## Monday, April 16, 2007

### How much should I pay for a house?

I was thinking about the advice I should give to the people I know who are considering the purchase of a place to live and I came up with a way of simply expressing the math that is in my head. I wanted to keep the advice quite simple since I recognize that most people get lost after 1 + 1 = 2 and 10 x 10 = 100.

So here we go, a simple model for evaluating how much a dwelling is worth. It factors in comparable market rent, opportunity cost of down payment, maintenance/fees/taxes (expressed as a % of market rent), and, very importantly, mortgage costs. The "low price" is what I consider the highest price that the property in question would be a "Value" buying opportunity from an investment perspective. The "high price" is top price for what I believe a 'rational buyer' would be willing to pay for the property given the choice of renting or buying the same property.

The formula is fairly simple. It is a Present Value calculation of the mortgage payment over a 25 Year period plus a factor for maintenance, taxes, and other fees. I assume the "Value" buyer wants at least a modest positive cash flow from day 1 and factors a decent amount for costs with no ownership premium. A 'rational buyer' is willing to pay a premium for the so-called 'privilege of ownership' and does not factor in as much for maintenance as the resident owner can do the work him or herself.

For kicks, I added the estimated current market price in Greater Vancouver and the necessary price correction to bring it in line with the "rational buyer's" highest possible price. Feel free to poke holes in my methodology.

UPDATE:

An alternative valuation method reflecting the total lifecycle usage of a property. These formulas determine the price, above which, it is better to rent than buy. This number is represented in the column "PV of Property" and it takes into account the age (lifecycle stage) of the buyer. I also added some various interest rate and inflation scenarios for interest sake (pun intended). If the price of the property is above the PV of Property amount then it is cheaper to rent - for life. Click on the picture to enlarge.

tulip-Mania2 said...

Excellent, I think, with your permission, I will email the chart to all the realtors who publish their Email address.

But don't forget Mohican, the calcufuckations don't apply to Vancouver, where corrections are not possible because we have run out of land, the olym...............

M- said...

For what it's worth, a month ago I did a similar calculation on some rental housesI found on Canada.com rentals.

A couple of houses that I saw actually listed their street addresses. One was a Westside bungalow near Langara. The 2007 BC Assessment value was about \$650,000. The asking rent was \$2150. Another property, a house in Shaughnessy, was assessed at about \$1.2M, and the asking rent was \$3500.

Prices out of whack with rents? A correction due before I would consider investing? You bet!

Paul said...

I was just at a 475k apt for sale and the rent was 1350! lol what a F-ing joke....

Warren said...

Hey Mohican,

As a current owner/landlord, I'd say the housing "buy" values are a little low. That being said I don't know all of the math behind it. I would not re-buy my apartment at its current value to rent out (as is probably the case with 99% of apartments in Van), but I don't know if the values you're listing are even realistic. My purchase price was \$112k, rent is at \$960. Current market value is approx \$240k. According to that chart it would have to drop at least \$100k, or 41.6%. I'm expecting a correction, but I'm sure it won't be to that level. I don't think people would ever be able to buy again based on what you list.

tulip-Mania2 said...

"I'm expecting a correction, but I'm sure it won't be to that level. I don't think people would ever be able to buy again based on what you list."
Warren, you can think what you like.
It won't change a thing.

You might want to read a little history on financial manias. Lots of volumes to choose from.

South Seas Bubble, Tulip mania, Florida Land Bubble, Stock Market Bubbles, Nasdaq, Vancouver's previous crashes,

Yeah it's different this time!

Tick Tock, Tick Tock.

happy renter said...

I rent for \$1,300 per month for a 812 sqft unit and the same unit in the condo next door, 750 sqft, is offered at \$500,000. This is way out of your chart. 50% correction expected? Or does an extra bathroom justifies the extra \$300,000?

jesse said...

NPV using what discount rate? This has a huge effect on the calculation.

