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 :)

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.

Thanks, Rehmanvohra, I do appreciate it. When I looked back on my answer a bit after the fact, it seemed kind of 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 :))

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! :)

Hello ArcSine:

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

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".

When I looked back on my answer a bit after the fact, it seemed kinda clumsy, and a cleaner exposition came immediately to mind.

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.