Question

Pure Water Products produces two types of water filters. One attaches to the faucet and cleans all water that passes through the faucet. The other is a pitcher filter that only purifies water meant for drinking. The unit that attaches to the faucet is sold for $80 and has variable costs of $30. The pitcher filter sells for $110 and has variable costs of $40. Pure Water sells two faucet models for every three pitchers sold. Fixed costs equal $1,050,000.

REQUIRED:

1. Pure Water is considering buying new production equipment. The new equipment will increase fixed costs by $180,000 per year and will decrease variable cost of the faucet and pitcher units by $5 and $8, respectively. Assuming the same sales mix, how many of each type of filter does Pure Water need to sell to breakeven?

Answer 1

	Faucet	Pitcher
Selling price per unit	80	110
Variable cost per unit	30	40
Decrease in variable cost per unit	5	8
New variable cost per unit	25	32
New contribution margin per unit ( Selling price per unit - New variable cost per unit)	$55	$78

Sales mix = Faucet:Pitcher

= 2:3

Weighted average contribution margin per unit = 55 x 2/5 + 78 x 3/5

= 22+46.8

= $68.8

Fixed cost = $1,050,000

Increase in fixed cost = $180,000

New fixed cost = 1,050,000+180,000

= $1,230,000

Break even point = Fixed cost/ Weighted average contribution margin per unit

= 1,230,000/68.8

= 17,878 units

Break even units of Faucet = 17,878 x 2/5

= 7,151 units

Break even units of Pitcher = 17,878 x 3/5

= 10,727 units

Kindly comment if you need further assistance.

Thanks‼!