Chapter 21, Problem 4APSA

Requirement 1

To determine

To compute:

Break-even point for the year 2015

Answer to Problem 4APSA

Solution:

Break-even point for the year 2015 = $ 1,250,000

Explanation of Solution

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

• Sales revenue = $ 1,000,000
• Contribution margin per unit = $ 200,000
• Fixed costs = $ 250,000

First, we will calculate the contribution margin ratio −

  $\begin{array}{l}Contributionmarginratio=\frac{Contributionmargin}{Sales}X100\\ Contributionmarginratio=\frac{\$\text{ 200,000}}{\$\text{ 1,000,000}}X100\\ Contributionmarginratio=20\%\end{array}$

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

  $\begin{array}{l}Break-evenpoint\left(in\text{ dollar}s\right)=\frac{Fixedcost}{Contributionmargin\text{ ratio}}\\ Break-evenpoint\left(in\text{ dollar}s\right)=\frac{\$\text{ 250},000}{\text{20 \% }}\\ Break-evenpoint\left(in\text{ dollar}s\right)=\$1,250,000\end{array}$

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 4APSA

Solution:

Predicted break-even point for the year 2016 = $

Explanation of Solution

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

• Sales revenue = $ 1,000,000
• Variable costs = $ 400,000 (50 % reduced due to installation of machine i.e. = $ 800,000 X 50 %)
• Fixed costs = $ 450,000 ($ 200,000 increased per year i.e. = $ 250,000 + $ 200,000)

The contribution margin will be calculated as −

  $\begin{array}{l}ContributionMargin=Salesrevenue-Variablecosts\hfill \\ ContributionMargin=\$1,000,000-\$400,000\hfill \\ ContributionMargin=\$600,000\hfill \end{array}$

The contribution margin ratio −

  $\begin{array}{l}Contributionmarginratio=\frac{Contributionmargin}{Sales}X100\\ Contributionmarginratio=\frac{\$\text{ 600,000}}{\$\text{ 1,000,000}}X100\\ Contributionmarginratio=60\%\end{array}$

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

  $\begin{array}{l}Break-evenpoint\left(in\text{ dollar}s\right)=\frac{Fixedcost}{Contributionmargin\text{ ratio}}\\ Break-evenpoint\left(in\text{ dollar}s\right)=\frac{\$\text{ 450},000}{\text{60 \% }}\\ Break-evenpoint\left(in\text{ dollar}s\right)=\$\text{ 7}50,000\end{array}$

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 Astro Co. for the year ended on December 31, 2016.

Answer to Problem 4APSA

Solution:

Astro. Co
Forecasted Contribution Margin Income statement
For the year ended December 31, 2016
Sales	1,000,000
Less: Variable costs	400,000
Contribution Margin	600,000
Less: Fixed Costs	450,000
Net Operating Income	150,000

Explanation of Solution

The contribution income statement is prepared as under −
Given,

• Sales price revenue = $ 1,000,000
• Variable costs = $ 400,000 (50 % reduced due to installation of machine i.e. = $ 800,000 X 50 %)
• Fixed costs = $ 450,000 ($ 200,000 increased per year i.e. = $ 250,000 + $ 200,000)

1. The contribution margin is calculated as under −

  $\begin{array}{l}ContributionMargin=Salesrevenue-Totalvariablecosts\hfill \\ ContributionMargin=\$\text{ 1},000,000-\$\text{ 40}0,000\hfill \\ ContributionMargin=\$\text{ 600},000\hfill \end{array}$
2. Fixed costs given as = $ 450,000
3. The net operating income will be calculated as under −

  $\begin{array}{l}NetOperatingIncome=ContributionMargin-Fixedcosts\hfill \\ NetOperatingIncome=\$\text{ 600},000-\$\text{ 450},000\hfill \\ NetOperatingIncome=\$\text{ 150},000\hfill \end{array}$

The expected net operating income for Astro Co. for the year ended December 31, 2016 = $ 150,000.

Conclusion

Thus, the forecasted contribution margin income statement for Astro 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 4APSA

Solution:

1. The amount of sales needed to produce the target income of $ 200,000 = $ 1,083,333
2. The number of units to be sold to produce the target income of $ 200,000 = 21,667 units

Explanation of Solution

1. The target sales will be calculated as under −

Given,

• Contribution margin ratio = 60%
• Fixed costs = $ 450,000
• Desired profit = $ 200,000

The target sales will be calculated as under −

  $\begin{array}{l}Target\text{ Sales }=\frac{FixedCosts+DesiredProfit}{ContributionMarginratio}\\ Target\text{ Sales }=\frac{\$\text{ 450},000+\text{ \$ 200,000}}{60\%}\\ Target\text{ Sales }=\$1,083,333\end{array}$

The amount of sales to earn a target pre-tax income of $ 200,000 = $ 1,083,333.

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 = $ 50 (i.e. $ 1,000,000 divided by 20,000 units)
• Sales = $ 1,083,333

  $\begin{array}{l}Numberofunitssold=\frac{Sales}{Salespriceperunit}\\ Numberofunitssold=\frac{\$1,083,333}{\$50perunit}\\ Numberofunitssold=21,667units\end{array}$

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 = $ 1,083,333.

Answer to Problem 4APSA

Solution:

The forecasted margin income statement with sales level = $ 1,083,333 −

Astro. Co
Forecasted Contribution Margin Income statement
For the year ended December 31, 2016
Sales	1,083,333
Less: Variable costs	433,333
Contribution Margin	650,000
Less: Fixed Costs	450,000
Net Operating Income	200,000

Explanation of Solution

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

1. Sales revenue = $ 1,083,333
2. Variable costs will be calculated as −

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

  $\begin{array}{l}\begin{array}{l}Variablecosts=SalesX\left(1–Contributionratio\right)\hfill \\ Variablecosts=\$1,083,333X\left(1–60\%\right)\hfill \end{array}\\ Variablecosts=\$433,333\end{array}$
3. The contribution margin is calculated as under −

  $\begin{array}{l}ContributionMargin=Salesrevenue-Totalvariablecosts\hfill \\ ContributionMargin=\$\text{ 1},083,333-\$\text{ 433},333\hfill \\ ContributionMargin=\$\text{ 650},000\hfill \end{array}$
4. Fixed costs given as = $ 450,000
5. The net operating income will be calculated as under −

  $\begin{array}{l}NetOperatingIncome=ContributionMargin-Fixedcosts\hfill \\ NetOperatingIncome=\$\text{ 650},000-\$\text{ 450},000\hfill \\ NetOperatingIncome=\$\text{ 200},000\hfill \end{array}$

The expected net operating income for Astro 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 = $ 1,083,333 has been calculated.