Question

Patriot Co. manufactures and sells three products: red, white, and blue. Their unit selling prices are red, \(20; white, \)35; and blue, \(65. The per unit variable costs to manufacture and sell these products are red, \)12; white, \(22; and blue, \)50. Their sales mix is reflected in a ratio of 5:4:2 (red:white:blue). Annual fixed costs shared by all three products are \(250,000. One type of raw material has been used to manufacture all three products. The company has developed a new material of equal quality for less cost. The new material would reduce variable costs per unit as follows: red, by \)6; white, by \(12; and blue, by \)10. However, the new material requires new equipment, which will increase annual fixed costs by $50,000. (Round answers to whole composite units.)

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.

Analysis Component

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

Short answer

Answer

1. Break-even point in dollars:$758,500

2. Break-even point in dollars after a change in the price of raw material:$504,680

3. Analysis suggests to management that new material must be used so that the break-even point can be achieved by selling fewer units.

Step-by-step solution

Definition of Variable Cost

The cost incurred by the business entity will increase or decrease as per a change in the level of activity, known as a variable cost. It includes costs such as direct material and direct labor.

Calculation of break-even point

Sales proportion of each product:

Product	Proportion	X	Selling price	=	Selling price per composite unit
Red	5	X	$20	=	$100
White	4	X	$35	=	$140
Blue	2	X	$65	=	$130
					$370

Product	Proportion	X	Variable cost	=	Variable cost per composite unit
Red	5	X	$12	=	$60
White	4	X	$22	=	$88
Blue	2	X	$50	=	$100
					$248

Contribution margin per composite unit:

Particular	Amount $
Sales price per composite unit	$370
Less: variable cost per composite unit	(248)
Contribution margin per composite unit	$122

Break-even point in units:

$$\begin{gathered} Break-even=\frac{\mathrm{Fixed}\mathrm{cost}}{\mathrm{Contribution}\mathrm{margin}\mathrm{composite}\mathrm{unit}} \\ =\frac{\$250,000}{\$122} \\ =2,050units \end{gathered}$$

Product	Composite unit	X	Proportion	=	Break-even in units
Red	2,050	X	5	=	10,250
White	2,050	X	4	=	8,200
Blue	2,050	X	2	=	4,100

Break-even in dollars:

Product	Break-even in units	X	Selling price	=	Break-even in dollars
Red	10,250	X	$20	=	$205,000
White	8,200	X	$35	=	$287,000
Blue	4,100	X	$65	=	$266,500
					$758,500

Break-even point after a change in the price of raw material

Calculation of composite selling price:

Product	Proportion	X	Selling price	=	Selling price per composite unit
Red	5	X	$20	=	$100
White	4	X	$35	=	$140
Blue	2	X	$65	=	$130
					$370

Calculation of composite variable cost:

Product	Proportion	X	New Variable cost	=	Variable cost per composite unit
Red	5	X	$6	=	$30
White	4	X	$10	=	$40
Blue	2	X	$40	=	$80
					$150

Contribution margin per composite unit:

Particular	Amount $
Sales price per composite unit	$370
Less: variable cost per composite unit	(150)
Contribution margin per composite unit	$220

Break-even point in units:

$$\begin{gathered} Break-evenpoint=\frac{Fixed\cos t}{Contributionmarginpercompositeunit} \\ =\frac{\$300,000}{\$220} \\ =1,364units \end{gathered}$$

Product	Composite unit	X	Proportion	=	Break-even in units
Red	1,364	X	5	=	6,820
White	1,364	X	4	=	5,456
Blue	1,364	X	2	=	2,728

Break-even in dollars:

Product	Break-even in units	X	Selling price	=	Break-even in dollars
Red	6,820	X	$20	=	$136,400
White	5,456	X	$35	=	$190,960
Blue	2,728	X	$65	=	$177,320
					$504,680

Insight provided by the above analysis

The above analysis provides information that reducing the material price increases the contribution margin, allowing a business entity to achieve a break-even point by selling fewer units.