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Thread: Finding value of a series of cashflows

  1. #1
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    Question Finding value of a series of cashflows

    I know that if each side of a comparison date contains the same type of cashflow (both inflow or both outflow), then you can find the value of the cashflows by just adding the accumulated values of all cash flows to the left (and including comparison date) and the present values of all cash flows to the right.

    Example:

    Suppose you have the following cashflows with an annual effective rate of interest of 1%. CF(t) means the cashflow at the end of year t:
    CF(0)=1
    CF(1)=3
    CF(2)=7
    CF(3)=4
    CF(4)=1

    Then the value at time t=2 is

    1*1.01^2+3*1.01+7+4*1.01^-1+1*1.01^-2.

    So, how do you calculate the value of the cashflows if one side of the comparison date contains both cash inflows and outflows? Do you add the difference of the accumulated values of past cash inflows and outflows to the difference of the present values of future cash inflows and outflows? Please let me know if you need clarification of my question. Thanks.

  2. #2
    Actuary.com - Level III Poster (/iropracy's Avatar
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    Quote Originally Posted by promathlete View Post
    I know that if each side of a comparison date contains the same type of cashflow (both inflow or both outflow), then you can find the value of the cashflows by just adding the accumulated values of all cash flows to the left (and including comparison date) and the present values of all cash flows to the right.

    Example:

    Suppose you have the following cashflows with an annual effective rate of interest of 1%. CF(t) means the cashflow at the end of year t:
    CF(0)=1
    CF(1)=3
    CF(2)=7
    CF(3)=4
    CF(4)=1

    Then the value at time t=2 is

    1*1.01^2+3*1.01+7+4*1.01^-1+1*1.01^-2.

    So, how do you calculate the value of the cashflows if one side of the comparison date contains both cash inflows and outflows? Do you add the difference of the accumulated values of past cash inflows and outflows to the difference of the present values of future cash inflows and outflows? Please let me know if you need clarification of my question. Thanks.
    Yeah not exactly sure what you mean.... but outflow is negative and inflow is positive. The valuing process does not change. I don't know if that is what you are looking for.
    (/

  3. #3
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    Quote Originally Posted by (/iropracy View Post
    Yeah not exactly sure what you mean.... but outflow is negative and inflow is positive. The valuing process does not change. I don't know if that is what you are looking for.
    If it helps you to understand my question, what I'm talking about has also been called the current value, not to be confused with the present value or accumulated value.

  4. #4
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    CF(0)=-1
    CF(1)=3
    CF(2)=7
    CF(3)=4
    CF(4)=1

    Then the value at time t=2 is

    -1*1.01^2+3*1.01+7+4*1.01^-1+1*1.01^-2.

  5. #5
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    Quote Originally Posted by promathlete View Post
    I know that if each side of a comparison date contains the same type of cashflow (both inflow or both outflow), then you can find the value of the cashflows by just adding the accumulated values of all cash flows to the left (and including comparison date) and the present values of all cash flows to the right.

    Example:

    Suppose you have the following cashflows with an annual effective rate of interest of 1%. CF(t) means the cashflow at the end of year t:
    CF(0)=1
    CF(1)=3
    CF(2)=7
    CF(3)=4
    CF(4)=1

    Then the value at time t=2 is

    1*1.01^2+3*1.01+7+4*1.01^-1+1*1.01^-2.

    So, how do you calculate the value of the cashflows if one side of the comparison date contains both cash inflows and outflows? Do you add the difference of the accumulated values of past cash inflows and outflows to the difference of the present values of future cash inflows and outflows? Please let me know if you need clarification of my question. Thanks.
    If I'm understanding your question correctly, you are correct, but you can only take the current values of the difference of inflow/outflow at the same times.

    To expand on your example, let's say you have to pay 2 for the first 3 years (at the beginning of the year) as an investment cost. So, we're subtracting 2 from time 0, 1, & 2.

    We can do one of two things: calculate the current value of the Net Cash Flow (Original Cash Flow - Investment Cash Flow) or subtract the current value of the Investment Cash Flow from the current value of the Original Cash Flow.

    So, we're assuming that:

    OCF(0)=1, ICF(0)=-2
    OCF(1)=3, ICF(1)=-2
    OCF(2)=7, ICF(2)=-2
    OCF(3)=4, ICF(3)=0
    OCF(4)=1, ICF(4)=0

    We can either do:

    1) PV(NCF(t), 1%), where NCF(t) = OCF(t) - ICF(t), or
    2) PV(OCF(t), 1%) - PV(ICF(t), 1%)

  6. #6
    Actuary.com - Level II Poster
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    Thanks wat. I understand it now.

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