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Thread: deferred perpetuity question

  1. #1
    Actuary.com - Newbie Poster
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    Exclamation deferred perpetuity question

    hello

    I am confuse. my question is as follows:Please help me with part b) of question.
    You have the right to receive a deferred perpetuity annual end of year payments of $10,500. The first payment for the perpetuity will be received at the end of year 5.
    a) Given that your opportunity cost of funds is 15% p.a., compounded quarterly, what is the current value of this right to receive the deferred perpetutiy?

    PV = PP/i
    PV = $10,500/0.0375
    PV = $280,000.00

    b) what would be the difference in your answer to part a) of this question, if the first payment could be brought forward to the end of year 3?

    thank you very much.

    Jess
    Last edited by jess; March 30th 2008 at 12:32 AM. Reason: need reply asap please

  2. #2
    Actuary.com - Level V Poster
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    Quote Originally Posted by jess View Post
    hello

    I am confuse. my question is as follows:Please help me with part b) of question.
    You have the right to receive a deferred perpetuity annual end of year payments of $10,500. The first payment for the perpetuity will be received at the end of year 5.
    a) Given that your opportunity cost of funds is 15% p.a., compounded quarterly, what is the current value of this right to receive the deferred perpetutiy?

    PV = PP/i
    PV = $10,500/0.0375
    PV = $280,000.00

    b) what would be the difference in your answer to part a) of this question, if the first payment could be brought forward to the end of year 3?

    thank you very much.

    Jess
    First you need to compute the effective annual interest rate which is

    i = (1 + 0.15/4)^4 - 1 = 0.158650415.

    Then the value of the perpetuity at the end of 4-th year is 10500/i (this is the formula for perpetuity-immediate).

    To get the present value, you discount back by 4 years, i.e. the present value is v^4*(10500/i), where v = 1/(1+i).

    If the first payment is received at the end of 3rd year, you just need to discount back by 2 years, i.e. the answer is v^2*(10500/i).

    If you are still confused, see the thread

    http://www.actuary.com/actuarial-dis...ead.php?t=7678

    ctperng

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