Chapter 21, Problem 4BPSB

Requirement 1

To determine

To compute:

Break-even point for the year 2015

Answer to Problem 4BPSB

Solution:

Break-even point for the year 2015 = $ 1,000,000

Explanation of Solution

The break-even point in dollars will be calculated as under −
Given,

• Sales revenue = $ 750,000
• Contribution margin = $ 150,000
• Fixed costs = $ 200,000
First, we will calculate the contribution margin ratio −

  $\begin{array}{l}Contributionmarginratio=\frac{Contributionmargin}{Sales}X100\\ Contributionmarginratio=\frac{\$\text{ 150,000}}{\$\text{ 750,000}}X100\\ Contributionmarginratio=20\%\end{array}$

Now, the break-even point in units will be calculated as −

  $\begin{array}{l}Break-evenpoint\left(in\text{ dollar}s\right)=\frac{Fixedcost}{Contributionmargin\text{ ratio}}\\ Break-evenpoint\left(in\text{ dollar}s\right)=\frac{\$\text{ 200},000}{\text{20 \% }}\\ Break-evenpoint\left(in\text{ dollar}s\right)=\$1,000,000\end{array}$

Conclusion

Thus, the break-even point in dollars has been calculated.

Requirement 2

To determine

To compute:

Predicted break-even point for the year 2016

Answer to Problem 4BPSB

Solution:

Predicted break-even point for the year 2016 = $ 583,333

Explanation of Solution

The break-even point in dollars will be calculated as under −
Given,

• Sales revenue = $ 750,000
• Variable costs = $ 300,000 (50 % reduced due to installation of machine i.e. = $ 600,000 X 50 %)
• Fixed costs = $ 350,000 ($ 150,000 increased per year i.e. = $ 200,000 + $ 150,000)
The contribution margin will be calculated as −

  $\begin{array}{l}ContributionMargin=Salesrevenue-Variablecosts\hfill \\ ContributionMargin=\$\text{ 75}0,000-\$\text{ 300},000\hfill \\ ContributionMargin=\$\text{ 45}0,000\hfill \end{array}$

The contribution margin ratio −

  $\begin{array}{l}Contributionmarginratio=\frac{Contributionmargin}{Sales}X100\\ Contributionmarginratio=\frac{\$\text{ 450,000}}{\$\text{ 750,000}}X100\\ Contributionmarginratio=60\%\end{array}$

Now, the break-even point in units will be calculated as −

  $\begin{array}{l}Break-evenpoint\left(in\text{ dollar}s\right)=\frac{Fixedcost}{Contributionmargin\text{ ratio}}\\ Break-evenpoint\left(in\text{ dollar}s\right)=\frac{\$\text{ 350},000}{\text{60 \% }}\\ Break-evenpoint\left(in\text{ dollar}s\right)=\$\text{ 583,333 }\end{array}$

Conclusion

Thus, the predicted break-even point in dollars has been calculated.

Requirement 3

To determine

To prepare:

A forecasted contribution margin income statement for Rivera Co. for the year ended on December 31, 2016.

Answer to Problem 4BPSB

Solution:

Rivera Co
Forecasted Contribution Margin Income statement
For the year ended December 31, 2016
Sales	750,000
Less: Variable costs	300,000
Contribution Margin	450,000
Less: Fixed Costs	350,000
Net Operating Income	100,000

Explanation of Solution

The contribution income statement is prepared as under −
Given,

• Sales price revenue = $ 750,000
• Variable costs = $ 300,000 (50 % reduced due to installation of machine i.e. = $ 600,000 X 50 %)
• Fixed costs = $ 350,000 ($ 150,000 increased per year i.e. = $ 200,000 + $ 150,000)

1. The contribution margin is calculated as under −

  $\begin{array}{l}ContributionMargin=Salesrevenue-Totalvariablecosts\hfill \\ ContributionMargin=\$\text{ 75}0,000-\$\text{ 30}0,000\hfill \\ ContributionMargin=\$\text{ 450},000\hfill \end{array}$
2. Fixed costs given as = $ 350,000
3. The net operating income will be calculated as under −

  $\begin{array}{l}NetOperatingIncome=ContributionMargin-Fixedcosts\hfill \\ NetOperatingIncome=\$\text{ 450},000-\$\text{ 350},000\hfill \\ NetOperatingIncome=\$\text{ 100},000\hfill \end{array}$

The expected net operating income for Rivera Co. for the year ended December 31, 2016 = $ 100,000.

