
Concept explainers
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
- 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.
- If the company uses the new material, determine its new break-even point in both sales units and sales dollars of each individual product.
- What insight does this analysis offer management for long-term planning?

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
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-
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 |

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
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-
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 |

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
As per new policy:
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Chapter 5 Solutions
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