sales mix with assumptions are casually made concerning sales mix in cost-volume profits (CVP) analysis

Q. What is meant by sales mix? What assumptions are casually made concerning sales mix in cost-volume profits (CVP) analysis?

Sales mix is the components of Cost volume profit analysis.

CVP analysis expands the use of information provided by breakeven analysis.  

Assumptions:

1. The behavior of both costs and revenue is linear throughout the relevant range of activity.

2. Costs can be classified accurately as either fixed or variable.

3. Changes in activity are the only factors those affects costs.

4. All units produced are sold.

5. When a company sells more than one type of product, the sales mix will remain constant.

Applications:

CVP simplifies the computation of breakeven in break-even analysis and more generally allows simple computation of target income sales. It simplifies analysis of short run trade-offs in operation decisions.

Limitations:

CVP is a short run marginal analysis, it assumes that unit variable costs and unit revenues are constant which is appropriate for small deviation from current production and sales and assumes a neat division between fixed costs and variable costs through in the long run all costs are variable. For longer term analysis that considers the entire life-cycle of a product one therefore often prefers activity-based costing.   

Problem: The Paduka Shoe Company sells five different styles of ladies chappals with identical costs and selling prices. The company is trying to find out the profitability of opening another store, which will have the following expenses and revenues:-

Per Pair

Taka

Selling price

30.00

Variable cost

19.50

Salesman’s commission

1.50

Total Variable cost

21.00

Annual fixed expenses are:

Rent

60,000

Salaries

2,00,000

Advertising

80,000

Other fixed expenses

20,000

Total

3,60,000

Required: (1) Calculate the annual Break-even point in units and in value. Also determine the profit or loss if 35,000 pairs of chappals are sold;

Required: (2) The sales commission are proposed to be discounted, but instead a fixed amount of Tk.90,000 is to be incurred in fixed salaries. A reduction in selling price of 5% is also proposed. What will be the Break-even point in units?

Required: (3) It is proposed to pay the store manager 50 paisa (Tk.0.50) per pair as further commission. The selling price is also proposed to be increased by 5%. What would be the Break-even point in units?

Required: (4) Refer to original data, if the store manager were to be paid 30paisa (Tk 0.30) commission on each pair of chappal sold in excess of Break-even point, What would be the store’s net profit, if 50,000 pairs were sold?

Solution: Required 1:

BEP in units = Fixed Cost/Contribution margin per unit

     = Fixed Cost/(Selling price per unit – Varibale cost per unit)

    = 3,60,000/(30-21) = 40,000 units

The required BEP in units 40,000.

Contribution margin = (Contribution margin/sales)*100

                                  = (30-21)/30*100 = 30%

So Break even Value = Fixed cost/CM ratio

                                   = 3,60,000/0.3 = 12,00,000 Tk.

The Break Even Value is Tk.12,00,000.

Now, we know,

Sales = Fixed cost + variable cost + profit or (loss)

Profit or (loss) = Sales – (Fixed cost + variable cost)

Profit or (loss) = (30*35,000) – (3,60,000 + 21*35,000)

Profit or (loss) = 10,50,000 – (3,60,000 + 7,35,000)

Profit or (loss) = - 45,000.

So, the loss is Tk.45,000.

Solution: Required 2:

New variable cost   = Tk.19.50

New fixed expanse = (3,60,000 + 90,000) = Tk.4,50,000.

New selling price    = 30 – (30*0.05) = Tk.28.50

So, BEP in units

= Fixed Cost/(Selling price per unit – Variable cost per unit)

= 4,50,000/(28.50-19.50) = 50,000 units

The required BEP in units 50,000.

The required BEP in sales volume = Total unit*Sales price

               = 50,000*28.50 = Tk.14,25,000.

Solution: Required 3:

New variable cost = Tk. (19.50+1.50+0.50) = Tk.21.50

New selling price = 30 + (30*0.05) = Tk.31.50

So, BEP in units

= Fixed Cost/(Selling price per unit – Variable cost per unit)

= 3,60,000/(31.50-21.50) = 36,000 units

New BEP in sale volume = 36,000*31.50 = Tk.11,34,000.

Solution: Required 4:

Particulars

amount

Total amount (Tk.)

Sales revenue (50,000*30)

15,00,000

Less,

Variable commission Tk.0.30 is imposed in escess BEP

40,000 units * 21.00

Tk.8,40,000

Excess 10,000 units * 21.30

Tk.2,13,000

(10,53,000)

Commission margin                                               4,47,000

Less, fixed cost                                                    (3,60,000)

Profit                                                                         87,000