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Thread: MARR Present worth analysis

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    MARR Present worth analysis

    Is there anyone kind enough to solve this problem for me? I have my semester final ahead, and struggling with this problem. I am attaching my understanding too.
    ps: also calculating for 30 years seems confusing
    .IMG_2124.jpg IMG_2125.jpg
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    Last edited by Tayeeba; 12-05-2017 at 02:22 AM.

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    Cool

    Quote Originally Posted by Tayeeba View Post
    Is there anyone kind enough to solve this problem for me? I have my semester final ahead, and struggling with this problem. I am attaching my understanding too.
    ps: also calculating for 30 years seems confusing
    .IMG_2124.jpg IMG_2125.jpg
    I can't read everything in the scan of the exercise; for instance, items in the table are too small for me to see. Also, I can't read the sideways stuff. Please reply with clarification. Thank you!
    Last edited by stapel; 12-06-2017 at 02:38 PM. Reason: Correcting typo.

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    As far as I can tell:

    Model A:
    Cost: 50000
    Revenue:
    10000 : 1st 5 years
    15000 : next 10 years
    15th year salvage value: 5000

    Calculation of PV:
    -50000
    + PV of 10000 annually: n = 5, i = .10
    + PV of 15000 annually: n = 10, i = .10 : let that = x
    + PV of x over 5 years: x/(1.10^5)
    + PV of 5000 over 15 years: 5000/1.10^15

    If I didn't goof, that results in net PV of 46334.22

    I'm NOT doing the other 2 models!!

    Note that 10000 for 15 years and 5000 for 10 years
    would work out the same.

    EDIT:
    on this one:
    + PV of 15000 annually: n = 10, i = .10 : let that = x

    That's the PV as at end of 5th year, of course;
    result has to be PV'd again, for 5 years.
    Last edited by Denis; 12-05-2017 at 04:52 PM.
    I'm just an imagination of your figment !

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    Quote Originally Posted by Denis View Post
    As far as I can tell:

    Model A:
    Cost: 50000
    Revenue:
    10000 : 1st 5 years
    15000 : next 10 years
    15th year salvage value: 5000

    Calculation of PV:
    -50000
    + PV of 10000 annually: n = 5, i = .10
    + PV of 15000 annually: n = 10, i = .10 : let that = x
    + PV of x over 5 years: x/(1.10^5)
    + PV of 5000 over 15 years: 5000/1.10^15

    If I didn't goof, that results in net PV of 46334.22

    I'm NOT doing the other 2 models!!

    Note that 10000 for 15 years and 5000 for 10 years
    would work out the same.

    EDIT:
    on this one:
    + PV of 15000 annually: n = 10, i = .10 : let that = x

    That's the PV as at end of 5th year, of course;
    result has to be PV'd again, for 5 years.

    you are right about the numbers of model A, for model B: first cost $40k, salvage value $2k, annual profet: $10k+$1k/year increase, life (years): 10.
    model C: first cost $10k, salvage $0, annual profit $9k, life (years): 5.

    i understand what you did for model A except the line PV of X over 5 years. Here you calculated the Future value of $15k for 5 years right? Why is that when the problem says $15k annuity for 10 years, (what you did the line before PV of X over 5 years). Please help me here. Youd did 15 K annuity for 10 years, but why again 15k future value for 5years?
    also i need to convert every modelís life in 30 years right to do a fair comparison. So how can i find the value of 30 years for model A?

    i just have these two problems with model A, Once understood, I can do B and C by myself.
    thanks again Denis.

    also can you please suggest me any YouTube video to get clear idea about marr,irr and err. I have read my textbooks but still have many confusions

  5. #5
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    Quote Originally Posted by Tayeeba View Post
    i understand what you did for model A except the line PV of X over 5 years. Here you calculated the Future value of $15k for 5 years right? Why is that when the problem says $15k annuity for 10 years, (what you did the line before PV of X over 5 years). Please help me here. Youd did 15 K annuity for 10 years, but why again 15k future value for 5years?
    No. I'll try and explain again.
    (not easy without chalk/blackboard!)

    Step 1: calculate PV of $15000 annuity over 10 years
    15000 * (1 - 1/(1.10)^10 / .10 = ~92168

    Since the $15000 begins in 5 years, then the above PV
    is effective 5 years later than today.
    So today, we look at that $92168 as a FV 5 years later,
    and calculate its PV:
    Step 2: calculate PV of 92168

    92168 / 1.10^5 = ~57229

    OK?