Has there ever been a time when the "ownership premium" has been zero? I think there was a window, between when rates started falling in 2001 and when house prices started rising, when this happened. The only thing was, at the time, there was less certainty rates would remain low. So the "value" investor, if buying at that time, would have been betting on rates staying low.

Going forward from now, even if prices drop to "value" guy's range and rates stay low, there is a risk rates will rise. But the difference is now that there is no broad expectation of substantial rate rises. There is risk to some degree, only the rate sentiment is very diffrent from the last "value" window in 2001-2003.

The point is that even if prices tank and you "value" buy, there is some risk.

dot com refugee said...

I recently moved to coal harbour and am paying \$1,750 to rent a view two bedroom.

Mohican's valuation model shows that I should be willing to pay about \$250,000 for this space.

Unfortunately for me, the last suite like this one to sell went for a hair under \$800,000.

patriotz said...

I don't think people would ever be able to buy again based on what you list.

Uh huh. Well, in 1983-84 houses in Vancouver were selling for 100x monthly rent. Granted mortgages were about 9% or so, if you adjust for the lower rates today you'd get a multiple in Mohican's range.

But that can't happen again right?

casual observer said...
This comment has been removed by the author.
mohican said...

warren - I am not suggesting that prices will correct to that level but I am suggesting that, for the rent level I indicate and the interest rate I indicate, rents will need to rise and / or prices will need to decrease for it to make sense for me to buy anything else.

jesse - I used the longest available mortgage rate (10 years = 5.75%) as the discount rate to remove as much risk as possible from the equation.

dot com - sweet deal you have there

patriotz - In 1984, the 5 year mortgage rate was between 12% and 14%. This would mean, in my calculation, that a place rented for \$1000 should have sold for approximately \$85,000 to \$95,000.

mohican said...

I think that it might be helpful for you to understand the perspective that I am coming from here. Some history:

A few years ago, just after getting married, my wife and I moved into a rental suite together and paid \$750 / month for a small but decent place to live. We didn't like our landlord and we wanted to buy a place eventually so we started shopping for a nice condominium.

After looking casually for a couple months and looking more seriously for another month we found a place we liked and that was reasonable. The place we bought was \$114,000 and approximately 25% larger than the suite we were renting. Our mortgage payment (amortized over 25 years), strata, and taxes were roughly equal to our rent. This seemed like a smart decision to us so we did not have a problem committing to it.

Fast forward to today, similar condos would sell for \$180,000 and would rent for approximately \$850 / month (strata + taxes = \$250/month). By my estimation, our place's real market value today should be around \$120,000 to \$135,000. This represents a correction of approximately 25% to 33%. I think this is fair.

freako said...

Interesting idea.

I know it wasn't intended this way, but I just want to caution against "shoe horning" various housing units into a formula without adjusting and accounting for certain factors.

Just as a low PE stock may not be a better buy than a high PE stock, there is more to valuation than cash flow. For example, all else the same, low density will have worse cash flow than high density. Rural will have better cashflow than urban. Old will have better cashflow than new. There is a valid reason for all these.

The NPV calculations are a great STARTING point. Then you need to evaluate the circumstances.

" I used the longest available mortgage rate (10 years = 5.75%) as the discount rate to remove as much risk as possible from the equation."

The longer terms do contain a liquidity/risk premium. If you want longer terms, you could use bonds.Could you explain what you mean by "Present Value calculation of the mortgage payment"? Do you just take the future payments and discount them back? At the end of the life of the mortgage, the property will continue to provide shelter while incurring only taxes and maintenance expenses. A renter will keep continue paying perpetually.

patriotz said...

Has there ever been a time when the "ownership premium" has been zero?

During the Great Depression the ownership premium was negative, big time. If you had the down payment, you could buy a place with 1/2 the monthly cost of renting. But things could never get that bad again, right?

Thanks for the tip re mortgages in 1984, Mohican. I was a bit low on the rates, but I'm sure I was right about the 100x multiple. For example, a 125K house could rent for 750 (main) + 500 (suite).

