\$13.6\\ =\$31.2\end{array}$

Calculate the unit contribution margin of mountaineering model.

$\begin{array}{c}\text{Contribution margin = Sales}-\text{Variable cost}\\ =\$88-\$52.80\\ =\$35.2\end{array}$