Problem 13.14 (14.14 in new text)
Subject: Reverse Gradient Question
I was looking over the economic problems, and have a problem. The problem in question starts with an unknown P, and then the payments decrease, rather than increase by G. So, it’s clearly a gradient, but one where the amount decreases.
Do you just put in negative G value, or do we need another formula which will be some sort of decreasing gradient?
Thanks for your help.
No, unfortunately, the equations are very specific, and very unforgiving. If your cash flow diagram doesn’t look exactly like the one used in the derivation, it won’t work. So, have you ever heard of superposition? Where you take something you don’t want (like an “A”) and add something else to it (like a “G”), to turn the whole mess into something you want?
In other words you pretend that you have an A = -$100 from year 1 to 6. Not true, but we can fix it. Then you correct it with a Gradient of +$10 starting at year 2 which will end up at +$50 by year 6. The result? The positive G cancels out some of the unwanted negative A, giving you the cash flow diagram you want.