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I'm trying to calculate (for myself, not relying on other people's graphs) when it becomes worth it to buy vs. rent.

On the positive side, there is:

  1. the down payment,
  2. property that (roughly, over the long term, unless you live where it was horribly overpriced during the early 2000s bubble) appreciates about 4%/year, and
  3. a declining mortgage balance.

But on the negative side are ongoing yearly expenses, some which decline over the years, and others that keep on rising:

  1. Mortgage interest,
  2. PMI (maybe),
  3. Property taxes,
  4. Maintenance & repair, and
  5. Home ownwer's insurance.

If after 30 years you wind up with a house that's worth $1M, but spent $700K in expenses, do you wind with an effective house-only Net Worth of $1M - $700K = $300K?

It seems like I'm mixing apples (assets and debts) and oranges (expenses).

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    A house is worth what it is worth, I think you are really mixing up value and return on investment. The house will be valued at $1M, but if you look at it as an investment (neglecting things like inflation), your ROI will only be $300K. – Ron Beyer Oct 7 at 13:40
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    @RonBeyer that should be an answer. – RonJohn Oct 7 at 13:57
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    Do you want/need to be able to move on short notice? Do you want to be able to make extensive changes to your house? The pros and cons of buying vs renting aren't always (easily) reduced to a dollar value. – chepner Oct 7 at 14:19
  • @chepner this is just the financial aspect, since as you say, certain things can't be reduced. (My sheet does, though, show that you have a negative ROI for many years on a 5% DP. – RonJohn Oct 7 at 14:33
  • @CharlesFox I rejected your edit because the error you tried to correct is fundamental to my question. – RonJohn Oct 7 at 16:29
9

A house's value is whatever it is sold for when you sell it. This doesn't change based on how much you put into the house. There are a lot of examples of that, but let's say you buy a house for $100K. If you assume that the home's "value" increases at 4% per year (and inflation stays at 0%), your house will objectively be worth $324K at the end of 30 years.

So the home's value is simply what the house can be sold for when you are ready to sell. If you can't sell it (for example if a housing bubble comes up or external factors like somebody building a nuclear power plant next door), the house is worth nothing.

The concept you are mixing up is return on investment (ROI) and value. Your ROI is the difference between what you invested and its value at the time of the sale. Value is value regardless of how much you put in it, ROI takes into account all the expenses you "invest" in order to get to the value in the future.

  • A compounding 4% annual increase will result in a house value of $324K and change after 30 years, not accounting for inflation. – GOATNine Oct 7 at 18:28
  • @GOATNine Thanks, edited, I used an incorrect online calculator to get the other number. – Ron Beyer Oct 7 at 20:51
2

It is valid to consider the projected expenses when determining whether or not purchasing a home is a wise decision. Expenses are a key component for estimating your expected net profit/loss from buying the home.

Expenses and rents help determine the market value of a home. If an investor needs to decide between buying the home and buying a stock, they will need to evaluate the potential expenses associated with the home. For the investor, the home's value is the present value of expected rents minus the present value of expected expenses. This present value calculation is the link between the value of an apple (and cost of fertilizer) and the value of the orchard.

Also note that the value to you might be higher or lower than the value to an investor. You might love/hate the neighborhood for personal reasons. Your tax situation might be different. You might also just like owning (renting) due to the ability to alter the home (freedom to easily move).

There are multiple values for the same asset. This is the basis of supply and demand curves. If a homeowner believes their home is worth $1mn to them, but the highest bidder thinks it is only worth $900k, neither is wrong. It is just a preference! However, they would not transact. The supply curve has 0 quantity at a price of $900k and the demand curve has a quantity of 0 at a price of $1mn.

There are a couple additional issues to consider when doing these calculations.

First, people with paying $10,000 or more in state income taxes will not generally be able to use their property taxes to further reduce their federal income taxes. The State and Local Tax (SALT) limit prevents people from deducting more than $10,000 of state income tax + property tax + other state and local taxes.

Second, the standard deduction is now quite high. As a result, you might still take the standard deduction for federal income taxes if you have a mortgage. If you are not giving to charity or have other deductions, you might find that your interest expense is not helping you significantly reduce your federal income tax burden.

As an example, if a married couple has $10,000 of SALT deductions, $15,000 of interest expense, and no other deductions, their itemized deductions are only $600 more than the standard deduction! The interest expense would have almost no impact on their federal income taxes.

The above is for educational purposes only. Without knowing your full circumstances, I cannot say how much, if any, of it applies to you.

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You don’t have apples or oranges :) . You have homogenous units of currency, which I’ll just call dollars for ease of reference.

So to work out when you break even, you’ll need to factor in every relevant financial detail, including both positive and negative tax effects. Since you’re comparing what you spend out of your own pocket in both buy and rent scenarios, you are comparing like with like when you lump it all in.

A caveat is that the tax effects might need to be calculated based on only certain portions of the total.

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Here is where the expenses become relevant. Assuming you live somewhere that you can rent or buy equivalent houses, imagine you pay $1500 a month rent, but your mortgage payment after buying the equivalent house would be $1200 a month. And then there is the maintenance and so on, perhaps it all adds up to $1800 a month. So you are paying $300 a month more to own the house than to rent it.

Now if your principal is going down $400 a month, then as long as you can sell the house for what you paid for it (after commission and whatnot), you are going to end up ahead. If your principal is only going down $200 a month it appears to be more expensive to own. Now you need to take into account how much you predict the house will increase in value. If it will go up by more than $100 a month, you will end up ahead.

For most people, the sorts of places they can rent are very different from the sort of places they can buy. And for some people, their houses go up a LOT more than $100 a month, but the total of their "owning expenses" (including maintenance, property taxes etc) is less than their rent would be. (This makes sense really, since most landlords are trying to recoup those expenses.) This means they pay less per month than if they were renting, while accumulating an asset. This is why so many people want you to buy a house.

That said, most people isn't all people. My brother lives in Vancouver and pays rent that is over $4000 a month (yes, thousand) less than the mortgage payment would be if he tried to buy the house. He's been saving that money in a different form for many years and doesn't mind staying out of that quite ridiculous housing market.

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The net worth of an entity is the difference between assets and liabilities.

Considering the special case of evaluating exclusively one house:

  • If you can sell the house tomorrow for $100,000 but there's a $200,000 lien on it, then your net worth is -$100,000.

  • If you can sell the house tomorrow for $100,000 and you own it free and clear, then your net worth is $100,000.

(After all taxes, fees, etc etc.)

That's all there is to net worth. If you're more interested in something like return-on-investment, that's a related but quite different topic.

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