# Private Real Estate Investment: Data Analysis and Decision Making_10

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## Private Real Estate Investment: Data Analysis and Decision Making_10

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1. 236 211 The Lender’s Dilemma 2. If the borrower experiences a period of inflation unanticipated by the lender (especially if the loan is granted at a fixed rate of interest), he will reap leveraged equity growth as the appreciation of the entire property value is credited to his equity. Of course, these beneﬁts come at the expense of risk because leverage magniﬁes both proﬁts and losses. The choice of how much debt to use often discloses a difference of opinion between borrowers and lenders about inﬂation expectations. When borrowers view inﬂation expectations differently than lenders, they place a different value on the property. This results, given ﬁxed net operating income (noi), in borrower capitalization rates differing from lender capitalization rates. Some rearranging of the identities for ltv, dcr, and value will convince you that market value may be represented as either of the two identities in Equation (9-1) noi noi ¼ market value ¼ ð9-1Þ cr 12 Ã constant Ã dcr Ã ltv where ‘‘constant’’ is the ratio of monthly installment payments required on the loan to the loan balance (also the factor from Elwood Table #6, the payment to amortize $1). Setting the two expressions for market value (mv) equal to each other and solving for capitalization rate (cr) produces Equation (9-2). cr ¼ 12 Ã constant Ã dcr Ã ltv ð9-2Þ Although lenders have some discretion in the setting of interest rates, due to competition and the inﬂuence of the Federal Reserve Bank, the lender’s discretion is across such a narrow range that it may be ignored for our purposes. Thus, using an amortization period of 360 months and exogenously determined interest rates, we assume that the choice of constant is essentially out of the control of the parties to the loan contract. (This is not to preclude the borrower from electing a shorter amortization term to retire debt faster, something he can do without agreeing to a shorter loan provided prepayment is allowed.) We pointed out in Chapter 3 that, if one does not model individual cash ﬂows separately as part of an economic forecast, DCF analysis adds nothing of value to capitalization rate. Indeed, a primary beneﬁt of using DCF analysis is to be able to vary cash ﬂows as part of arriving at value. The lender that ﬁxes both the ltv and the dcr is, in effect, dictating that the buyer use outdated 2. 236 212 Private Real Estate Investment capitalization rate methodology. Two important consequences follow: 1. It forces the buyer to use an inferior valuation tool. 2. It requires the buyer to accept the lender’s inflation expectations. THE LENDER’S PERSPECTIVE To illustrate we will analyze a sale of a property that has been arranged at a price of$1,000,000. The property has $100,000 of net operating income, thus the buyer’s capitalization rate is 10%. The buyer requires an 80% loan to complete the transaction. Assume that 30-year loans are available at 8% interest. The monthly loan constant is .00733765. The lender’s underwriting policy provides that the loan may not exceed 80% of appraised value and net income must exceed debt service by 50%. (These are admittedly stringent standards to make our point.) Using the right side of Equation (9-1), we ﬁnd that the lender’s value of$946,413 is $53,587 below the buyer’s, a shortfall of about 5%. The lender places a higher capitalization rate of 10.566% on the property, and the loan approved of$757,131 satisﬁes both the ltv and the dcr requirement, but is insufﬁcient for the buyer’s needs. This is because the lender employs a valuation technique that depends on annual NOI, the constant, and both a ﬁxed predetermined dcr and ltv. THE BORROWER’S PERSPECTIVE The buyer’s approach to value is different. By agreeing to pay $1,000,000 for the property and to borrow$800,000 at market rates and terms, the borrower is saying that the equity is worth $200,000 to him. Thus, he has examined the present and anticipated cash ﬂows in light of his chosen discount rate and, after considering payments on an$800,000 loan, makes the following calculation using Equation (3-9) from Chapter 3. X atcf t atert n 200,000 ¼ nþ ð1 þ dÞt ð1 þ d Þ n ¼1 The connection between the difference in the parties’ opinion of value and the differences in their inﬂation expectations is found in their differing opinions of g in Equation (3-12) of Chapter 3.
