Question

Waterways has a sales mix of sprinklers, valves, and controllers as follows.

Annual expected sales:
Sale of sprinklers 460,000 units at $26.50
Sale of valves 1,480,000 units at $11.20
Sale of controllers 60,000 units at $42.50
Variable manufacturing cost per unit
Sprinklers $13.96
Valves $7.95
Controllers $29.75
Fixed manufacturing overhead cost (total) $760,000
Variable selling and administrative expenses per unit:
Sprinklers $1.30
Valves $0.50
Controllers $3.41
Fixed selling and administrative expenses (total) $1,600,000
A) Determine the sales mix based on unit sales for each product.
B) Using the annual expected sales for these products, determine the weighted-average unit contribution margin for these three products.
C) Assuming the sales mix remains the same, what is the break-even point in units for these products?

Answer 1

A.

Sales Mix is 23 : 74 : 3

B.

$567.17

C.

sprinklers = 95,726 units

valves = 303,826 units

controllers = 12,486 units

Step-by-step explanation:

the sales mix based on unit sales for each product

sprinklers = 460,000 units

valves = 1,480,000 units

controllers = 60,000 units

this can then be expressed as :

460,000 : 1,480,000 : 60,000

expressed in lowest terms as :

23 : 74 : 3

the weighted-average unit contribution margin for these three products.

weighted-average unit contribution margin is the sum of contribution per units with the mix applied to each contribution margin.

unit contribution margin are

sprinklers = $12.54

valves = $3.25

controllers = $12.75

weighted-average unit contribution margin = $12.54 x 23 + $3.25 x 74 + $12.75 x 3 = $567.17

the break-even point in units for these products

break-even point in units = Fixed Cost ÷ Contribution per unit

= ($760,000 + $1,600,000) ÷ $567.17

= 4,162 units

Multiplying this with each mix we have :

sprinklers = 95,726 units

valves = 303,826 units

controllers = 12,486 units