If A and B account for 60% and 40% of total sales, respectively, and variable costs are 60% and 85% respectively, what is the breakeven point (in sales), given fixed costs of $150,000?

Hello. Im stuck with this question. Please help?

Thanks, michelle

ArcSine

Breakeven occurs when your Contribution Margin (in dollars) exactly equals your total Fixed Costs; in this case, 150K.

Let A, B, and S represent total sales dollars from Product A, Product B, and total Sales combined, respectively.

From the supplied info we know two things: For one, A = 60% x S, and B = 40% x S.

We also know that A's contribution margin, in dollars, is 40% x A, and B's contribution margin is 15% x B. (Remember that Contribution Margin % is (1 minus Variable Cost %).)

Going back to my first statement, we need to set the total Contribution Margin to equal 150K, or...

(0.40)A + (0.15)B = 150,000

Now recall that in the third line above we expressed both A and B in terms of S; that is, A = (0.60)S, and B = (0.40)S. So let's replace 'A' and 'B' in the above Contribution Margin equation, to get an equation with one variable. The equation becomes...

(0.40)(0.60)S + (0.15)(0.40)S = 150,000

Solve for S, and that'll give you the sales dollars S at which total Contribution Margin is exactly 150K. Important: Check your answer! Make sure that for whatever answer you derive, if the contribution margin on 60% of your answer is 40%, and the CM on 40% of your answer is 15%, then your total contribution margin is indeed 150,000.

ArcSine

Thanks, Rehmanvohra, I do appreciate it. When I looked back on my answer a bit after the fact, it seemed kinda clumsy, and a cleaner exposition came immediately to mind. So I'm glad to hear that the original version "worked" (at least for one reader )

michi424

Hello ArcSine:

I just wanted to tell you that you are the bomb! Nobody could figure this out. You should definitely teach accounting. Excellent explanation. Very tricky question though. Thank thank you soooo much!!

michi424

Hello ArcSine:

I also forgot to tell you that my answer was $500,000. Is that right?

ArcSine

Always a pleasure....thanks for the kind words.

Let's confirm that $500K of sales puts us at a breakeven point: We know that 60% of our sales (product A) is throwing off a 40% profit margin, so A's profit at this level of sales would be

500,000 x 0.60 x 0.40 = $120,000.

The other 40% of our sales is generating a 15% profit margin, so B's profit at this sales level is

500,000 x 0.40 x 0.15 = $30,000.

So at total sales of $500,000, A and B together are producing a total profit of $150,000. Since that exactly covers our fixed costs, we're definitely at breakeven.

Looks like we can stamp this one "done".

morgaine300

Oh... if I had a dollar for every time I thought that...

If I had the time I'd like to sit down and re-write and re-write some explanations, until they all make clear sense, and then just paste them in. I started to put some stickies together for this board of a variety of topics, but have never had time to work on it.