Conclusion

Thus, the forecasted contribution margin income statement for Rivera Co. for the year ended on December 31, 2016 has been prepared.

Requirement 4

To determine

To compute:

1. The amount of sales needed to produce the target income of $ 200,000
2. The number of units to be sold to produce the target income of $ 200,000

Answer to Problem 4BPSB

Solution:

1. The amount of sales needed to produce the target income of $ 200,000 = $ 916,667
2. The number of units to be sold to produce the target income of $ 200,000 = 24,445 units

Explanation of Solution

1. The target sales will be calculated as under −
Given,
• Contribution margin ratio = 60%
• Fixed costs = $ 350,000
• Desired profit = $ 200,000
The target sales will be calculated as under −

  $\begin{array}{l}Target\text{ Sales }=\frac{FixedCosts+DesiredProfit}{ContributionMarginratio}\\ Target\text{ Sales }=\frac{\$\text{ 350},000+\text{ \$ 200,000}}{60\%}\\ Target\text{ Sales }=\$916,667\end{array}$

The amount of sales to earn a target pre-tax income of $ 200,000 = $ 916,667


2. The number of units to be sold to earn a target profit of $ 200,000 will be calculated as under −

• Sales price per unit = $ 37.50 (i.e. $ 750,000 divided by 20,000 units)
• Sales = $ 916,667

  $\begin{array}{l}Numberofunitssold=\frac{Sales}{Salespriceperunit}\\ Numberofunitssold=\frac{\$\text{ 916},667}{\$\text{ 37}\text{.5 }perunit}\\ Numberofunitssold=24,445units\end{array}$

Conclusion

Thus, the amount of sales and the number of sales units needed to produce the target income of $ 200,000 have been calculated.

Requirement 5

To determine

To prepare:

A forecasted contribution margin income statement that shows the results at the sales level = $ 916,667.

Answer to Problem 4BPSB

Solution:

The forecasted margin income statement with sales level = $ 916,667 −

Rivera Co.
Forecasted Contribution Margin Income statement
For the year ended December 31, 2016
Sales	916,667
Less: Variable costs	366,667
Contribution Margin	550,000
Less: Fixed Costs	350,000
Net Operating Income	200,000

Explanation of Solution

The forecasted contribution margin income statement has been prepared as under −

1. Sales revenue = $ 916,667
2. Variable costs will be calculated as −

  $Variablecosts=SalesX\left(1–Contributionratio\right)$
• Contribution ratio = 60 %

  $\begin{array}{l}\begin{array}{l}Variablecosts=SalesX\left(1–Contributionratio\right)\hfill \\ Variablecosts=\$\text{ 9}16,667X\left(1–60\%\right)\hfill \end{array}\\ Variablecosts=\$\text{ 366},667\end{array}$
3. The contribution margin is calculated as under −

  $\begin{array}{l}ContributionMargin=Salesrevenue-Totalvariablecosts\hfill \\ ContributionMargin=\$\text{ 916},667-\$\text{ 366,667}\hfill \\ ContributionMargin=\$\text{ 550},000\hfill \end{array}$
4. Fixed costs given as = $ 350,000
5. The net operating income will be calculated as under −

  $\begin{array}{l}NetOperatingIncome=ContributionMargin-Fixedcosts\hfill \\ NetOperatingIncome=\$\text{ 550},000-\$\text{ 350},000\hfill \\ NetOperatingIncome=\$\text{ 200},000\hfill \end{array}$

The expected net operating income for Rivera Co. for the year ended December 31, 2016 = $ 200,000.

Conclusion

Thus, the forecasted contribution margin income statement that shows the results at the sales level = $ 916,667 has been calculated.