However, if either the actual results or the budget is negative, I don't know how to compute the index. For example, if the actual was ($100) and the budget was $50 what is the index?

Using the "old" math it would be a (200%) but this doesn't really make sense. The actual is actually 3 times worse than budget so I'd think the answer would be (300%).

Also, a convention is that if actual equals budget then the index is 100%. For example, if actual = ($100) and budget = ($100) then the index is 100%. In this structure, what would the index be if the actual was $0, or some would say 1 times better than budget hence shouldn't it be 100% too??

Where can I go to get help with this?

Thanks

Darrell Boomgaarden

Your notion of index is entirely man-made, by which I mean that there is no compelling reason to go one way rather than another beyond what is suggested by you intuition and business sense.

However you define your index, it must not be given by the same formula in all possible cases. E.g., from what you wrote I sense you won't be comfortable with a negative index in case of a positive actual and a negative budget, right? Something that goes way beyond your expectations must be big, very big, not negative.

The best advice I can give you is to not seek a single math expression that works in all cases. Formulas may be different depending on the signs of quantities involved. Or, perhaps, to describe a situation fully you need more than one attribute.

You may want to contact Edward MacNeal at macneal@erols.com, an expert on mathsemantics and business consultant.