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 faucet-model that must be sold in order for Pure Water Products
to earn a target profit of $212,000.

Answer 1

Target profit analysis with a sales mix uses a contribution margin approach for different products that are not equally profitable for a company. Calculating target sales both in units and in dollars requires three steps.

Step 1. Calculate the contribution margin per unit for each product in the sales mix.

Contribution Margin _{per Unit} = Sales Price _{per Unit} - Variable Cost _{per Unit}

Step 2. Calculate the weighted average contribution margin for the sales mix,

Weighted Average Contribution Margin =	N	CMi × wi
	Σ
	i = 1

where CM_i is the contribution margin per unit of a relevant product, and w_i is the proportion of a relevant product in the sales mix.

Step 3. Calculate in units the number of target sales for each product.

Target Sales in Units =	Fixed Costs + Target Profit	× Percentage of Sales Mix
	Weighted Average Contribution Margin

In the given question:

Particulars	Faucet	Pitcher	Total
Sales PU	$70	$80	$150
Variable Cost PU	$30	$45	$75
Contribution PU	$40	$35	$75
% of mix	57%	43%	100%
Fixed cost			$424,000
Target Profit			$212,000

Contribution Per unit is Sales less Variable cost per unit. % of mix is 4/7 for Faucet and 3/7 for Pitcher

Weighted Average Contribution = ($40 x 57%) + ($35 x 43%) = $37.86

Target profit units of Faucet = {($424,000+$212,000)/$37.86} x 57% = 9,600 units.

Target Profit units of Pitcher = {($424,000+$212,000)/$37.86} x 43% = 7,200 units.