Question

Crandall Company sells flags with team logos. Crandall has fixed costs of \(583,200 per year plus variable costs of \)4.80 per flag. Each flag sells for \(12.00.

Requirements

1. Use the equation approach to compute the number of flags Crandall must sell each year to break even.

2. Use the contribution margin ratio approach to compute the dollar sales Crandall needs to earn \)33,000 in operating income for 2018. (Round the contribution margin ratio to two decimal places.)

3. Prepare Crandall’s contribution margin income statement for the year ended December 31, 2018, for sales of 70,000 flags. (Round your final answers up to the next whole number.)

4. The company is considering an expansion that will increase fixed costs by 21% and variable costs by $0.60 per flag. Compute the new breakeven point in units and in dollars. Should Crandall undertake the expansion? Give your reasoning. (Round your final answers up to the next whole number.)

Short answer

1. Breakeven units equals 81,000 Units
2. Dollar sales equals $1,027,000
3. Operating loss equals $79,200.
4. If estimated sales increases to 106,920units, then expansion can be undertaken.

Step-by-step solution

Computation of number of flags for breakeven 

$\begin{array}{rcl}\mathbf{Netsalesrevenue}\mathbf{-}\mathbf{Variablecosts}\mathbf{-}\mathbf{Fixedcosts}& \mathbf{=}& \mathbf{Targetprofit}\\ \left(\mathbf{\$}\mathbf{12}\mathbf{\times }\mathbf{Unitssold}\right)\mathbf{-}\left(\mathbf{\$}\mathbf{4}\mathbf{.}\mathbf{80}\mathbf{\times }\mathbf{Unitssold}\right)\mathbf{-}\mathbf{\$}\mathbf{583}\mathbf{,}\mathbf{200}& \mathbf{=}& \mathbf{\$}\mathbf{0}\\ \left(\mathbf{\$}\mathbf{7}\mathbf{.}\mathbf{2}\mathbf{\times }\mathbf{Unitssold}\right)& \mathbf{=}& \mathbf{\$}\mathbf{583200}\\ \mathbf{Unitssold}& \mathbf{=}& \mathbf{81}\mathbf{,}\mathbf{000}\\ & & \end{array}$

Computation of dollar sales required to earn operating income of $33,000.

$\begin{array}{rcl}\mathbf{Contributionmarginratio}& \mathbf{=}& \frac{\mathbf{Contributionmargin}}{\mathbf{Salesperunit}}\\ & \mathbf{=}& \frac{\left(\$12-\$4.80\right)}{\mathbf{\$}\mathbf{12}}\\ & \mathbf{=}& \mathbf{60}\mathbf{\%}\\ & & \end{array}$

$\begin{array}{rcl}\mathbf{Breakevensales}& \mathbf{=}& \frac{\mathbf{Fixedcost}\mathbf{+}\mathbf{Targetprofit}}{\mathbf{Contributionmarginratio}}\\ & \mathbf{=}& \frac{\mathbf{\$}\mathbf{583}\mathbf{,}\mathbf{200}\mathbf{+}\mathbf{\$}\mathbf{33}\mathbf{,}\mathbf{000}}{\mathbf{60}\mathbf{\%}}\\ & \mathbf{=}& \mathbf{\$}\mathbf{1}\mathbf{,}\mathbf{027}\mathbf{,}\mathbf{000}\\ & & \end{array}$

Contribution margin income statement

Net sales revenue (70,000 x $12)	$840,000
Variable costs (70,000 x $4.80)	$336,000
Contribution margin(70,000 x $7.20)	$504,000
Fixed costs	$583,200
Operating income	($79,200)

Calculation of new breakeven in units and sales

Expansion decision is fully dependent on the expected sales. In case business is able to sell more than 106,920 units, then only expansion can be undertaken, so as to have positive operating income.

$\begin{array}{rcl}\mathbf{Contributionmarginratio}& \mathbf{=}& \frac{\mathbf{Contributionmargin}}{\mathbf{Salesperunit}}\\ & \mathbf{=}& \frac{\left(\$12-\left(\$4.80+\$0.60\right)\right)}{\mathbf{\$}\mathbf{12}}\\ & \mathbf{=}& \mathbf{55}\mathbf{\%}\\ & & \end{array}$

$\begin{array}{rcl}\mathbf{Breakevensales}\text{in dollars}& \mathbf{=}& \frac{\mathbf{Fixedcost}}{\mathbf{Contributionmarginratio}}\\ & \mathbf{=}& \frac{\mathbf{\$}583,200\times \left(1+21\%\right)}{55\mathbf{\%}}\\ & \mathbf{=}& \mathbf{\$}\mathbf{1}\mathbf{,}283,040\\ & & \end{array}$

$\begin{array}{rcl}\mathbf{Breakevensale}s\text{in units}& \mathbf{=}& \frac{\mathbf{Fixedcost}}{\mathbf{Contributionmargin}per\text{unit}}\\ & \mathbf{=}& \frac{\mathbf{\$}583,200\times \left(1+21\%\right)}{\left(\$12-\left(\$4.80+\$0.60\right)\right)}\\ & \mathbf{=}& 106,920\text{Units}\\ & & \end{array}$