Chapter 3, Problem 23PSB

a.

To determine

Calculate the contribution margin per unit.

Explanation of Solution

The calculation of contribution margin per unit is as follows:

$\begin{array}{c}\text{Contribution margin per unit}=\text{Sales price}-\text{Variable cost}\\ =\$200-\$160\\ =\$40\end{array}$

Hence, the contribution margin per unit is $40.

b.

To determine

Calculate the break-even points in dollars and units and prepare income statement using contribution margin format.

Explanation of Solution

The calculation of break-even points in units is as follows:

$\begin{array}{c}\text{Break-even point in units}=\frac{\text{Fixed cost}}{\text{Contribution margin per unit}}\\ =\frac{\$250,000}{\$40}\\ =6,250\text{ units}\end{array}$

Hence, the break-even units are 6,250 units.

The calculation of break-even point in dollars is as follows:

$\begin{array}{c}\text{Break-even in dollars}=\text{Break-even units}\times \text{Sales price}\\ =6,250\text{ units}\times \$200\text{ per unit}\\ =\$1,250,000\end{array}$

Hence, the break-even in dollars is $1,250,000.

The calculation of income statement is as follows:

(Table 1)

Working note:

The calculation of variable cost is as follows:

$\begin{array}{c}\text{Variable cost}=\text{Number of units}\times \text{Variable cost per unit}\\ =\text{6,250 units}\times \text{\$160}\\ =\$1,000,000\end{array}$

Hence, the variable cost is $1,000,000.

…… (1)

c.

To determine

Calculate the sales volume in units and dollars that is required to earn profit and prepare income statement.

Explanation of Solution

The calculation of sales volume in units is as follows:

$\begin{array}{c}\text{Sales volume in units}=\frac{\text{Fixed cost}+\text{Target profit}}{\text{Contribution margin per unit}}\\ =\frac{\$250,000+\$50,000}{\$40}\\ =\frac{\$300,000}{\$40}\\ =7,500\text{ units}\end{array}$

Hence, the sales volume in units is 7,500 units.

The calculation of break even in dollars is as follows:

$\begin{array}{c}\text{Sales volume in dollars}=\text{Sales volume in units}\times \text{Sales price}\\ =7,500\text{ units}\times \$200\text{ per unit}\\ =\$1,500,000\end{array}$

Hence, the sales volume in dollars is $1,500,000.

The calculation of income statement is as follows:

(Table 2)

Working note:

The calculation of variable cost is as follows:

$\begin{array}{c}\text{Variable cost}=\text{Number of units}\times \text{Variable cost per unit}\\ =7,500\text{ units}\times \text{\$160}\\ =\$1,200,000\end{array}$

Hence, the variable cost is $1,200,000.

…… (2)

d.

To determine

Calculate the level of sales that is necessary to earn profit in case of drop in sales price.

Explanation of Solution

The calculation of sales volume in units is as follows:

$\begin{array}{c}\text{Sales volume in units}=\frac{\text{Fixed cost}+\text{Target profit}}{\text{Contribution margin per unit}}\\ =\frac{\$250,000+\$50,000}{\$20(3)}\\ =\frac{\$300,000}{\$20}\\ =15,000\text{ units}\end{array}$

Hence, the sales volume in units is 15,000 units.

The calculation of sales volume in dollars is as follows:

$\begin{array}{c}\text{Sales volume in dollars}=\text{Sales volume in units}\times \text{Sales price}\\ =15,000\text{ units}\times \$180\text{ per unit}\\ =\$2,700,000\end{array}$

Hence, the sales volume in dollars is $2,700,000.

The calculation of income statement is as follows:

(Table 3)

Working note:

The calculation of contribution margin per unit is as follows:

$\begin{array}{c}\text{Contribution margin per unit}=\text{Sales price}-\text{Variable cost}\\ =\$180-\$160\\ =\$20\end{array}$

Hence, the contribution margin per unit is $20.

