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Math Help - Rearranging to find IRR

  1. #1
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    Post Rearranging to find IRR

    Hi All..

    I just needed some help solving a question to find the internal rate of return (IRR). I have attached the problem.

    How do I find IRR from the equation?

    I have the solution of 13.45%

    Thank you
    Attached Thumbnails Attached Thumbnails Rearranging to find IRR-irr.gif  
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by dadon View Post
    Hi All..

    I just needed some help solving a question to find the internal rate of return (IRR). I have attached the problem.

    How do I find IRR from the equation?

    I have the solution of 13.45%

    Thank you
    first combine the fractions on the right and multiply the left by \frac {(1 + IRR)^5}{(1 + IRR)^5}, we get:

    \frac {10000(1 + IRR)^5}{(1 + IRR)^5} = \frac {2000(1 + IRR)^4 + 2500(1 + IRR)^3 + 3000(1 + IRR)^2 + 3500(1 + IRR) + 4000}{(1 + IRR)^5}

    now, since the denominators are the same on both sides, we can just equate the numerators, to get:

    10000(1 + IRR)^5 = 2000(1 + IRR)^4 + 2500(1 + IRR)^3 + 3000(1 + IRR)^2 + 3500(1 + IRR) + 4000

    haha, we could have gotten this by multiplying through by (1 + IRR)^5 . an easier way. can you finish?
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    Hey
    Thanks for your reply

    Ok I expanded the brackets dividing the whole thing by 1000 first
    ...very tedious method used Pascals triangle

    Then I collected the like terms together this is what I got.. (I hope I didnít make a mistake!!)

    25IRR + 7.51RR^2 + 89.5IRR^3 + 48IRR^4 + 10IRR^5 Ė 4001 = 0

    Then divided the whole thing by 0.5
    50(IRR) + 155(IRR)^2 + 179(IRR)^3 + 96(IRR)^4 + 20(IRR)^5  - 8002 = 0

    LOL after all that Iím still nowhere close to the answer 13.45%...
    Iím I going the right way about this.. surely there is a simpler method?
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    Hey All..

    Sorry I think the example I gave before was abit tedious on here.. I have found a better one which I have attached..

    The question is still the same how do I find IRR?

    Thank you
    Attached Thumbnails Attached Thumbnails Rearranging to find IRR-irr2.gif  
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  5. #5
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by dadon View Post
    Hey All..

    Sorry I think the example I gave before was abit tedious on here.. I have found a better one which I have attached..

    The question is still the same how do I find IRR?

    Thank you
    the same approach as above will work, except you end up with a quadratic equation, which is easier to manage
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    Quote Originally Posted by Jhevon View Post
    the same approach as above will work, except you end up with a quadratic equation, which is easier to manage
    Hey

    Ok I tried what you said

    It gives me this equation:
    6000(IRR) + 4000(IRR)^2 - 2000 = 0
    3(IRR) + 2(IRR)^2 - 1 = 0

    and I get the answer 0.2808 and -1.7808

    Thank you
    Last edited by dadon; April 6th 2009 at 06:20 AM. Reason: found right anwer.. plugged in wrong value
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  7. #7
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    Hey me again :P

    Ok I get the quadratic stage.. but normally the powers are high like the first example posted.. how do I solve for higher powers..Is there like a way to do it on calculator?

    are there more formulas?

    Thank you
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  8. #8
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by dadon View Post
    Hey
    Thanks for your reply

    Ok I expanded the brackets dividing the whole thing by 1000 first
    ...very tedious method used Pascals triangle

    Then I collected the like terms together this is what I got.. (I hope I didn’t make a mistake!!)

    25IRR + 7.51RR^2 + 89.5IRR^3 + 48IRR^4 + 10IRR^5 – 4001 = 0

    Then divided the whole thing by 0.5
    50(IRR) + 155(IRR)^2 + 179(IRR)^3 + 96(IRR)^4 + 20(IRR)^5  - 8002 = 0

    LOL after all that I’m still nowhere close to the answer 13.45%...
    I’m I going the right way about this.. surely there is a simpler method?
    that is not right. dividing through by 100 and expanding everything, we get:

    100(IRR)^5 + 480(IRR)^4 + 895(IRR)^3 + 775(IRR)^2 + 250(IRR) - 50 = 0

    i am sorry, but i do not see a nice way to solve this. there is no general formula for solving general polynomials of degree 5 or above. and this guy does not look like a nice guy to factor.

    Quote Originally Posted by dadon View Post
    Hey me again :P

    Ok I get the quadratic stage.. but normally the powers are high like the first example posted.. how do I solve for higher powers..Is there like a way to do it on calculator?

    are there more formulas?

    Thank you
    so yeah, there is no general formula for solving quintic polynomials. if you can use technology for this, do so. otherwise, this question is just mean.
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    Quote Originally Posted by Jhevon View Post
    that is not right. dividing through by 100 and expanding everything, we get:

    100(IRR)^5 + 480(IRR)^4 + 895(IRR)^3 + 775(IRR)^2 + 250(IRR) - 50 = 0

    i am sorry, but i do not see a nice way to solve this. there is no general formula for solving general polynomials of degree 5 or above. and this guy does not look like a nice guy to factor.

    so yeah, there is no general formula for solving quintic polynomials. if you can use technology for this, do so. otherwise, this question is just mean.
    LOL haha.. Thanks! really appreciate the help
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