Question

A company is selling 2 types of bicycles with sales as follows:

Selling price   Purchase cost   commission on sale
Model Y   600 370 50  
Model Z   400    300    25  
The 2/3 of bicycles sold is model Z. Fixed cost is : EUR 36.000. Considering that the sales mix is fixed:

A.   What is the break even point in money for the shop .
B.   How many bicycles from each category should be sold so that the net profit is EUR 13.500?
C.   270 bicycles model Y and 540 model Z were sold this year. What is the operating leverage level for this year?

Answer 1

Answer A)

Calculation of Break-even point in money for the shop

Break-even point in money = Total fixed cost/ Composite Contribution margin ratio

                                                   = € 36,000/ 22.50%

                                                    = € 160,000

Therefore break-even point in money is € 160,000.

Working Note:

Calculation of Contribution margin per unit and Contribution margin ratio:

	Model Y	Model Z
Selling Price per unit   (B)	€        600	€        400
Less: Variable Costs per unit
Purchase Cost per unit	€        370	€        300
Commission on Sale per unit	€          50	€          25
Contribution margin per unit   (A)	€        180	€          75
Contribution margin ratio   (A/B)	30.00%	18.75%

Calculation of Composite Contribution margin ratio

Composite contribution margin ratio = (Contribution margin ratio of Model Y x Sales mix of Model Y) + (Contribution margin ratio of Model Z x Sales mix of Model Z)

                                                           = (30.00% X 1/3) + (18.75% X 2/3)

                                                            = 10% + 12.50%

                                                            = 22.50%

Calculation of Composite Contribution margin

Composite contribution margin = (Contribution margin per unit of Model Y x Sales mix of Model Y) + (Contribution margin per unit of Model Z x Sales mix of Model Z)

                                                           = (€ 180 per unit X 1/3) + (€ 75 per unit X 2/3)

                                                            = € 60 + € 50

                                                            = € 110 per unit

Answer B)

Calculation of number of bicycles from each category to be sold to earn net profit of € 13,500

Total Number of Bicycles to be sold = (Total fixed cost + Target Net Profit)/ Composite Contribution margin per unit

                                                                                         = (€ 36,000 + € 13,500)/ € 110

                                                                                          = 450 units

Number of units of Model Y = Total number of units to be sold to earn target Net Profit X Sales mix of Product Y

                                                    = 450 units X 1/3

                                                    = 150 units       

Number of units of Model Z = Total number of units to be sold to earn target Net Profit X Sales mix of Product Z

                                                    = 450 units X 2/3

                                                    = 300 units       

Therefore 150 bicycles of Model Y and300 Bicycles of Model Z should be sold to achieve net profit of € 13,500.

Answer C)

Calculation of Degree of Operating Leverage

Degree of Operating Leverage = Total Contribution margin/Net Operating Income

                                                        = € 89,100/ € 75,600

                                                         = 1.1786 times or 1.18 times (rounded off)

Therefore degree of operating leverage is 1.18 times.

Working Note:

Calculation of Total Contribution margin and Net Operating Income

	Model Y	Model Z	Total
Number of Units Sold	270	540
Contribution margin per unit	€        180	€          75
Total Contribution margin (Number of units sold X Contribution margin per unit)	€ 48,600	€ 40,500	€ 89,100
Less: Fixed Costs			€ 13,500
Net Operating Income			€ 75,600