Question

Patriot Co. manufactures and sells three products: red, white, and blue. Their unit selling prices are red, $45, white, $75, and blue, $100. The per unit variable costs to manufacture and sell these products are red, $30, white, $50, and blue, $70. Their sales mix is reflected in a ratio of 4:5:2 (red white blue). Annual fixed costs shared by all three products are $140,000. 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 $7: white, by $17, and blue, by $7. However, the new material requires new equipment, which will increase annual fixed costs by $10,000. Required: 1. Assume 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. (Round composite units up to next whole number.) 1. Determine its break even point in both sales units and sales dollars of each individual product Determine the selling price per composite unit. Ratio Selling price per unit Total per composite unit White Blue 57 21 Determine the variable costs per composite init. Variable cost per unit otal per composite White Determine the break even point in composite unit Choose Numero Choose Denominator - Break Even Units Break even units Determine its break even point in units and sales dollars of each individual product Number per Number of composte units to Unithe composite break even break even point De break even point Prey 4 of 4 !!! Next

Answer 1

1) Calculation of break even point at old prices:

Given that:

Products	Variable cost	Sales MIx	Selling Price
Red	30	4/11	45
White	50	5/11	75
Blue	70	2/11	100

Fixed Cost = $140,000

Step 1: Calculate the Contribution Margin(CM) for each product

Products	Selling Price - Variable Cost = Contribution Margin
Red	45 - 30 = 15
White	75 - 50 = 25
Blue	100 - 70 = 30

Step 2: Calculate Weighted average of CM

Products	Sales Mix	Cont. Margin	Sales Mix * CM
Red	4/11	15	60/11
White	5/11	25	125/11
Blue	2/11	30	60/11

Total Weighted average of CM = 245/11

Step 3: Calculate Breakeven point

breakeven point

= fixed cost / Total weight CM

= 140,000 / 245/11

= 6,286

Products	Sales Mix	Breakeven Point	Sales (units)	Selling Price ($)	Sales ($)
Red	4/11	6286	2286	45	102,870
White	5/11	6286	2857	75	214,275
Blue	2/11	6286	1143	100	114,300

1) Calculation of break even point at new prices:

Given that:

Products	Variable cost	Sales MIx	Selling Price
Red	23	4/11	45
White	33	5/11	75
Blue	63	2/11	100

Fixed Cost = $150,000

Step 1: Calculate the Contribution Margin(CM) for each product

Products	Selling Price - Variable Cost = Contribution Margin
Red	45 - 23 = 22
White	75 - 33 = 42
Blue	100 - 63 = 37

Step 2: Calculate Weighted average of CM

Products	Sales Mix	Cont. Margin	Sales Mix * CM
Red	4/11	22	88/11
White	5/11	42	210/11
Blue	2/11	37	74/11

Total Weighted average of CM = 372/11

Step 3: Calculate Breakeven point

breakeven point

= fixed cost / Total weight CM

= 150,000 / 372/11

= 4,435

Products	Sales Mix	Breakeven Point	Sales (units)	Selling Price ($)	Sales ($)
Red	4/11	4,435	1612	45	72540
White	5/11	4,435	2016	75	151,200
Blue	2/11	4,435	806	100	80,600