Rent vs. Buy Redux: the rule of 777?

There were a number of excellent comments on my last post, and I thank everyone who had the patience to read through it and check out the spreadsheet.  Hopefully it was (or will be) useful.

However, I did make a fairly substantial omission.  I have created an updated version of the spreadsheet at the following address: (and thanks to JR for pointing out that readers can open the spreadsheet and play with their own version by going to File->Copy Spreadsheet in the dashboard): http://spreadsheets.google.com/pub?key=pHgERPShu-vGRshNShxpKOQ

The omission is subtle but important.  When you calculate the present value (PV) of the home ownership scenario, you have to include the extra payments that occur because of the transaction itself (including cap gains taxes, agent and legal fees, financing fees, the underuse of the home during the selling period, etc.).  I had included this before in the spreadsheet, although for this version I reduced the average length of stay to 7 years to match industry trends, and increased the average transaction cost to 9% to better match the established academic literature. 

The main issue is that I had to include not only the current costs and the costs of the next transaction, as I had before, but rather ALL of the discounted cashflows from transaction costs every 7 years from now until eternity.  This does have a substantial effect, and my last spreadsheet formula for that cell suffered from this omission and some other silly errors due to a late night post.

You might ask, why do we include the future transaction costs that will be borne by another owner?  This is a subtle question, and I think the simplest sketch of a proof is this: if, whenever I sell, I buy another house that is roughly equivalent to my current house (it has the same price and I value it the same), then the economic choice of being a renter or owner must account for all of the transaction payments that I would make over my lifetime as an owner.

For the curious, there is some fun little math involved in computing the PV of those transaction costs that I will leave to a future post if there is interest.  I will also try to give more thought to Ralph Liu’s comment on the last post about a financial instrument allowing someone to switch between ownership and renting on a given house; that is very interesting.  Also, I found it amazing that rents have been decreasing (on a real basis) in the long term, and I have some ideas about why it might be true.  I’ll save it all for a later date!

 

Rent vs. Buy: the rule of 666

At what price is renting preferable to purchasing a house?  There are many factors influencing the price of a home or apartment, and the relative valuation of homes remains a matter of both art and preference.  But we can still ask, for a given home at a given price, what would be the equivalent rent that I should be willing to pay for that home.

If I rent, I don’t have to invest a large down payment, pay maintenance or insurance costs, property taxes, or transaction costs associated with buying/selling the home.  On the other hand, my rent will gradually increase over time, and I won’t benefit from the mortgage interest deduction or the relatively cheap lending rates available for mortgages.

I have come up with a spreadsheet model that you can view at http://spreadsheets.google.com/pub?key=pHgERPShu-vEtwvFmEbRBVQ [write a comment if you want me to send you an excel version you can play with].  First the answer: under reasonable assumptions, an equivalent rent should be around $666 per month for every $100k of house price.  Thus a $400k house should rent at $2666 per month.  Alternatively, given a choice between purchasing a $300k house and renting at $1500 per month (as opposed to the computed $2000), we should choose to rent and be happy to pocket the extra $500.  Or if we know that a house/apartment should rent for $2000 based on comparable properties, we can compute that a selling price of $350k is about $50k too high.

The model makes extensive use of a concept called “Present Value”.  I won’t go into the details here (see Wikipedia for a better introduction), but the idea is that the PV of a set of cash payments over time equals how much money I would have to have in my investment account today, at a given rate of appreciation, to afford the payments using just the money in the account.  We first calculate the PV in the case of renting, where the payments are assumed to start at a value X and grow at a given rate forever, and in the case of outright purchasing, where the sale price is paid upfront and maintenance and tax costs grow and are paid over time just like rent.  We then compute the value of X such that the two PV calculations are made equal.  This is the equivalent current rent under the assumption that the buyer purchases the home outright with cash.

Then we calculate the benefits of using mortgage financing to purchase the home.  For simplicity, I assume an interest-only loan that lasts forever, which makes the math simpler but doesn’t change the numbers much.  There are now two benefits that we subtract from the PV of the buy scenario: the first is due to the mortgage interest deduction that we get from Uncle Sam, the second is the financial benefit of having a loan interest rate that is lower than the return we can get from our fictional investment account.  Adjusting our PV to account for these benefits, we get a much smaller equivalent rent.

Finally, we need to add the expected transaction costs of buying/selling to the PV.  The exact way that I calculate this might be the subject of a future entry, but to make a long story short, assume that the present value of the house today includes not just the current transaction costs, but the expected discounted transaction costs that will occur in the future every time the house is sold.  This increases the equivalent rent a bit to just around our lovely 666.

