Question

9) A firm is selling two products, chairs and bar stools, each at $50 per unit. Chairs have a variable cost of $25, and bar stools $20. Fixed cost for the firm is $20,000. a. If the sales mix is 1:1 (one chair sold for every bar stool sold), what is the break-even point in dollars of sales? In units of chairs and bar stools? (Round your unit answers to a whole number before calculating the breakeven point and round the break-even point to the nearest whole number.) b. If the sales mix changes to 1:4 (one chair sold for every four bar stools sold), what is the break-even point in dollars of sales? In units of chairs and bar stools? (Round your unit answers to a whole number before calculating the breakeven point and round the break-even point to the nearest whole number.)

Answer 1

Ans.

a) BEP (units) =727; BEP($)= $36,350

b) BEP (units) =690; BEP($)=$34,500

Step-by-step explanation:

Hi, in order to find the break even point in units, we have to use the following equation in both cases.

`BEP(Units)=(Fixed Costs)/((AveragePrice-Average VariableCost))`

Since the sales mix is different in both scenarios, let´s find the average variable cost for a) (notice that there is no need to find the average price because both, the stool and the chair have the same price)

`AverageVariableCost=25*(1)/(2) +20*(1)/(2) =22.5`

Now, the fraction aside each of the price is 1/2 in both cases, because the sale mix 1:1 means that the company makes 1 stool for every chair it makes, in fraction that is, for every 2 items that the company makes, 1 is a stool (1/2) and 1 is a chair (1/2).

So, our BEP in units is:

`BEP(Units)=(20,000)/((50-22.5)) =727`

`BEP(Dollars)=727*50=36,350`

That means that the company has to make 727 units, which 363 are chairs and 364 are stools (you could say 364 chairs and 363 stools too, because we are heavily rouding numbers). This is represented in $36,350 in sales.

Now, for b), our average cost is:

`AverageVariableCost=25*(1)/(5) +20*(4)/(5) =21`

As you can see, the fraction changed, that is because of the new sales mix of 1:4, that is: the company makes 4 stool for every chair it makes, in fraction that is, for every 5 items that the company makes, 4 are a stools (4/5) and 1 is a chair (1/5).

Now, let´s find our new BEP in units and dollars.

`BEP(Units)=(20,000)/((50-21)) =690`

`BEP(Dollars)=690*50=34,500`

That means that the company has to make 690 products, which 138 are chairs and 552 are stools. This is represented in $34,500 in sales.

Best of luck.