Question

Calculating breakeven point for two products, margin of safety, andoperating leverage

The contribution margin income statement of Delectable Donuts for May 2018follows:

DELECTABLE DONUTS Contribution Margin Income Statement Month Ended May 31, 2018

Net Sales Revenue		\(125,000
Variable cost
Cost of goods sold	\)32,100
Selling cost	17,400
Administrative cost	500	\(50,000
Contribution Margin		\)75,000
Fixed cost
Selling cost	\(37,800
Administrative cost	12,600	\)50,400
Operating income		\(24,600

Delectable sells five dozen plain donuts for every dozen custard-filled donuts. A dozenplain donuts sells for \)4.00, with a variable cost of \(1.60 per dozen. A dozen custardfilled donuts sells for \)8.00, with a variable cost of $3.20 per dozen.

Requirements

1. Calculate the weighted-average contribution margin.

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

3. Compute Delectable’s margin of safety in dollars for May 2018.

4. Compute the degree of operating leverage for Delectable Donuts. Estimate thenew operating income if total sales increase by 20%. (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 marginincome statement with a 20% increase in total sales. (The sales mix remainsunchanged.)

Short answer

1. Weighted average contribution margin is $2.8.
2. Break-even point in units: 18,000 units.
3. Operating income is $0.
4. Margin of safety in dollars: $41,000.
5. Degree of operating leverage is 3.05.

Step-by-step solution

Step 1:1. Computation of the weighted-average contribution margin-

Weighted average contribution margin

Plain donuts

Custardfilled donuts

Total

Selling price	$4	$8
Less: Variable cost	($1.6)	($3.2)
Contribution margin per unit	$2.4	$4.8
Sales mix (a)	5	1	6
Contribution margin (b)	$12	$4.8	$16.8
Weighted average contribution margin (b/a)			$2.8

2. Computation of break even point-

$\begin{array}{rcl}\mathbf{Break}\mathbf{}\mathbf{even}\mathbf{}\mathbf{point}& \mathbf{=}& \frac{\mathbf{Fixed}\mathbf{}\mathbf{costs}}{\mathbf{Weighted}\mathbf{}\mathbf{average}\mathbf{}\mathbf{contribution}\mathbf{}\mathbf{margin}}\\ & \mathbf{=}& \frac{\mathbf{\$}\mathbf{50}\mathbf{,}\mathbf{400}}{\mathbf{2}\mathbf{.}\mathbf{8}}\\ & \mathbf{=}& \mathbf{\$}\mathbf{18}\mathbf{,}\mathbf{000}\end{array}$

	Units(a)	Selling Price Per unit(b)	Total sales (a x b)	Variable cost per unit (c)	Total Variable cost (axc)
Plain donuts $\left(18,000\times \frac{5}{6}\right)$	15,000	$4	$60,000	$1.6	$24,000
Custardfilled donuts $\left(18,000\times \frac{1}{6}\right)$	3,000	$8	$24,000	$3.2	$9,600

Contribution margin income statement-

Contribution margin income statement

	Plain donuts	Custardfilled donuts	Total
Revenue	$60,000	$24,000	$84,000
Less: Variable cost	($24,000)	($9,600)	($33,600)
Contribution margin per unit	$36,000	$14,400	$50,400
Less: Fixed cost			($50,400)
Operating income			$0

3. Computation of margin of safety-

$\begin{array}{rcl}\mathrm{Margin}\mathrm{of}\mathrm{safety}& =& \mathrm{Sales}-\mathrm{Break}\mathrm{even}\mathrm{sales}\\ & =& \$125,000-\$84,000\\ & =& \$41,000\\ & & \end{array}$

Step 5:Computation of Degree of Operating Leverage-

$\begin{array}{rcl}\mathbf{Degree}\mathbf{}\mathbf{of}\mathbf{}\mathbf{operating}\mathbf{}\mathbf{levearge}& \mathbf{=}& \frac{\mathbf{Contribution}\mathbf{}\mathbf{margin}}{\mathbf{Operating}\mathbf{}\mathbf{Income}}\\ & \mathbf{=}& \frac{\mathbf{75}\mathbf{,}\mathbf{000}}{\mathbf{24}\mathbf{,}\mathbf{600}}\\ & \mathbf{=}& \mathbf{3}\mathbf{.}\mathbf{048780}\\ & & \end{array}$

Step 6:4. Computation of increase in operating income-

$\begin{array}{rcl}\mathbf{Increase}\mathbf{}\mathbf{in}\mathbf{}\mathbf{operating}\mathbf{}\mathbf{income}& \mathbf{=}& \mathbf{Increase}\mathbf{}\mathbf{in}\mathbf{}\mathbf{sales}\mathbf{\times }\mathbf{Degree}\mathbf{}\mathbf{of}\mathbf{}\mathbf{operating}\mathbf{}\mathbf{leverage}\\ & \mathbf{=}& \mathbf{20}\mathbf{\times }\mathbf{3}\mathbf{.}\mathbf{048780}\\ & \mathbf{=}& \mathbf{60}\mathbf{.}\mathbf{9756}\end{array}$

Step 7:5. Contribution margin income statement-

Contribution margin income statement

Sales Revenue	$150,000
Less: Variable cost	$60,000
Contribution margin per unit	$90,000
Less: fixed cost	$50,400
Operating income	$39,600
Less: Old operating income	$24,600
Incease	$15,000