Of course there are places right now where the ownership premium is zero or less, such as Nowheresville, Sask, or Detroit.

Warren said...

mohican - your point is valid, I just hope people don't wait for real estate to hit these values before buying, as they may never buy again.

Rent multiples of course vary across different housing types and regions in the GVRD. I think a reasonable investor waits for trends and tries to predict future values. If we get a 30% drop, and then things begin to rise, I'd seriously recommend buying to anyone who's thinking about it. Don't keep waiting for that mythical 45% drop that may never happen.

Interest rates are obviously key. There will always be a premium on ownership.

freako said...

"Interest rates are obviously key. There will always be a premium on ownership. "

I think we have to define "premium on ownership". Technically, there has always been a discount on ownership, else a renter would have been better off in the long run, and that has clearly not been the case.

A cash flow difference is really not a "premium". Second, an owner's premium is an a renter's discount. A renter's discount is a landlord's loss. Clearly, an owner's premium would make RE investing unattractive. The investors would be expected to sell until there no longer is an ownership premium.

Warren said...

By premium I mean that individuals are typically willing to pay more to own. They want to be in total control of the property, feel more secure owning than renting, etc.

If current/future/permanent cash flows and values were equal, I think the overwhelming majority would choose ownership. People are simply willing to pay more to own.

rentah said...

Taking into account various mortgage rate possibilities, the market price of the house I rent would have to drop 65%-85% (not a typo) to be cash flow flat/positive.
Even though I'm currently RE bearish and rent my primary residence, I actually would value owning, and my personal ownership premium would likely be as much as 25%. Meaning, that's what I'd pay over a simple cash flow valuation model price to own a property I liked.
So, at current mortgage rates, I'd likely be prepared to buy my rental for about 50% of current market 'value'.
---
That said, I see many properties on the market at present that in my opinion would still be expensive at half the price.

mohican said...

"Technically, there has always been a discount on ownership, else a renter would have been better off in the long run, and that has clearly not been the case."

I am not sure the case is so clear, at least not for the reason you are mentioning freako.

There have been times in history when owners have fared better than renters and I also think there are times in history when renters have fared better than owners - today being one of those times.

mohican said...

"Could you explain what you mean by "Present Value calculation of the mortgage payment"? Do you just take the future payments and discount them back?"

This is what I did - it was only a PV calculation on the mortgage payment.

An alternative method would be to use a lifecycle model of calculating the usable life of the asset and all of its future benefits - for the owners entire life. Lets say the prospective purchaser is 30 and expects to live until 80 years old = 50 years of usable life = 600 monthly payments. Adjusting for inflation (2.5%) the present value of total rent (\$1000 / month in todays dollars) paid would be \$342,298. Remove the present value of all ownership fees, taxes, etc and the present value of the residence becomes \$273,839. Factor in the cost of borrowing funds (5.5%) and assume that the owner wants a 'return of capital' adjusted for inflation and I come up with a present value of \$187,248.

In this valuation model this is the 'total lifetime breakeven point' for ownership. Recognize this does not take into account some risks or some potential winfalls - only cashflows.

jesse said...

"During the Great Depression the ownership premium was negative, big time. If you had the down payment, you could buy a place with 1/2 the monthly cost of renting."

I was not alive during this time. In the mid-80s, when the ownership premium was lower, there was also uncertainty on the direction of interest rates. Rates were crazy only 2 years prior and there was fear of a repeat occurrence. I agree with you that there are much better times to buy than others but when better times happen it will never seem clear cut.

Re "ownership premium" you can rephrase this as a "control premium" if you want. There is benifit to control when to buy/sell, stability, and the ability to rennovate and customize. Not all see this benefit but enough do to put a premium on owning. During times of hardship or falling knives this can change but the general bias is for a positive control premium.

blueskies said...

CBC news item

double ?!!?

vineland said...

CIBC must want people to sign up for their mortgages. How could housing double due to younger people's demand while our population falls?

jesse said...

