Question

The contribution margin income statement of Sugar Lips Donuts for August 2018 follows:

Sugar Lips sells three dozen plain donuts for every dozen custard-filled donuts. A dozen plain donuts sells for \(4.00, with total variable cost of \)1.80 per dozen. A dozen custard-filled donuts sells for \(8.00, with total variable cost of \)3.60 per dozen.

Requirements

1. Calculate the weighted-average contribution margin.

2. Determine Sugar Lips’s monthly breakeven point in dozens of plain donuts and custard-filled donuts. Prove your answer by preparing a summary contribution margin income statement at the breakeven level of sales. Show only two categories of costs: variable and fixed.

3. Compute Sugar Lips’s margin of safety in dollars for August 2018.

4. Compute the degree of operating leverage for Sugar Lips Donuts. Estimate the new operating income if total sales increase by 30%. (Round the degree of operating leverage to four decimal places and the final answer to the nearest dollar. Assume the sales mix remains unchanged.)

5. Prove your answer to Requirement 4 by preparing a contribution margin income statement with a 30% increase in total sales. (The sales mix remains unchanged.)

Short answer

1. Weighted average contribution equals $2.75.
2. Breakeven for plain donuts equals 9,000 units and custard filled donuts equals 3,000 units.
3. Margin of safety equals $65,000
4. Degree of operating leverage equals1.9231, and revised operating income equals $56,374.
5. Revised operating income equals $56,375

Step-by-step solution

(1) Computation of weighted average contribution margin

	Plain donuts	Custard filled donuts	Total
Selling price	$4	$8
Variable cost	$1.80	$3.60
Contribution per unit	$2.2	$4.4
Sales mix	X 3	X 1	4
Total contribution	$6.6	$4.4	$11
Weighted average contribution margin			$2.75

(2) Computation of breakeven point

$\begin{array}{rcl}\mathbf{Breakevensalesofplaindonuts}& \mathbf{=}& \mathbf{12}\mathbf{,}\mathbf{000}\mathbf{\times }\frac{\mathbf{3}}{\mathbf{4}}\\ & \mathbf{=}& \mathbf{9}\mathbf{,}\mathbf{000}\\ \mathbf{Breakevensalesofcustardfilleddonuts}& \mathbf{=}& \mathbf{12}\mathbf{,}\mathbf{000}\mathbf{\times }\frac{\mathbf{1}}{\mathbf{4}}\\ & \mathbf{=}& \mathbf{3}\mathbf{,}\mathbf{000}\\ & & \end{array}$

$\begin{array}{rcl}\text{Composite breakeven}& \mathbf{=}& \frac{\mathbf{Fixedcost}}{\mathbf{Weightedaveragecontributionmargin}}\\ & \mathbf{=}& \frac{\mathbf{\$}\mathbf{33}\mathbf{,}\mathbf{000}}{\mathbf{\$}\mathbf{2}\mathbf{.}\mathbf{75}}\\ & \mathbf{=}& \mathbf{12}\mathbf{,}\mathbf{000}\\ & & \end{array}$

Contribution margin income statement

Net sales revenue (9,000 x $4)+($3,000x$8)	$60,000
Variable cost (9,000 x $1.80)+($3,000x$8)	$27,000
Contribution Margin	$33,000
Fixed cost	$33,000
Operating income	$0

(3) Calculation of margin of safety 

$\begin{array}{rcl}\mathbf{Marginofsafety}& \mathbf{=}& \mathbf{Expectedsales}-\mathbf{breakevensales}\\ & \mathbf{=}& \mathbf{\$}\mathbf{125}\mathbf{,}\mathbf{000}-\mathbf{\$}\mathbf{60}\mathbf{,}\mathbf{000}\\ & \mathbf{=}& \mathbf{\$}\mathbf{65}\mathbf{,}\mathbf{000}\\ & & \end{array}$

$\begin{array}{rcl}\mathbf{Marginofsafety}& \mathbf{=}& \mathbf{Expectedsales}-\mathbf{breakevensales}\\ & \mathbf{=}& \mathbf{\$}\mathbf{125}\mathbf{,}\mathbf{000}-\mathbf{\$}\mathbf{60}\mathbf{,}\mathbf{000}\\ & \mathbf{=}& \mathbf{\$}\mathbf{65}\mathbf{,}\mathbf{000}\\ & & \end{array}$

Calculation of operating leverage

$\begin{array}{rcl}\mathbf{Degreeofoperatingleverage}& \mathbf{=}& \frac{\mathbf{Contributionmargin}}{\mathbf{Operatingincome}}\\ & \mathbf{=}& \frac{\mathbf{\$}\mathbf{68}\mathbf{,}\mathbf{750}}{\mathbf{\$}\mathbf{35}\mathbf{,}\mathbf{750}}\\ & \mathbf{=}& \mathbf{1}\mathbf{.}\mathbf{9231}\\ & & \end{array}$

$\begin{array}{rcl}\text{Revised operating income}& =& \text{Operating income}\times \left(1+\text{Increase in operating income}\right)\\ & =& \$35,750\times \left(1+57.69\%\right)\\ & =& \$56,374\\ & & \end{array}$

Statement showing contribution margin income statement with a 30% increase in total sales 

Net sales revenue (125,000 x (1+30%)	$162,500
Variable cost ($56,250 x (1+30%)	$73,125
Contribution margin	$89,375
Fixed costs	$33,000
Operating income	$56,375