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Homework Help: Economics and uniform series formula problems

  1. Sep 12, 2010 #1
    1. The problem statement, all variables and given/known data

    A Machine at a cost of $5,000 was purchased 3 years ago. It can be sold now for $3,000. If the machine is kept, the annual operating and maintenance costs will be $1,500. If it is kept and operated for next five years, determine the amount at time 0 (now) equivalent to the cost of owning and operating the machine can be sold for $1,000 at the end of the five year period. Use an interest rate of 10%.

    A. 8065
    B. 6550
    C. 9522
    D. 5002


    2. Relevant equations

    Not exactly sure which to use but here are the ones from the chapter we are studying:

    F = P(1 + i)^n

    F = A [((1 + i)^n - 1))/i]

    P = A [((1 + i)^n - 1))/((i(1 + i)^n))]

    3. The attempt at a solution

    1500 * 5 = 7500
    7500 - 1000 = 6500
    6500 is not one of the choices

    What now?
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Sep 14, 2010 #2

    Redbelly98

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    As nobody else has replied, I'll try to offer a hint or two ...

    It looks like you have to consider two situations...

    (A) The machine is sold today for $3000
    (B) The machine is kept, operated for 5 years, and then sold for $1000.

    ... and then take the difference between the $3000 you could make, versus the money (a negative number) which must be set aside today to cover 5 years of operating costs.

    So, how much money must be set aside to cover operating costs over the next 5 years? Hint, it is not simply $1500*5, you must take into account the 10% interest.

    As a final twist, the $1000 earned in the future must be taken into account as well.
     
  4. Sep 14, 2010 #3
    That's what i thought also so I used the 3rd equation.

    A = 1500
    n = 5
    i = .1

    but I get 5686.18 as an answer for P. Then I realized that didn't make any sense because 1500 dollars is not an annuity. In other words, the 1500 dollars doesn't collect interest because it's merely a recurring cost.
     
  5. Sep 15, 2010 #4

    Redbelly98

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    You should have to set aside less than $1500 for each year of operating cost in the future. That money then accrues interest at 10%, until it is worth the necessary $1500 to cover operating costs at the appropriate time.

    It's not clear to me if operating costs are paid annually, monthly, continuously, or what -- hopefully that has been explained to you in the textbook or your course lectures.
     
  6. Sep 26, 2010 #5
    The solutions were finally posted. Here is what you were supposed to do:

    P = $3,000
    Operating and maintenance costs / year = $1,500
    n = 5 years
    Salvage value = $1,000
    Interest rate = 10%
    PW of costs = 3,000 + 1,500 (P/A, 10%, 5) - 1,000(P/F, 10%, 5)
    = 3,000 + 1,500 (3.791) -1,000(0.6209)
    = $8,065.60
    The answer is, “A”.

    What I didn't understand was that everything must be taken to the present including the salvage value which is also affected by the interest rate. Money is not worth the same in the future as it is in the present.
     
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