Question

R&R Tax Service offers tax and consulting services to individuals and small businesses. Data for fees and costs of three types of tax returns follow. R&R provides services in the ratio of 5:3:2 (easy, moderate, business). Fixed costs total \(18,000 for the tax season. Use this information to determine the (1) selling price per composite unit, (2) variable costs per composite unit, (3) break-even point in composite units, and (4) number of units of each product that will be sold at the break-even point.

Types of return	Fee charged	Variable cost per return
Easy (Form 1040EZ)	\)50	$30
Moderate (Form 1040)	125	75
Business	275	100

Short answer

1. Selling price per composite unit:$1,175.
2. Variable cost per composite unit:$575.
3. Break-even point in composite units:30 units.
4. Break-even point in unitsEasy: 150, Moderate: 90, Business: 60.

Step-by-step solution

Definition of Composite Unit

The combination of the different units of the sales mix according to their proportion in the sales mix is known as a composite unit. It is a unit reflecting the expression of the sales mix.

Selling price per composite unit

Product	Proportion	X	Price per unit	=	Selling price
Easy (Form 1040EZ)	5	X	$50	=	$250
Moderate (Form 1040)	3	X	$125	=	$375
Business	2	X	$275	=	$550
Selling price per composite unit					$1,175

Variable cost per composite unit

Product	Proportion	X	Cost per unit	=	Variable cost
Easy (Form 1040EZ)	5	X	$30	=	$150
Moderate (Form 1040)	3	X	$75	=	$225
Business	2	X	$100	=	$200
Variable cost per composite unit					$575

Break-even point in a composite unit

$\begin{array}{rcl}\mathrm{Break}-\mathrm{even}\mathrm{point}\mathrm{in}\mathrm{composite}\mathrm{units}& =& \frac{\mathrm{Fixed}\mathrm{cost}}{\mathrm{Sales}\mathrm{price}\mathrm{per}\mathrm{composite}\mathrm{unit}-\mathrm{Variable}\mathrm{cost}\mathrm{per}\mathrm{composite}\mathrm{unit}}\\ & =& \frac{\$18,000}{\$1,175-\$575}\\ & =& 30\mathrm{units}\end{array}$

Number of units of each product

Product	Proportion	X	Break-even unit	=	Variable cost
Easy (Form 1040EZ)	5	X	30	=	150
Moderate (Form 1040)	3	X	30	=	90
Business	2	X	30	=	60
Break-even units					300