4. 236 214 Private Real Estate Investment Due Diligence Level # Units 5 100 FIGURE 9-1 Due diligence in the Tier I and Tier III markets. Due Diligence Level # Units 5 100 FIGURE 9-2 Tier II constantly increasing due diligence by size. property. Hence, due diligence might be a function of property size. If we restrict our argument to these extremes, a graph of this claim looks like Figure 9-1. The focus of this book is on the Tier II property in the middle. One wonders if the move in sophistication is continuous across all sized properties. Thus, retaining the tier concept but concentrating on Tier II, we ask if due diligence increases continuously with size? If so, Tier I represents a minimum level of due diligence and Tier III represents the maximum. If we claim that due diligence quality is linear in size, one would expect an increase in due diligence across Tier II as property size increases, as shown in Figure 9-2.
5. 236 215 The Lender’s Dilemma Figure 9-2 illustrates a ‘‘static’’ model, a snapshot of reality at any given moment. Whatever we believe about how investors approach the acquisition process, it is likely that such a process changes over time. Thus, it is a dynamic process. The acquisition standards of 1994 are probably not the same as those of 2004. Acquisition standards themselves should be viewed as cyclical, responding to changes in the surrounding environment. Investors in a hurry resort to rules of thumb (ROT) to quickly evaluate whether a property is worth a closer look. The use of a rule of thumb for acquisition is a different matter. It represents a reduced level of due diligence over more sophisticated methods such as DCF techniques. The Tier I market rarely uses DCF, more often using the rule of thumb known as gross rent multiplier (GRM). At the lowest size of Tier I, the single-family rental, value is perhaps, say, 100 times its monthly rent. Some apply that to duplexes, triplexes, and four-plexes. Somewhere along the line monthly GRM is abandoned in favor of annual GRM. This is hardly a rise in sophistication because the annual GRM is just the monthly GRM divided by 12. Few, if any, Tier III acquisitions are made on the basis of GRM. The question is: At what size property do GRMs drop out completely in favor of DCF and other sophisticated methods? Is it 20 units, 50 units, or 90 units? Also, wherever the drop-out point, does the drop-out point change at different times in different markets? Perhaps most important, why does it change? In very strong seller’s markets an often asked, but seldom answered question is: When will it end? Or, where is the top? One way to approach that question is to ask when do the simple rules of thumb measures that shouldn’t be relied upon for decision making creep into the larger acquisitions populated by what should be the more sophisticated investors? A 20-unit building, made up of 2-bedroom units renting for $1,000 per month, that sold for$100,000 per unit, is purchased at the 100 times gross monthly income rule that once applied to houses. What that says is that the housing consumer is paying the same in rent-to-beneﬁt terms for an apartment as he once paid to rent a house. Apartments don’t have yards, and apartment renters have to share walls with people who may not be good neighbors. The question of ‘‘How high is up?’’ becomes more urgent when house economics, ratios, and standards begin to drive investment decisions. An interesting empirical question might ask if there is a relationship between the top of the market and a time when rules of thumb dominate appraisal and acquisition standards at the larger property levels? Figure 9-3 illustrates such an idea. The essence of the rules of thumb is to impound future events implicitly into one simple measure, a kind of short cut. By contrast, the central value of forward projection methods is to allow the analyst to explicitly consider the effect of changing future events on the expected outcome. Departing from
6. 236 216 Private Real Estate Investment ROT Top Analysis Methods Prices DCF Bottom Time FIGURE 9-3 Cyclical analysis methods/acquisition criteria. more complete methods in favor of the rules of thumb basically says either ‘‘I don’t care what the future brings’’ or ‘‘The future will be just like the present.’’ These sentiments are usually counterproductive over the long run. This is the converse of the problem we had when examining the lender’s and the buyer’s perspective earlier. Then the borrower was negotiating with the lender to allow an underwriting restriction to vary in order to improve both parties’ analysis and decision making. In the present case the lender ﬁnds his borrowers failing to use or failing to appreciate the value of forward projection methods. His reaction, to impose restraint on what he sees as irrational exuberance, is to modify his loan underwriting standards. This does not necessarily mean that the lender ﬁxes both ltv and dcr (although that can be the case), rather it means he chooses wisely between them. To get to the bottom of this we return to the earlier comment that the lender and borrower disagree on g in Equation (3-12) in Chapter 3. There is a curious three-way relationship between capitalization rates, interest rates, and inﬂation.3 When inﬂation expectations increase, interest rates rise as lenders build inﬂation expectations into their rates. Since capitalization rates include the cost of funds (interest rates), one would expect capitalization rates to increase also. That this is not always true is an anomaly. Buyers of income property, anticipating higher future income, bid up prices, causing capitalization rates to fall. Tension is created by this anomaly because everyone knows that it cannot continue forever. Price inﬂation traceable to this anomaly introduces concern about a bubble in the market. Much has been written about the difference between expected and unexpected inﬂation. Our interest is about how two parties to a transaction behave when their separate opinions differ in these areas. 3 The author is indebted to Bob Wilbur for pointing this out.
