Question

Question: Milano Co. manufactures and sells three products: product 1, product 2, and product 3. Their unit selling prices are product 1, \(40; product 2, \)30; and product 3, \(20. The per unit variable costs to manufacture and sell these products are product 1, \)30; product 2, \(15; and product 3, \)8. Their sales mix is reflected in a ratio of 6:4:2. Annual fixed costs shared by all three products are \(270,000. One type of raw material has been used to manufacture products 1 and 2. The company has developed a new material of equal quality for less cost. The new material would reduce variable costs per unit as follows: product 1 by \)10 and product 2 by \(5. However, the new material requires new equipment, which will increase annual fixed costs by \)50,000.

Required

1. If the company continues to use the old material, determine its break-even point in both sales units and sales dollars of each individual product.

2. If the company uses the new material, determine its new break-even point in both sales units and sales dollars of each individual product. (Round to the next whole unit.)

Analysis Component

3. What insight does this analysis offer management for long-term planning?

Short answer

1. Overall break-even point when old material is used:22,500 units.

2. Overall break-even point when new material is used:17,148 units.

3. Material price reduction led to the company’s break-even point decline.

Step-by-step solution

Definition of Break-Even Units

Break-even units are the number of units a business must sell to cover the total cost, i.e., fixed and variable costs.

Break-even point when old material is used

Calculation of composite sales price:

Production	Selling price	X	Proportion	=	Composite Selling price
1	$40	X	6	=	$240
2	$30	X	4	=	$120
3	$20	X	2	=	$40
					$400

Calculation of composite variable cost:

Production	Variable cost	X	Proportion	=	Composite Selling price
1	$30	X	6	=	$180
2	$15	X	4	=	$60
3	$8	X	2	=	$16
					$256

Calculation of contribution margin per composite unit:

Particular	Amount $
Sales price per composite unit	$400
Less: Variable cost per composite unit	(256)
Contribution margin per composite unit	$144

$\begin{array}{rcl}\mathbf{\text{Break-evenpointinubits}}& \mathbf{=}& \frac{\mathbf{\text{Fixedcost}}}{\mathbf{\text{Contributionmarginpercompositeunit}}}\\ & \mathbf{=}& \frac{\mathbf{\$}\mathbf{270}\mathbf{,}\mathbf{000}}{\mathbf{\$}\mathbf{144}}\\ & \mathbf{=}& \mathbf{1875}\mathbf{}\mathbf{\text{units}}\end{array}$

Break-even point for each product in units:

Production	Break-even point	X	Proportion	=	Composite Selling price
1	1875	X	6	=	11,250
2	1875	X	4	=	7,500
3	1875	X	2	=	3,750
					22,500

Break-even point in dollars for each product:

Production	Break-even in units	X	Sales price per unit	=	Composite Selling price
1	11,250	X	$40	=	$450,000
2	7,500	X	$30	=	$225,000
3	3,750	X	$20	=	$75,000
					$750,000

Break-even point when new material is used

Calculation of composite sales price:

Production	Selling price	X	Proportion	=	Composite Selling price
1	$40	X	6	=	$240
2	$30	X	4	=	$120
3	$20	X	2	=	$40
					$400

Calculation of composite variable cost:

Production	Variable cost	X	Proportion	=	Composite Selling price
1	$20	X	6	=	$120
2	$10	X	4	=	$40
3	$8	X	2	=	$16
					$176

Calculation of contribution margin per composite unit:

Particular	Amount $
Sales price per composite unit	$400
Less: Variable cost per composite unit	(176)
Contribution margin per composite unit	$224

$\begin{array}{rcl}\mathbf{\text{Break-evenpointinunits}}& \mathbf{=}& \frac{\mathbf{\text{Fixedcost}}}{\mathbf{\text{Contributionmarginpercompositeunit}}}\\ & \mathbf{=}& \frac{\mathbf{\$}\mathbf{270}\mathbf{,}\mathbf{000}\mathbf{+}\mathbf{\$}\mathbf{50}\mathbf{,}\mathbf{000}}{\mathbf{\$}\mathbf{224}}\\ & \mathbf{=}& \mathbf{1}\mathbf{,}\mathbf{429}\mathbf{}\mathbf{\text{units}}\end{array}$

Break-even point for each product in units:

Production	Break-even point	X	Proportion	=	Composite Selling price
1	1429	X	6	=	8,574
2	1429	X	4	=	5,716
3	1429	X	2	=	2,858
					17,148

Break-even point in dollars for each product:

Production	Break-even in units	X	Sales price per unit	=	Composite Selling price
1	8,574	X	$40	=	$342,960
2	5,716	X	$30	=	$171,480
3	2,858	X	$20	=	$57,160
					$571,600

Insight provided by the above analysis

The above analysis provides information that the reduction in the material price of products 1 and 2 will bring down the variable cost of the business entity, leaving a higher portion of the sales revenue to cover the fixed cost. It will also decrease the units required to be sold to achieve the break-even point.