Chapter 6, Problem 5E

To determine

(a)

Concept introduction:

Contribution Margin:

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

The missing figure in the table.

Answer to Problem 5E

The missing figure in the table is as follows:

Particulars
Number of canoes sold	$400$	$600$	$750$
Total Costs:
Variable Cost	$\$67,500$	$\$101,250$	$\$126,563$
Fixed Cost	$\$150,000$	$\$150,000$	$\$150,000$
	$\$217,500$	$\$251,250$	$\$276,563$
Cost per unit
Variable Cost per unit	$\$168.75$	$\$168.75$	$\$168.75$
Fixed Cost per unit	$\$375.00$	$\$250.00$	$\$200.00$
	$\$543.75$	$\$418.75$	$\$368.75$

Explanation of Solution

The total cost is an addition of variable cost and fixed cost. Variable cost varies with the quantity volume but the variable cost per unit remains same. On the other hand, the fixed costs remain same but the per unit fixed cost decreases with the increase in quantity level.

As given in the question, the variable cost of $400$ canoes is $\$67,500$ and the fixed cost is $\$150,000$. By this, the variable cost and fixed cost per unit can be computed by the following formula:

$\begin{array}{c}\text{Variable Cost per unit}=\frac{\text{Total variable cost}}{\text{No}\text{. of canoes sold}}\\ =\frac{\$67,500}{400}\\ =\$168.75\end{array}$

$\begin{array}{c}\text{Total Fixed Cost}=\frac{\text{Total fixed cost}}{\text{No}\text{. of canoes sold}}\\ =\frac{\$150,000}{400}\\ =\$375.00\end{array}$

To determine

(b)

Concept introduction:

Contribution Margin:

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

The contribution margin per unit and margin ratio if the sales price is $\$550$ per canoe.

Answer to Problem 5E

The contribution margin per unit, if the sales price is $\$550$ per canoe, is $\$381.25$ and the contribution margin is $69.32\%$.

Explanation of Solution

Contribution Margin Income Statement

Particulars		Amount
Sales Price $\left(\text{A}\right)$	$\$550.00$
Variable Cost per Canoe $\left(\text{B}\right)$	$\left(\$168.75\right)$
Contribution Margin $\left(\text{A}-\text{B}\right)$		$\$381.25$
Contribution Margin Ratio $\frac{\left(\text{A}-\text{B}\right)}{\left(\text{A}\right)}$		$69.32\%$

To determine

(c)

Concept introduction:

Contribution Margin:

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

The contribution margin income statement if the number of canoes to be sold is $820$.

Answer to Problem 5E

The contribution margin is $\$312,625$.

Explanation of Solution

Contribution Margin Income Statement

Particulars		Amount
Sales Price $\left(\text{A}\right)$	$\$550.00$
Variable Cost per Canoe $\left(\text{B}\right)$	$\left(\$168.75\right)$
Contribution Margin $\left(\text{A}-\text{B}\right)$		$\$381.25$
No. of canoes sold		$820$
Contribution Margin Income $\left(\$381.25\times 820\text{ canoes}\right)$		$\$312,625$

To determine

(d)

Concept introduction:

Contribution Margin:

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

The breakeven point in units and in sales amount

Answer to Problem 5E

The breakeven point in units is $394\text{ units}$ and in sales amount is $\$216,700$.

Explanation of Solution

Contribution Margin Income Statement

Particulars		Amount
Sales Price $\left(\text{A}\right)$	$\$550.00$
Variable Cost per Canoe $\left(\text{B}\right)$	$\left(\$168.75\right)$
Contribution Margin $\left(\text{A}-\text{B}\right)$		$\$381.25$

The break-even point in units is calculated as:

$\begin{array}{c}\text{Breakeven Point}=\frac{\text{Fixed Cost}}{\text{Contribution Margin}}\\ =\frac{\$150,000}{\$381.25}\\ =394\text{ units}\end{array}$

Thebreak-even point in sales is calculated as:

$\begin{array}{c}\text{Breakeven Point}=\text{Breakeven sales in units}\times \text{Sales price}\\ =394\text{ units}\times \$550\text{ per unit}\\ =\$216,700\end{array}$

To determine

(e)

Concept introduction:

Contribution Margin:

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

The number of canoes to be sold to achieve target profit of $\$75,000$.

Answer to Problem 5E

The breakeven point in units is $\text{590 units}$.

Explanation of Solution

Contribution Margin Income Statement

Particulars		Amount
Sales Price $\left(\text{A}\right)$	$\$550.00$
Variable Cost per Canoe $\left(\text{B}\right)$	$\left(\$168.75\right)$
Contribution Margin $\left(\text{A}-\text{B}\right)$		$\$381.25$

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

$\begin{array}{c}\text{Target Sales}=\frac{\text{Fixed Cost}+\text{Target Profit}}{\text{Contribution Margin}}\\ =\frac{\$150,000+\$75,000}{\$381.25}\\ =590\text{ units}\end{array}$

Thesales for achieving the target profit are calculated as:

$\begin{array}{c}\text{Target Sales}=\text{Target sales in units}\times \text{Sales price}\\ =590\text{ units}\times \$550\text{ per unit}\\ =\$324,500\end{array}$