How to Value Options in Real Estate

I love working in commercial real estate because there appears to be more rationality in this arena than the residential side (note I said more and not suggesting that either market was rational).  I am and always will be a numbers guy at heart, so one question that has bothered me has been how to value real options in real estate.  If two identical 11 story properties are next door to each other, but one is zone for 11 stories, while the other is zoned for 15 how much is that additional zoning worth? This question goes well beyond simple zoning, think about assumable mortgages or some other forms of seller financing.

To answer this question one must first think about the probability of exercising, the cost of exercising, and the volatility of the situation.  Immediately my mind went to the Black-Scholes pricing model for standard options.  Unfortunately real estate does not trade as often and is much harder to price than stocks.  Additionally, it's not always handy when you need to make some quick calculations.  So where do you go from here?  My recommendation is a far simpler approach: the binomial pricing model. 

The binomial pricing model simply takes the probability of the upside of the event multiplied by the upside payoff plus the probability of the downside of the same event multiplied the downside payoff.  Adding in the cost of capital fills out the rest of the model, making it very easy to use and apply.  The attached link provides the full model, but use of the simplier decision tree framework can be done as described above to get an idea of what the option is worth.

Let's look at an easy example of an assumable mortgage.  Many banks charge points or an additional fee for an assumable mortgage.  Let's say (for ease of examples) they charge 1 point for this loan vs. a traditional fixed loan.  Most of the value of this option occurs when interest rates go above the rate of the assumable loan.  There may be additional value for consumers who may not be able to qualify for other loans, but let's ignore that for now.  Looking at the feds current view of inflation, let's assume the probability of interest rates increasing is 75%.  Finally, we can guess that this assumable clause will add 5% to the value of the property (a slightly conservative assumption).  We can estimate the value of this option by multiplying the 75% x 5% x the value of the building minus 25% x 1% x the total loan amount.  Again, this is a simplistic version of the model, but gives you a ballpark figure of what this option is worth.  Keep in mind if the result is negative, the purchaser would simply take the traditional loan.  If the result is zero the purchaser will be indifferent between the having and not having the option.

So how can you use this in business?  Use this tool to think out of the box more and win more bids.  When approaching a deal, valuing a mortgage, or considering a zoning issue, put some numbers to it.  Many investors, brokers, and agents simply guess at the additional value of zoning or assumable mortgages.  Putting numbers behind the decision takes emotion and guesswork out of the process. 

 I also want to thank Brian Brady for starting this econimics contest.  I would have never been able to locate a place to test out my many real estate economic theories had it not been for this contest.