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Math Help - Internal Rate of Return/Variables and Exponents

  1. #1
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    Internal Rate of Return/Variables and Exponents

    Hey guys,

    I've been out of school for some time and I'm just getting back into the groove. I need a quick refresher....

    I'm working on Internal Rates of Returns with long term cash flows and I'm very, very rusty on working with exponents and unknown variables. Basically the problem looks like this:

    26,000,000/(x+1)+26,000,000/(x+1)^2+26,000,000/(x+1)^3+26,000,000/(x+1)^4+26,000,000/(x+1)^5=73,000,000

    I have to solve for x. Any and all help will be GREATLY appreciated!
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  2. #2
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    Quote Originally Posted by Cleg22 View Post
    Hey guys,

    I've been out of school for some time and I'm just getting back into the groove. I need a quick refresher....

    I'm working on Internal Rates of Returns with long term cash flows and I'm very, very rusty on working with exponents and unknown variables. Basically the problem looks like this:

    26,000,000/(x+1)+26,000,000/(x+1)^2+26,000,000/(x+1)^3+26,000,000/(x+1)^4+26,000,000/(x+1)^5=73,000,000

    I have to solve for x. Any and all help will be GREATLY appreciated!

    First of all, divide both sides by 1,000,000 so that it's nicer to look at.

    After this, you can multiply both sides by (x+1)^5 to get rid of denominators and you will be left with a polynomial of degree 5.

    In addition, you can substitute y = x + 1, solve for y, then subtract one from y to recover x.

    I don't know how straightforward solving the quintic in y will be, and what tools you have available, but possibly it will factor easily and/or there will be rational roots you can find through trial/error, otherwise you might need some sort of computing device, like a graphing calculator or Mathematica, to find roots.

    As a final note, if you find that x = -1 is a solution, you'll have to exclude it from your solution list because that would make the denominators in the original problem equal to zero.
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