"double ?!!? "

Double sure but from what pricepoint is a very good question. Currently the market is well above the long term average that CIBC dude is using as a benchmark. That said, boomers can live in their houses until well after retirement so the result could be inefficient usage of housing for the next 20 years at least.

freako said...

"By premium I mean that individuals are typically willing to pay more to own."

Ok, but if we include appreciation (as we should), it has been cheaper to own. In that sense, the ownership premium is a myth, and really is a gauge of cash flow, not ownership cost.

patriotz said...

People are simply willing to pay more to own.

Well they certainly are now in any reasonable future scenario of interest rates and rents, but historically that just hasn't been true. Prior to the inflationary era starting in the late 1960's, people were not willing to pay a monthly cashflow for ownership in excess of rent, and as I noted during the 1930's that reached an extreme.

The era of inflation changed that as people were willing to assume a cash flow shortfall in the short run in return for expected inflationary gains in prices and rents that would put them ahead in the long run - and they were correct up until the crash of 1981-1984. Since then we have seen asset inflation without matching wage or rent inflation, which makes buying increasingly more expensive than renting.

Perhaps some market psychologist can study the current crop of buyers to find out if they really think they're going to come out financially worse than renting, or expect price or rent gains to rescue them.

We'll see how expected gains hold up in the next few years in the face of a certain RE debacle in the US, and inevitable effects here.

Warren said...

freako:
Ok, but if we include appreciation (as we should), it has been cheaper to own. In that sense, the ownership premium is a myth, and really is a gauge of cash flow, not ownership cost.

Here's one for the books.. Freako advocating "buy!". When you say cheaper to own, we need to be talking about some sort of time period. If you have a 25 year amortization and live another 50 years, you could well be ahead, but if you croak on that 25th payment, you might be behind (but who cares, you're dead). When you buy and the ensuing RE market is the big determination in any of these factors. I'd like to think rents would match RE values in terms of investments, but they've been way out of whack for a while now. We all assume there will be a correction back to long term historical averages, but in the mean time there's lots of money being made and lost on this differential.

patriotz:
Since then we have seen asset inflation without matching wage or rent inflation, which makes buying increasingly more expensive than renting.

If RE is going up, commodities, consumer goods and wages are not, then is it truely "inflation" or is it real gains? RE gains over the past 5-7 years are huge nominal gains, and almost as huge real gains. Of course to realize them you have to cash out (sell), but calling them inflationary is not really accurate.

We'll see how expected gains hold up in the next few years in the face of a certain RE debacle in the US, and inevitable effects here.

Yes. I'll go on record agreeing with my post about that we won't see anything in the 42% range. 20% easy, 30% I give a 50/50 chance of happening.

bc locust said...

An interesting comparison between economic cycles and earthquakes. Pretty bearish...

http://tinyurl.com/2d9ln8

patriotz said...

is it truly "inflation" or is it real gains?

"Inflation" simply means a number is getting bigger. You can have monetary inflation, commodity inflation, wage inflation, asset inflation, etc. Or grade inflation in schools or what have you.

To compute the real gain of anything you have to pick a price index to deflate it against. This is usually the CPI. So for example if wage inflation exceeds CPI growth, we say real wages are increasing. As was the case 1945-1975, for example.

Indeed it's quite unusual to have real gains in any item without inflation of its price - that would require a declining CPI, which we haven't seen since the 1930's.

but calling them inflationary is not really accurate.

Saying that there is "inflation" in the price of some item is something entirely different from calling that increase "inflationary".

Calling price gains "inflationary" means they result in an increasing CPI. This is usually not the case in asset inflation, indeed the reverse is often true (dot-com boom -> too much fiber optics -> cheaper long distance, RE bubble -> oversupply -> cheaper rents). Also asset inflation often leads to asset busts which are deflationary due to wealth destruction.

And I think you're way too optimistic about nominal price declines in BC RE. Many US markets are already down 20%, and the fiasco is just getting started. And there's no magic amulet to ward off the damage to BC.

freako said...

