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Math Help - Equivalent uniform annual cost

  1. #1
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    Equivalent uniform annual cost

    heres the problem

    http://i14.photobucket.com/albums/a3...ristx/eco2.jpg

    heres my cash flow diagram and attempt

    http://i14.photobucket.com/albums/a3...aristx/eco.jpg

    Im having trouble because the A;s change from 4k to 3k........

    the answer...9287
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  2. #2
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    You seem confused at things that ought not be confusing you. You will struggle more and more if you do not get past this.

    You MUST learn to resort to "Basic Principles". This will allow you to decode and evaluate ANY string of cash values. If all you know is a bunch of formulas for regular cash flows, you are toast.

    When I looked at this problem, I did not even consider the concept that has stumped you - that the payments change from 4000 to 3000. I just saw individual cash flows.

    If i = 0.10, v = 1/1.10, then

    Original PV = 60000 + 4000v + 3000v^2 + 3000v^3 + 3000v^4 - 60000v^4

    I'm not sure what is wanted for "Uniform Annual Cost". It could be this:

    Uniform PV = P + Pv + Pv^2 + Pv^3 + Pv^4 = Original PV, where P is the Uniform Annual Cost.

    You book or teacher will have to tell you exactly what is meant.

    Basic Principles!!! Trust me on this.
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  3. #3
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    Thanks.....I see what your saying, i do feel like I keep making these problems more complex than they really are.....

    I just took the answer from the first part and plugged it into the Capital Recovery Formula which gives the Equivalent Uniform Annual Cost.....

     A= P\frac{i(1+i)^n}{(1+i)^n-1)}
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  4. #4
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    The solution I came up with seems to suggest that the so-called “equivalent uniform annual cost” is nothing more than the equal (thus, uniform) periodic payments of $R at the end of each year for 4 years had the electronics firm obtained a loan of $A (to be determined from the given information) at a rate of 10% compounded annually.

    You then first solve the equivalent debt of $A. It is equal to TK’s Original PV:
    Original PV = 60000 + 4000v + 3000v^2 + 3000v^3 + 3000v^4 - 60000v^4 ≈ 29,437.88, where i = 0.10, and v = 1/1.10.

    Similarly,
    <br />
A = 60,000 + 4,000(1.10)^{ - 1}  + 3,000(1.10)^{ - 2}  + 3,000(1.10)^{ - 3}  + 3,000(1.10)^{ - 4}<br />
    <br />
 - 60,000(1.10)^{ - 4}  \approx 29,437.88<br />

    You then solve for R in the following equation: <br />
A = R \cdot \frac{{1 - \left( {1 + i} \right)}}<br />
{i}^{ - n} <br />
    With n = 4, and i = 10% = .10, you should have no trouble in arriving at the given answer key. Good luck.
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  5. #5
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    Quote Originally Posted by jason03 View Post
    Capital Recovery Formula which gives the Equivalent Uniform Annual Cost.....

     A= P\frac{i(1+i)^n}{(1+i)^n-1)}
    Just look at that beautiful formula. After a little modification, we gain some insight into what it actually means.

    A\frac{(1+i)^{n}-1}{i} = P(1+i)^{n}

    The LHS is the accumulation of n payments of $A at the end of each of n years.

    The RHS is the accumulation of a single payment of $P at the beginning of n years.

    Note: My Basic Principles version examined the value at the beginning of the n years. The given formula examines the equivalence at the end of the n years. This difference is of no consequence. If you examine ALL the cash flows, it will not matter when you examine them ALL.

    Additional Note: My guess at what Uniform Annual Cost might be includes one additional annual payment at the beginning of the n years. This is not consistent with the definition and formula provided. See how important it is to know your definitions and what your formulas mean?!
    Last edited by TKHunny; May 14th 2008 at 06:29 AM. Reason: Add Additional Note
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  6. #6
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    i understand this is an old post but i thought i should provide a clear answer to this problem and how to solve it.

    first, solve for present worth (PW)

    PW= -60,000 - 4000(P/F,10%,1) - 3000(P/F,10%,2) - 3000(P/F,10%,3) - 3000(P/F,10%,4) + 60000(P/F,10%,4)

    PW= -29,437

    now convert PW to annual worth to obtain the answer

    annual worth, or in this case (because of negative PW it is a cost) EUAC (equivalent uniform annual cost)

    EUAC= PW(A/P,10%,4)

    EUAC= 9287

    any engineering economics book will have interest and annuity tables in the back of the book for the values to solve the above equations.
    here is a table i found online for a 10% interest rate
    http://www.uic.edu/classes/ie/ie201/1000interest.html

    hopefully this will be helpful to anyone else who searches for this.
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  7. #7
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    Re: Equivalent uniform annual cost

    I need help with a unifrom cost probelm
    an alternative has a discount project cost of 2195000.00 with no salvage value. The estiamte was in constant dolars and the discount used a mid year factor

    while the period of analysis is 5 years the alternative only provides benefits for the last 3 years


    So do I calcuate using the data table for a 5 year project or just the 3 years on that table
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  8. #8
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    Re: Equivalent uniform annual cost

    Helen, you should start a NEW thread instead of tagging on to an old thread.

    Anyway, go here: 3) An Alternative Has A Discounted Project Cost... | Chegg.com
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  9. #9
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    Re: Equivalent uniform annual cost

    The estiamte was in constant dolars and the discount used a mid year factor .


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  10. #10
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    Re: Equivalent uniform annual cost

    Felton, if you put up the solution to Helen's problem,
    I'll buy 12 DVD's from you!
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  11. #11
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    Re: Equivalent uniform annual cost

    This problem is really difficult!




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    Last edited by DVDHD; July 18th 2013 at 11:09 PM.
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