Problem 18-7A Break-even analysis with composite units LO P4 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. 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 eac individual product.

Instructions are below.

Explanation:

Giving the following information:

Selling prices:

red= $20

white= $35

blue= $65.

Unitary variable cost:

red= $12

white= $22

blue= $50

Sales proportion:

red= 5/11= 0.46

white= 4/11= 0.36

blue= 2/11= 0.18

Fixed costs= $250,000

1) To calculate the break-even point in units, we need to use the following formula:

Break-even point (units)= Total fixed costs / Weighted average contribution margin

Weighted average contribution margin= (weighted average selling price - weighted average unitary variable cost)

Weighted average contribution margin= (0.46*20 + 0.36*35 + 0.18*65) - (0.46*12 + 0.36*22 + 0.18*50)= 33.5 - 22.44= 11.06

Break-even point (units)= 250,000/11.06= 22,604 units

Sales proportion (units):

red= 0.46*22,604= 10,398

white= 0.36*22,604= 8,137

blue= 0.18*22,604= 4,069

To calculate the break-even point in dollars, we need to use the following formula:

Break-even point (dollars)= Total fixed costs / Weighted average contribution margin ratio

Break-even point (dollars)= 250,000 / (11.06/33.5)

Break-even point (dollars)= $757,233.27

Sales proportion (dollars):

red= 0.46*757,233.27= $348,327.30

white= 0.36*757,233.27= 272,603.98

blue= 0.18*757,233.27= 136,301.99

2)Unitary variable cost:

red= $6

white= $10

blue= $40

Fixed costs= 300,000

Break-even point (units)= Total fixed costs / Weighted average contribution margin

Weighted average contribution margin= (weighted average selling price - weighted average unitary variable cost)

Weighted average contribution margin= (0.46*20 + 0.36*35 + 0.18*65) - (0.46*6 + 0.36*10 + 0.18*40)= 33.5 - 13.56= $19.94

Break-even point (units)= 300,000/19,94= 15,045 units

Sales proportion (units):

red= 0.46* 15,045= 6,921

white= 0.36* 15,045= 5,416

blue= 0.18* 15,045= 2,708

To calculate the break-even point in dollars, we need to use the following formula:

Break-even point (dollars)= Total fixed costs / Weighted average contribution margin ratio

Break-even point (dollars)= 300,000 / (19.94/33.5)

Break-even point (dollars)= $504,012

Sales proportion (dollars):

red= 0.46*504,012= 231,845.52

white= 0.36*504,012= 181,444.32

blue= 0.18*504,012= 90,722.16

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