I am advocating buying, just not right now. In the long run, there clearly is an owner's discount. You couldn't even cherry pick a 10 year period when nominal prices have been down, because there are none.

I was responding to your comment, "Interest rates are obviously key. There will always be a premium on ownership. "

I maintain that when measuring true costs of shelter (not just CF), the odds are HEAVILY stacked in favor of owning. As it should be. Note I didn't say always.

I don't think CF comparisons measure just that, a do no capture the true costs of shelter.

"but calling them inflationary is not really accurate."

As patriotz points out,, "inflation" in the term "asset inflation" is not to be confused with the traditional definition.

"Yes. I'll go on record agreeing with my post about that we won't see anything in the 42% range. 20% easy, 30% I give a 50/50 chance of happening. "

For lack of a better method, I predict that real prices will rejoin the long run trendline. This can occur with a 40% nominal drop in a one year period, or flat nominal prices for 20 years. The return to fundamentals can take many routes. I am going with a two year period for the bulk of the decline. But when does it start? How about between now and summer?

Warren said...

patriotz:
Many US markets are already down 20%, and the fiasco is just getting started. And there's no magic amulet to ward off the damage to BC.

Many US markets have yet to see any drops at all. Are we a Seattle or a Pheonix? or a Detroit? To parrot a cliche "all real estate is local". The US has its own share of problems, but we need to keep in mind that not all metro areas are dropping like a rock, the ranges are all over the map. I searched for a blog link posted recently but couldn't find it.

freako:
But when does it start? How about between now and summer?

I think we are another year away from seeing real drops. I think this summer will be flat, which should scare some people, but 2008 might mirror 2006 in some of the bust US markets (California, Arizona). Personally I'm aiming to buy again in 2009, I hope the market lines up to dish me some bargains, I don't want to wait too much longer than that.

M- said...

Mohican: I like your graphs for life-cycle housing valuation. It adds a point of what the "real value" to a person is for a housing unit, including the old argument of "after you've paid off your mortgage, your house is free!".

What is the difference between gross and net rent? Also, does it take into account anticipated maintenance for home-ownership?

mohican said...

M - Gross Rent is what the renter pays. Net rent is Gross Rent minus a factor of 20% for ownership costs, including taxes, fees, and maintenance.

freako said...

"Many US markets have yet to see any drops at all. Are we a Seattle or a Pheonix? or a Detroit?"

Based on prices and fundamentals, I'd say we are a mix San Diego, Miami, and Phoenix. We are not Seattle or Portland.

Warren said...

Check this timely article out:

The article makes a good point that is obvious to most of us here. It could use some graphs though.

Anyway, the best part is the comments. Same drivel from real estate "experts" who bought their first property 4 years ago.

New Meat said...

I picked up a copy of the NY Times last week because of this front page article: "A Word of Advice During a Housing Slump: Rent" April 11, 2007, Wednesday.

Obviously, there are different reasons to rent vs buy. According to this article it makes better financial sense in many US markets right now to rent because over the near term (5 years and longer) you'll get no return on your investment when you buy.

In Vancouver, it's better to rent because of affordability issues.

freako said...

" This number is represented in the column "PV of Property" and it takes into account the age (lifecycle stage) of the buyer."

I don't totally understand the life cycle aspect. Isn't that mostly irrelevant? If markets are remotely efficient, the asset will be priced on ITS economic life, not your physical life.

Anyhow, I have come to the conclusion that rent vs buy calculators both oversimplify and overcomplicate things.

Here is how I see it:

1. You make an assumption about real RE returns.
2. You make an assumption about inflation.
3. You assume that rents will follow inflation.
4. You assume that alternate investments will return approximately real RE returns plus inflation plus rents.
5. You need a current apples to apples homeprice and rent.
5. You assume that the owner buys house outright.
6. You assume that the renter has the same amount of money as the owner used to buy the house outright. He invests all of it at the investment rate.
7. You need a factor for other ownership costs, such as taxes and repairs/maintenance.

Fire up Excel and away you go.