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Math Help - Present Value Noncompounding Problem

  1. #1
    Apr 2009

    Present Value Noncompounding Problem

    So here is some background information on this problem I need to solve, please skip to the bottom for my question:

    Bob and Linda Smith are divorcing after 41 years of marriage. That date of divorce will be April 1, 2009.

    Bob is retired military currently receiving $4,500 a month in traditional (or High-3) military retirement benefits. Bob was born April 1, 1949 and Linda was born April 1, 1951. They married on March 31, 1969, and Bob joined the army the next day. He retired 20 years later on March 31, 1989.

    Bob, because he didn't want to pay for it, convinced Linda years ago to sign away her right to SPB, which is a type of military insurance that would assure that Linda continued to receive Bob's military retirement payments in the event that he died. If Linda chooses to participate in Bob's retirement benefits, and he dies, all benefits to her would cease. The only way to mitigate this is to purchase a life insurance policy on Bob that would pay her enough to ensure her financial future. Unfortunately, Bob is a smoker and Linda cannot afford the cost of such a policy.

    Bob also doesn't really want Linda participating in his retirement (although there is some debate over whether he has a choice) so he is willing to "buy her out" of his policy.

    Military benefits increase in January of each year by what is known as a COLA, or cost of living adjustment. This is a federally mandated increase that is tied to changes in the Consumer Price Index. The increase this year was a whopping 5.8%.

    The question that needs to be answered: How much would he have to pay her today assuming all future COLA's will equal the average COLA of the last 10 years?

    You should use March 30, 2009 as the date for your discount rate. Also assume that the effective tax rate will be 18%. Also assume that Bob and Linda are Caucasian.

    What I need:

    So I am have trouble figuring out how to find out the first payment. What I need to do is start with year 1 and find the PV of the payment and not compound all the years. Then do the next year, etc. The second year is when I need to apply COLA (not sure how to do this either). The information I have found that I need to do this is the following:

    Life Expecancy: 20.9
    COLA Rate Average of last 10 years: 3.02
    Treasury Yield Curve rate - 20 year: 3.64
    Payment: $4500 a month

    Anything would help, thanks. If you could show me or help me find out how to get year 1 and 2 I think I could finish it all. Thanks again!
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  2. #2
    MHF Contributor
    Aug 2007
    Do you have a spreadsheet? I really don't see anything difficult in there. Keeping track of all the information is the hard part. A spreadsheet will help you do that.

    I don't understand your need "not to compound". If you apply a percentage COLA each year, how is that not compounding?
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