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Math Help - Unique Problem

  1. #1
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    Unique Problem

    I have a very tough problem that I am having a hard time setting up for a break even problem. I am doing a break even analysis on having a solar panel system vs not using solar.


    Solar Panel System:

    I have a loan that I will be paying $105,281.03 total over 20 years

    after that I will be receiving $590 each year after the 20 years



    No System:

    The other situation is that I pay $1,347 every year



    so how long until I break even?



    Here is what I am up against so far:

    $105,281.03 - $590x(after 20 years) = $1,347x


    I am trying to set this problem up correctly but I do not understand how I can account for the after 20 years deposits for the loan side. Any help would be appreciated.
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  2. #2
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    Re: Unique Problem

    Don't use dollar signs; they mean something special on this site and will screw you up if you do not know to use them correctly.

    There is not enough information to solve your problem as it stands in any but the crudest of ways because it is break even analysis sensitive to both time and risk. Long, long ago, I used to do this kind of analysis for a living, and I probably would have used a Monte Carlo method and needed a ton more information than you have supplied

    To give a half-way meaningful answer, I would need to know the terms of the loan, ie interest rate, amount paid each month, initial principal balance etc? I would also need more information about the payment of 590 dollars each year. Until the sun explodes, until 2100, until the company paying it goes bankrupt, over what period?

    However, completely ignoring the time value of money and uncertainty,

    $105,281.03 - 590x = 1347 * (20 + x) \implies x =\dfrac{78,341.03}{590 + 1347} \approx 40\ years,\ starting\ 20\ years\ from\ now.$

    If I did the proper analysis, it would look even worse. If you buy into this deal, call me up: I have a bridge you may want to look at. It's an old bridge, but it has a lot of wear left in it and looks really cool.

    EDIT: Think about it this way. If you pay 1,347 for 60 years that is 80,820. So if you get the system, you would be net out of pocket over the next 60 years by 105,281.03 - 40 * 590 = 81,681.03. At the end of sixty years you still would not have broken even.
    Last edited by JeffM; June 21st 2014 at 06:35 PM.
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  3. #3
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    Re: Unique Problem

    So accounting for all that Jeff I actually forgot to add the amount that is saved per year on the electric after the 20 years. That being said I had to modify the equation a little so here it is and let me know how I can shape this in an equation. Now I did take into account the interest on the loan over the 20 years, and I am not including inflation due to the complexity that it will cause over all my calculations that I had to do to get these numbers.

    105,281.03 initial loan that will be paid off in 20 years
    After the 20 years it will only cost 533.50 per year after the 20 years


    The other side of the equation will have 1,347 each year ( this represents a non solar system electric bill)

    When will I break even?
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  4. #4
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    Re: Unique Problem

    Quote Originally Posted by zach48191 View Post
    So accounting for all that Jeff I actually forgot to add the amount that is saved per year on the electric after the 20 years. That being said I had to modify the equation a little so here it is and let me know how I can shape this in an equation. Now I did take into account the interest on the loan over the 20 years, and I am not including inflation due to the complexity that it will cause over all my calculations that I had to do to get these numbers.

    105,281.03 initial loan that will be paid off in 20 years
    After the 20 years it will only cost 533.50 per year after the 20 years


    The other side of the equation will have 1,347 each year ( this represents a non solar system electric bill)

    When will I break even?
    I believe I already answered that. Now perhaps my answer is wrong because I failed to address one or more issues. But you have not explained what you think was wrong with my previous answer. You mention that there is a saving in the electricity bill during the first 20 years, but you give no numbers for that. Nor have you explained how you took interest into account. And with a very long period for break even, you undoubtedly should address the expected life of the system. And I still do not understand the annual payment you say someone is going to make to you starting in year 21 and then presumably in perpetuity.

    Keeping things simple, a first crude cut would be to take the annual payment (interest plus reduction of principal) on the loan, subtract the annual reduction in the electricity bill, and multiply that difference by 20. That tells you what the net aggregate cash outflow is over the first 20 years. (Obviously, the break even period will exceed 20 years if annual loan service exceeds the annual reduction in the electricity bill.) Now divide that product by the annual reduction in the electricity bill. Take that quotient and add 20: that's the break even period.
    Last edited by JeffM; June 21st 2014 at 10:05 PM.
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  5. #5
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    Re: Unique Problem

    Sorry Jeff I did not want to make like a huge 5 page of all my calculations that I have made to get those numbers. I figured it out by actually just using an excel table and just compared the price over time. I am uploading my document that has ever calculation that I have done and you can see the break even point. Btw I probably am just going to lease a system as economically I will die probably before I can make any money!


    Thank you for your help it really did help me in trying to ensure that I have a crude formula for my break even. I basically am just doing a cost analysis to see roughly if it is worth buying or leasing a system. My fellow teammate is working on the leasing portion and together we are going to present it to our class.


    https://www.dropbox.com/s/v9x5149nu9...s%20Final.docx
    Last edited by zach48191; June 21st 2014 at 11:21 PM.
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  6. #6
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    Re: Unique Problem

    I want ! But, yeah, cost is a bit of an issue. What are you planning on doing with solar panels? Are you trying to power your house?
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  7. #7
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    Re: Unique Problem

    Zach

    I could not follow all of your thinking. A note for the future (or perhaps for real life). You have to get the correct answer, and then you have to present it in a way for the stupidest person in the room to understand. I don't say that presentation is more important than being correct because that is gross foolishness. A wrong answer if accepted will always do damage, sometimes serious damage. Nevertheless, a bad presentation of the correct answer may mean that the correct answer is not accepted.
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  8. #8
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    Re: Unique Problem

    Quote Originally Posted by SlipEternal View Post
    I want ! But, yeah, cost is a bit of an issue. What are you planning on doing with solar panels? Are you trying to power your house?
    Uhhhh...SlipEternal? Are you feeling okay?

    -Dan
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