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

(i know i'm late but the answer's "things about yourself" because you want to list things you're capable of, why you want to open up the business, the amount of money you're putting into it,etc.) i'm guessing you take online school small business, the answers to the quizzes are all over quizlet. just look up your question and type quizlet after it and it'll pop up.