Re Academic Press Private Real Estate Investment_3

Fundamental Real Estate Analysis 81 BEGINNING OF YEAR ---> END OF YEAR ---> VALUE LOANS EQUITY ACCRUED DEPRECIATION SALE COST PERCENT: 1 0 1250000 875000 375000 2 1 1287500 871061 416439 31818 3 2 1326125 866667 459458 63636 4 3 1365909 861764 504145 95455 5 4 1406886 856294 550592 127273 6 5 1449093 850191 598902 159091 7 6 1492565 843381 649184 190909 8 7 1537342 835784 701559 222727 7.50% B-TAX SALES PROCEEDS BASIS CALCULATION: GROSS SALE PRICE ORIGINAL COST LESS DEPRECIATION PLUS COST OF SALE OTHER BASIS ADJUST 96562 319876 1287500 1250000 −31818 96562 99459 359999 1326125 1250000 −63636 99459 102443 401701 1365909 1250000 −95455 102443 105516 445076 1406886 1250000 −127273 105516 108682 490220 1449093 1250000 −159091 108682 111942 537242 1492565 1250000 −190909 111942 115301 586258 1537342 1250000 −222727 115301 ACB AT SALE CAPITAL GAIN REAL GAIN TAX RATE 1314744 −27244 −59063 15.00% 15.00% 1285823 40302 −23334 15.00% 1256989 108920 13466 15.00% 1228244 178642 51370 15.00% 1199591 249502 90411 15.00% 1171033 1142573 321532 394769 130623 172042 15.00% 15.00% RECOVERY RATE 25.00% TAX REVERSION CALCULATION: B-TAX SALES PROCEEDS TAX AFTER TAX EQ REVERSION 25.00% 25.00% 25.00% 25.00% −905 12409 25883 39524 319876 359999 401701 445076 905 −12409 −25883 −39524 320781 347590 375818 405552 25.00% 25.00% 25.00% 53334 67321 81488 490220 537242 586258 −53334 −67321 −81488 436886 469921 504770 FIGURE 4-7 Sale computations for sample project. THE NET PRESENT VALUE In order to determine net present value, we need a function, Equation (4-1), that iterates each annual cash flow, cfn, takes the present value of each at the investor’s required rate of return, r, sums these present values adds the total to the present value of the after-tax equity reversion, ert, and subtracts the initial investment (dp). X npv ¼ n¼1 ð1 þ rÞn þ ð1 þ rÞt ÿ dp ð4-1Þ Figure 4-8 displays the results of Equation (4-1) for the sample project. We certainly went to a lot of trouble only to learn that the property has a negative net present value. For our sample project this means its return does not support its cost of capital. Note that all ‘‘Yields’’ in Figure 4-8 are less than the investor’s required rate of return, r. Therefore, the potential buyer/ investor will reject the project. Simply stated, a negative net present value means this project is a bad deal from the buyer’s perspective. 82 Private Real Estate Investment BEGINNING OF YEAR---> 1 2 3 4 END OF YEAR---> 0 1 2 3 5 6 6 YIELDS NPV 4 5 6 GPI EGI NOI −1250000 117000 120510 BTCF −375000 17006 20516 ATCF −375000 20812 22934 124125 127849 24131 27855 25106 27328 131685 1516258 11.3087% 31691 572883 11.9799% 29599 501841 10.1146% −47353 FIGURE 4-8 Net present value and IRR computations for sample project. INSIGHT INTO THE ANALYSIS It is time to engage in some decomposition, looking behind the equations and the spreadsheet icons into the inner workings of the process. Previously, we referred to the variables as ‘‘deterministic’’ because we can determine the outcome—the net present value—by choosing values for particular variables.1 The outcome changes every time the values of the variables change. With any change in the nominal value of a variable, we explicitly cause a change in return, as measured by the net present value. But there is usually also a corresponding implicit change in the risk. Understanding the inner workings of the variables provides a more explicit view of risk and an insight into the bargaining process. Seeing dependencies at the general level allows us to ask ‘‘if–then’’ type questions about the entire process, not just about a single acquisition. To illustrate the concept of dependency in a very simple case, we begin by looking at the deterministic inputs that affect the gross rent multiplier. We know this equation as value gross scheduled income ð4-2Þ Hence, it would seem that grm is simply dependent upon two variables, the value and the gross income. Because value is defined in our example as a combination of two other deterministic variables, down payment and initial loan, the expression ‘‘grm’’ actually depends on variables which are the antecedent primitives that make up value. grm ¼ dp þ initln 1Many of the relationships described in this section are dependent on the way our sample project is described. The most general approach would be independent of the construction of any particular example. Our purpose here is to strike a balance between theory and practice by using a stylized example and highlighting aspects of the process to illuminate its general meaning. Fundamental Real Estate Analysis 83 So we see that, given how we have defined the variables, three things determine the grm, not the two we originally thought. Perhaps the decomposition of grm is too obvious. One can easily see what determines grm. More difficult and complex examples exist at the other extreme. When we look at what affects after-tax cash flow, cf0, we find a really ugly equation that incorporates all of the inputs