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So I am looking at buying a house jointly with my cousin. I have a higher income and better career prospects, they have a larger proportion of the deposit. Neither of us would be able to break into the property market on our own.

So when we come to sell the place in X (say 10) years, they paid the 3/4 of the (20%) deposit & I paid the 2/3 of the repayments. Also (hopefully) the value of the property has increased.

Now dividing up the place 3 parts to 1 (deposit ratios) does not seem fair. But dividing up 1 part to 2 (repayment ratio) also does not seem fair. Meeting half way just seems mathematically naive, especially considering the growth is leveraged.

We could get a property valuation every year and maths out each weeks repayments and work out the leveraged growth of each repayment + simple growth on the deposits. But that seems too complex and lead to different mistakes and interpretations (what happens if interest rates go up, what if growth is flat for a few years etc).

So:

Given different deposits and repayment ratios what is a simple 'rule of thumb' way/formula to work out a roughly fair ownership in X years time, considering the leveraged growth in value?

Note: The ratios given are just examples, and to make the question reusable, one person could also be paying the lions share of the deposit and repayments.

For the sake of this question: Lets also assume that if we agree on this formula there will be no difficulties arising from going into an investment with a family member.

Bonus question: How would you account for one person living in the smaller room (or unit) of the property?

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    We need to know the length of the loan. It would also help if we knew the ratio of one month's (or whatever period) payment to the overall value of the loan (or the deposit).
    – Brythan
    Commented Jan 28, 2018 at 13:19
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    In some jurisdictions, property held in the name of two or more non-spouses is held as tenancy in common with equal percentages (unless otherwise specified in the registration) and people have to work at it to get the property registered as joint tenancy (which usually includes right of survivorship meaning that if you die, Cousin Fitzwilliam gets it all and your heirs get bupkis). So, do think of the legal ramifications of the proposed joint ownership and talk to a lawyer to fully understand what can of worms you might be opening with this deal.
    – Dilip Sarwate
    Commented Jan 28, 2018 at 16:51
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    Don't mix family and money. If you do, put everything in writing and get a lawyer to review it. Anything you don't specify today could blow up in your face tomorrow, if it creates a dispute about how an unintended event will be treated.
    – Grade 'Eh' Bacon
    Commented Jan 28, 2018 at 17:35
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    Possible duplicate of Split buying a house 3 ways. How do I approach this?
    – Grade 'Eh' Bacon
    Commented Jan 28, 2018 at 17:36
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    I understand that your question here is about the math, but you should be aware that your assumption (“there will be no difficulties arising...”) is a pretty big leap. A house is not a simple investment, like a share of stock. There are so many unforeseen things that can happen with a house investment that can strain a good relationship.
    – Ben Miller
    Commented Jan 28, 2018 at 20:41

2 Answers 2

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This isn't as hard as it may seem at first. You just have to think of the future loan payments in terms of what they are worth today (the loan amount is equal to the present value of the future payments). Since the payment fraction will be fixed, the math is easy.

Let's say you are purchasing the house for $100. Together, you are paying $20 down payment and $80 through a loan.

Person A pays (3/4)x$20 for the down payment and (1/3)x$80 of the loan. Their share is

[(3/4)x$20 + (1/3)x$80]/$100 = 41.67%

Person B pays (1/4)x20 for the down payment and (2/3)x$80 of the loan. Their share is

[(1/4)x$20 + (2/3)x$80]/$100 = 58.33%

These are the fractions of the sale price that person A and B will take, respectively.

The above treats the home as an investment asset, so it doesn't matter who uses the house in the mean time.

If I were you, I would use the above math for the purchase and sale. Then separately split up the ongoing costs of the home (upkeep, utilities, insurance, taxes, upgrades) according to the proportion of the home being used by each person.

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  • The way of looking at the loan is an excellent simplification - assuming each side does keep up their payment obligations, you can effectively think of it as two separate loans which each is responsible for. One complication will come if the house is sold before the loan is paid off: in that case they should divide the equity as if they divided up the total sale price by the ownership proportions, then use their shares of that to pay off the right shares of the loan (in the loan proportions).
    – Ganesh Sittampalam ♦
    Commented Jan 28, 2018 at 19:10
  • For the bonus question, they should also consider a notional "rent" figure unless they occupy the house in the same proportions as the ownership they calculate.
    – Ganesh Sittampalam ♦
    Commented Jan 28, 2018 at 19:10
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The answer shouldn't be a fixed number (percentage) for each. It should be a formula in which the percentage assigned to each person will change each month.

For example if the decision is made after two months to end the arrangement, then the percentage should highly favor the percentages for the down payment. But if the house is sold as the last mortgage payment is being made 30 years later, the percentages would look like the raw percentages for the amount of money contributed.

A good approach is just to keep track of how much money each person contributed and just use that to determine the percentages.

For the cost of insurance, taxes, and repairs just make the split equal to the split of the monthly payment.

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