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Math Help - Interest rate that gives a net present value of zero.

  1. #1
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    Post Interest rate that gives a net present value of zero.

    A project has cash flows of -$12,000 in Year 1, +$5000 in Years 2 and 3, -$2000 in Year 4, and +$6000 in Years 5 and 6. Find the interest rate that gives a net present value of zero?

    The answer is provided to me, it is 19.2%.
    I would like to see what the process was to get that answer
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  2. #2
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    wrong forum i think.

    You did not say whether the casflows happen at the start or the end of each year. I will assume they happen at the start of each year.

    Using standard notation
    i = annual interest rate
    v=1/(1+i)

    you want to solve PV = 0
    -12000 + 5000v + 5000v^2 -2000v^3 + 6000v^4 + 6000v^5 = 0

    Use trial and error. For a first guess i will use 10%
    @ 10%: PV = 2099
    @ 20%: PV = -213

    So the answer is between 10% and 20%. it looks closer to 20%

    @18%: 328
    @19%: 51.98

    So the answer is between 19% and 20%

    Keep going and you will get 19.2%
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  3. #3
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    If 19.2%, then flows are at end, so:
    -12000v + 5000v^2 + 5000v^3 - 2000/v^4 +6000/v^5 + 6000/v^6 = 0

    As SFan told you, can't be calculated directly: so "hit and miss!".
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  4. #4
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    If 19.2%, then flows are at end,
    in fact, it doesn't matter

    for cashflows at the start of each period you solve:
    (A)~~-12000 + 5000v + 5000v^2 -2000v^3 + 6000v^4 + 6000v^5 = 0

    For cashflows at the end of each period you solve

    (B)~~-12000v + 5000v^2 + 5000v^3 -2000v^4 + 6000v^5 + 6000v^6 = 0
    But, this factorises to (A)
    (B)~~~v(-12000 + 5000v+ 5000v^2 -2000v^3 + 6000v^4 + 6000v^5) = 0

    We know v is not 0, so any solution of B is also a solution of A. You can actually shift the payments by any (constant) length of time and it still works, provided that all payments are shifted by the same amount.
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  5. #5
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    Agree; shudda known!
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