FILE: Determining Percent Ownership
DATE: 2006-12-04
ARCHIVE: 2020-08-26
(c) Copyright Brett Paufler

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I acquired a beneficial fractional ownership in a property.  The problem was to determine a fair value upon dissolution of the agreement by sale of the property or otherwise given differential inputs at the start and over time.

Being mathematically oriented, I came up with the following formula, which was eventually agreed upon.

Subsequently, the market tanked, we were upside down, and I terminated my participation at a $0 buy out, which was the floor for my share: i.e. I could never have negative equity, otherwise I would have owed money upon dissolution.  So, I'm pretty glad I had that term written into the agreement.

At this point, I doubt the equations are human readable.  Still, give it a shot if that is your thing.

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Determining Percent Ownership

Value Contributed to [property] is comprised of two components
Purchase Price Amount (PPA), and
Equity Improvements (IMP)

PPA
Purchase Price Amount (PPA) is composed of two variables, 
Down Payment (DP), and
Loan (Loan)

DP
PERSON_A to pay down payment of [$-].  DP=[$-], which equates to 20% of PPA.

Loan
Closing costs beyond DP are to be split
.75 PERSON_A
.25 PERSON_B

Each month, the minimum payment to service Loan will be split 
.75 PERSON_A
.25 PERSON_B

If additional payments to the Loan can be agreed upon, they will be split
.75 PERSON_A
.25 PERSON_B

If additional payments to Loan cannot be agreed upon, either party may make additional payments to Loan, and amount will be credited to their IMP 

PPA = [$-]
Assuming all payments made on time
PERSON_A PPA = PPA-A = 100%DP + .75 Loan = 80% of PPA = [$-]
PERSON_B PPA = PPA-B = 0%DP + .25 Loan = 20% of PPA = [$-]
PPA-A + PPA-B = PPA = [$-]

IMP
Improvements is comprised of three components, 
Extra Payments to Loan, (EPL)
Cash for Work & Materials (Cash)
Sweat Equity (SE)

IMP intended to cover
1) Changes to property which change the cost basis of the property by IRS rules, or
2) Any change to which PERSON_A and PERSON_B agree

Regardless of whether a change is credited to IMP; 
1) PERSON_A may make any changes desired, regardless of PERSON_B’s approval
2) PERSON_B may not make any change, without PERSON_A’s approval
3) There is no obligation for either PERSON_A or PERSON_B to contribute to any improvement, or to contribute in any set prorated amount.

EPL
Is any amount paid on any loan payment over and above the prorated amount due (e.g. If PERSON_A pays $100 extra to Loan, and PERSON_B pays $25 extra to loan, EPL-A=$0, EPL-B=$0)(e.g. If PERSON_A pays $100 extra to Loan, and PERSON_B pays $50, EPL-A=$0, EPL-B=$25) 

Cash
Is any amount paid to an outside source for labor or materials for any qualified IMP project.  

SE
Sweat Equity is labor performed by either PERSON_A or PERSON_B.  Amount to be credited to be agreed upon at time of labor.  If no agreement can be reached, SE is not allowed for that project.

IMP amount is summed by simple arithmetic over course of ownership, all EPL, Cash, & SE, added together to come up with a total value for both PERSON_A and PERSON_B.  It is not possible to determine in advance what these values will be and may conceivably become quite large.

IMP-A = All contributions by PERSON_A to EPL, Cash, & SE = EPL-A + Cash-A + SE-A
IMP-B = All contributions by  PERSON_B to EPL, Cash, & SE = EPL-B + Cash-B + SE-B

Utilities
Utilites are not included in above and are to be paid in equal portions by all [users] (any [user] for a duration of over two weeks).  Payments to Utilities do not figure into ownership.  

Computing Ownership
Total Value (TV) = PPA ([$-]) + IMP-A + IMP-B

PERSON_A’s Contribution = AC = PPA-A + IMP-A
PERSON_B’s Contribution = BC = PPA-B + IMP-B

PERSON_A’s ownership share is AC/TV
PERSON_B’s ownership share is BC/TV
Where AC/TV + BC/TV = 1.00

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I don't know what could be simpler.