Question

White Company sells flags with team logos. White has fixed costs of \(639,600 per year plus variable costs of \)4.20 per flag. Each flag sells for \(12.00.

Requirements

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

2. Use the contribution margin ratio approach to compute the dollar sales White needs to earn \)32,500 in operating income for 2018. (Round the contribution margin to two decimal places.)

3. Prepare White’s contribution margin income statement for the year ended December 31, 2018, for sales of 73,000 flags. (Round your final answers up to the next whole number.)

4. The company is considering an expansion that will increase fixed costs by 23% and variable costs by $0.60 per flag. Compute the new breakeven point in units and in dollars. Should White undertake the expansion? Give your reasoning. (Round your final answers up to the next whole number.)

Short answer

1. Breakeven units equals 82,000 Units
2. Desired sales level to earn $32,500 operating income equals $1,034,000
3. Operating loss equals ($70,200)
4. New breakeven in units equals 109,265 units and in dollars equals $1,311,180. Expansion can be undertaken if expected sales increases beyond breakeven level.

Step-by-step solution

Computation of number of flags for breakeven 

$\begin{array}{rcl}\mathbf{Netsalesrevenue}-\mathbf{Variablecosts}-\mathbf{Fixedcosts}& \mathbf{=}& \mathbf{Targetprofit}\\ \left(\mathbf{\$}\mathbf{12}\mathbf{\times }\mathbf{Unitssold}\right)-\left(\mathbf{\$}\mathbf{4}\mathbf{.}\mathbf{20}\mathbf{\times }\mathbf{Unitssold}\right)-\mathbf{\$}\mathbf{639}\mathbf{,}\mathbf{600}& \mathbf{=}& \mathbf{\$}\mathbf{0}\\ \left(\mathbf{\$}\mathbf{7}\mathbf{.}\mathbf{8}\mathbf{\times }\mathbf{Unitssold}\right)& \mathbf{=}& \mathbf{\$}\mathbf{639}\mathbf{,}\mathbf{600}\\ \mathbf{Unitssold}& \mathbf{=}& \mathbf{82}\mathbf{,}\mathbf{000}\\ & & \end{array}$

Contribution margin approach

$\begin{array}{rcl}\mathbf{Contributionmarginratio}& \mathbf{=}& \frac{\mathbf{Contributionmargin}}{\mathbf{Salesperunit}}\\ & \mathbf{=}& \frac{\mathbf{\$}12-\$4.20}{\mathbf{\$}\mathbf{12}}\\ & \mathbf{=}& \mathbf{65}\mathbf{\%}\\ & & \end{array}$

$\begin{array}{rcl}\text{Desired sales level for target profit}& \mathbf{=}& \frac{\mathbf{Fixedcost}\mathbf{+}\mathbf{Targetprofit}}{\mathbf{Contributionmarginratio}}\\ & \mathbf{=}& \frac{\mathbf{\$}\mathbf{639}\mathbf{,}\mathbf{600}\mathbf{+}\mathbf{\$}\mathbf{32}\mathbf{,}\mathbf{500}}{\mathbf{65}\mathbf{\%}}\\ & \mathbf{=}& \mathbf{\$}\mathbf{1}\mathbf{,}\mathbf{034}\mathbf{,}\mathbf{000}\\ & & \end{array}$

 Step 3: Contribution margin income statement

Net sales revenue (73,000 x $12)	$876,000
Variable costs (73,000 x $4.20)	$306,600
Contribution margin	$569,400
Fixed cost	$639,600
Operating income/(Loss)	($70,200)

Calculation of new breakeven in units and sales

$\begin{array}{rcl}\mathbf{Breakevensale}s\text{in units}& \mathbf{=}& \frac{\mathbf{Fixedcost}}{\mathbf{Contributionmargin}per\text{unit}}\\ & \mathbf{=}& \frac{\mathbf{\$}639,600\times \left(1+23\%\right)}{\left(\$12-\left(\$4.20+\$0.60\right)\right)}\\ & \mathbf{=}& 109,265\text{Units}\\ & & \end{array}$

$\begin{array}{rcl}\mathbf{Contributionmarginratio}& \mathbf{=}& \frac{\mathbf{Contributionmargin}}{\mathbf{Salesperunit}}\\ & \mathbf{=}& \frac{\$12-\left(\$4.20+\$0.60\right)}{\mathbf{\$}\mathbf{12}}\\ & \mathbf{=}& \mathbf{60}\mathbf{\%}\\ & & \end{array}$

$\begin{array}{rcl}\mathbf{Breakevensales}& \mathbf{=}& \frac{\mathbf{Fixedcost}}{\mathbf{Contributionmarginratio}}\\ & \mathbf{=}& \frac{\left(\$639,600\times \left(1+23\%\right)\right)}{\mathbf{60}\mathbf{\%}}\\ & \mathbf{=}& \mathbf{\$}\mathbf{1}\mathbf{,}\mathbf{311}\mathbf{,}\mathbf{180}\\ & & \end{array}$