Rent vs buy calculations

There’s an interesting debate going on in the comments section of yesterday’s housing post about the relative costs of buying and renting a house.

David Sucher is in Seattle:

We have had a great discrepancy between buying & renting since the early 1970s i.e. it has always been far more expensive to buy than to rent and very few (like show me one and I’ll buy it) residential properties ‘cash-flow’ at a 20% down purchase. But people do buy when they can afford it. As markets are not likely to be wrong over such a long period of time, my conclusion is that the psychological value of owning is simply worth the extra $$$ and responsibility.

And Nicholas Weaver responds:

In terms of raw cash flow, buying costs more than renting under ALL conditions I’ve looked at. Even in a “sane” market, on a cash-flow basis, buying is expensive.

But notice that for “cheaper then renting”, I only consider lost-money (interest, tax, HOA) as ‘cost’ for buying, the rest of that huge mortgage payment you should see again, evenutally, so I don’t consider that a cost.

Well, maybe not all conditions. In fact, I’ve been doing some back-of-the-envelope sums and have come to the conclusion that buying is likely to be cheaper than renting. Take the example of someone who can buy their house with cash, and who doesn’t consider themselves a particularly astute or successful investor. Let’s say that the house costs $1 million, that renting it would cost $5,000 per month, and that property taxes and other costs of ownership are $500 per month. Let’s also say that the interest rate on cash deposits is 5%.

Do you buy the home or rent it? If you buy it, after one year you are down $6,000 in taxes and other expenses, so the cost of buying is $6,000. If you rent it, after one year you are up $50,000 in interest on your $1 million, and down $60,000 in rent, so the cost of renting is $10,000. Then come taxes. If you rent, your rent payments aren’t tax deductible, but your interest income is taxable. So if you pay 30% tax on that $50,000 interest income, that puts you another $15,000 in the hole. Meanwhile, if you own, those property taxes are tax deductible. Buying just became significantly more attractive still. Then, of course, you’re better off still if the value of your house appreciates over the course of the year.

How does a mortgage affect these calculations? Let’s say that you have $200,000 for a down payment, and the rest of the purchase price comes from a 6% mortgage. Now, if you buy, you’re still down $6,000 in property taxes, but you also need to pay 6% interest on an $800,000 mortgage, which is another $48,000. Total cost of buying: $54,000, all of which is tax-deductible. If you rent, you pay $60,000 in rent, while earning $10,000 in taxable interest income. Total cost of renting: $50,000, plus another $3,000 in taxes. You’re still better off buying, certainly if there’s any kind of nominal house-price appreciation going on.

Of course, if you tweak the numbers, you get different results. Crucially, if you can invest your money and get a higher return than prevailing mortgage rates, then it becomes much less attractive to buy. But no one would lend money to homeowners if it was that easy to get a higher return elsewhere.

In my example, how much would that house have to cost before it became cheaper to rent? Let’s say the house was $1.2 million, and we still had that 20% down payment. Cost of buying is $63,600, tax-deductible; cost of renting is $52,000 after taxes, which is over $74,000 before taxes at a 30% tax rate. How about $1.5 million? Cost of buying is $78,000, tax-deductible; cost of renting is $49,500 after taxes, which is about $71,000 before taxes. Finally, it’s cheaper to rent than to buy — assuming, of course, that house prices have zero nominal appreciation.

I’m not intimately connected with the housing market, but my gut feeling is that it’s not easy to find $1.5 million houses renting for $5,000 per month. Then again, depending on what state you’re in, the property taxes on a $1.5 million house might well be vastly greater than $500 per month, and I’m unclear on the extent to which property taxes get passed through into higher rents.

Still, this is all highly theoretical; I’d love to see some real-world calculations.

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16 Responses to Rent vs buy calculations

  1. wcw says:

    Last things first: in re, “it’s not easy to find $1.5 million houses renting for $5,000 per month,” come to San Francisco. There are plenty of single-family-detacheds left in my neighborhood for which that’s about the going sale price, and the few I see for rent are around $4,000 — sometimes below, sometimes above. What’s hard is finding an actual “house” for rent. Usually you’re talking a nice, 3-plus-bedroom Victorian flat instead, which rent in the $3,000 range and as condos sell in the $1m range.

    As for the calculations, I wrote a toy rent-vs-buy monte-carlo simulation a couple summers ago to settle an argument. It turns out that those tax breaks are *fierce*. Even in San Francisco, where the prices are really high and the rent is controlled if you don’t move, using rational assumptions about return expectations buying beat renting in about a third of the thousands of model futures I ran.

    Off the top of my head, the biggest things you are missing are the standard deduction for renters, and the capital gains shield for homeowners. There is also the expected returns from investing your cash (comparing housing to t-bills isn’t quite fair), the cap on the interest deduction over $1m, the potential that rents outstrip CPI, and on and on.