7. 236 217 The Lender’s Dilemma BUBBLE THEORY—HOW HIGH IS UP? Markets are cyclical. It is widely accepted that timing is everything. This is easy to say and hard to implement, knowing when to get out is very often the key to investment success. If we accept the argument of the prior section that rules of thumb, as decision tools, dominate as the market approaches a peak, we can take advantage of that to examine the interaction of these rules with an eye toward discovering if and when the lender–borrower difference of opinion about the future suggests the market has gone as high as it can be expected to. Lenders operate as a sort of governor, acting out the unpopular role of guarding the punch bowl, adding just enough joy juice (easy credit) to keep the party interesting, but not enough to allow it to become unruly. This restriction manifests itself as lender underwriting moves from ltv to dcr. POSITIVE LEVERAGE To further develop this story we need to look closely at the idea of positive leverage. This is simply the ‘‘buy-low-sell-high’’ maxim at work in ﬁnancing terms. One hopes to borrow money at one rate and reinvest it at a higher rate. Indeed, if this is not accomplished, the long run outcome is as disastrous as a policy of buy-high-sell-low. The expression of positive leverage has two versions:  For some, positive leverage occurs when the capitalization rate exceeds the interest rate.  Alternatively, positive leverage means that the capitalization rate exceeds all debt service, including principal payments. We will have to choose between these eventually, but a short review of why each has merit is useful. The ﬁrst version is appropriate in cases where the loan contract requires only interest payments or if one wishes to compare pure yield rates. It also offers the beneﬁt of simplicity, allowing us to work with only the annual rate and not have to deal with amortization of principal. The second version is more appealing to lenders interested in knowing that the property generates enough net income to meet all its obligations. In the interest of realism and to accommodate the investor–lender conﬂict, we will gravitate toward this second version. The loan constant is the division of the loan payment by the loan balance. This number only remains truly constant in the case of ‘‘interest only’’ ﬁnancing. In the case of self-amortizing debt, it changes with each payment, offering the bizarre result of not being constant
8. 236 218 Private Real Estate Investment at all. Because our story will unfold using only ﬁrst year measures, we will deal only with the initial loan constant, meaning the initial loan payment divided by the initial balance. We make three further simplifying assumptions to facilitate the discussion. First, we will assume away tax consequences and deal with only pre-tax measures. This is justiﬁed for a variety of reasons. Investors purchasing even moderately sized real estate usually must have substantial ﬁnancial resources, making them eligible for the higher—and ﬂat—income tax brackets. Investors are thus presumed to have substantially similar after-tax motives. Also, since tax returns are conﬁdential, as we have noted earlier, tax beneﬁts are not obser- vable so empirical veriﬁcation of after-tax results is essentially unavailable. Second, we will momentarily assume away principal payment, using the interest only version of positive leverage. This simpliﬁcation is easily dropped later. We begin this way in order to keep the equation as simple as possible. The preponderance of debt service in the ﬁrst year goes to interest. So the effect of principal payments on ﬁrst year cash ﬂow is minimal and may be ignored at the outset. Third, we assume that interest rates, at least for the ﬁrst year, are ﬁxed. The simplest expression of pre-tax cash-on-cash (cc) return is the division of before-tax cash ﬂow (btcf ) by the equity down payment as shown in Equation (9-3). btcf simple cc ¼ ð9-3Þ equity Recalling that value ¼ noi and btcf ¼ noi À debt service, the numerator of cr Equation (9-3) can be expressed in terms of noi, cap rate, ltv, and interest rate. The denominator can also be expressed with the same terms and omitting the interest rate, creating Equation (9-4). By ignoring principal payment at this stage, i indicates that the debt service (the constant) is merely the interest rate.   noi noi À ltv Ã i btcf cr simple cc ¼ ð9-4Þ ¼ noi equity ð1 À ltvÞ cr Rearranging Equation (9-4), we obtain Equation (9-5) in which noi cancels out.   noi noi À ltv Ã i btcf i Ã ltv À cr cr simple cc ¼ ð9-5Þ ¼ ¼ noi equity ltv À 1 ð1 À ltvÞ cr
