Chapter 5, Problem 7PSA

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 5:4:3 (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 answer 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.
3. What insight does this analysis offer management for long-term planning?

To determine

Concept introduction:

A contribution margin income statement is a statement which shows the profit or loss for a entity for a particular product or overall performance.

The contribution margin ratio means calculated contribution in terms of percentage. The numerator part will be contribution amount and denominator part will net sales.

The break-even point formula is calculated as the total fixed cost of production part in numerator and price per unit less the variable costs to produce the product in denominator.

Requirement 1:

The break -even sales in units and dollars.

Answer to Problem 7PSA

$\begin{array}{l}Break\text{ even points in composite units }=\text{ Total fixed costs/ contribution margin per unit}\\ =250,000/122=2050units\end{array}$

Calculation of break even points in units and sales dollar of each individual product-:

Particulars	Ratio	Number of composite units to break even	Units sales at the break-even point	Dollar sales at the break-even point
Red	5	2050	10, 250	205, 000
White	4	2050	8, 200	287, 000
Blue	2	2050	4, 100	266, 500

Explanation of Solution

Calculation of selling price per unit- $$

Particulars	Ratio	Selling price per unit($)	Total per composite unit($)
Red	5	20	100
White	4	35	140
Blue	2	65	130
			370

Calculation of variable cost per unit-

Particulars	Ratio	Variable cost per unit($)	Total per composite unit($)
Red	5	12	60
White	4	22	88
Blue	2	50	100
			248

Calculation of break even points in composite units-

$\begin{array}{l}Break\text{ even points in composite units }=\text{ Total fixed costs/ contribution margin per unit}\\ =250,000/122=2050units\end{array}$

Calculation of break even points in units and sales dollar of each individual product-:

Particulars	Ratio	Number of composite units to break even	Units sales at the break-even point	Dollar sales at the break-even point
Red	5	2050	10, 250	205, 000
White	4	2050	8, 200	287, 000
Blue	2	2050	4, 100	266, 500

To determine

Concept introduction:

A contribution margin income statement is a statement which shows the profit or loss for a entity for a particular product or overall performance.

The contribution margin ratio means calculated contribution in terms of percentage. The numerator part will be contribution amount and denominator part will net sales.

The break-even point formula is calculated as the total fixed costs of production part in numerator and price per unit less the variable costs to produce the product in denominator.

Requirement 2:

The break-even sales in units and dollars.

Answer to Problem 7PSA

$\begin{array}{l}Break\text{ even points in composite units }=\text{ Total fixed costs/ contribution margin per unit}\\ =300,000/220=1364units\end{array}$

Calculation of break even points in units and sales dollar of each individual product-:

Particulars	Ratio	Number of composite units to break even	Units sales at the break-even point	Dollar sales at the break-even point
Red	5	1364	6820	136, 400
White	4	1364	5456	190, 960
Blue	2	1364	2728	177, 320

Explanation of Solution

Calculation of selling price per unit- $$

Particulars	Ratio	Selling price per unit($)	Total per composite unit($)
Red	5	20	100
White	4	35	140
Blue	2	65	130
			370

Calculation of variable cost per unit-

Particulars	Ratio	Variable cost per unit($)	Total per composite unit($)
Red	5	6	30
White	4	10	40
Blue	2	40	80
			150

Calculation of break even points in composite units-

$\begin{array}{l}Break\text{ even points in composite units }=\text{ Total fixed costs/ contribution margin per unit}\\ =300,000/220=1364units\end{array}$

Calculation of break even points in units and sales dollar of each individual product-:

Particulars	Ratio	Number of composite units to break even	Units sales at the break-even point	Dollar sales at the break-even point
Red	5	1364	6820	136, 400
White	4	1364	5456	190, 960
Blue	2	1364	2728	177, 320

To determine

Concept introduction:

A contribution margin income statement is a statement which shows the profit or loss for a entity for a particular product or overall performance.

The contribution margin ratio means calculated contribution in terms of percentage. The numerator part will be contribution amount and denominator part will net sales.

The break-even point formula is calculated as the total fixed costs of production part in numerator and price per unit less the variable costs to produce the product in denominator.

Requirement 3:

To analyze:

Long term planning.

Answer to Problem 7PSA

This will help the management in the long term planning as manager will come to know the break-even point in old as well as new policy and he will be aware that at what unit company is able to realize all its costs.

Explanation of Solution

This will help the management in the long term planning as manager will come to know the break-even point in old as well as new policy and he will be aware that at what unit company is able to realize all its costs.

As per old policy

$\begin{array}{l}Break\text{ even points in composite units }=\text{ Total fixed costs/ contribution margin per unit}\\ =250,000/122=2050units\end{array}$

As per new policy:

$\begin{array}{l}Break\text{ even points in composite units }=\text{ Total fixed costs/ contribution margin per unit}\\ =300,000/220=1364units\end{array}$