This model doesn’t include the value associated with “pride of ownership”, or more tangibly, the value that a developer/owner adds to her home through renovation or investment.  It doesn’t account for the fact that there may not be a choice between renting and buying a specific property (though it does give guidelines about how to negotiate a fair rent from an owner).  It also doesn’t account for the fact that a buyer might speculate that a home, despite being overpriced today, may be even more overpriced in the future (or from another perspective, that the speculator has a higher estimate of the rental growth than is currently priced into the property).  However, if a buyer is left holding an overpriced hot potato at the end of a bubble, he will eventually wish that he rented.

Furthermore, the given calculation is based on reasonable but specific assumptions.  The primary drivers of the calculation are the rental growth and WACC (the appreciation rate of our fictional investment account), and there are very good reasons why the WACC may be quite a bit lower (probably closer to 8 or 9% if we were doing this calculation for a REIT that has a well-diversified portfolio of properties, but don’t make the mistake of thinking that it should be as low as the interest rate on the loan or, god forbid, the fed funds rate) which will lower the equivalent rent.  Different people will have different assumptions (such as marginal tax rate, longevity of the lease contract, interest rates, maintenance costs, etc.).  In particular, people with high marginal tax rates are more likely to want to own than those with low tax rates.  People who expect to live in the same house for a long time are more likely to buy.  People who expect to create value by investing in their property are more likely to buy.  But this model should allow someone to appropriately value these effects and come to a rational assessment of the proper value of her house and whether she would prefer to rent or to buy.

 

Prediction Markets

I’ve been traveling this week back in the Bay Area and had an interesting discussion the other day with my friend Manu about the coming election.  I made a bold claim about the coming presidential election, namely that it was more or less already over and there’s no point in spending too much time thinking about it.  I was mostly trying to be polemical, but Manu is smarter than I am so he insisted that if I truly believed this that I should be backing up my predictions with actual bets on “prediction markets” that are designed to track people’s beliefs in elections and sporting events.  (Google “prediction markets” and you’ll find the same ones we did).

The basic idea is that you bid on a contract that pays a dollar only if an event occurs (such as Barack Obama winning the Democratic nomination) and pays nothing otherwise.  If you think the probability is high, then you might be willing to pay a high price (perhaps something close to the probability you ascribe to the event) and buy a contract if it’s cheap.  If you think the probability is low, you might consider “selling a contract short” by selling at a currently high price, with the promise to buy the contract back at the time of the election.  The idea is that if these markets have enough bidders/sellers then the bid and ask prices for the contracts will be close to each other and be close to an imputed probability of the event happening.

Initially we asked ourselves if there was some way we could perform arbitrage within these markets to make a little bit of dough.  For example, you can bid on Pr(Dems win Presidency), Pr(Reps win Presidency), and Pr(Indpts win Presidency).  These should clearly add up to probability 1.  Similarly Pr(Dems Presidency) = Sum [candidate c in Dem Party] Pr(c wins Presidency).  This is just mathematical formalism, but these constraints allow you to perform arbitrage if, for example, the bid price of Pr(Dems win Presidency) is less than one minus the ask price of Pr(Reps win Presidency).

You can go a bit further and play around with the assumption that Pr(Clinton meets Giuliani in national election) = Pr(Clinton wins nomination) * Pr(Giuliani wins nomination).  This doesn’t have to be true, but if the two events are independent (which they probably are, roughly) then the equation should hold.  There are a bunch of these little tricks you can play.  And presumably having crazy nerds like us playing these tricks to make little itty-bitty amounts of money will create rational pricing (at least insofar as these mathematical relationships hold).

But we discovered a problem.  As above, we should have Pr(D wins Pres)+Pr(R wins Pres)+Pr(I wins Pres)=1.  But does that mean the prices of the contracts should necessarily sum to 1?  Actually, no.  If I were to buy all three contracts, then with certainty I win exactly one dollar at the end of the contract.  How much would I be willing to pay for that?  It should be the present value of one dollar paid in November 2008, which we can calculate using the riskfree interest rate (let’s say about 5% for fun).  By this logic, I’d be willing to pay only 93 cents for this combined contract.  And yet the sum of the current bid-ask prices for the contracts are between 100.0 and 102.5 cents.  [I think the mathematically mature reader can convince herself that all contract prices should simply be the present value of the probability of the underlying event, i.e. divide the probability by the discount rate for the time period]

Does this mean that I can short sell the three contracts (receiving 100.0 cents), take the money and invest it in a bond, and then pay out 100 cents in 11/08 when the contracts expire and I have to pay a dollar for one of them?  This essentially would allow me to borrow money for free and make the riskfree rate of interest on it.

