Gofigure2 ?
A couple of these questions have at least two answers ? one based on
units and one based on sales revenues. In fact, there?s a third
potential answer to question #1 based on profitability.
SALES MIX ? VOLUME
The store sells 480 computers each year, with 120 high quality (HQ)
and 360 medium quality (MQ). By volume the mix is:
MQ : 75%
HQ : 25%
SALES MIX ? REVENUES
The mix is different if analyzed by revenues because of the different prices:
MQ: 300 * 360 = $108,000 ; $108,000/$168,000 = 64.3%
HQ: 500 * 120 = $60,000; $60,000/$168,000 = 35.7%
SALES MIX ? PROFITABILITY
Your account would say that neither revenue nor volume mixes count
(even though they do if you?re deciding what to advertise; how to
attract new customers; how to predict accessory or service revenues;
and dozens of other management decisions). Look at your profitability
mix, the accountant would say:
Gross margin, MQ = $300 - $135 - $15 = $150
Gross margin, HQ = $500 - $275 - $25 = $250
Gross profits, MQ = $150 * 360 = $54,000; $54,000/$84,000 = 64.3%
Gross profits, HQ = $250 * 120 = $30,000; $30,000/$84.000 = 35.7%
It matches your revenue sales mix ONLY because both MQ and HQ
computers have the same contribution margin of 50% (contribution
margin = gross margin/sales price). Because contribution margins are
rarely identical in the real world, having a profitabiity mix match
revenue mix is rare.
---
BREAK EVEN SALES VOLUME
This question has a single answer ? only because the contribution
margin is 50%. If the two lines of computers had different margins,
there would be several possible answers.
Each dollar sold is generating 50% in contribution. $100,000 in sales
generates $50,000 in contribution dollars. What will it take to get
$65,000 in contribution to cover fixed costs?
$65,000 = Sales * 0.50; Sales = $130,000
***
A second way to look at this is to take existing sales of $168,000;
profits of $19,000 and ask ? ?how much would sales decrease to erase
the $19,000 net profit??
$19,000 = Sales decrease * 0.50
Sales decrease = $38,000 ? so that if revenues dropped from $168,000
to $130,000 the company would be back at break-even
---
TARGET NET INCOME
To get to a net income of $48,750, revenues will need to be at:
$48,750 = [(0.50) * Sales] - $65,000
$113,750 = 0.50 * Sales
Sales = $227,500
MQ: we could sell only MQ models, then we?d need 759 to hit the target
HQ: we could sell only HQ models, then we?d need to sell only 455 systems
As you can tell, depending on the mix, there are a large number of
potential answers here.
But let?s go back to the original volume assumptions of 75%-25% --
0.75 * $300 * x + 0.25 * $500 * x = $227,500
$225x + $125x = $227,500; x = 650
So, selling 650 computers in a mix of 75% MQ and 25% HQ would hit your target.
Note that we could recalculate the number of computers based on the
REVENUE MIX ? and get yet another answer. But there are lots of
potential answers to this one: you could arbitrarily assume that 50 HQ
computers get sold and calculate another total to produce the net
income of $48,750.
Best regards,
Omnivorous-GA |
Clarification of Answer by
omnivorous-ga
on
08 Aug 2005 00:48 PDT
Gofigure2 --
The 0.50 represents the contribution margin, which is the same for
each computer. The 0.25 and the 0.75 represents the weighting of each
(75%-25%).
Your 700 computers are too many -- they produce a profit of $57,500 --
525 MQ = $87,500
175 HQ = $157,500
Contribution margin = $122,500
Net profit = $122,500 - $65,000 = $57,500
--
The number 650 doesn't split well -- we end up with 1/2 computer of
each type. But we'll round numbers up:
MQ: 487 * $300 = $146,100
HQ: 163 * $500 = $81,500
Contribution margin = 0.50 * $227,600 = $113,800
Net profit = $113,800 - $65,000 = $48,800
That's $50 more profit than required -- but it's as close as you'll
get with the 75%-25% split.
Best regards,
Omnivorous-GA
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