Chapter 6, Problem 17E

To determine

(a)

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 product mix is $40/60$.

Answer to Problem 17E

The breakeven point in units is $862\text{ units}$.

Explanation of Solution

Contribution Margin Income Statement

Particulars	Standard	Deluxe
Rental Price $\left(\text{A}\right)$	$\$30$	$\$38$
Variable Cost per Canoe $\left(\text{B}\right)$	$\left(\$10.50\right)$	$\left(\$15.20\right)$
Contribution Margin $\left(\text{A}-\text{B}\right)$	$\$19.50$	$\$22.80$

As the product mix is $40/60$

So, the weighted contribution margin is calculated as:

$\begin{array}{c}\text{Weighted Contribution Margin}=\left(19.50\times \frac{40}{100}\right)+\left(22.80\times \frac{60}{100}\right)\\ =\$21.48\end{array}$

The break-even point in units is calculated as:

$\begin{array}{c}\text{Breakeven Point}=\frac{\text{Fixed Cost}}{\text{Weighted Contribution Margin}}\\ =\frac{\$18,500}{\$21.48}\\ =862\text{ units}\end{array}$

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 sales of both model increases by $20\%$ and the product mix changes to $50/50$.

Answer to Problem 17E

The breakeven point in units is $\text{662 units}$.

Explanation of Solution

Contribution Margin Income Statement

Particulars	Standard	Deluxe
Rental Price $\left(\text{A}\right)$	$\$36\left(\$30\times 1.2\right)$	$\$45.6\left(\$38\times 1.2\right)$
Variable Cost per Canoe $\left(\text{B}\right)$	$\left(\$10.50\right)$	$\left(\$15.20\right)$
Contribution Margin $\left(\text{A}-\text{B}\right)$	$\$25.50$	$\$30.40$

As the product mix is $50/50$

So, the weighted contribution margin is calculated as:

$\begin{array}{c}\text{Weighted Contribution Margin}=\left(25.50\times \frac{50}{100}\right)+\left(30.40\times \frac{50}{100}\right)\\ =\$27.95\end{array}$

The break-even point in units is calculated as:

$\begin{array}{c}\text{Breakeven Point}=\frac{\text{Fixed Cost}}{\text{Weighted Contribution Margin}}\\ =\frac{\$18,500}{\$27.95}\\ =662\text{ units}\end{array}$

To determine

(c)

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 increased by $\$5,200$ and the product mix changes to $50/50$.

Answer to Problem 17E

The breakeven point in units is $\text{1121 units}$.

Explanation of Solution

Contribution Margin Income Statement

Particulars	Standard	Deluxe
Rental Price $\left(\text{A}\right)$	$\$30$	$\$38$
Variable Cost per Canoe $\left(\text{B}\right)$	$\left(\$10.50\right)$	$\left(\$15.20\right)$
Contribution Margin $\left(\text{A}-\text{B}\right)$	$\$19.50$	$\$22.80$

As the product mix is $50/50$

So, the weighted contribution margin is calculated as:

$\begin{array}{c}\text{Weighted Contribution Margin}=\left(19.50\times \frac{50}{100}\right)+\left(22.80\times \frac{50}{100}\right)\\ =\$21.15\end{array}$

The break-even point in units is calculated as:

$\begin{array}{c}\text{Breakeven Point}=\frac{\text{Fixed Cost}}{\text{Weighted Contribution Margin}}\\ =\frac{\$23,700}{\$21.15}\\ =1121\text{ units}\end{array}$

To determine

(d)

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 variable cost increases by $30\%$ and the product mix changes to $50/50$.

Answer to Problem 17E

The breakeven point in units is $\text{1070 units}$.

Explanation of Solution

Contribution Margin Income Statement

Particulars	Standard	Deluxe
Rental Price $\left(\text{A}\right)$	$\$30$	$\$38$
Variable Cost per Canoe $\left(\text{B}\right)$	$\begin{array}{l}\left(\$13.65\right)\\ \left(\$10.50\times 1.30\right)\end{array}$	$\begin{array}{l}\left(\$19.76\right)\\ \left(\$15.20\times 1.30\right)\end{array}$
Contribution Margin $\left(\text{A}-\text{B}\right)$	$\$16.35$	$\$18.24$

As the product mix is $50/50$

So, the weighted contribution margin is calculated as:

$\begin{array}{c}\text{Weighted Contribution Margin}=\left(16.35\times \frac{50}{100}\right)+\left(18.24\times \frac{50}{100}\right)\\ =\$17.295\end{array}$

The break-even point in units is calculated as:

$\begin{array}{c}\text{Breakeven Point}=\frac{\text{Fixed Cost}}{\text{Weighted Contribution Margin}}\\ =\frac{\$18,500}{\$17.295}\\ \text{=1070 units}\end{array}$