You examine the financial statements of a firm and find that for every unit of P

Question

You examine the financial statements of a firm and find that for every unit of Product X sold, the firm sells 4 units of Product Y. For example, if the firm sold 100 units of X, it would see 400 of Y. The sales price and variable cost per unit for Product X are $100 and $70, respectively; the sales price and variable cost per unit for Product Y are $80 and $60, respectively.

a. 1.Assuming a constant product mix and fixed costs of $550,000, how many of each product line must be sold to break even?

b. 2.What is total sales revenue (in dollars) at the break-even point? Show your work.

Explanation / Answer

Hi,

Please find the answer as follows:

Part A:

Contribution Per Unit of X = 100 - 70 = 30

Contribution Per Unit of Y = 80 - 60 = 20

Weighted Contribution = Proportion of X*Contribution Per Unit of X + Proportion of Y*Contribution Per Unit of Y = 1/5*30 + 4/5*20 = 22

Break Even Points (Total) = Fixed Cost/Weighted Contribution = 550000/22 = 25000 Units

Product X Sales at Break Even Point = Break Even Points (Total)* Proportion of X = 25000*1/5 = 5000

Product Y Sales at Break Even Point = Break Even Points (Total)* Proportion of Y = 25000*4/5 = 20000

Part B:

Value of Break Even Sales = Units of X*Sales Price + Units of Y*Sales Price = 5000*100 + 20000*80 = 2100000

Thanks.

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