# How much house can a retired person afford

Consider a single person with a net worth of N where N is between one and ten million dollars. He is retired and has no source of income other than his investments. He wants to buy a home which means he must sell assets. As a function of N, how much of a home can he buy? Is 20% of N to high? I think it is.

• Why ask "how much can I spend without going broke" instead of "how much house do I/we need"? Nov 10, 2017 at 0:36
• @RonJohn Part of the purpose of this question is to see how I am doing relative to my friends who do own homes.
– Bob
Nov 10, 2017 at 1:04
• "to see how I am doing relative to my friends" afraid you aren't keeping up with the Joneses? Nov 10, 2017 at 1:06
• There isn't a certain percentage that makes sense, if you have \$10M, of course you can afford a \$2M home, \$8M is far more than most people retire with. How much annual income do you want to have in retirement? Nov 10, 2017 at 2:03
• As @Hart CO says, decide how much income you need to live the way you want, and compute how much invested capital is needed to produce that income, reliably. Then you can potentially spend the rest on a house. Beware of one potential gotcha, though: if you sell a sizeable chunk of invested assets in a single year, you will probably put yourself in a high tax bracket, and wind up giving a big chunk to the government. Nov 10, 2017 at 2:40

Consider property taxes (school, municipal, county, etc.) summing to 10% of the property value. So each year, another `.02N` is removed. Assume the property value rises with inflation. Allow for a 5% after inflation return on a 70/30 stock bond mix for `N`.

### No house

After inflation return.

``````N * .05 = .05N
``````

Let's assume a 20% rate. And let's bump the `.05N` after inflation to `.07N` before inflation. Inflation is still taxable.

``````.07N * .2 = .014N
``````

Result

``````.05N - .014N = .036N
``````

### With house

Drop in value of investment funds due to purchase.

``````N - .2N = .8N
``````

Return after inflation.

``````.8N * .05 = .04N
``````

After-inflation return minus property taxes.

``````.04N - .02N = .02N
``````

Taxes are on the return including inflation, so we'll assume `.06N` and a 20% rate (may be lower than that, but better safe than sorry).

``````.06N * .2 = .012N
``````

Amount left.

``````.02N - .012N = .008N
``````

### Summary

If no property, you would have `.036N` to live on after taxes. But with the property, that drops to `.008N`. Given the constraints of the problem, `.008N` could be anywhere from \$8k to \$80k.

So if we ignore housing, can you live on \$8k a year? If so, then no problem. If not, then you need to constrain `N` more or make do with less house.

On the bright side, you don't have to pay rent out of the `.008N`. You still need housing out of the `.036N` without the house.

These formulas should be considered examples. I don't know how much your property taxes might be. Nor do I know how much you'll pay in taxes. Heck, I don't know that you'll average a 5% return after inflation. You may have to put some of the money into cash equivalents with negligible return. But this should allow you to research more what your situation really is.

### Other values

If we set returns to 3.5% after inflation and 2.4% after inflation and taxes, that changes the numbers slightly but importantly. The "no house" number becomes `.024N`. The "with house" number becomes

``````.024N * .8 - .02N = .0192N - .02N = -.0008N
``````

So that's \$24,000 (which needs to include rent) versus -\$800 (no rent needed). There is not enough money in that plan to have any remainder to live on in the "with house" option. Given the constraints for `N` and these assumptions about returns, you would be \$800 to \$8000 short every year.

This continues to assume that property taxes are 10% of the property value annually. Lower property taxes would of course make this better. Higher property taxes would be even less feasible.

### Comparing

When comparing to people with homes, remember the option of selling the home. If you sell your `.2N` home for `.2N` and buy a `.08N` condo instead, that's not just `.12N` more that is invested. You'll also have less tied up with property taxes. It's a lot easier to live on \$20k than \$8k.

Or do a reverse mortgage where the lender pays the property taxes. You'll get some more savings up front, have a place to live while you're alive, and save money annually.

There are options with a house that you don't have without one.

• I think a 5% rate of return after inflation is too high of an estimate. The numbers I like are 3.5% after inflation and 2.4% after taxes and inflation.
– Bob
Nov 10, 2017 at 12:45
• Do you have examples to support the 10% property tax rate? I am more used to 2% to 3% property tax rates.
– Eric
Nov 10, 2017 at 15:34
• @Eric Indeed. wallethub and taxfoundation.org both show property tax rates capping out under 3% in the US. Nov 10, 2017 at 18:46
• @Brian: Indeed, anywhere west of the Rockies they're likely to be around 1% or less. Also, the tax may be on assessed value, which is often much less than current market price, or limited to the property's purchase price (Calif, Prop 13 &c). Nov 10, 2017 at 19:17
• This doesn't answer the question. It instead selects 20% arbitrarily, then goes through the ramifications of purchasing a house at 0.2N. Nov 11, 2017 at 0:40

Consider a single person with a net worth of N where N is between one and ten million dollars.

has no source of income other than his investments

How much dividends and interest do your investments return every year? At 5%, a US\$10M investment returns \$500K/annum. Assuming you have no tax shelters, you'd pay about \$50% (fed and state) income tax.

https://budgeting.thenest.com/much-income-should-spent-mortgage-10138.html

A prudent income multiplier for home ownership is 3x gross income. Thus, you should be able to comfortably afford a \$1.5M house.

Of course, huge CC debt load, ginormous property taxes and the (full) 5 car garage needed to maintain your status with the Joneses will rapidly eat into that \$500K.

• Good answer. However a retired person may or may not want to leave behind the "N" ... in which case depending on life expectancy, he may choose to spend substantial amount ... and not leave anything behind. So it depends on what retirement life style one chooses and what one desires to leave behind to family / charity. Nov 10, 2017 at 3:29
• I think the "prudent income multiplier" really applies only when you're in need of a mortgage. With a high net worth, it's more about what you choose to spend your money on. For instance, that hypothetical person with a \$10 million net worth could easily buy a \$5 million house, and have enough left to live comfortably. Nov 10, 2017 at 19:10