## How To Use Statistics To Value Commercial Real Estate Commercial real estate valuation differs from stock and bond valuations because ral estate often has fewer buyers, only one seller, little comparable properties and location biases, compared to pricing a share of stock which is quoted visibly and enjoys hundreds of trades every minute. If commercial real estate information was more widespread and there were more buyers and sellers, properties would be easier to value. However real estate is not a purely competitive market where there is transparent information available to all and many buyers and sellers. Often there are no comparable properties for sale and no comparable properties sold in the past few years. The result is difficulty in pricing commercial real estate. One solution is to use math to calculate a regression formula to value property, based on variables such as building size and land.

# Three Common Methods of Pricing Properties

The Cost Approach of valuation was ineffective in this situation because nobody could estimate the cost of rebuilding due to the difficulty in finding laborers. The Income Capitalization method was useless because properties produced no income since most tenants had defaulted on their leases. One method that worked was the Sales Comparison Approach, but the downside of this method is that it is based on the Principle of Substitution which makes the assumption that adjustments need to be made for some unusual differences in comparable properties. After the Katrina disaster, the adjustments were not your normal factors: it might be whether the property was flooded or not, was it flooded 3 feet or ten feet, does it have electricity, or is there a roof. In order to have an accurate selling price, you’ll need to have accurately adjusted for differences.  After a disaster, however, the unique differences in comparable properties may have changed dramatically, resulting in a need to utilize an alternative pricing method. One method is a statistical strategy called regression analysis, which can be used to forecast price with a high degree of confidence.

Let’s examine how to value a flooded 92,000 SF warehouse on 271,000 SF land, just weeks after Hurricane Katrina. Market conditions at the time for industrial property were mixed, with an increase in demand for leasing warehouse space, but a decrease in demand for purchasing warehouse space because few buyers could commit capital to unpredictable demographics. Market supply had dramatically fallen which offset some drop in demand. The target property was impacted by high winds and was flooded with three feet of water; like most property in New Orleans, the water stayed on the property for two weeks. Part of the target property was intact because it was concrete block structure, and part of the warehouse needed to be re-skinned since it was a metal frame. The property had roof damage and all the copper wiring was stripped by vandals. Normally, these conditions would make the property undesirable, but due to Katrina, industrial property was uniformly in this condition. When comparable properties are homogenous, the regression method of forecasting produces a reliable result.

# Predicting Price Based on Average Price Per Square Foot

In determining our price of the target property, we are using real data in the accompanying table (Table One). The prices are from a sample of warehouses which were available in New Orleans following Hurricane Katrina. For each property, the selling price, the size of the warehouse, and the size of the parcel of land are shown.

 Table One Comparable Warehouse Properties Size (square feet) Price (\$)  per square foot Selling price (\$) Building Lot Building Lot 1 1,700,000 40,000 261,000 42.50 6.51 2 1,000,000 20,000 100,000 50.00 10.00 3 4,500,000 60,000 212,000 75.00 21.23 4 2,100,000 70,000 70,000 30.00 30.00 5 800,000 22,000 25,000 36.36 32.00 6 2,000,000 50,000 60,000 40.00 33.33 7 5,800,000 54,000 352,000 107.41 16.48 8 1,750,000 82,000 123,000 21.34 14.23 9 769,000 18,000 27,000 42.72 28.48 10 2,650,000 41,624 60,984 63.67 43.45 11 1,600,000 33,534 47,195 47.71 33.90 12 360,000 14,924 33,000 24.12 10.91 13 325,000 6,121 12,278 53.10 26.47 14 215,000 7,980 14,375 26.94 14.96 15 2,860,000 101,500 141,960 28.18 20.15 Average 45.94 22.81 Margin of Error 9.61 4.54

Many property owners would use this market information to conclude that since the average price of land is \$22.81/SF, the predicted price for 271,000 square feet of land is \$6,181,510, but that estimate rarely works accurately in real life. A cautious buyer has to wonder if the average price in the table might be somehow unusual and not truly representative of the market. What can make the predicted price more reliable?

The reliability of an average can be assessed by measuring its precision. Consider two sets of numbers: one set is 30, 50, and 70 and the other set is 49, 50, and 51. In both cases, 50 is an accurate measure of the average; however in the second case, the average is more precise – here’s why. When the results of a poll are reported, a “margin of error” often is given. For example, a poll may show that 48% of people prefer candidate A over candidate B with a margin of error of +/- 3%. The margin of error measures the precision of the estimate, 48%. If the estimate is precise, then the margin of error is small. The margin of error of +/- 3% indicates that the true percentage of people who prefer candidate A is very likely to fall between 45% and 51%.

Note the margins of error for the estimates of the average price per square foot of floor space (9.61) and the average price per square foot of land (4.54) in the table. Because the margin is greater for building size, the average lot size is probably a more reliable number to use when estimating value.

# Predicting Price Based on Regression The use of regression analysis and a forecasting method called linear regression is illustrated in the accompanying graph. Each property in the table is represented by a dot, and selling price is plotted against the size of the lot. By themselves, graphs can be very informative; for example, the graph confirms that price increases with lot size, and the slope explains by how much. The graph also provides a general impression of the extent of the “scatter” of the data points: you can see that data points tend to be clustered together when lot size is small, and you can easily see outliers, or unusual data points.

Regression analysis uses math to provide a line that best fits the data. The green line on the graph shows the relationship between price and lot size, assuming an average price of \$22.81 per square foot of land. The solid brown line represents the line of best fit. If y represents price and x represents the size of the lot, then the solid line is described by the equation y = Ax + B. When you calculate a regression formula for these data, A is \$12.77 per square foot of land and B is about \$584,000. A is an estimate of the rate of increase in price as the lot size increases. B estimates the baseline price (\$584,000), which is the price of a warehouse property as the lot size decreases to zero.

For a warehouse situated on 271,000 square feet of land, the predicted price is y = (12.77)(271,000) + 584,000 = \$4,044,670. This is \$2 million below the price predicted using the average price per square foot of land (\$6,181,510). Regression analysis can provide a more sophisticated method of forecasting price of any property, and it is more useful because you plug in your square footage for the variable x, and the result is the price. This formula also explains with every one square foot increase in land size, the price increases \$12.77.

Regression analysis can also show how lot size affects price. The value of R2 is often used to measure the precision of a regression line in the same way that the margin of error is often used to measure the precision of an average. The value of R2 can vary between 0 and 1. In this example, R2 measures the proportion of the variation in price that is explained by lot size. If R2 = 0, then the regression line has no precision and lot size explains none of the variation in price. If R2 = 1, then the regression line is extremely precise and variation in price is explained entirely by lot size. In our example, R2 = 0.67, which indicates that lot size explains 67% of the variation in price. The price of warehouse property in New Orleans in this situation was related much more strongly to the size of the lot than the size of the building. This makes sense because few buildings were of value after Hurricane Katrina, since most were flooded.

In summary, using statistics can help you determine a market price with greater reliability than using the average price per square foot method, and can be a useful tool when supply and demand factors change dramatically.

To create your own formula in Microsoft Excel, simple linear regression is performed using an Excel add-in called the Analysis Toolpak. First install this add-in. Then in an Excel worksheet, enter the data in two columns, one column for price and one column for lot size. On the menu bar select “Tools”, then “Data Analysis”, and then “Regression”. For “input Y range” select the price column. For “input X range” select the lot size column. Select a location for the output data and click on “OK”.