Chapter 21, Problem 4BPSB

To determine

Concept Introduction:

Breakeven point-

Breakeven point is the point where total revenues are equal to total costs. Total cost includes fixed costs as well as variable costs. It is calculated as follows-

  $Breakevenpointinsalesdollars=Fixedcosts/Contributionmarginratio$

Requirement 1-:

To compute:

Break even points in sales dollars.

Answer to Problem 4BPSB

  $\begin{array}{l}Breakevenpointinsalesdollars=\frac{Fixedcosts}{Contributionmarginratio}\hfill \\ Breakevenpointinsalesdollars=\frac{\$200,000}{20\%}\hfill \\ Breakevenpointinsalesdollars=\$1,000,000\hfill \end{array}$

Explanation of Solution

Given,

• Fixed costs = $200,000
• Sales = $750,000
• Contribution margin = $150,000
First we need to find contribution margin ratio-

  $\begin{array}{l}Contributionmarginratio=Contributionmargin/Sales\hfill \\ Contributionmarginratio=\$150,000/\$750,000\hfill \\ Contributionmarginratio=20\%\hfill \end{array}$

Breakeven point is calculated as follows-

  $\begin{array}{l}Breakevenpointinsalesdollars=\frac{Fixedcosts}{Contributionmarginratio}\hfill \\ Breakevenpointinsalesdollars=\frac{\$200,000}{20\%}\hfill \\ Breakevenpointinsalesdollars=\$1,000,000\hfill \end{array}$

Conclusion:

Thus, breakeven point in sales dollars is calculated.

To determine

Concept Introduction:

Breakeven point-

Breakeven point is the point where total revenues are equal to total costs. Total cost includes fixed costs as well as variable costs. It is calculated as follows-

  $Breakevenpointinsalesdollars=Fixedcosts/Contributionmarginratio$

Requirement 2-:

To compute:

Break even points in sales dollars.

Answer to Problem 4BPSB

  $\begin{array}{l}Breakevenpointinsalesdollars=\frac{Fixedcosts}{Contributionmarginratio}\hfill \\ Breakevenpointinsalesdollars=\frac{\$350,000}{60\%}\hfill \\ Breakevenpointinsalesdollars=\$583,333\hfill \end{array}$

Explanation of Solution

  $\begin{array}{l}Revisedfixedcosts=\$200,000+\$150,000\hfill \\ Revisedfixedcosts=\$350,000\hfill \end{array}$

First we need to find revised variable costs-

  $\begin{array}{l}Revisedvariablecosts=Variablecosts–50\%*Variablecosts\hfill \\ Revisedvariablecosts=\$600,000–\left(50\%*\$600,000\right)\hfill \\ Revisedvariablecosts=\$600,000-\$300,000\hfill \\ Revisedvariablecosts=\$300,000\hfill \end{array}$

Then, we need to find revised contribution margin-

  $\begin{array}{l}Revisedcontributionmargin=Sales-Revisedvariablecosts\hfill \\ Revisedcontributionmargin=\$750,000-\$300,000\hfill \\ Revisedcontributionmargin=\$450,000\hfill \end{array}$

Contribution margin ratio is calculated as follows-

  $\begin{array}{l}Contributionmarginratio=Revisedcontributionmargin/Sales\hfill \\ Contributionmarginratio=\$450,000/\$750,000\hfill \\ Contributionmarginratio=60\%\hfill \end{array}$

Breakeven point is calculated as follows-

  $\begin{array}{l}Breakevenpointinsalesdollars=\frac{Fixedcosts}{Contributionmarginratio}\hfill \\ Breakevenpointinsalesdollars=\frac{\$350,000}{60\%}\hfill \\ Breakevenpointinsalesdollars=\$583,333\hfill \end{array}$

Conclusion:

Thus, breakeven point in sales dollars is calculated.

To determine

Concept Introduction:

Contribution margin income statement-

It is a statement wherein all the variable costs are deducted from the sales to get the contribution margin and after getting contribution margin, fixed expenses are deducted from contribution margin to get net income or loss.

Requirement 3-:

To prepare:

Forecasted contribution margin income statement.

Answer to Problem 4BPSB

Rivera Company
Forecasted contribution margin income statement
Particulars	Amount ($)
Sales	750,000
Variable costs	(300,000)
Contribution margin	450,000
Fixed costs	(350,000)
Net income	100,000

Explanation of Solution

First we need to find revised fixed costs-

  $\begin{array}{l}Revisedfixedcosts=\$200,000+\$150,000\hfill \\ Revisedfixedcosts=\$350,000\hfill \end{array}$

Then, we need to find revised variable costs

  $\begin{array}{l}Revisedvariablecosts=Variablecosts–50\%*Variablecosts\hfill \\ Revisedvariablecosts=\$600,000–\left(50\%*\$600,000\right)\hfill \\ Revisedvariablecosts=\$600,000-\$300,000\hfill \\ Revisedvariablecosts=\$300,000\hfill \end{array}$

Then, we need to find revised contribution margin-

  $\begin{array}{l}Revisedcontributionmargin=Sales-Revisedvariablecosts\hfill \\ Revisedcontributionmargin=\$750,000-\$300,000\hfill \\ Revisedcontributionmargin=\$450,000\hfill \end{array}$

Net income is calculates as follows-

  $\begin{array}{l}Netincome=Contributionmargin–Fixedcosts\hfill \\ Netincome=\$450,000-\$350,000\hfill \\ Netincome=\$100,000\hfill \end{array}$

Conclusion:

Thus, contribution margin income statement is prepared.

To determine

Concept Introduction:

Breakeven point-

Breakeven point is the point where total revenues are equal to total costs. Total cost includes fixed costs as well as variable costs.

