Question

Patriot Co. manufactures and sells three products: red, white, and blue. Their unit selling prices are red, $64; white, $94; and blue, $119. The per unit variable costs to manufacture and sell these products are red, $49; white, $69; and blue, $89. Their sales mix is reflected in a ratio of 5:4:2 (red:white:blue). Annual fixed costs shared by all three products are $159,000. 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 $16; and blue, by $6. However, the new material requires new equipment, which will increase annual fixed costs by $29,000. 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. 2. Assume if the company uses the new material, determine its new break-even point in both sales units and sales dollars of each individual product.

Answer 1

1. PATRIOT CO.

Red White Blue

Selling price $64 $94 $119

varaible cost $49 $69 $89

Contribution 15 29 30

ratio 5 4 2

weighted average contribution = (15*5) + ( 29*4) + (30*2)

5+ 4+2

= 75 + 116 +60

11

= 251/11 = $22.82

Weighted average contribution ratio = (15*5) + ( 29*4) + (30*2)

5*64+ 4*94+2*119

= 251/934 = 26.87%

Break-even unit = fixed cost / weighted average contribution

= $159,000/$22.82 = 6,968unit

Red = 5/11* 6,968 = 3,167

White = 4/11* 6,968 = 2,534

Blue = 2/11 * 6,968 = 1,267

Break-even in sales dollar = fixed cost / weighted average contribution ratio

= $159,000/26.87% = $591,738

Red = 5/11* $591,738 = $268,972

White = 4/11* $591,738 = $215,177

Blue = 2/11 * $591,738 = $107,589

2.

Red White Blue

Selling price $64 $94 $119

variable cost $43 $53 $83

Contribution 21 45 36

ratio 5 4 2

weighted average contribution = (21*5) + ( 45*4) + (36*2)

5+ 4+2

= 105 + 180 +72

11

= 357/11 = $32.54

Weighted average contribution ratio = (21*5) + ( 45*4) + (36*2)

5*64+ 4*94+2*119

= 357/934 = 38.22%

Break-even unit = fixed cost / weighted average contribution

= $188,000/$32.45= 5,794unit

Red = 5/11* 5,794 = 2,634

White = 4/11* 5,794 = 2,107

Blue = 2/11 * 5,794 = 1,53

Break-even in sales dollar = fixed cost / weighted average contribution ratio

= $188,000/38.22% = $491,889

Red = 5/11* $491,889 = $223,586

White = 4/11* $491,889 = $178,869

Blue = 2/11 * $491,889 = $89,434

Step-by-step explanation: