Wednesday, July 25, 2007

Renting vs. Buying Simulation

It seems to me that the best way to address the financial aspects of the renting vs. buying conundrum is to use simulations. There are too many variables and complications for most people including me to get a handle on this problem analytically. Of course you need to make a lot of assumptions but these can be adjusted in a "sensitivity analysis" to see what effect each assumption has. My initial assumptions are as follows:

Both the renter and the homebuyer start off at age 30 with a disposable monthly income of $5000 and savings of $40,000. The homebuyer uses all this as a downpayment on a house with a 30 year mortgage. The renter invests the money in a taxable account with an after tax rate of return of 9% and pays rent of $1500 for an identical house (which isn't too far off for some of the bubble areas). House prices and rents rise at 4% per annum and wages at 5% p.a. Initially I assume that the homebuyer spends the rest of their after tax income and the renter spends an identical amount. The renter saves the remainder in the taxable account. Initially the homebuyer can't save any extra money but as the homebuyer's mortgage payments do not increase (but property taxes etc. do) gradually they can afford to make some additional savings which they also put in a taxable account. Both the renter and homebuyer increase their spending at the same rate as wages increase. I run the simulation till the end of the mortgage:

At age 60 the renter has a net worth of $4.74 million and the homeowner $3.88 million. Obviously there are possible assumptions and scenarios which would result in the homeowner ending up ahead in net worth terms. But these assumptions seem pretty typical to me and result in the renter coming out ahead.

Let me know if there are particular scenarios you want me to check out or I can even e-mail you the spreadsheet.


Anonymous said...

hello professor!
found this clip "money as debt" ( on line and just wonder if you would not mind take a look at it when you have time and comment on the validity of it. it's a bit long and i only know the very basic of econ theories but i still find it quite amuzing. thanks and good luck moving to australia!

mOOm said...

Somebody sent me this link before and I didn't get beyond the first few minutes then before giving up. The banking system as a whole creates money but each individual bank doesn't just create money. They each lend out money that was lent to them. Here is a Wikipedia article that tries to explain this though it looks more complicated than most standard introductory textbook treatments: said...

I'd use 6% as the house price gain assumption - this has been the average Australian house price rise over the past 70+ years. Despite the Eastern states being in a "bust" following the 1998-2003 "boom" house prices have started to appreciate again in the Eastern states. Canberra market has experienced boom conditions with the median house price surging by 7.4 per cent last quarter (ref:

You may also want to check out the after-tax amount delivered by renting vs. buying - the renter's investment gains would be taxed at half the marginal tax rate (say 20%) whereas the gain on your own residence in free of capital gains tax.

A third comparison would be to rent and salary sacrifice the excess money into a SMSF invested in an index fund - earnings are taxed at 15% in the SMSF, and realised gains taxed at 10%. Once you reach retirement age you can convert the SMSF into pension mode, in which case the capital gains are tax free! said...

I forgot - the other consideration is that once you have some equity in your home you can use get a "portfolio loan" to borrow funds to invest in stocks etc. The benefit of this compared to a margin loan is
a) same interest rate as your home loan
b) no margin calls

The benefit of this form of gearing compared to an internally geared share fund is that the interest is deductible against your other income, whereas with a geared share fund there is no tax deduction available (although you may get some franking credits passed through).

mOOm said...

The 4% nominal gain is based on Shiller's work for the US housing market. If I assume 6% house price and rent gains without any other changes to the model I get net worth of the buyer at $4.45 million and renter at $3.79 million after 30 years. The $400k house rises to a price of $2.29million and rent is over $8000 per month at the 30 year point. This is a good point which shows that coming out ahead from buying could be the case if houses appreciate very rapidly.

On taxes I assumed that the investor pays 10% of the total return each year. The US Federal rate for capital gains and qualified dividends is 15%. State taxes could range from 0 to 9.3%. So I am assuming that the investment is in a high tax state and half the gain is realized in dividends or capital gains each year. In Australia the taxpayer would be in the 40% bracket with franked dividends at an effective 10% and CGT 20% we would need to lower the tax rate. or trade more. So your second point I think is built into the baseline simulation.

Putting the savings into an Australian superannuation fund I can assume they are taxed at 15% on all gains and 15% going in - so lets assume the salary sacrifice (equivalent of pre-tax contribution to a 401k in the US) results in saving 25% of tax. This will boost the amount going into saving. With no other changes the owner reaches $4.54million and the renter $5.65million. If I also assume 6% house price appreciation the owner reaches $5.01million and the renter $4.46million.

Bottom line - there is no simple answer to the question of whether renting or buying is best - it depends on assumptions.

mOOm said...
This comment has been removed by the author.
mOOm said...

Oops - sorry for the double posting - yes I haven't assumed any refinancing of the mortgage or any margin loans in my base case. The fact that interest isn't explicitly deductible in the geared product makes no difference to your total tax bill unless you want to go to negative gearing. The interest rate will be much lower in most cases than what you can obtain yourself and so is the way to go unless you expect very high capital appreciation.

Anonymous said...

Hey Moom, I'm late to the party. Catching up on blog posts.

What formula did you use to determine a house price of $2.29M based on 4% appreciation per year? My numbers show this to be significantly higher.

mOOm said...

Hi Clifford. 6% p.a. (not 4%) results in a 5.74 fold increase after 30 years. (1.06^30). Multiply that by $400k and you get $2.297 million.

Anonymous said...

Hey Moom,

I certainly enjoy posts that make me think.

I thought your assumptions showed a 4% appreciation on the house. But that's not important.

I'll have to disagree with your decision to ignore the tax benefits. Your response above focused on capital gains tax. But yearly income tax was not addressed. Using your numbers, I show the home-owner saving on average $6500/year over the renter (assuming 33% fed/state tax rate). With an income level of $60,000/year, the tax savings of $6500/year becomes too significant to ignore.

Speaking as an engineer of course.

If the home-owner has access to the same 9% after tax account as the renter, then $6500/year over 30 years at 9% is approx. $1M. Add this to the $3.88M you arrived at and the two scenarios are neck and neck.

One of the major benefits of buying a home is the yearly tax breaks. I don't know what all your other assumptions are based on this article. But the tax breaks are, in my opinion, significant and can't be ignored if the attempt is to do a fair analysis.

Did I miss something?

mOOm said...

There are no mortgage interest tax breaks for owner occupiers in Australia. But even in the US all the tax break does is reduce the effective interest rate you pay. For couples in low tax states without a lot of deductions it's likely they don't get much of a tax break at all due to the value of the standard deduction. Most people don't get all the possible deduction.

Anonymous said...

That's what I missed. You're talking about Australia.

Thanks for the indulging! :)

mOOm said...

Mortgage interest tax breaks are vastly over-rated by most homebuyers in the US IMHO. I can run the simulation with any numbers. I'm pretty sure that reasonable numbers for California will require a high rate of expected homeprice appreciation to reach breakeven.