Requirement 4-:

To compute:

Break even points in sales dollars and in sales units to earn a targeted profit

Answer to Problem 4BPSB

  $\begin{array}{l}Breakevenpointsinsalesdollars=\left(Fixedcosts+Pretaxincome\right)/Contributionmarginratio\hfill \\ Breakevenpointsinsalesdollars=\left(\$350,000+\$200,000\right)/60\%\hfill \\ Breakevenpointsinsalesdollars=\$550,000/60\%\hfill \\ Breakevenpointsinsalesdollars=\$916,667\hfill \end{array}$

  $\begin{array}{l}Breakevenpointsinsalesunits=\left(Fixedcosts+Pretaxincome\right)/Contributionmargin\hfill \\ Breakevenpointsinsalesunits=\left(\$350,000+\$200,000\right)/\$22.5\hfill \\ Breakevenpointsinsalesunits=\$550,000/\$22.5\hfill \\ Breakevenpointsinsalesunits=24,445units\hfill \end{array}$

Explanation of Solution

• Breakeven point in sales dollars-

Given, Pretax income = $200,000

First we need to find revised fixed costs-

  $\begin{array}{l}Revisedfixedcosts=\$200,000+\$150,000\hfill \\ Revisedfixedcosts=\$350,000\hfill \end{array}$

Then, we need to find revised variable costs

  $\begin{array}{l}Revisedvariablecosts=Variablecosts–50\%*Variablecosts\hfill \\ Revisedvariablecosts=\$600,000–\left(50\%*\$600,000\right)\hfill \\ Revisedvariablecosts=\$600,000-\$300,000\hfill \\ Revisedvariablecosts=\$300,000\hfill \end{array}$

Then, we need to find revised contribution margin-

  $\begin{array}{l}Revisedcontributionmargin=Sales-Revisedvariablecosts\hfill \\ Revisedcontributionmargin=\$750,000-\$300,000\hfill \\ Revisedcontributionmargin=\$450,000\hfill \end{array}$

Contribution margin ratio is calculated as follows-

  $\begin{array}{l}Contributionmarginratio=Revisedcontributionmargin/Sales\hfill \\ Contributionmarginratio=\$450,000/\$750,000\hfill \\ Contributionmarginratio=60\%\hfill \end{array}$

Breakeven point in sales dollars is calculated as under-

  $\begin{array}{l}Breakevenpointsinsalesdollars=\left(Fixedcosts+Pretaxincome\right)/Contributionmarginratio\hfill \\ Breakevenpointsinsalesdollars=\left(\$350,000+\$200,000\right)/60\%\hfill \\ Breakevenpointsinsalesdollars=\$550,000/60\%\hfill \\ Breakevenpointsinsalesdollars=\$916,667\hfill \end{array}$

• Breakeven point in sales units-

Given, Pretax income = $200,000

  $\begin{array}{l}Revisedfixedcosts=\$200,000+\$150,000\hfill \\ Revisedfixedcosts=\$350,000\hfill \end{array}$

Contribution margin per unit is calculated as under-

  $\begin{array}{l}Contributionmarginperunit=Totalcontributionmargin/Salesunits\hfill \\ Contributionmarginperunit=\$450,000/20,000\hfill \\ Contributionmarginperunit=\$22.5\hfill \end{array}$

Breakeven point in sales units is calculated as follows-

  $\begin{array}{l}Breakevenpointsinsalesunits=\left(Fixedcosts+Pretaxincome\right)/Contributionmargin\hfill \\ Breakevenpointsinsalesunits=\left(\$350,000+\$200,000\right)/\$22.5\hfill \\ Breakevenpointsinsalesunits=\$550,000/\$22.5\hfill \\ Breakevenpointsinsalesunits=24,445units\hfill \end{array}$

Conclusion:

Thus, breakeven point in sales units and sales dollars is calculated.

To determine

Concept Introduction:

Contribution margin income statement-

It is a statement wherein all the variable costs are deducted from the sales to get the contribution margin and after getting contribution margin, fixed expenses are deducted from contribution margin to get net income or loss.

Requirement 5-:

To prepare:

Forecasted contribution margin income statement.

Answer to Problem 4BPSB

Rivera Company
Forecasted contribution margin income statement
Particulars	Amount ($)
Sales	916,688
Variable costs	(366,675)
Contribution margin	550,013
Fixed costs	(350,000)
Net income	200,013

Explanation of Solution

  $\begin{array}{l}Salespriceperunit=\$750,000/20,000units\hfill \\ Salespriceperunit=\$37.5\hfill \\ Salesatbreakeven=24,445units*\$37.5\hfill \\ Salesatbreakeven=\$916,688\hfill \end{array}$

  $\begin{array}{l}Variablecostsperunit=\$300,000/20,000units\hfill \\ Variablecostsperunit=\$15\hfill \\ Variablecostsatbreakeven=24,445*\$15\hfill \\ Variablecostsatbreakeven=\$366,675\hfill \end{array}$

  $\begin{array}{l}Contributionmargin=Sales–Variablecosts\hfill \\ Contributionmargin=\$916,688-\$366,675\hfill \\ Contributionmargin=\$550,013\hfill \end{array}$

  $\begin{array}{l}Revisedfixedcosts=\$200,000+\$150,000\hfill \\ Revisedfixedcosts=\$350,000\hfill \end{array}$

Net income is calculated as follows-

  $\begin{array}{l}Netincome=Contributionmargin–Fixedcosts\hfill \\ Netincome=\$550,013-\$350,000\hfill \\ Netincome=\$200,013\hfill \end{array}$

Conclusion:

Thus, contribution margin income statement is prepared.