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Thread: Internal Rate of Return, Simplifying Equation Help

  1. #1
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    Internal Rate of Return, Simplifying Equation Help

    Hi, I have an Internal Rate of Return question I need help with please.

    I have been given the answer for r, which is 0.208, however I cannot understand how the following equation:

    -300 + -300/(1+r) + 800/(1+r)^2 = 0

    when multiplied by (1+r)^2, becomes:
    300r^2 + 900r - 200 = 0

    Could someone please explain step by step how this is achieved?

    Thanks

    Charlie
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  2. #2
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    Re: Internal Rate of Return, Simplifying Equation Help

    Have you done as advised? Multiplying both sides by (1 + r)^2 ? After you've done that, expand...
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    Re: Internal Rate of Return, Simplifying Equation Help

    That's what I am struggling to do, how would you multiply this by (1+r)^2..... I can't get to 300r^2 + 900r - 200 = 0
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    Re: Internal Rate of Return, Simplifying Equation Help

    So what did you get?

    (If the problem is, as you stated, -300 + -300/(1+r) + 800/(1+r)^2 = 0 multiplied by (1+ r)^2, then the "given" answer, 300r^2 + 900r - 200 = 0, is NOT correct.)
    Last edited by HallsofIvy; Apr 17th 2017 at 09:57 AM.
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    Re: Internal Rate of Return, Simplifying Equation Help

    That's what I thought, it's from a past exam paper at my university.

    I would have made 1/(1+r) = x and then multiplied it out.

    What is the correct answer please?
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    Re: Internal Rate of Return, Simplifying Equation Help

    -300 + -300/(1+r) + 800/(1+r)^2 = 0
    divide every term by $100$ ...

    $-3 - \dfrac{3}{1+r} + \dfrac{8}{(1+r)^2} = 0$

    $\dfrac{1}{1+r} = \dfrac{3 + \sqrt{9 +96}}{16} \implies r = \dfrac{16}{3+\sqrt{105}} - 1 \approx 0.208$
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    Re: Internal Rate of Return, Simplifying Equation Help

    Quote Originally Posted by charlie3 View Post
    I would have made 1/(1+r) = x and then multiplied it out.
    Easier this way: let x = 1+r

    Then divide by 100 (as per Skeeter) to get:
    3x^2 + 3x - 8 = 0

    Solve using quadratic to get x = 1.2078...

    1 + r = 1.2078...
    r = .2078 which is ~20.8%

    Yokay?
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    Re: Internal Rate of Return, Simplifying Equation Help

    I love you all so much.

    Thank you this really helped me!!!!
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    Re: Internal Rate of Return, Simplifying Equation Help

    Save your love for Skeeter!
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