    If not for the tax breaks, there’d be no question.

  2. Troege says:

    Aren’t you forgetting inflation here? After all buying versus renting is a long term decision and in the long run you would expect your house price to go up by at least the current 2% inflation rate. Alternatively you could reason in constant dollars and assume constant house prices, but then the real value of your credit should decrease about 2% per year. This is another $20,000 per year in favor of buying or did I get something wrong?

  3. baxter says:

    Let’s say that the house costs $1 million, that renting it would cost $5,000 per month

    Yeah, right. That’s a reflection of reality now.

    if you buy, you’re still down $6,000 in property taxes, but you also need to pay 6% interest on an $800,000 mortgage, which is another $48,000.

    See? A mortgage payment(amortizing) about $4796.4 compared to a rent of 5000.

    Or mortgage ~= rent!!

    Where is that magical place in California?

    You are so disconnected from reality. In bubble areas mortgage is more than twice the rent, for the typical home. (it may not be so at the extreme high and low ends, due to availability reasons)

  4. Nicholas Weaver says:

    Is my spreadsheet, and the actual numbers from last year for buying my apartment at the special “discount because otherwise you could give us real headaches, as is” price.

    Not included is the one huge advantage of buying (a massive hedge against inflation, I assumed a 3% inflation and not more), and the one huge disadvantage (vulnerability to megacatastrophies. I don’t know about you, but an apartment at about 2 feet above sea level, on bay fill, in the SF bay area, doesn’t strike me as long term stable).

  5. Nicholas Weaver says:

    Sorry bout the duplicate post.

    One other thing, you excluded property tax (~1.25%! but at least in california its effectively fixed as its on the price you paid, not the price its assessed at today). Thus for the example of a $1.5M house, thats another $19K/year in (admittedly deductible) costs.

    And don’t forget insurance (in CA, earthquake insurance isn’t cheap, but if you are on some particularly vulnerable soils, you either want that insurance or want to assume a 1% chance/year that your entire investment goes bye-bye, take your pick)

  6. Nicholas Weaver says:

    Finally, your rental rate is WAY out of line. Here in Napa, I’m renting what would probably be a $600k-700k house.

    Monthly rent? $1675.

    Data for SF proper, first hit (I could have looked further but this seems optimistic/high actually)

    $3000 a month

    A bit of Zillow has the places in that neighborhood at at LEAST $800k, most at $1M+.

  7. Felix says:

    Now that is a crazy datapoint. You can take your $650,000, invest it in 30-year TIPS, and guarantee yourself a 3.375% REAL rate of return, which is $1,828 — more than enough to cover your rent. In other words, your principal goes up with inflation, AND you’re paying your rent on top. It’s hard to justify buying in that situation.

  8. Nicholas Weaver says:

    Yet at the same time, it makes sense for the landlord to keep renting.

    He bought it in 1990 (while still under construction). Its a nice stable income, its 100% inflation sheltered, and his costs are very low (as its income on an asset he paid very little on and has little cost on).

    However, if/when it is sold, it will not be used as a rental unless the new owner really likes losing money.

  9. Lord says:

    Rents rise with inflation though, faster than inflation in metropolises, so eventually it is always cheaper to rent, but eventually can be a very long time. Some times to buy are much better than others. However, I think most people buy because they can’t stand having a landlord, utterly can’t stand it.

  10. wcw says:

    No, Felix, no — that was the point of my overlong rant to start this thread. Even with California prices and rents, a rational accounting of the overgenerous tax subsidies makes about one in three futures better off for owners. Why? Mainly, the interest deduction and the gains tax shield. TIPS principal adjustments are taxed away, as is the interest income. Poof, goes your guaranteed sinecure. Your $650k house throws off more than a rental equivalent (which implicit income, mind you, is also never taxed): you get a stream of tax deductions off your mortgage interest and your capital gains are essentially never taxed.

    As I said, it’s a no-brainer in the *absence* of taxes — but taxes exist, and my guesstimate is that ownership rates among likely voters likely push 80%, so they are politically safe.

  11. Roger says:

    Some further thoughts to factor in

    In the long run house prices have tended to have a relationship with average earnings. Does this justify assuming they increase at more than inflation? and what costs may be incurred in keeping a house to an improving standard so that it does this?

    And maintenance costs need to be counted.

  12. wcw says:

    Historically residential housing is a 1% real grower at constant house quality. The 1997-2006 5+%-real-appreciation decade is the great exception to that 1%-real rule of thumb, but I do not actually find that too irrational. The 1997 tax-law change turned homes into cap-gains tax shelters, and prices needed to adjust above normal growth to compensate. The expansion of alt-A and subprime lending the last few years, despite the fallout to come, should end having expanded the pool of potential borrowers. However, I don’t see any sea changes thereafter, so I think it goes back to being a 1% real grower, and I could see the worst 2003-2006 excesses inflated away over the next decade.