Unfortunately, no.  The way the services are constructed (that we found anyway), you would have to actually put 100 cents into your account in order to make the short sale and while you would earn a measly 3% interest rate on that money, you would not have the ability to use the extra 100 cents from the short sale to make further profit. 

Why does this matter?  It matters because rational investors/speculators may avoid making bets in this system too far from the date of the contract expiration because of the lack of return from money that’s invested in the bet, and the lack of true short-selling ability when the prices are too high.  But this defeats the fundamental claim of these prediction markets: that people with superior knowledge or predictive ability will incorporate that knowledge quickly into the prices of these contracts.  As we saw above, some of these contracts could be as far as 7 cents off from my predicted value and I still would prefer not to make a bet.

 

Fear and Loathing of MBAs

Why does everyone seem to hate MBAs?  I have had several conversations within the last week in which someone was trying to convince me that MBAs were 1) overrated, 2) overpaid, 3) unqualified to run a small business, and 4) unable to start a company.   The weird thing is that the majority of these people had MBAs themselves.  What gives?

It seems like there are two main components to an MBA degree: there are all of the things that are taught (and maybe learned) within the program as well as any networking connections that are formed, and there is the “signal” value (all things which might be reasonably inferred based on selection bias to apply for and join a program).

In the first case, it seems likely that an MBA is a positive thing.   I really doubt that a person actually gets negative value from an MBA program, and my sense is that even if the value may not always be worth the price of admission, a typical MBA graduate knows more about the fundamentals of business than before the program and probably has a better chance of being a good businessperson and/or manager than before.

But the signal value is the problem.  For one thing, the people that decide to get MBAs tend to be: 1) dissatisfied with their current career, 2) as good or better than their peer group in climbing the corporate ladder, 3) not in a startup or other all-consuming job that requires emotional commitment (like some non-profits), and 4) fairly analytical and comfortable in an academic environment.  This signal gets even worse if you look, for example, at Harvard MBAs (not to pick on Harvard), who need to be very smart, know that they are very smart, have had some success in their work experience, and want to be in a top-tier school.

So if you see a random MBA, they’re likely to be analytical, think they can solve all problems with Excel and Powerpoint, be less likely to be entrepreneurial, be good at climbing the corporate ladder, and know that they are smart.  All of these things might be neutral or negative in a startup or small business environment.

But that doesn’t mean that this same MBA is less qualified, with the MBA, to start or run a business than he/she would have been without it.  So there.

 

An Entrepreneurial Conundrum

My father recently read that Atlanta has more entrepreneurs per capita than any other major metropolitan area in the US.  We can’t seem to verify the source of this claim, but for the sake of argument, let’s suppose that it is true.  At first glance, it seems to be an extremely positive indicator.  Atlanta is the most entrepreneurial city in the US!  Who can argue with the positivity of this statement?

Except that the number of entrepreneurs is proportional to the number of companies that are founded.  If the number of companies founded is large, we can reasonably infer one or both of the following:

1. The average lifetime of companies (or lifespan of the entrepreneur within the company) is small
2. The average size of firms is small (meaning a great percentage of entrepreneurs to workers)

Unfortunately, neither of these two indicators are positive from an economic standpoint.  Companies tend to fail or be acquired due to poor management or poor capital markets (yielding larger, acquiring firms elsewhere); a short average lifespan implies anemic performance. 

Furthermore, small companies are less likely to take advantage of economies of scale or to generate a sustainable competitive advantage over their competitors.  A smaller average firm size would again imply diminished economic performance.

So my claim is that there may be an inverse relationship between the number of per capita entrepreneurs and the per capita economic output of a region or nation.  Now if only someone could get the data…

 

Pura Vida in Costa Rica

Last weekend, I enjoyed the sunny climes of Costa Rica to visit a couple of investment opportunities, along with my INSEAD buddy Martin Acosta, who is working at Aureos Capital (www.aureos.com).   While I had been to Costa Rica before, I had never really spent any time in San Jose, nor had I ever done any business there.  I was anxious to practice my rusty Spanish.

Of course, I hardly ever used my Spanish while I was there thanks to Martin having a set of friends and colleagues who all spoke nearly perfect English.  As it turns out, San Jose is an ugly town filled with lovely people in a beautiful country.  Traffic is dismal, there are no signs (in fact, there are actually no addresses, and people write down their address in relation to known landmarks), and roads are pocked with craters from neglect.  I thought it was amusing that the Costa Rican name for speed bump is policias muertas (dead policemen).