    As far as extending to 30 years, seems we need
    something more about salvage value, plus what
    will the revenue be...still $15000 annually?
    I'm just an imagination of your figment !

  6. #6
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    Quote Originally Posted by Denis View Post
    No. I'll try and explain again.
    (not easy without chalk/blackboard!)

    Step 1: calculate PV of $15000 annuity over 10 years
    15000 * (1 - 1/(1.10)^10 / .10 = ~92168

    Since the $15000 begins in 5 years, then the above PV
    is effective 5 years later than today.
    So today, we look at that $92168 as a FV 5 years later,
    and calculate its PV:
    Step 2: calculate PV of 92168

    92168 / 1.10^5 = ~57229

    OK?

    As far as extending to 30 years, seems we need
    something more about salvage value, plus what
    will the revenue be...still $15000 annually?

    Hey, thanks I got it clearly now.1CE3FD6D-B379-44DF-B7B1-855BDF1A4215.jpg
    also found the the value in 30 years too. Itís the value in 15 years+future value over next 15 years.
    thanks a ton for helping me out.

  7. #7
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    In case this helps you...
    Problem can be looked at as a savings account
    starting in overdraft of -$50000 and the "annuities"
    being deposited in this account; like this:
    Code:
    YEAR   DEPOSIT   INTEREST   BALANCE
      0                         -50000
      1     10000     -5000     -45000
      2     10000     -4500     -39500
      3     10000     -3950     -33450
      4     10000     -3345     -26795
      5     10000     -2679     -19474
      6     15000     -1947     - 6421
      7     15000     - 642       7937
      8     15000       794      23731
      9     15000      2373      41104
     10     15000      4110      60214
     11     15000      6021      81235
     12     15000      8123     104358
     13     15000     10436     129794
     14     15000     12979     157773
     15     15000     15777     188550
     15      5000         0     193550
    Present value: 193550 / 1.10^15 = 46334

    Got that??
    I'm just an imagination of your figment !

  8. #8
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    Quote Originally Posted by Denis View Post
    No. I'll try and explain again.
    (not easy without chalk/blackboard!)

    Step 1: calculate PV of $15000 annuity over 10 years
    15000 * (1 - 1/(1.10)^10 / .10 = ~92168

    Since the $15000 begins in 5 years, then the above PV
    is effective 5 years later than today.
    So today, we look at that $92168 as a FV 5 years later,
    and calculate its PV:
    Step 2: calculate PV of 92168

    92168 / 1.10^5 = ~57229

    OK?

    As far as extending to 30 years, seems we need
    something more about salvage value, plus what
    will the revenue be...still $15000 annually?
    hello Denis, i did exactly in your way, but got different answer, will you please cross check my answer?0CE13816-11FD-4CF7-AD33-360F3B1B9421.jpg
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    Last edited by Tayeeba; 12-06-2017 at 01:49 PM.

  9. #9
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    Can't read your attachment; here's the steps:

    PV of 10000 annuity, 5 years:
    10000 * (1 - 1/1.10^5) / .10 = 37907.87 [1]

    PV as at end of year5 of 15000 annuity, 10 years:
    15000 * (1 - 1/1.10^10) / .10 = 92168.51
    PV of above as at today: 92168.51 / 1.10^5 = 57229.39 [2]

    PV salvage value, 15 years:
    5000 / 1.10^15 = 1196.96 [3]

    Net PV today:
    -50000.00 + [1] + [2] + [3] = 46334.22

    OK???
    I'm just an imagination of your figment !

  10. #10
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    Quote Originally Posted by Denis View Post
    Can't read your attachment; here's the steps:

    PV of 10000 annuity, 5 years:
    10000 * (1 - 1/1.10^5) / .10 = 37907.87 [1]

    PV as at end of year5 of 15000 annuity, 10 years:
    15000 * (1 - 1/1.10^10) / .10 = 92168.51
    PV of above as at today: 92168.51 / 1.10^5 = 57229.39 [2]

    PV salvage value, 15 years:
    5000 / 1.10^15 = 1196.96 [3]

    Net PV today:
    -50000.00 + [1] + [2] + [3] = 46334.22

    OK???
    perfect, I canít thank you enough for your time and patience. The God bless you

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