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Expert: - 10/2/2009


Question
Can you tell me the formula that will provide the practically and intuitively meaningful results for a series of possible scenarios?

Take four companies:
A Inc. Last year made a loss of -$500. This year it made profits of $500.
B Inc.  Last year made a loss of -$50. This year it made profits of $500.
C Inc.  Last year made a loss of -$500. This year it made profits of $250.
D Inc.  Last year made a loss of -$500. This year it made profits of $1,000.

I need to express the improved profitability of each, as a percentage
value, in such a way that the result reflect the relative
improvement; i.e. the best turnabout is D which reversed a -$500 loss
and achieved a profit twice that of its previous loss. The smallest
turnabout was B which started from a more modest loss of -$50.
The order, when ranked in percentage terms needs to display the
companies as biggest turnaround to smallest as D, A, C, B

The problem I face, is that using the conventional solution for
dividing by a negative number and converting positive and negative
values, is that I get results that suggest B made the biggest
percentage change.

Is there another formula that can be applied when calculating a
change from a negative base?

Many thanks for your help.


Answer
Take the amount gained over the amount lost (make the amount lost positive).
Also, you might want to divide the amount gained by some inerest rate, say 1.05 or something.

THis would give you
A: 500/500 = 1,
B: 500/50 = 10,
C: 250/500 = 1/2 = 0.5, and
D: 1,000/500 = 2.

So of the numbers 1, 10, 0.5, and 2, 10 is clearly the greatest.
So not only is B the smallest loss, it gets the biggest bang for the buck.
B is clearly the optimum choice.

If the profit for B were only 50, then it could be seen that 50/50 = 1, so in this case,
D would be the optimum choice, but its not, so its B.

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