And even though violent crime is fairly low, Costa Ricans are afraid to park their cars on the street due to nearly certain theft and vandalism.  This means that nearly every housing community is gated and employs security, and nearly every restaurant and mall with parking employs 24-hour security.  I have never seen so many security guards or parking attendants in my life.

The primary purpose of this trip was for me to visit a Spanish language school that is up for sale, and that Martin and Aureos were originally interested in purchasing.  As it turns out, the deal is too small for their fund (a running theme for these private equity funds in emerging markets is that they can’t find deals that are large enough to justify their time…. and there’s no point risking money on small stuff when they can just pick up an annual 2% management fee in the meantime).  But despite that, we thought that the deal had sufficient merit that we could find angel investors and/or vendor financing, so I decided I would come down to see the place for myself.

It’s a beautiful building with a thoroughly modern architecture and glass windowed offices looking out over the San Pedro neighborhood of San Jose, which is a vibrant area near the University.  The grounds include a covered open-air terrace that serves as a restaurant and meeting place, and a walkway down a hill to a separate classroom building, lined with outdoor ranchitos for classes outdoor.  There are over 35 classrooms in total, so even if the class sizes are kept small (a surprisingly important factor in language immersion courses) there is room for at least 150 students. 

Unfortunately, San Pedro has seen better days, and while the building still looks striking, it is equally out of place.  Because the building lacks parking, it is difficult to convert the building into office space or other use for which tenants would require parking (again, street parking would require a security attendant at all times).  The school has been around for a long time, and although the quality of instruction is high, and the brand is fairly well-known, the school only attracts around 15 students on any given week, less than 10% of capacity.  There are 8 salaried professors who are paid above-market wages.  More professors can be added on in the boom times, but those 8 are permanent.

So Martin and I talked with the owner about the various options for buying this company.  At first, he was insistent on selling the real estate along with the operations of the business (both of which are owned entirely by him, except for a relatively small 14% interest mortgage on the property).  Because his asking price for the building was based on construction costs (roughly $60 per square meter), this was an inordinately large number, which didn’t capture the fact that the building would be almost worthless for any other kind of use.  Furthermore, the reported earnings for the operations were based on an artificially low rent, inflating the value of the company.  It took us a while to figure all of this out, and in the end, we had to deal with the fact that all of the numbers we were looking at had been collected by an accountant with little training, and somewhat suspect moral character.

Since earnings had been falling in recent years due to increased competition from other schools and other countries, the owner wanted us to use a multiple of the average earnings over the past 3 years, which he argued is a more accurate reflection of the steady state for the business.  If we did this, then he would consider renting the building to the company at a reduced rate while he looks for other tenants to fill the remaining space.  We then countered that in order to do this, we would only purchase a portion of the company now at a price below what we believe it is worth, with an option to purchase the rest in a year or two at a price above what he believes it is worth.  In this way, with the right incentives in place, we are all happy…. at least in theory.  Unfortunately, there was still a fairly large gap when we left the negotiating table and it’s not clear if the size of the investment is worth too much further energy.

After visiting the school, Martin and I also visited an ice factory, which, if you believe the numbers that the owner is quoting, is doing a shockingly good business.  It’s not clear to me why the owner wants to sell for 1.5x reported earnings, but it definitely feels fishy.  I guess this is a case when a good deal may not go through due to the asymmetric information problem (read “The Market for Lemons” by George Akerlof).

We spent the rest of the weekend chatting with other entrepreneurs and investors in town to see if we could structure a deal based on a bundle of different investments.  I won’t go into the details, because in the end it boils down this: 1) there are many small companies that can be bought cheaply (typical IRR is 40-60%), 2) venture capital and private equity partners don’t have an incentive to invest in small deals even if the returns are high, especially if it takes any amount of thinking to improve the company enough to sell it later, and 3) you need to be able to hire good managers who are trustworthy to manage these businesses once you buy them.

After staying an extra day in Costa Rica due to logistical problems at a poorly managed airline headquartered in another emerging market (ahem, Delta) I returned home with the feeling that there are tremendous opportunities in Latin America among smaller business.  However, in order to really capitalize on them, you need partners in those countries who you can really trust, you need energetic managers to reinvigorate the businesses, and you need to be able to attract capital by bundling together a large number of small, though similar, businesses together.

I think the same may prove true here in Atlanta.