Management Accounting Math Solution (Break Even Math)

Problem: The Sunmoon Ltd is the distributor for a foreign product. The product sells in the market for Tk.200.00 per unit with a variable selling expense of Tk.20.00 and a item based commission of Tk.40.00 per item. The Company’s cost of import at its godown is Tk.90.00 Fixed selling and administrative expenses are Tk.2,00,000.00 per year.

Required:

1) What is Break-even point in unit and taka;

2) What sales level in unit is required to earn an annual before tax profit of Tk.1,50,000.00

3) What sales level must be achieved to have the same level of after tax profit as above, if tax rate is 40%.

4) What sales level must be achieved to have the after tax target profit Tk.3,00,000.00. If tax rate is 30%.

5) What is the Margin of safety and after tax profit for sales level of 10,000 units, if tax rate is 40%.

Solution:

Calculation of unit contribution:

Variable cost of the product/unit:

               Variable Selling expenses : 20.00

               Commission                       :40.00

               Cost of import                    :90.00

               Variable cost per unit   =   150.00 Taka

Selling price per unit = Tk.200

So, Unit Contribution = Selling price per unit – Variable Cost per unit = 200-150=Tk.50.00 

 

Required 1:

BEP in units = FC/Contribution per unit = 2,00,000/50

                                                                 =4000 units

Therefore BEP in sales = 4,000*200 = 8,00,000 Taka

 

Required 2:

Level of Sales = (Fixed Cost + expected profit)/(Contribution Margin per unit) = (2,00,000+1,50,000)/50=7,000 units

 

Required 3:

Required sales Level = Fixed Cost+(Profit after tax)/(1-tax rate)

                                        Contribution Margin per unit

                                   = 2,00,000 + (1,50,000)/(1-0.40)

                                                       50

                                   = 2,00,000 + 2,50,000

                                                       50               

                                   = 9,000 units

 

Required 4:

Required sales level  = Fixed cost + Profit after tax/(1-tax rate)

                                          Contribution Margin per unit

                                  = 2,00,000 + (3,00,000)/(1-0.30)

                                                       50

                                  = 2,00,000 + 3,00,000/0.70

                                                       50               

                                  = 2,00,000 + 4,28,571.42

                                                       50

                                  = 6,28,571.42

                                            50

                                  = 12,571.43 units

                                  = 12572 units (approx.)

 

Required 5:

Margin safety in units = Sales – BEP=10,000-4,000=6000

Marginal safety in Tk. = 6000*Selling price per unit

                                     = 6000*200 = 12,00,000 Taka

Profit of marginal safety       =6000*50          = 3,00,000

Less, Tax (40% of 3,00,000)= 3,00,000*0.40= 1,20,000

                Now, Profit after tax                        =1,80,000