Chapter 21, Problem 6AP

1.  a.

To determine

Calculate break-even point in dollar sales for plan 1.

Explanation of Solution

Break-even Point: It refers to a point in the level of operations at which a company experiences its revenues generated is equal to its costs incurred. Thus, when a company reaches at its break-even point, it reports neither an income nor a loss from operations. The formula to calculate the break-even point in dollar is as follows:

  $\text{Break-even}\text{point}\text{in}\text{dollars }=\frac{\text{Fixed}\text{Costs}}{\text{Contribution}\text{Margin}\text{Ratio}}$

Calculate breakeven point in dollar sales for plan 1.

  $\begin{array}{c}\text{Break-even}\text{point}\text{in}\text{dollar sales }=\frac{\text{Fixed}\text{Costs}}{\text{Contribution}\text{Margin}\text{Ratio}}\\ =\frac{\text{\$200,000+\$325,000}}{70\%}\\ =\$750,000\end{array}$

Working notes:

Calculate variable cost per unit.

$\begin{array}{c}\text{Variable cost}\text{per}\text{unit}\text{=}\left(\begin{array}{l}\text{Material}\text{+}\text{Direct labor +Variable overhead costs}\\ \text{+}\text{Variable selling and administrative costs}\end{array}\right)\\ =\left[\$8.00\times \left(1–50\%\right)\right]+\left[\$5.00\times \left(1–60\%\right)\right]+\$1.00+\$0.50\\ =\$4.00+\$2.00+\$1.00+\$0.50\\ =\$7.50\end{array}$

Determine the contribution margin ratio.

  $\begin{array}{c}\text{Contribution}\text{Margin}\text{Ratio }=\frac{\text{Contribution}\text{Margin}}{\text{Sales}}\times 100\\ =\frac{\left(\$25.00-\$7.50\right)}{\$25.00}\times 100\\ =70\%\end{array}$

Conclusion

Hence, the break-even point in dollar sales for plan 1 is $750,000.

1.  b.

To determine

Calculate break-even point in dollar sales for plan 2.

Explanation of Solution

Break-even Point: It refers to a point in the level of operations at which a company experiences its revenues generated is equal to its costs incurred. Thus, when a company reaches at its break-even point, it reports neither an income nor a loss from operations. The formula to calculate the break-even point in dollar is as follows:

  $\text{Break-even}\text{point}\text{in}\text{dollars }=\frac{\text{Fixed}\text{Costs}}{\text{Contribution}\text{Margin}\text{Ratio}}$

Calculate breakeven point in dollar sales for plan 2.

  $\begin{array}{c}\text{Break-even}\text{point}\text{in}\text{dollar sales }=\frac{\text{Fixed}\text{Costs}}{\text{Contribution}\text{Margin}\text{Ratio}}\\ =\frac{\text{\$200,000+\$325,000}}{75\%}\\ =\$700,000\end{array}$

Working notes:

Calculate sales price per unit.

$\begin{array}{c}\text{Sales price}\text{per}\text{unit}\text{=}\left[\$25.00\times \left(1+20\%\right)\right]\\ =\$30.00\end{array}$

Calculate variable cost per unit.

$\begin{array}{c}\text{Variable cost}\text{per}\text{unit}\text{=}\left(\begin{array}{l}\text{Material}\text{+}\text{Direct labor +Variable overhead costs}\\ \text{+}\text{Variable selling and administrative costs}\end{array}\right)\\ =\left[\$8.00\times \left(1–50\%\right)\right]+\left[\$5.00\times \left(1–60\%\right)\right]+\$1.00+\$0.50\\ =\$4.00+\$2.00+\$1.00+\$0.50\\ =\$7.50\end{array}$

Determine the contribution margin ratio.

  $\begin{array}{c}\text{Contribution}\text{Margin}\text{Ratio }=\frac{\text{Contribution}\text{Margin}}{\text{Sales}}\times 100\\ =\frac{\left(\$30.00-\$7.50\right)}{\$30.00}\times 100\\ =75\%\end{array}$

Conclusion

Hence, the break-even point in dollar sales for plan 2 is $700,000.

2.

To determine

Prepare a forecasted contribution margin income statement for plan 1 and plan 2.

Explanation of Solution

Contribution Margin: It is defined as the difference between the sales and the variable cost.

Contribution margin income statement: Contribution margin income statement highlights the cost behavior as sales minus variable costs and shows the contribution margin. It also shows contribution margin minus fixed costs and finds the net income of the company.

Prepare a forecasted contribution margin income statement for plan 1 and plan 2.

Company B
Forecasted Contribution Margin Income Statement
	Plan 1	Plan 2
Sales	$1,000,000	$1,080,000
Less: Variable costs	$300,000	$270,000
Contribution margin	$700,000	$810,000
Less: Fixed costs	$525,000	$525,000
Income before taxes	$175,000	$285,000
Less: Income taxes (30%)	$52,500	$85,500
Net income	$122,500	$199,500

Working notes:

Calculate the amount of sales for plan 1 and plan 2.

$\begin{array}{c}\text{Sales for plan 1}\text{= 40,000 units }\times \text{\$25 per unit}\\ =\$1,000,000\end{array}$

$\begin{array}{c}\text{Sales for plan 2}\text{= 36,000 units }\times \text{\$30 per unit}\\ =\$1,080,000\end{array}$

Calculate the amount of variable costs for plan 1 and plan 2.

$\begin{array}{c}\text{Varaible costs for plan 1}\text{= 40,000 units }\times \text{\$7}\text{.50 per unit}\\ =\$300,000\end{array}$

$\begin{array}{c}\text{Variable costs for plan 2}\text{= 36,000 units }\times \text{\$7}\text{.50 per unit}\\ =\$270,000\end{array}$