…… (3)

The calculation of variable cost is as follows:

$\begin{array}{c}\text{Variable cost}=\text{Number of units}\times \text{Variable cost per unit}\\ =15,000\text{ units}\times \text{\$160}\\ =\$2,400,000\end{array}$

Hence, the variable cost is $2,400,000.

…… (4)

e.

To determine

Calculate the level of sales that is necessary to earn profit in case of drop in fixed cost.

Explanation of Solution

The calculation of sales volume in units is as follows:

$\begin{array}{c}\text{Sales volume in units}=\frac{\text{Fixed cost}+\text{Target profit}}{\text{Contribution margin per unit}}\\ =\frac{\$200,000+\$50,000}{\$20(3)}\\ =\frac{\$250,000}{\$20}\\ =12,500\text{ units}\end{array}$

Hence, the sales volume in units is 12,500 units.

The calculation of sales volume in dollars is as follows:

$\begin{array}{c}\text{Sales volume in dollars}=\text{Sales volume in units}\times \text{Sales price}\\ =12,500\text{ units}\times \$180\text{ per unit}\\ =\$2,250,000\end{array}$

Hence, the sales volume in dollars is $2,250,000.

The calculation of income statement is as follows:

(Table 4)

Working note:

The calculation of variable cost is as follows:

$\begin{array}{c}\text{Variable cost}=\text{Number of units}\times \text{Variable cost per unit}\\ =12,500\text{ units}\times \text{\$160}\\ =\$2,000,000\end{array}$

Hence, the variable cost is $2,000,000.

…… (5)

f.

To determine

Calculate the level of sales that is necessary to earn profit in case of drop in variable cost.

Explanation of Solution

The calculation of sales volume in units is as follows:

$\begin{array}{c}\text{Sales volume in units}=\frac{\text{Fixed cost}+\text{Target profit}}{\text{Contribution margin per unit}}\\ =\frac{\$200,000+\$50,000}{\$50(6)}\\ =\frac{\$250,000}{\$50}\\ =5,000\text{ units}\end{array}$

Hence, the sales volume in units is 5,000 units.

The calculation of sales volume in dollars is as follows:

$\begin{array}{c}\text{Sales volume in dollars}=\text{Sales volume in units}\times \text{Sales price}\\ =5,000\text{ units}\times \$180\text{ per unit}\\ =\$900,000\end{array}$

Hence, the sales volume in dollars is $900,000.

The calculation of income statement is as follows:

(Table 5)

Working note:

The calculation of contribution margin per unit is as follows:

$\begin{array}{c}\text{Contribution margin per unit}=\text{Sales price}-\text{Variable cost}\\ =\$180-\$130\\ =\$50\end{array}$

Hence, the contribution margin per unit is $50.

…… (6)

The calculation of variable cost is as follows:

$\begin{array}{c}\text{Variable cost}=\text{Number of units}\times \text{Variable cost per unit}\\ =5,000\text{ units}\times \text{\$130}\\ \text{=\$650,000}\end{array}$

Hence, the variable cost is $650,000.

…… (7)

g.

To determine

Calculate the margin of safety in dollars, units and as a percentage.

Explanation of Solution

The calculation of break-even points in units is as follows:

$\begin{array}{c}\text{Break-even point in units}=\frac{\text{Fixed cost}}{\text{Contribution margin per unit}}\\ =\frac{\$200,000}{\$50}\\ =4,000\text{ units}\end{array}$

Hence, the break-even units are 4,000 units.

The calculation of margin of safety in dollars and units is as follows:

(Table 6)

The calculation of margin of safety in percentage is as follows:

$\begin{array}{c}\text{Margin of safety in percentage}=\frac{\text{Margin of safety in dollars}}{\text{Budgeted sales}}\\ =\frac{\$180,000}{\$900,000}\\ =0.2\\ =20\%\end{array}$

Hence, the margin of safety in percentage is 20%

h.

To determine

Draw a break-even graph using the data in requirement (g).

Explanation of Solution

The break-even graph is as follows:

s

(Figure 1)