Question

In: Accounting

A company sells three products A, B and C in a 3:3:4 sales mix. Sales price:       ...

A company sells three products A, B and C in a 3:3:4 sales mix.

Sales price:        A - $10 B -$8    C - $6

Variable cost:     A - $7 B- $3      C - $3   

Quantity sold   A 6,000 B6000 C8000

Fixed costs are $36,000

A) 6% - Calculate breakeven in total sales dollars and in units of the 3 products

B) 5% - What is the total income the company can earn with this sales mix?

             Say the sales mix changes to 4;3:3 with total quantity sold of 20,000

C) 6% -What is the breakeven point in sales dollars and units?

D) 5% - What is the total income the company can earn with this sales mix?

E) 3% - Explain why though the sale mix changed the income in parts B and D is the same

Solutions

Expert Solution

A) Break even total sales in units

= Total fixed expenses / (Weighted average selling price – Weighted average variable cost)

Weighted average selling price

= (Sale price of product A * Sales ratio of product A) + (Sale price of product B * Sale ratio of product B) + (Sale price of product C * Sales ratio of product C)

= [10 * (3/10)] + [8 * (3/10)] + [6 * (4/10)]

= 3 + 2.4 + 2.4

= $7.8

Weighted average variable cost

= (Variable cost of product A * Sales ratio of product A) + (Variable cost of product B × Sales ratio of product B) + (Variable cost of product C × Sales ratio of product C)

= [7 * (3/10)] + [3 * (3/10)] + [3 * (4/10)]

= 2.1 + 0.9 + 1.2

= $4.2

So, Break even total sales in units

= Total fixed expenses / (Weighted average selling price – Weighted average variable cost)

= 36000 / (7.8 – 4.2)

= 10000 units

So the company has to sell 10000 units to break even. Now number of units sold of each product to breakeven :

Product A [10000*(3/10)] = 3000 units

Product B [10000*(3/10)] = 3000 units

Product C [10000*(4/10)] = 4000 units

Break even point in dollars

= (Breakeven units of product A * Sales price of product A) + (Breakeven units of product B * Sales price of product B) + (Breakeven units of product C * Sales price of product C)

= (3000*10) + (3000*8) + (4000*6)

= $78000

B)

Total Income of Company with sale mix between A,B,C being 3:3:4

Particulars

Amount ($)

Amount ($)

Sales

Product A (6000*10)

60000

Product B (6000*8)

48000

Product C (8000*6)

48000

156000

Less : Variable Cost

Product A (6000*7)

42000

Product B (6000*3)

18000

Product C (8000*3)

24000

84000

Contribution

72000

Less: Fixed Cost

36000

Total Income

36000

C)

Sale Mix between A, B, C = 4:3:3

Break even total sales in units

= Total fixed expenses / (Weighted average selling price – Weighted average variable cost)

Weighted average selling price

= (Sale price of product A * Sales ratio of product A) + (Sale price of product B * Sale ratio of product B) + (Sale price of product C * Sales ratio of product C)

= [10 * (4/10)] + [8 * (3/10)] + [6 * (3/10)]

= 4 + 2.4 + 1.8

= $8.2

Weighted average variable cost

= (Variable cost of product A * Sales ratio of product A) + (Variable cost of product B × Sales ratio of product B) + (Variable cost of product C × Sales ratio of product C)

= [7 * (4/10)] + [3 * (3/10)] + [3 * (3/10)]

= 2.8 + 0.9 + 0.9

= $ 4.6

So, Break even total sales in units

= Total fixed expenses / (Weighted average selling price – Weighted average variable cost)

= 36000 / (8.2 – 4.6)

= 10000 units

So the company has to sell 10000 units to break even. Now number of units sold of each product to breakeven :

Product A [10000*(4/10)] = 4000 units

Product B [10000*(3/10)] = 3000 units

Product C [10000*(3/10)] = 3000 units

Break even point in dollars

= (Breakeven units of product A * Sales price of product A) + (Breakeven units of product B * Sales price of product B) + (Breakeven units of product C * Sales price of product C)

= (4000*10) + (3000*8) + (3000*6)

= $82000

D) Sales units of A, B, C with sales mix ratio of 4:3:3

Sales of Product A = 20000*(4/10) = 8000 units

Sales of Product A = 20000*(3/10) = 6000 units

Sales of Product A = 20000*(3/10) = 6000 units

Total Income of Company with sale mix between A,B,C being 4:3:3

Particulars

Amount ($)

Amount ($)

Sales

Product A (8000*10)

80000

Product B (6000*8)

48000

Product C (6000*6)

36000

164000

Less : Variable Cost

Product A (8000*7)

56000

Product B (6000*3)

18000

Product C (6000*3)

18000

92000

Contribution

72000

Less: Fixed Cost

36000

Total Income

36000

E ) The income of Part B and Part D are same because :

  1. The change in sale mix changed only the sales of Product A and Product C
  2. The contribution of Product A and Product C is same i.e $3 (Contribution = sales – variable cost)

So the increased contribution of Product A due to increase in sales is settled by an equal amount of decreased contribution of Product C due of decrease in sales after change of sale mix.

The sales of Product B is same in both the sale mix.

Therefore, the income of Part B ($36000) and Part D ($36000) is same.


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