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. Revenue and cost information for each product appears below: the unit that attaches to the faucet is sold for $70 and has variable costs of $30 the pitcher-filter sells for $80 and has variable costs of $45 • fixed costs total $424,000 • Pure Water sells 4 faucet models for every 3 pitcher-filters sold Calculate the number of units of the pitcher-filters that must be sold in order for Pure Water Products to break-even. 6,000

Answer 1

Number of units of the pitcher filters that must be sold in order for Pure Water Products to break-even = 4,800 units

Work:

• Where multiple products are produced by incurring common fixed costs, the Break-even point is calculated using a weighted average contribution.
• The weights may be sales mix quantity or values.

Per unit Selling price (a) Variable cost (b) Contribution (a - b) Faucet model Pitcher-filter $ 70 $ 80 $ 30 $ $ 40 $ 35 45

• Sales mix in quantity: 4 faucet models for every 3 pitcher filters.
• i.e. Sales ratio = 4:3
• 
  Weighted average contribution per unit = $40 X = + 35 X - = $22.857 + $15 = $37.857 Common fixed costs Overall Break – even point = 7 Weighted average contribution per unit = 11,200 units $4,24,000 $37.857 Break-even units of Faucet Model = 11,200 units 6,400 units Break-even units of Pitcher Filter = 11,200 units 4,800 units N
  

Verification:

Total 832,000 Sales Faucet model Pitcher-filter I $ 448,000 $ 384,000 $ (6,400 units x $70) (4,800 units X $80) $ 192,000 $ 216,000 $ (6,400 units * $30) (4,800 units * $45) $ 256,000 $ 168,000 $ 408,000 Less: Variable costs Contribution Less: Fixed costs Profit 424,000 424,000 $ 0

• The breakeven point (BEP) is the volume at which there is neither profits nor losses.
• At breakeven point, contribution earned exactly equals total fixed costs.
• Breakeven point (in units) = Fixed costs ÷ Contribution per unit
  • i.e BEP units × Contribution per unit = Fixed costs
• Breakeven point (value in $) = Fixed costs ÷ Contribution margin ratio
  • i.e. BEP sales (in $) × Contribution margin ratio = Fixed costs
• Contribution margin ratio = Contribution margin ÷ Sales revenue
• Sales - Variable cost = Contribution
• Contribution - Fixed costs = Profit
• At BEP, profit = 0; therefore, Contribution = Fixed costs