Regression analysis is a useful tool for hard-to-value properties.
After Hurricane Katrina devastated most of New Orleans’ industrial real estate stock, valuing for-sale warehouse space almost was impossible. Overnight, supply fell sharply for all real estate categories, and, unlike any normal market, demand also dropped due to demographic unpredictability. Since the eventual size of the city’s post-Katrina population was unknown, making decisions to acquire industrial, office, or retail space was more speculation than a sound business decision.
In such situations, commercial real estate professionals must look beyond traditional methods to make property valuations. In the chaos of the post-Katrina marketplace, three commonly used methods of pricing properties were not viable. The cost approach of valuation was ineffective because no one could estimate the cost of rebuilding due to the difficulty of finding laborers. The income capitalization method was useless because most tenants had defaulted on their leases and thus, properties produced no income. The sales comparison approach worked, but this method is based on the principle of substitution, which assumes that adjustments need to be made for unusual differences in comparable properties. After Katrina, the adjustments were not the normal factors; it might be whether or not the property was flooded, whether it flooded three feet or 10 feet, or if it had electricity and a roof. Obviously after a disaster of this magnitude, the unique differences in comparable properties had changed so dramatically it was impossible to obtain accurate selling prices through comparisons.
To value properties it was necessary to utilize an alternative pricing method such as a statistical strategy called regression analysis. Calculated using Microsoft Excel, regression analysis can be used to forecast property prices with a high degree of confidence. Illustrating the process is the example of valuing a flooded 92,000-square-foot warehouse on 271,000 square feet of land, just weeks after Hurricane Katrina.
Market and Property Factors
Market conditions for industrial property were mixed at the time, with an increase in demand for leasing warehouse space, but a decrease in demand for purchasing warehouse space because few buyers could commit capital due to unpredictable demographics. Market supply had fallen dramatically, which offset some drop in demand.
The target property had been somewhat damaged by high winds and flooded by three feet of water. Similar to most properties in New Orleans, the building had contained water for about two weeks. A concrete-block portion of the property was intact, but a metal-frame part of the warehouse needed to be re-skinned. The property had roof damage and all the copper wiring had been stripped by vandals.
Normally such conditions would make the property undesirable, but due to Katrina, most industrial property was in similar condition. When comparable properties are homogenous, the regression method of forecasting produces a reliable result.
Predicting Price Based on Averages
Real pricing data were used to determine the target property’s price. (See Table 1.) The data, from a sample of warehouses that were available in New Orleans following Hurricane Katrina, include the selling price, the size of the warehouse, and the size of the land parcel for each property. In the months following Hurricane Katrina, there were very few completed sale transactions to provide comparable data, so the information in Table 1 was compiled from the most valid sources available at the time, including current listings and even conversations among buyers and sellers.
From this market information, many property owners might assume that since the average price of land is $22.81 per sf, the price for 271,000 sf of land is $6,181,510. But estimates based on averages rarely produce prices that are representative of the market.
The reliability of an average is assessed by measuring its precision, or margin of error. Consider two sets of numbers: One set is 30, 50, and 70; the other set is 49, 50, and 51. In both cases, the average is 50; however in the second case, the average is more precise because the data points are closer to the average, making the margin of error smaller.
Table 1: Comparable Warehouse Properties
|Margin of error
Since the average price psf of land in the above example is based on a sample size of properties, a margin of error estimates the approximate average psf for all industrial properties. In the case of the land psf, the average price has a margin of error of $4.54, so the land psf average actually varies between $18.27 and $27.35 psf.
Note the margin of error for the average price psf of building space (+/- $9.61) is larger than the margin of error for the average price psf of land (+/- $4.54). Because the margin is greater for building size, the average lot size is probably a more reliable number to use when estimating value. In this example, the margin of error was calculated at the 90 percent confidence interval. The confidence interval was calculated using the confidence function in Excel. The use of this function is fully documented in the Excel help menu. In brief, to access the menu via the toolbar, click on help, Microsoft Excel help, table of contents, working with data, analyzing data, function reference, statistical functions, confidence.
Predicting Price Based on Regression
The use of regression analysis and a forecasting method called linear regression is illustrated by the scatter plot graph. (See Table 2.) Each property in Table 1 is represented by a square, and the selling price is plotted against the size of the lot. The graph illustrates the scatter of the data points: Small lot sizes are clustered together, and outliers, or unusual data points — larger, more-expensive properties — are easily determined. The graph also confirms that price increases with lot size.
The green line on the graph shows the relationship between price and lot size, assuming an average price of $22.81 psf of land. However, regression analysis creates a line that best fits the data. The solid brown line represents the line of best fit, which approximates the correlation between price and size of the lots. If y represents price and x represents the size of the lot, then the solid line is described by the equation y = Ax + B.
A is $12.77 psf of land, an estimate of the rate of increase in price as the lot size increases. B is about $584,000, an estimate of the baseline price, which is the price of a warehouse property as the lot size decreases to zero. For a warehouse situated on 271,000 sf of land, the predicted price is y = (12.77)(271,000) + 584,000 = $4,044,670. This is $2 million below the $6,181,510 price predicted using the average price psf of land. This formula also explains with every square-foot increase in land size, the price increases $12.77.
Regression analysis can provide a more sophisticated method of forecasting the price of any property: Users plug in the square footage for the variable x, and the result is the price. Simple linear regression is performed using an Excel add-in called the Analysis Toolpak. (See sidebar.) 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, data analysis, and regression. For “input y range” highlight all the entries in the price column. For “input x range” highlight the lot size column. Select a location for the output data and click OK. Creation of xy scatter graphs is described in the Excel help file. On the toolbar, click help, Microsoft Excel help, table of contents, charts and graphics, charts, creating charts, creating xy scatter and line charts.
Regression analysis also can show how lot size affects price. The value of R2 often is used to measure the precision of a regression line in the same way that the margin of error often is 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 this example, R2 = 0.67, which indicates that lot size explains 67 percent of the variation in price.
If the regression analysis is performed using the regression tool in Microsoft Excel’s Analysis Toolpak, assume the regression line is y = Ax + B, where y is a column of cells (in the original worksheet) containing the values of the dependent variable (in this example, the selling price) and x is a corresponding column of cells containing the values of the independent variable (in this example, building size or lot size). In the output that is generated by the regression tool, estimates of the coefficients A and B are in the first column of the table. The value of B is in the row labeled intercept. The value of A is in the row labeled x variable. For additional information, view the Excel help file by clicking on help, Microsoft Excel help, table of contents, working with data, analyzing data, perform a regression analysis.
Using statistics can help determine a market price with greater reliability than using the average price psf method and can be a useful tool when supply and demand factors change dramatically. Clearly, 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 and inoperable.
The following Web sites offer additional information on general statistical analyses, linear regression analyses, confidence intervals, and margins of error.