Chapter 18, Problem 7QS

To determine

Break-even Point:

The break-even point is the amount of sales that does not result in any loss or profit for a company. It is used for the various cost control goals as it covers the total cost of operation that would be incurred.

To identify: The break-even point.

Explanation of Solution

In order to calculate the break- even point, contribution margin needs to calculate.

Given,

The sale price per unit is $90.
The variable cost per unit is $36.

Formula to calculate the contribution margin,

$\text{Contribution}\text{marginm}\text{per}\text{unit}=\text{Sales}\text{per}\text{unit}-\text{Variable}\text{cost}\text{per}\text{unit}$

Substitute $90 for sales per unit and $36 for variable cost per unit.

$\begin{array}{c}\text{Contribution}\text{margin}\text{per}\text{unit}=\$90-\$36\\ =\$54\end{array}$ ................ (1)

The contribution margin per unit is $54.

The fixed cost is $162,000. (Given)
The contribution margin per unit is $54. (Calculated in equation (1))

Formula to calculate the break-even point,

$\text{Break-even}\text{point}=\frac{\text{Fixed}\text{cost}}{\text{Contribution}\text{margin}\text{per}\text{unit}}$

Substitute $162,000 for fixed cost and $54 for contribution margin per unit.

$\begin{array}{c}\text{Break-even}\text{point}=\frac{\$162,000}{\$54}\\ =3,000\text{units}\end{array}$

Hence, the break-even point is 3,000 units.

1. Total fixed cost increased to $190,000.

In order to calculate the break- even point, contribution margin needs to calculate.

The fixed cost is $190,000. (Given)
The contribution margin per unit is $54. (Calculated in equation (1))

Formula to calculate the break-even point,

$\text{Break-even}\text{point}=\frac{\text{Fixed}\text{cost}}{\text{Contribution}\text{margin}\text{per}\text{unit}}$

Substitute $190,000 for fixed cost and $54 for contribution margin per unit.

$\begin{array}{c}\text{Break-even}\text{point}=\frac{\$190,000}{\$54}\\ =3,519\text{units}\end{array}$

Hence, the break-even point is 3,519 units. As the break-even point has increased the answer will be (I).

2. Variable cost decrease to $34.

In order to calculate the break- even point, contribution margin needs to calculate.

Given,

The sale price per unit is $90.
The variable cost per unit is $34.

Formula to calculate the contribution margin,

$\text{Contribution}\text{marginm}\text{per}\text{unit}=\text{Sales}\text{per}\text{unit}-\text{Variable}\text{cost}\text{per}\text{unit}$

Substitute $90 for sales per unit and $34 for variable cost per unit.

$\begin{array}{c}\text{Contribution}\text{margin}\text{per}\text{unit}=\$90-\$34\\ =\$56\end{array}$ ................. (2)

The contribution margin per unit is $56.

The fixed cost is $162,000. (Given)
The contribution margin per unit is $56. (Calculated in equation (2))

Formula to calculate the break-even point,

$\text{Break-even}\text{point}=\frac{\text{Fixed}\text{cost}}{\text{Contribution}\text{margin}\text{per}\text{unit}}$

Substitute $162,000 for fixed cost and $56 for contribution margin per unit.

$\begin{array}{c}\text{Break-even}\text{point}=\frac{\$162,000}{\$56}\\ =2,893\text{units}\end{array}$

Hence, the break-even point is 2,893 units. As the break-even point has increased the answer will be (D).

3. Selling price per unit decrease to $80.

In order to calculate the break- even point, contribution margin needs to calculate.

Given,

The sales per unit is $80.
The variable cost per unit is $36.

Formula to calculate the contribution margin,

$\text{Contribution}\text{marginm}\text{per}\text{unit}=\text{Sales}\text{per}\text{unit}-\text{Variable}\text{cost}\text{per}\text{unit}$

Substitute $80 for sales per unit and $36 for variable cost per unit.