    Due to this discussion I have been toying with the idea of a product that hedges out house price and instead levers up in something like TIPS. I can’t quite figure out how to do it, mainly because TIPS interest is taxable. Otherwise you really would have a sinecure. You’d collect tax-free owner’s equivalent rent by living in the house. You’d hedge out that price risk. You’d borrow at around 0% real, after the IRS and FTB get done subsidizing your interest payments. Voila — serious alpha, since the tax-free OER probably adds another 0.5% real to TIPS. A 2.8% real return isn’t far below what you expect from equities going forward, but in a much lower-volatility vehicle you hence can lever up with the mortgage.

    A chicken in every pot, and every household its own hedge fund.

  13. RichB says:

    I moved from California to the UK last year, and it’s interesting to extend this analysis to the UK housing market where mortgage interest payments are not tax deductible. You might think that would convince more people to rent, and yet the ratio of purchase price to rent is even worse here. And housing prices are still appreciating here in the 10%-12% range (5%-6% if you exclude the more exclusive areas of London where the hedge fund managers and Russian oligarchs are buying).

    I took a house that was listed on the internet both for sale and for rent and created a model to understand what you would have to believe for it to make more sense to buy rather than rent. The house is a family home with 5 bedrooms and a big lot located just outside of London on the other side of the M25. List price is 795,000 pounds and the monthly rent is 2,750.

    For the model, I calculated the monthly mortgage payment for a 20 year mortgage with 20% down at current rates, 6.1%, and that came out at around 4,600 pounds a month. (There are cheaper rates out there, but they involve points and starter rates that are just moving the costs around. I used the lowest APR.) Upkeep on the house was assumed at 0.5% of purchase price (i.e. no kitchen/bath remodeling allowed). Stamp duty, paid up front by the buyer, is 4%. Capital gains on a primary residence are tax free.

    For the rental comparison, the difference between the monthly mortgage payment and monthly rent, as well as all up front costs, are assumed to be invested at 5.5% (with a 40% tax rate) and rent is assumed to increase by 3% a year (CPI has been averaging just above 2%).

    Given the huge difference between the rent and the mortgage payment, any rationale for buying rests on the capital gains. It turns out that for a 10 year holding period, you have to assume that the house will appreciate by 7.5% a year for the two options to be equivalent on a present value basis. If you had to sell after 5 years, you’d lose 50,000 pounds (on a present value basis) by buying, assuming the 7.5% annual appreciation rate. Houses in the southeast of England outside of London are now seeing annual gains of about 6% (more than double CPI) and this is supposed to be something of a boom time for property prices. At that rate of appreciation, you’re 115,000 pounds worse off by buying, assuming you hold the house for 10 years. This house actually has a higher rental yield (i.e. rent – upkeep / purchase price) than most rental properties. The rent yield is 3.7%, while the rental yield on most new buy-to-let properties is supposedly somewhere in the low 3% range.

    It’s interesting, that given these assumptions, financial advisers here are still telling people that renting is a waste of money (for example, one of the financial advice columns in this past weekend’s Financial Times). Housing prices here have gone up a lot in the past, but it seems hard to argue that they will continue to go up by more than 3 times the CPI given current levels of affordability and the outlook for interest rates.

  14. David Sucher says:

    ” Let’s say that the house costs $1 million, that renting it would cost $5,000 per month…”

    I, too, wonder how likely that is. Sounds like a sorta rent for a million dollar house.

    Of course I can’t speak about million dollar houses but I can with some expertise about $450,000 houses in Seattle which would rent for maybe $1600 if it is charming. On a strictly-economic (cash-flow & “let someone else worry about the roof” basis,) it would only make sense to rent.

    But a house or (to a lesser degree) condominium is something you can play with and shape. It is not an economic investment except over the very long-run.

    There is also a very important status factor, some hold-over from the days when fewer peoplewere employees and ownership of assets was the key to feeding one’s family.

    But all in all, the reasoin to rent is that when I come home and I feel like taking out a wall between two rooms, I can simply go ahead and do it, with no one to ask.

  15. A great real estate calculator that includes reant-vs-own calculations is RealtyJuggler Calculator. It runs on SmartPhones and PDA’s from Palm as well as Windows Mobile / Pocket PC. The calculator includes a tremendous level of detail including computing tax benefits of owning, returns you would get in the stock market if you rented and didn’t pay a down payment, PMI / insurance / tax costs, transaction cost for buying and selling a home and much more. The way the software works is that you fill in the blanks to some basic questions and a plain english explanation comes out explaining the financial situation of renting compared with buying. It’s extremely easy to use and built in a way where you can tweak the settings to determine where it would make sense to rent and where it would make sense to buy as well as give you straight honest answers to specific scenerios.

    This is a real must have product for potetial home owners, especially in the current market climate.

    You can download a 30 day free trial from the company web site. the product costs $9.

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