9. 236 219 The Lender’s Dilemma Let’s look at the classic beneﬁt of positive leverage. Using plausible, so-called ‘‘normal market’’ numbers (ltv ¼ 75%, cap rate ¼ 9%, interest rate ¼ 8%) in which investors enjoy positive leverage with a ‘‘normal’’ spread, we compute the simple cc at 12%. Note that Equation (9-5) is devoid of a variable for appreciation. To this point one obtains enough return in the capitalization rate to service debt and have funds left over in the ﬁrst year to reward down payment capital in double digits without any appreciation assumption. The simple cc rate above becomes 12% because one earns 9% on the down payment equity which represents 25% of the total investment PLUS a 1% ‘‘override’’ on reinvesting the lender’s funds (which represent 75% of the total investment). As the lender’s money is exactly three times the borrower’s, that 1% override is multiplied three times and added to the 9% the investor received on his equity for a total of 12%. As our interest is in price bubbles, let’s see what happens to positive leverage as prices rise. When capitalization rates drop to the point where they equal interest rates, the simple cc becomes 8%. As leverage is now ‘‘breakeven,’’ the investor receives a cash-on-cash return equal to the capitalization rate with no override. There is no ﬁrst year beneﬁt from leverage under these conditions. Investors must look elsewhere to justify borrowing. That elsewhere is future appreciation in value. Before continuing, we will complicate Equation (9-5) to introduce the reality of monthly payments and principal amortization into the story. Most real estate loans amortize, most real estate lenders use the full principal and interest payment in their dcr computations, and borrowers calculate before- tax cash ﬂow using all lender payments in the debt service part of the equation. To accommodate these realities we must replace interest (i) with debt service (ds). Debt service involves not only the interest rate (i), but a second variable, term (t). The equation for the amount required to retire a \$1 loan produces what we call ‘‘the constant.’’ As most real estate loans are based on 30-year amortization with monthly payments, we will use t ¼ 360 as the number of months in the debt service, deﬁning the constant (const) as debt service (ds) in Equation (9-6) 0 1 B C i ds ¼ 12B C ð9-6Þ @ A 1 1À ð1 þ iÞt Substituting ds for interest rate (i) in Equation (9-5) and rearranging, we obtain Equation (9-7), noting that noi has once again canceled out.
10. 236 220 Private Real Estate Investment 0.1 cash on cash 0 8% −0.1 cap rate 6% 6% 8% int rate 4% 10% FIGURE 9-4 Cash-on-cash return as a function of capitalization and interest rates. This equation expresses cash-on-cash return for an investment using amortizing debt. 0 1 B C  12 Ã i Ã ltv C crB1 À @ A 1 cr 1 À 360 ð1 þ iÞ cc ¼ ð9-7Þ 1 À ltv Using the same plausible inputs from our ﬁrst example with positive leverage, we compute a 9.584% cash-on-cash return. Note two differences from the simple cc. First, we must input the interest rate as a monthly variable because the ds calculation computes monthly payments and multiplies them by 12 to arrive at the annual debt service. Second, because of the reduction of cash ﬂow due to principal payments, the cc result we obtain is smaller.4 Figure 9-4, a three-dimensional plot of our cc function, illustrates the obvious, which is that cash-on-cash returns rise as debt service, a function of interest rates, falls and capitalization rates rise. Note the negative 4 Some would argue that this reduction is unimportant because the retirement of debt merely shifts items in the balance sheet between cash and equity. This argument is compelling in other settings, but does not serve our purpose here.