Conference rusure::math

You could use present values and assign the profit proportionately.

    	==		==		==		==
    
The first person paid a down payment (D) x months ago, worth

	D * (1 + i) ^ x				[P1]

today, where i is the monthly rate of interest (e.g. 1%).

The second person paid monthly payments (M) for x months, worth

	M * (1 + i) ^ x   +   M * (1 + i) ^ (x-1)   +   M * (1 + i) ^ (x-2)
	    +  ...  +   M * (1 + i) ^ 2   +   M * (1 + i)

today, which is equal to

		      (1 + i) ^ x - 1
	M * (1 + i) * ---------------		[P2]
                             i

E.g. for i = 1%, D = $30,000, M = $1000, and x = 60 months:

	P1 = $54,501
	P2 = $82,486

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You could split the new selling price in the ratio P1:P2.

John

    What is a fair way to determine i?
    
    

    (1 + i) ^ 12   =   1 + annual interest rate
    
    John

    I am sorry.  What I really meant is, Whose interest rate?  Treasury
    bonds?  Prime rate?
    
    Also, if one person lives in the house, and the other person does
    not live in the house, then the M needs to be adjusted downward
    to reflect the fact that he is living rent-free.  The person paying
    the downpayment doesn't have the privilege of living in the house.

    Well, the fairest way is to follow the contract the two sides both
    signed :-).  T'is definitely not a math problem.
                        
    Eugene

    The contract does not exist yet.  I am referring to a proposed future
    arrangement.
    

    re .6
    Oh boy!  This is tough.  There are so many variables involved. 
    To start with, there is the renting income, the potential damage to
    the hourse, the future inflation rage vs. interest rate, the tax benifit, 
    depreciation of the hourse and on and on and on.  Personally, 
    I do not feel that mathematics is of much help beyoun arithmetics.  
    One way to do it is perhapsto find some lawyer/real estate agent to 
    figure it out.  That cost money, but you can avoid potential legal 
    problem.
    Eugene

     When calculating the present values of the amounts paid
     by both parties, how do you take the following into account:
     
          The person making the down payment paid for and
          got a percentage of the value of the house.
     
          The person making the monthly payments has paid
          mostly interest, and has not much increased the
          combined share in the house.
     
     Perhaps consider many ways of dividing the profits, until
     finding one that both sides can agree to.  Or the standard,
     one person selects the method and the other selects whether
     to make the down payment or the make the monthly payments.
     
     Dan

     Another idea:  see if the IRS has regulations for something
     like this.  How would they decide how much income accrues
     to each partner?

    I also think that checking existing regulations is a wise thing
    to do.  Afterall, the most satisfactory mathematical solution can
    be rendered unlawful if it contradicts any relevant regulations
    or polices.
    
    However, just for fun, let us consider the problem this way -- That
    it is just coincidence that the person who pays the monthly mortgage
    also lives in the house.  For our present purposes, we just consider
    A pays the down-payment, B pays the monthly mortgages and C rents
    the house.  C has no claim whatsoever on the profit/loss from
    selling the house and has to pay a monthly rent.  A, B and C agree
    on the rent of the house.
    
    ACP = A's contribution in present value
        = present value of down-payment
    
    BCP = B's contribution in present value
        = SUM ( present value of payment i )
           i
        
    INCOME from the house =
        Selling Price + SUM( rent for month i ) - unpaid mortgage 
                         i
    
    A should get ACP/(ACP + BCP) portion of INCOME
    
    B should get BCP/(ACP + BCP) portion of INCOME

   
    After putting down this lines, I suddenly realize that the BUYING
    PRICE didn't come into play.  Have I got something wrong ?  Anyway,
    I still think that separating the person who pays the mortgage and
    the person who rents the house is a reasonable approach.
    
    
    Eddie Leung.    

     The unpaid mortgage reflects what's left of the buying
     price after the down payment and monthly payments so
     far have been made.  I suppose points fit in there
     somewhere, too.

    Here's a method I would agree to:
    
    Call the interest rate i.  Make a list of the dates and amounts each
    person paid, whether down payments, mortgage payments, maintenance, or
    whatever.  Include each month's rental on the house as a negative
    payment for the person(s) living in it.  The amount of this negative
    payment should be fair market value of the rental at the time (the same
    amount other house's of similar characteristics were renting for).
    
    Giving this list, figure how much money would have accumulated had it
    been put in a bank account with interest rate i.  Adjust i up or down
    until the total accumulation for all people is equal to the amount
    obtained by selling the house.  Then each person receives the amount
    they would have accumulated.
    
    
    				-- edp 

    I have in the past participated in similar profit-sharing arrangements.
    It may be too simple, but consider this:  divide up the eventual profit
    or loss pro-rata according to the out-of-pocket dollars actually spent
    by each party.  (Net after deducting taxes paid and deductions received). 
    
    It is true that one person pays mostly principal and the other interest,
    but on the other hand it's that interest payment that allows the leverage
    that will presumably benefit both partners -- and the monthly-payer is
    obligated to make further payments, while the down-payer is not.

    I also suggest appropriate escape clauses to provide for death,
    insolvency, or one party's desire to pull out.  For example, have
    the house appraised and settle at appraised value, if that is what
    seems to be appropriate.

      John

re .10
Don't you need to Present_Value the rent, too?

John F.

    The important point, it seems to me, is how was the money for purchase
    really acquired.  Ownership is determined by resources and risk.
     If "renter" obtained the Mortgage, then he/she is "at risk" for
    the mortgage.  So the correct way to divide the gain is based on
    the amount "at risk" for each purchaser at the front end, whether
    or not the resources are cash or credit.  The renter is simply paying
    his/her credit liability, not changing the amount "at risk"./
    	Perhaps this is simple-minded...but I am using it.