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Profit down 20%, costs up 10%, so % change in revenues =?

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Profit down 20%, costs up 10%, so % change in revenues =? [#permalink] New post 02 Apr 2011, 05:09
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If profits are down 20%, and costs are up 10%, how do we know sales must be down 10%?

This is just one part of a larger case interview question but I just can't figure it out. I'd think the ratio of new revenues to new costs should factor into the calculation but I've run into this in a mock interview and a case that I read online, and both times they assumed this was a very simple calculation that was independent of the actual costs and revenues. Can anyone explain why?
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Re: Profit down 20%, costs up 10%, so % change in revenues =? [#permalink] New post 03 Apr 2011, 22:31
I don't think you can come to the conclusion that sales MUST be down 10%... there is a piece of information missing here. I'm thinking the margin, and maybe the equation they are working with... I am assuming you are working with the very basic equation of:
Profits = Sales - Cost

Lets try thinking this out loud:


profits = sales - cost

lets say profits last period were 100. Sales 200, Cost 100.

profits down 20% = profits 80 in current period.
Costs up 10% = costs 110 in current period.
X = Sales

80 = X - 110
X = 190 = Sales

That looks like 5% to me...

but look at this scenario:

Profit = Sales - Costs
100 = 1000 - 900

80 = X - 990
X = 1070, Sales go up 7% here.....


but what do I know... derp...
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Re: Profit down 20%, costs up 10%, so % change in revenues =? [#permalink] New post 04 Apr 2011, 10:08
Taking a preschool approach, its sounds like someone is saying 20% of profits have disappeared, we know that 10% of it is attributable to higher costs, therefore the other 10% must be attributable to lower sales since that's the remaining variable in play.

But if it's phrased as posted, then you guys are correct that there is missing information. As posted, the mathematics do not produce a constant.
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Re: Profit down 20%, costs up 10%, so % change in revenues =? [#permalink] New post 01 May 2011, 18:33
% change in revenues could be unknown due to the following reasons:

- change in interest expense
- change in tax rate
- change in FX gain/loss
- ...etc

There are too many line items between gross margin and profit to be able to calculate the % change in revenues.
Re: Profit down 20%, costs up 10%, so % change in revenues =?   [#permalink] 01 May 2011, 18:33
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