Chapter 21, Problem 3BPSB

To determine

Introduction:

Break-even point in terms of sales units: The break-even point in sales units is the company’s fixed costs divided by the contribution margin of the company. Here, the contribution margin of the company is the selling price less the variable cost.

Break-even point in terms of sales dollars: The break-even point in sales dollars is the company’s fixed costs divided by the contribution margin ratio of the company. Here, the contribution margin of the company is the selling price less the variable cost. And the contribution margin ratio of the company is the contribution margin divided by the selling price.

CVP Chart: CVP chart is the short form of a cost volume profit chart. It shows the relationship between the units produced in a particular period, total cost involved and the sales revenues in that period.

Contribution margin income statement: It is a statement where variable costs are deducted from the sales dollars to get the contribution margin and then all fixed costs are deducted from the contribution margin to get the net profit/loss.

1.

To calculate:

(a) Estimated Break-even point in terms of sales units

(b) Estimated Break-even point in terms of sales dollars

Answer to Problem 3BPSB

Solution:

(a) Estimated Break-even point in terms of sales units is 300.

(b) Estimated Break-even point in terms of sales dollars is $105,000

Explanation of Solution

Explanations:

Given:

Fixed costs= $42,000

Selling price= $350 per unit

Forecasted variable cost= $210 per unit

Calculation:

$\begin{array}{c}(a)Break-evenpo\mathrm{int}\mathrm{in}termsofsalesunits=\frac{Fixed\cos ts}{Sellingprice-Variable\cos t}\\ =\frac{\$42,000}{\$350-\$210}\\ =300\end{array}$

Here, the given variable cost is the forecasted one, so the calculated value is for the estimated break-even point in terms of sales unit.

$\begin{array}{c}(b)Contributionm\arg inratio=\frac{Sellingprice-Variable\cos t}{sellingprice}\\ =\frac{\$350-\$210}{\$350}\\ =0.40\\ Break-evenpo\mathrm{int}\mathrm{in}termsofsalesdollars=\frac{Fixed\cos ts}{Contributionm\arg inratio}\\ =\frac{\$42,000}{0.40}\\ =\$105,000\end{array}$

Here, the given variable cost is the forecasted one, so the calculated value is for the estimated break-even point in terms of sales dollars.

To determine

2.

To Prepare:

A CVP chart

Answer to Problem 3BPSB

Solution:

Explanation of Solution

Explanations:

Given:

Maximum number of sales = 700

Maximum sales revenue = $245,000

Fixed costs= $42,000

Forecasted variable cost= $210 per unit

A CVP graph has graph lines for fixed cost, total cost and sales revenue. Here, fixed cost and maximum sales are known. Now total cost at maximum number of sales has to be calculated.

Calculation:

The formula for total cost is given below.

$Total\cos t=Fixed\cos t+Variable\cos t\times Salesunits$

$\begin{array}{c}Total\cos tat\max imumunitsofsales=Fixed\cos t+Variable\cos t\times MaximumSalesunits\\ =\$42,000+\$210\times 700\\ =\$189,000\end{array}$

Based on these information, a table showing fixed cost, total cost and sales in dollars at different label of sales can be constructed as shown below.

Sales units	Fixed cost	Total cost	Sales in dollars
0	$42,000	$42,000	$ -
100	$42,000	$63,000	$ 35,000
200	$42,000	$84,000	$ 70,000
300	$42,000	$105,000	$ 105,000
400	$42,000	$126,000	$ 140,000
500	$42,000	$147,000	$ 175,000
600	$42,000	$168,000	$ 210,000
700	$42,000	$189,000	$ 245,000

In the above table, total costs at different units of sales are calculated using the above given formula and sales in dollars are the sales units times the selling price.

By selecting this table in excel sheet, the required CVP chart is prepared as shown below.

To determine

3.

To Show:

Contribution margin income statement at break-even point

Answer to Problem 3BPSB

Solution:

Contribution margin income statement
Sales	$105,000
Less Variable costs	$63,000
Contribution margin	$42,000
Less Fixed cost	$42,000
Net profit	$0

Explanation of Solution

Explanations:

Given:

Fixed costs= $42,000

Selling price= $350 per unit

Forecasted variable cost= $210 per unit

Break-even point sales units= 300

Calculation:

$\begin{array}{c}Salesatbreak-evenpo\mathrm{int}=break-evenpo\mathrm{int}\times Sellingprice\\ =300\times \$350\\ =\$105,000\end{array}$

$\begin{array}{c}Total\mathrm{var}iable\cos tsatbreak-evenpo\mathrm{int}=break-evenpo\mathrm{int}\times Variable\cos t\\ =300\times \$210\\ =\$63,000\end{array}$

Based on these calculations, a contribution margin income statement is prepared as shown below.

Contribution margin income statement
Sales	$105,000
Less Variable costs	$63,000
Contribution margin	$42,000
Less Fixed cost	$42,000
Net profit	$0

Conclusion

At break-even point, net profit must be zero as shown by the above contribution margin income statement.