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A company sells DVD players for $200 per unit. The players have a unit variable cost of $160. The company estimates that it will sell one home entertainment system for every four DVD players sold. Home entertainment systems have a unit variable cost of $460 and sell for $600 per unit. The company's fixed costs are $90,000. Assuming that the sales mix estimate is correct, how many DVD players need to be sold for the company to break even?

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facundobuzzetti

Answer:

Break-even point= 1,200 DVDs

Explanation:

First, we need to calculate the sales proportion:

DVD= 4/5= 0.8

Home entertainment= 1/5= 0.2

Now, we need to calculate the break-even point for the whole company:

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= (200*0.8 + 600*0.2) - (160*0.8 + 460*0.2)

Weighted average contribution margin= 60

Break-even point (units)= 90,000/60= 1,500

Finally, the number of DVDs:

DVD= 1,500*0.8= 1,200 DVDs

DVD players need to be sold for the company to break even point :

Formula :

  • Break-even point (units)= Total fixed costs / Weighted average contribution margin
  • Break-even point (units)= 90,000/60
  • Break-even point (units)= 1,500

Therefore, the number of DVDs:

  • DVDs= Break-Even Point-Sales Proportion
  • DVD= 1,500*0.8
  • DVD= 1,200 DVDs

                                            Working Notes  :

  • Sales Proportion:

DVD= 4/5= 0.8

Home entertainment= 1/5= 0.2

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

  • Weighted average contribution margin= (200*0.8 + 600*0.2) - (160*0.8 + 460*0.2)
  • Weighted average contribution margin= 60

 

DVD players need to be sold for the company to break even is 1200DVDs.

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