leading to this output. cf0 ¼ gsi ÿ 1 ÿ1 þ ð1 þ iÞtln ÿ txrtinitln þ ÿ1 þ ð1 þ iÞt ðinitlnðð1 þ iÞ12 ÿ ð1 þ iÞtð1 þ 12iÞ þ dprtðÿ1 þ ð1 þ iÞtÞðÿ1 þ landÞÞ þ dpdprtðÿ1 þ ð1 þ iÞtÞðÿ1 þ landÞÞþðÿ1 þ exprtÞgsiðÿ1 þ vacrtÞ þ exprtgsiðÿ1 þ vacrtÞ ÿ gsivacrt ð4-3Þ Ugly as Equation (4-3) may seem, it is really nothing more than a fairly long algebraic equation. One could, with some difficulty, construct such an equation from the formulae underlying the cells of a spreadsheet program. Sometimes we can gain more useful insight by giving fixed, numeric values to some of the variables. This has the beneficial effect of eliminating some of the variables as symbols in favor of constants. One approach is to substitute real numbers for those variables out of the owner’s control. For instance, income tax rates, depreciation rates, and land assessments are handed down by government. Taking the relevant data from Table 4-1, in Equation (4-4) we reproduce Equation (4-3), providing fixed values for tax rates and land assessments, thereby reducing the number of symbolic variables to cap rate, loan amount, interest rate, expense and vacancy rates, and the gross scheduled income.2 Do these affect cash flow? They certainly do, and the owner has some influence on them. Suppose we have already decided to purchase the property or we already own it. Under those conditions we may know the income, loan details, and expense and vacancy factors.Inserting these values asnumbers, Equation (4-5) shows us that our cash flow is related to some constants and the interest rate. This permits us to consider explicitly the risk of variable interest rate loans. We also get a feel for the meaning of what is sometimes referred to as ‘‘positive leverage.’’ Using capitalization rate>loan constant as the 2Note that some of the constants combine into other numbers not shown in Table 4-1 because Equation(4-4) has been simplified. 84 Private Real Estate Investment definition of positive cf0 gsiÿ12ið1 þ iÞtinitln þ exprtgsiðÿ1 þ vacrtÞ ÿ gsivacrt ÿ 0:35ðÿ0:0225806dpþ gsi þ 0:977419initln ÿ 12ið1 þ iÞtinitln ÿ ð1 þ iÞtð1 ÿ ð1 þ iÞiÞÿtÞinitlnþ exprtgsiðÿ1 þ vacrtÞ ÿ gsivacrtÞ ð4-4Þ leverage, we know that if leverage is positive then cash flow must be positive. (If you don’t know that then you have just discovered an important reason to use symbolic analysis.) As the first constant term in Equation (4-5) is the net operating income, the aggregate of everything after that term must be smaller than that number for cash flow to be positive. This is, of course, critically dependent on the interest rate.3 cf0 ¼ 117000: þ 10500000i 0 ÿ1 þ ð1 þ iÞ360 1 ÿ 0:35B963774: þ 10500000i þ 875000 1 ÿ ð1 þ iÞ348 C ÿ1 þ ð1 þ iÞ360 ð1 þ iÞ360 ð4-5Þ By varying the loan interest to a rate above and below the going-in capitalization rate, cri, Table 4-3 shows first positive leverage then negative leverage, this time using capitalization rate>interest rate as our definition. Note the difference in cash flow. Another awful looking equation is what goes into the witches brew we call the equity reversion, shown in Equation (4-6). Note that since the loan is assumed to be paid off at the time of sale, the equation contains a constant, the final loan balance. This would certainly be a constant when the loan has a fixed interest rate. If the loan carried a variable rate of interest, an equation 3Further analysis, left to the reader as an exercise, will disclose under what conditions our definition of positive leverage is a stronger or weaker constraint than the alternate definition for positive leverage, capitalization rate>interest rate. Fundamental Real Estate Analysis 85 TABLE 4-3 Initial Cash Flow with Loan Interest above and below the Capitalization Rate cri ¼ .0936 i ¼ .09 i ¼ .095 cf0 ¼ 28,921 cf0 ¼ 26,652 would replace the constant. er ¼ cro ðcroðÿ843381 þ cgrtðdp þ initlnÞð1 þ dprtkðÿ1 þ landÞÞ ÿ ppmtÞ þ ð1 þ gÞkgsið1 ÿ scrtÿ vacrt þ scrtvacrt þ exprt ðÿ1 þ scrt þ vacrtÿ scrtvacrtÞ þ cgrtðÿ1 þ scrt þ vacrt ÿ scrtvacrt þ exprtð1 ÿ scrt ÿ vacrtþ scrtvacrtÞÞÞÞ ð4-6Þ The capital gain in Equation (4-7) is a little more accessible. Note that it is, not surprisingly, quite dependent on the going-out capitalization rate. croðdp þ initlnÞð1 þ dprtkðÿ1 þ landÞÞ cg ¼ ÿ þ ðÿ1 þ exprtÞð1 þ gÞkgsiðÿ1 þ scrtÞðÿ1 þ vacrtÞ cro ð4-7Þ If we are interested in what drives before-tax cash flow, Equation (4-8) shows that it is, of course, heavily dependent on the loan terms and net operating income. btcf ¼ ÿ12ið1 þ iÞtinitln þ ðÿ1 þ exprtÞgsiðÿ1 þ vacrtÞ ð4-8Þ A look at the variables that influence the tax consequence is the result of subtracting the symbolic expression for before-tax cash flow (btcf) from the symbolic expression for after-tax cash flow (cf0 in the initial year). Note the recognizable components in Equation (4-9). The large term inside the parentheses multiplied by the tax rate is the taxable income from operating the property. Inside the parenthesis we see the components of real estate taxable income. If you stare at it long enough, you will see the ... - tailieumienphi.vn