Chapter 6, Problem 19E

To determine

(a)

Concept introduction:

Contribution Margin:

The margin of profit which is computed after considering the variable cost only and not the fixed cost is known as contribution. In other words, it means the contribution made by selling the product after covering its variable cost to the company.

The weighted contribution margin per unit if the product mix is changed to $40/30/30$.

Answer to Problem 19E

The weighted contribution margin per unit is $\text{\$37}\text{.10}$.

Explanation of Solution

As the product mix is changed to $40/30/30$

So, the weighted contribution margin is calculated as:

$\begin{array}{c}\text{Weighted Contribution Margin}=\left(\$38\times 40\%\right)+\left(\$30\times 30\%\right)+\left(43\times 30\%\right)\\ =\$37.10\end{array}$

To determine

(b)

Concept introduction:

Breakeven Point:

The level of sales where the company is neither on profit nor loss is termed as breakeven point. In other words, that level of sales at which the fixed cost of the business is recovered.

The breakeven point if the fixed cost is $\$187,000$.

Answer to Problem 19E

The breakeven point for Lens A is $\text{2,016 units}$, Lens B is $\text{1,512 units}$, and Lens C is $\text{1,512 units}$.

Explanation of Solution

As the product mix is changed to $40/30/30$

So, the weighted contribution margin is calculated as:

$\begin{array}{c}\text{Weighted Contribution Margin}=\left(\$38\times 40\%\right)+\left(\$30\times 30\%\right)+\left(43\times 30\%\right)\\ =\$37.10\end{array}$

The break-even point in units is calculated as:

$\begin{array}{c}\text{Breakeven Point}=\frac{\text{Fixed Cost}}{\text{Weighted Contribution Margin}}\\ =\frac{\$187,000}{\$37.10}\\ =5,040\text{ units}\end{array}$

Now, this breakeven sale will be divided into the products. Lens A, Lens B, and Lens C in their respective percentage of sale.

The Breakeven sale for each product is:

$\begin{array}{c}\text{Lens A}=5,040\times 40\%\\ =2,016\text{ units}\end{array}$.

$\begin{array}{c}\text{Lens B}=5,040\times 30\%\\ =1,512\text{ units}\end{array}$

$\begin{array}{c}\text{Lens C}=5,040\times 30\%\\ =1,512\text{ units}\end{array}$

To determine

(c)

Concept introduction:

Target Profit:

The target profit is that profit which a company decides to achieve and this analysis helps in determinig the level of sales by which this target can be achieved.

The total sale units to achieve target profit of $\$73,000$.

Answer to Problem 19E

The target sale point for Lens A is $\text{2,803 units}$, Lens B is $\text{2,103 units}$, and Lens C is $\text{2,103 units}$.

Explanation of Solution

As the product mix is changed to $40/30/30$

So, the weighted contribution margin is calculated as:

$\begin{array}{c}\text{Weighted Contribution Margin}=\left(\$38\times 40\%\right)+\left(\$30\times 30\%\right)+\left(43\times 30\%\right)\\ =\$37.10\end{array}$

The number units to be sold for achieving the target profit are calculated as:

$\begin{array}{c}\text{Target Sales}=\frac{\text{Fixed Cost}+\text{Target Profit}}{\text{Contribution Margin}}\\ =\frac{\$187,000+\$73,000}{37.10}\\ =7,008\text{ units}\end{array}$

Now, this breakeven sale will be divided into the products. Lens A, Lens B, and Lens C in their respective percentage of sale.

The Breakeven sale for each product is:

$\begin{array}{c}\text{Lens A}=7,008\times 40\%\\ =2,803\text{ units}\end{array}$.

$\begin{array}{c}\text{Lens B}=7,008\times 30\%\\ =2,103\text{ units}\end{array}$

$\begin{array}{c}\text{Lens C}=7,008\times 30\%\\ =2,103\text{ units}\end{array}$

To determine

(d)

Concept introduction:

Contribution Margin:

The margin of profit which is computed after considering the variable cost only and not the fixed cost is known as contribution. In other words, it means the contribution made by selling the product after covering its variable cost to the company.

The reason for the difference in the results due to change in the product mix.

Answer to Problem 19E

The reason for the difference is the change in the weighted contribution margin due to the change in the product mix which changes the proportion of one product to the total sales.

Explanation of Solution

The reason for the difference in the results is due to change in product mix which changes the proportion of one product sale to the total sale.

This is because when the product mix has higher proportion of that product which has higher contribution then the overall weighted contribution also increases which leads to lower breakeven sales point. On the other hand, when the product mix has lower proportion of that product which has higher contribution then the overall weighted contribution also decreases which leads to higher breakeven sales point.