Chapter 21, Problem 6BP

1.  a.

To determine

Calculate break-even point in dollar sales for existing business strategy.

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 existing business strategy.

  $\begin{array}{c}\text{Break-even}\text{point}\text{in}\text{dollar sales }=\frac{\text{Fixed}\text{Costs}}{\text{Contribution}\text{Margin}\text{Ratio}}\\ =\frac{\text{\$950,000}}{55\%}\\ =\$1,727,273\left(rounded\right)\end{array}$

Working notes:

Calculate variable cost per unit.

$\begin{array}{c}\text{Variable cost}\text{per}\text{unit}\text{=}\frac{\text{Unit costs +}\text{Packaging costs}}{\text{Number}\text{of}\text{units}}\\ =\frac{\$800,000+\$100,000}{100,000}\\ =\$9.00\end{array}$

Determine the contribution margin ratio.

  $\begin{array}{c}\text{Contribution}\text{Margin}\text{Ratio }=\frac{\text{Contribution}\text{Margin}}{\text{Sales}}\times 100\\ =\frac{\left(\$20.00-\$9.00\right)}{\$20.00}\times 100\\ =55\%\end{array}$

Conclusion

Hence, the break-even point in dollar sales for existing business strategy is $1,727,273.

1.  b.

To determine

Calculate break-even point in dollar sales for new strategy.

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 new strategy.

  $\begin{array}{c}\text{Break-even}\text{point}\text{in}\text{dollar sales }=\frac{\text{Fixed}\text{Costs}}{\text{Contribution}\text{Margin}\text{Ratio}}\\ =\frac{\text{\$950,000}}{55\%}\\ =\$1,727,273\end{array}$

Working notes:

Calculate sales price per unit.

$\begin{array}{c}\text{Sales price}\text{per}\text{unit}\text{=}\left[\$20.00\times \left(1-20\%\right)\right]\\ =\$16.00\end{array}$

Calculate variable cost per unit.

$\begin{array}{c}\text{Variable cost}\text{per}\text{unit}\text{=}\text{Unit costs per unit + Packaging costs per unit}\\ =\left[\begin{array}{c}\left\{\left(\$800,000/100,000\right)\times \left(1–25\%\right)\right\}\\ +\left\{\left(\$100,000/100,000\right)\times \left(1+20\%\right)\right\}\end{array}\right]\\ =\$6.00+\$1.20\\ =\$7.20\end{array}$

Determine the contribution margin ratio.

  $\begin{array}{c}\text{Contribution}\text{Margin}\text{Ratio }=\frac{\text{Contribution}\text{Margin}}{\text{Sales}}\times 100\\ =\frac{\left(\$16.00-\$7.20\right)}{\$16.00}\times 100\\ =55\%\end{array}$

Conclusion

Hence, the break-even point in dollar sales for new strategy is $1,727,273.

2.

To determine

Prepare a forecasted contribution margin income statement for existing business strategy and new strategy.

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 existing business strategy and new strategy.

Company B
Forecasted Contribution Margin Income Statement
	Existing business strategy	New strategy
Sales	$2,000,000	$2,880,000
Less: Variable costs	$900,000	$1,296,000
Contribution margin	$1,100,000	$1,584,000
Less: Fixed costs	$950,000	$950,000
Income before taxes	$150,000	$634,000
Less: Income taxes (30%)	$37,500	$158,500
Net income	$112,500	$475,500
Return on sales (Net income/Sales)	5.6%	16.5%

Working notes:

Calculate the amount of sales for existing business strategy and new strategy.

$\begin{array}{c}\text{Sales for existing business strategy}\text{= 100,000 units }\times \text{\$20 per unit}\\ =\$2,000,000\end{array}$

$\begin{array}{c}\text{Sales for new strategy}\text{= 180,000 units }\times \text{\$16 per unit}\\ =\$2,880,000\end{array}$

Calculate the amount of variable costs for existing business strategy and new strategy.

$\begin{array}{c}\text{Varaible costs for existing business strategy}\text{= 100,000 units }\times \text{\$9}\text{.00 per unit}\\ =\$900,000\end{array}$

$\begin{array}{c}\text{Variable costs for new strategy}\text{= 180,000 units }\times \text{\$7}\text{.20 per unit}\\ =\$1,296,000\end{array}$