# Formula for determining equity in a home (multiple parties)

I am buying a house with two other folks, my partner and her step mom. We are going to own it together, all of us on the mortgage. We are drafting a joint venture agreement with an attorney to make sure the details are airtight.

One thing I am having trouble with (I am trying to model it in Excel) is how to determine how much equity each person has in the house and how much money (percentage) they would get if the house sells. The appropriate formula will be written into the joint venture agreement.

Here is the precise situation: My partner and I will live together in Unit 2 of the two family house. The stepmom lives in the other Unit (Unit 1).

Each person is putting different amounts towards the down payment, monthly maintenance costs, and mortgage.

Unit 1 makes up 60% of the value of the home. Unit 2 makes up 40% of the value of the home.

What formulas can we use to determine how much equity each person has in the entire home and how much money each person gets if the house is sold?

Edit: Here is a little more information. We want to be able to independently make improvements to the units, so while Unit 1 might make up 60% of the value of the home on the day we buy it, if we finish the attic in Unit 2, those percentages would change. We're looking for a way of reflecting changes in the value of each unit (as determined by an appraiser) as well.

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Ideally, the stepmom would put in 60% of the downpayment and 60% of the monthly maintenance costs and mortgage. You and your partner would evenly split the 40%. Then, it is very obvious.

However, my guess is that this isn't going to be the situation. Without knowing the numbers, I suggest that, upon sale of the house, the exact value of each person's downpayment is immediately returned without interest. What's left of the equity is returned to everyone as per the amount they paid in mortgage. The monthly maintenance costs are excluded from this calculation entirely. You are, of course, free to take any other approach all three of you deem to be fair.

In my example, consider a home that costs \$200,000. Your stepmom puts in \$40,000 for a downpayment, you put in \$10,000, and your parter puts in \$10,000. The mortgage payments are \$1500/month. Your stepmom puts in \$500 a month, you put in \$250 a month, and your partner puts in \$750 a month.

You sell the place for \$300,000 after paying off the entire mortgage. Your stepmom gets \$40,000 + \$80,000. You get \$10,000 + \$40,000. Your partner gets \$10,000 + \$120,000.

Keep in mind, though, that you may have to sell the house for a loss. In which case, some or all of the downpayment may not even be returned. In fact, you may end up having to cover money over and above the downpayment and the payments you've made. Any good lawyer will make you consider this. Additionally, any good lawyer will make you spell out under what circumstances, people can force sale of the home.

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While I agree with your answer, I look at the question and think, "no good can come of this." Relationships have a 50/50 chance of succeeding, less so with mom living upstairs. And when one person wants out, how does s/he get that portion is the other folk can't come up with the money? – JoeTaxpayer May 6 '14 at 2:01

If there was no question of improvements to the property, the problem would be simple. Each person invests whatever amount. Calculate the percentage of each person's investment out of the entire investment, and that's what share each one owns.

Like: A puts in \$10,000 for the deposit and pays \$5,000 toward the mortgage over the next however many years. B puts in \$5,000 toward the deposit but pays \$7,000 of the mortgage. C puts in \$15,000 but pays only \$1,000 of the mortgage payments. So total investments: A - \$15,000, B - \$12,000, C - \$16,000. Total - \$43,000. So A's share of the house is 15,000/43,000 = 34.9%. Etc. If you then sell it you pay off any outstanding debt, and then everybody gets their share of what's left.

But once you start making improvements, there is no simple formula. Suppose you put down new flooring in the dining room. You pay \$500 for materials and put in 20 hours of labor. Presumably you have now added something more than \$500 to your share, but how much more? How much are the hours worth? What if someone damages the house -- puts a hole in the all or something -- and then fixes it. Does the time and effort they put into fixing it add to their investment, or did that just cancel out the damage they did? What if one person does a lot to keep the house in generally good condition in small snippets of time, like cleaning furnace filters and polishing the floors, while another does nothing and lets their share get run down and dirty? It gets very complicated. Theoretically you could come up with a rate at which you value your work -- like say every hour spent maintaining the house is worth \$10 or \$20 or whatever. But who's going to keep track of it over the course of potentially many years? And what if one person does a small number of big, easily quantifiable jobs, while another does many small, hard-to-count jobs? Like if A mops the floor every week for 2 years, is that worth more or less than B installing 3 ceiling fans, a door, and 2 windows? You could go around and around on this sort of thing.

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