Question

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.Calculate breakeven in total sales dollars and in units of the 3 products B.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.What is the breakeven point in sales dollars and units? D.What is the total income the company can earn with this sales mix? E.Explain why though the sale mix changed the income in parts B and D is the same.

Answer 1

A)

Cal of cont per unit

Particulars	A	B	C
Sale price	10	8	6
less variable cost	7	3	3
cont per unit	3	5	3

wrighted avg cont per unit

=  [(3*3%) + (3*5%) + (4*3%)] / 10

= 3.6

Fixed cost = 36000

Break evn unit= Fixed cost / cont per unit

= 36000/3.6 = 10000 units

Units of A = 10000*3/10 = 3000

Units of B = 10000*3/10 = 3000

Units of C = 10000*4/10 = 4000

Breakeven sales = (3000*10) + (3000*8) + (4000*6) = 78000

B) Calculation of income

= (Units of A * contribution per unit) + (Units of B * CPU) + (Units of C *CPU) - Fixed cost

= (6000*3) + (6000*5) + (8000*3) - 36000 = 36000

C)

wrighted avg cont per unit

=  [(4*3) + (3*5) + (4*3)] / 10

= 3.9

Fixed cost = 36000

Break evn unit= Fixed cost / cont per unit

= 36000/3.9 = 9230 units

Units of A = 9230*3/10 = 2770

Units of B = 9230*3/10 = 2770

Units of C = 9230*4/10 = 3690

Breakeven sales = (2770*10) + (2770*8) + (3690*6) = 72000

D) Total units = 20000

Ratio = 4:3:3

A = 20000*4/10 = 8000

B = 20000*3/10 = 6000

C= 20000*3/10 = 6000

Calculation of income

= (Units of A * contribution per unit) + (Units of B * CPU) + (Units of C *CPU) - Fixed cost

= (8000*3) + (6000*5) + (6000*3) - 36000 = 36000

E) Income under both the options is same because In both the ratio change is only in Units of A and C without any change in units of B.

Contribution per unit under A and C is same i.e. 3 per unit hence it wont make any difference if you change and shift quantity between A and C.