It?s helpful in this situation to understand the contribution margin
for each product, as it tells you what the gross profits are for each:
?Contribution margin,? (undated)
Contribution margins for each product are:
Thus, at the volumes stated, each of the products is producing the
following contribution to all overhead costs:
#1: $10 * 50,000 units = $500,000
#2: $20 * 50,000 units = $1,000,000
#3: $17 * 100,000 units = $1,700,000
Total gross profits are $3,200,000. But for net income we have to
subtract the overhead and taxes:
Gross profits . . . . $3,200,000
Mfrg overhead . . . $2,000,000
Fixed admn/sales . $ 600,000
Profit before tax . . $ 600,000
Taxes (@ 40%) . . $ 240,000
NET INCOME . . . $ 360,000
So that?s your budget net income for this year and next: $360,000.
One of the reasons that contribution margin is so useful is that it
gives you the sensitivity that changes in your sales will have on
profits. It?s easiest to look at profit before tax because at
breakeven, you?ll pay no tax.
Three examples here:
#1: What if sales of product #1 drop by 50,000 units? It?s
contributing $500,000 in profits ? so the firm would still be
marginally profitable, making $2.7 million on the other 2 products and
covering all fixed costs.
#2: What if sales of product #2 drop by 30,000 units to only 20,000
sold? The lost 30,000 units would contribute $600,000 ? putting the
firm at breakeven.
So, this is one of an infinite number of solutions for breakeven:
50,000 units of #1; 20,000 units of #2; and 100,000 units of #3.
#3: What if sales of product #3 drop by 35,294 units to only 64,706?
The profits would drop by $599,998 ? so the firm would be at ?virtual
breakeven.? (I realize that it would make $2.) So that?s another
solution: 50,000 units of #1 and #2 and 64,706 of #3.
And, of course, we can change any of the volumes for each product to
decrease the profit before taxes by $600,000, providing an infinite
number of solutions.
Google search strategy:
Clarification of Answer by
25 Jul 2005 09:26 PDT
If the mix is to remain the same in UNITS, then it becomes a question
of what equal volume drop erases the $600,000 gross profit. Note that
because the sales prices are all different, this will change the mix
percentages in REVENUES.
So the question is, what is X when we have a contribution of the
following producing $600K in gross profits? (And will we be lucky
enough to have it come out to an even number?)
$10 * x + $20 * x + $17 * x = $600,000
$47 * x = $600,000; x = 12,766 (actually this produces a $2 loss
because the units don?t divide evenly)
So, if volumes drop to the following levels, you preserve your mix in
units but are at breakeven:
#1: 50,000 ? 12,766 = 37,234
#2: 50,000 ? 12,766 = 37,234
#3: 100,000 ? 12,766 = 87,234