Private Real Estate Investment: Data Analysis and Decision Making_4

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Private Real Estate Investment: Data Analysis and Decision Making_4 55 The ‘‘Rules of Thumb’’ and net income in turn is a function of vacancy and expenses, Net Operating Income ¼ Gross Potential Income À Vacancy À Expenses ð3-15Þ leads us to simplify the difference between gross and net income as Net Operating Income ¼ Gross Potential Income (1 À evrÞ ð3-16Þ where evr ¼ expense and vacancy rate (0 < evr < 1). Val Rearranging the value equation, recalling that GPI ¼ GRM, and substituting our simplifying assumption produces Val=GRMð1 À evrÞ Capitalization Rate ¼ ð3-17Þ Val Given that value and gross income are accurately reported, this makes the honest cap rate we yearn for a function of the expense and vacancy rate chosen. Further rearrangement gives us an equation for evr that is dependent on only two variables, both commonly found in reported sales of investment property: the GRM and the cap rate, of which one, GRM, is more reliable than the other. Using these two rules of thumb together in Equation (3-18), we can gain some additional insight. À Á evr ¼ 1 À cr grm ð3-18Þ One should be cautioned that, mathematically, it is possible for evr to be negative. However, in real estate it can never be less than zero. Should a negative evr be calculated by Equation (3-18) from observations in a dataset, it virtually must result from misreporting of either or both the capitalization rate or GRM. A moment’s thought about what it would mean for an apartment building to sell for ten times its gross income AND at a 13% cap rate will convince you that such things do not occur in nature. In Equation (3-19) we solve for GRM in terms of the other variables. 1 À evr GRM ¼ ð3-19Þ cr GRM is always greater than 1 (all buildings in first world countries sell for more than their annual gross income), and cr, the reciprocal of a positive 56 Private Real Estate Investment real number, must always be greater than 0 and less than 1. Thus, the only way for both sides of the above equation to be greater than 1 is for the numerator of the ratio on the right to be greater than its denominator. Since evr is a rate that, by definition, is a positive number between 0 and 1, 1 À evr must be a number between 0 and 1. For the whole right side of Equation (3-19) to be greater than 1, 1 À evr must be larger than the caprate. THE NORMAL APPROACH DATA TO Let’s look at a dataset of 1,000 actual apartment sales that took place in the San Francisco area between October 1996 and September 2001. Each observation shows the area, price, date sold, age, building size in square feet, number of units, GRM, and capitalization rate. The first five observations are displayed in Table 3-4. Using Equation (3-18), we can combine the cap rate and GRM to create a list of expense and vacancy ratios. It is useful to look at the range of the evr observations in Table 3-5 and plot them in Figure 3-6. Most practitioners in sunny California would agree that expenses of 59.18% of income for an apartment building are at least unusual, if not unlikely. Likewise at the other extreme, expenses of 10.43% are probably understated. We need to adopt a healthy suspicion about the extreme observations. The plot of an ordered list in Figure 3-6 shows, as always, a few extreme observations, but the majority of the observations is between 25 and 45%. TABLE 3-4 First Five Observations in San Francisco Data Area Price ($) Date Age SF Units GRM CR 5 880,000 09/21/01 94 2,100 6 11.24 0.0697 5 1,075,000 09/21/01 48 5,302 9 8.07 0.0918 1 920,000 09/19/01 0 5,502 6 10.6 0.0603 5 1,000,000 09/14/01 42 5,368 8 14.56 0.0546 5 1,150,000 09/07/01 50 5,200 8 8.87 0.0835 TABLE 3-5 San Francisco EVR Extreme of EVR for San Francisco data Minimum 0.1043 Maximum 0.5918 57 The ‘‘Rules of Thumb’’ 0.6 0.45 EVR 0.25 0.1 0 200 400 600 800 1000 Observations # FIGURE 3-6 Plot of ordered list of EVRs. Expense and Vacancy Ratios EVRs 140 120 100 80 60 40 20 0.2 0.3 0.4 0.5 0.6 FIGURE 3-7 San Francisco EVRs. The histogram in Figure 3-7 provides a visual way to see the discrete distribution of grouped evr data. Measures of central tendency, shape, and variance, known as descriptive statistics, are shown in Table 3-6. The ...