$\begin{array}{c}\text{Contribution}\text{margin}\text{per}\text{unit}=\$80-\$36\\ =\$44\end{array}$ ................... (3)

The contribution margin per unit is $44.

The fixed cost is $162,000. (Given)
The contribution margin per unit is $44. (Calculated in equation (3))

Formula to calculate the break-even point,

$\text{Break-even}\text{point}=\frac{\text{Fixed}\text{cost}}{\text{Contribution}\text{margin}\text{per}\text{unit}}$

Substitute $162,000 for fixed cost and $44 for contribution margin per unit.

$\begin{array}{c}\text{Break-even}\text{point}=\frac{\$162,000}{\$44}\\ =3,682\text{units}\end{array}$

Hence, the break-even point is 3,682 units. As the break-even point has increased the answer will be (I).

4. Variable cost increased to $67.

In order to calculate the break- even point, contribution margin needs to calculate.

Given,

The sales per unit is $90.
The variable cost per unit is $67.

Formula to calculate the contribution margin,

$\text{Contribution}\text{margin}\text{per}\text{unit}=\text{Sales}\text{per}\text{unit}-\text{Variable}\text{cost}\text{per}\text{unit}$

Substitute $90 for sales per unit and $67 for variable cost per unit.

$\begin{array}{c}\text{Contribution}\text{margin}\text{per}\text{unit}=\$90-\$67\\ =\$23\end{array}$ .................... (4)

The contribution margin per unit is $23.

The fixed cost is $162,000. (Given)
The contribution margin per unit is $23. (Calculated in equation (4))

Formula to calculate the break-even point,

$\text{Break-even}\text{point}=\frac{\text{Fixed}\text{cost}}{\text{Contribution}\text{margin}\text{per}\text{unit}}$

Substitute $162,000 for fixed cost and $23 for contribution margin per unit.

$\begin{array}{c}\text{Break-even}\text{point}=\frac{\$162,000}{\$23}\\ =7,044\text{units}\end{array}$

Hence, the break-even point is 7,044 units. As the break-even point has increased the answer will be (I).

5. Total fixed cost decreased to $150,000.

In order to calculate the break- even point, contribution margin needs to calculate.

The fixed cost is $150,000. (Given)
The contribution margin per unit is $54. (Calculated in equation (1))

Formula to calculate the break-even point,

$\text{Break-even}\text{point}=\frac{\text{Fixed}\text{cost}}{\text{Contribution}\text{margin}\text{per}\text{unit}}$

Substitute $150,000 for fixed cost and $54 for contribution margin per unit.

$\begin{array}{c}\text{Break-even}\text{point}=\frac{\$150,000}{\$54}\\ =2,778\text{units}\end{array}$

Hence, the break-even point is 2,778 units. As the break-even point has increased the answer will be (D).

6. Selling price increased to $120

In order to calculate the break- even point, contribution margin needs to calculate.

Given,

The sale price per unit is $120.
The variable cost per unit is $36.

Formula to calculate the contribution margin,

$\text{Contribution}\text{marginm}\text{per}\text{unit}=\text{Sales}\text{per}\text{unit}-\text{Variable}\text{cost}\text{per}\text{unit}$

Substitute $120 for sales per unit and $36 for variable cost per unit.

$\begin{array}{c}\text{Contribution}\text{margin}\text{per}\text{unit}=\$120-\$36\\ =\$84\end{array}$ ............ (5)

The contribution margin per unit is $84.

The fixed cost is $162,000. (Given)
The contribution margin per unit is $44. (Calculated in equation (5))

Formula to calculate the break-even point,

$\text{Break-even}\text{point}=\frac{\text{Fixed}\text{cost}}{\text{Contribution}\text{margin}\text{per}\text{unit}}$

Substitute $162,000 for fixed cost and $84 for contribution margin per unit.

$\begin{array}{c}\text{Break-even}\text{point}=\frac{\$162,000}{\$84}\\ =1,929\text{units}\end{array}$

Hence, the break-even point is 1,929 units. As the break-even point has increased the answer will be (D).