## Monday, July 21, 2014

### One Resource a (Week)Day #15: Math in Appraising Properties (and Companies)

It occurred to me today that property appraisal is a problem of mathematical interest. Before you read further, I challenge you to think about how you would assign monetary value to a piece of property, if you were an appraiser. Considered the different types of buildings: private houses, rental property, commercial property, and public spaces.

The heuristic brainstorm is the richest part of this math problem, I think. I was so intrigued to learn that there are actually 3 different processes for evaluating property value, each suitable for a different type of property.

1. The way you're probably most familiar with is sales comparison. You basically look at similar houses in the vicinity of the house being appraised, and use recent sales histories, with some up-or-down adjustment factors (for granite floors, kitchen islands, or below-ground oil tanks) to estimate the market value of the current property. Most private home sales involve this type of appraisal.

2. The income approach involves something called the "cap rate", and can be used to appraise buildings that are primarily intended as rental property. This method involves calculating the expected net income from the rent per year, and then using the cap rate of similar rental buildings in the neighborhood to calculate the total value of the property. Cap rate is a fancy way of saying ROI (return on investment percentage), which means if you know the cap rate and you know the net annual income, you can do basic proportional reasoning to find the value of the property. (The only thing that is a bit tricky is that the definition of cap rate is not always consistent from listing to listing, in terms of which costs are subtracted when calculating net income.)

3. The cost approach involves calculating the value of the empty lot, then estimating the cost of a new construction of the same house, then factoring in depreciation to find the current value of the house. They use this method for public buildings such as churches or libraries or school buildings, which have no easy sales comparisons to be made in the vicinity.

I read online that the people who are studying to become property appraisers are often intimidated by the math involved. If you have the opportunity to introduce some of these terms in your class, it can really help your students to learn some long-term investment terms that can help them be a bit more savvy with their own investments*, or ease their fear of entry into the field of appraisal. (*For example, the cap rate is extremely important when you glance at a bunch of listings in search of rental property investment, if you are looking to make a monthly profit on your personal investment.)

Here and here are some real-estate percent problems that appraisers have to be able to answer on their licensing exams. You can rephrase them and use most of them for your secondary students!

And, as an extension, how do companies determine how much another company is worth? (How did Facebook determine that What's App is worth \$19 billion?) Have your students consider the problem and brainstorm some possibilities before researching the process of appraising a company.

--As another extension, have students look at how neighborhoods affect things like the cost of land and cap rate. What social justice questions can they ask about this?