# The valuation of income property in overbuilt markets.

Many commercial real estate markets have been distressed by the
construction explosion that occurred during the last half of the
1980s.(1) Nationally, real office market rents have declined 45% since
1982 and office vacancy rates have stood at unprecedented levels.(2)
While more difficult to document, shopping center and hotel markets have
displayed similar signs of distress.(3) Moreover, some analysts predict
that the effects of this dramatic overbuilding will take as long as 10
years to be absorbed.(4) Income property appraisers in these overbuilt markets need to systematically employ valuation techniques that are
consistent both across properties and with basic microeconomic theory.

Rental rates in overbuilt markets are below the levels required to stimulate new construction. Because rents cannot immediately rise to required levels, many existing properties are selling at discounts to reproduction costs. The magnitude of the discount depends on how slowly investors think rent will rise to required or equilibrium levels. The longer the expected adjustment period, the greater the discount from reproduction costs. Appraisers' expectations of future cash flows should therefore vary with both the expected growth rate of the local market and the extent of the initial disequilibrium. In this article, the effects of current and projected local market conditions on market rents and values are discussed and a variant of the standard discounted cash flow (DCF) valuation model--the rent adjustment valuation model--is developed that allows (forces) appraisers to explicitly incorporate these anticipated effects into their market value estimates.

VALUATION AND THE IMPORTANCE OF LOCAL MARKET CONDITIONS

It is important to distinguish between the "space" market and the "asset" market when analyzing local markets for income-producing real estate. Equilibrium in the former is determined by the interaction between tenant demand for, and the available supply of, leasable space. The supply of rental space is relatively unresponsive to changes in rental prices (i.e., inelastic) in the short run. Thus, competitively determined rental rates in the space market are primarily determined by the current level of effective tenant demand. A primary determinant of the pace of future construction is the relationship between current rental rates in the local market and "required" (or equilibrium) rental rates. The required level of effective rental income in the first year of operations is that which equates the net present value of the income property investment to zero for typical investors, employing a typical set of assumptions about future rental rates, operating expenses, and resale values. This required first-year effective gross rent per dollar of investment serves as a hurdle rate for prospective developers and investors in income-producing property. If current supply and demand conditions in the market are such that properties generally earn rents greater than the required minimum rent, investors will add new construction to the existing stock in an attempt to capture these "excess" rents.

Put another way, prices or values in the asset market are multiples of the rental rates competitively determined in the space market. If current rents exceed required minimum rents, market values will exceed construction costs (that includes the price of land and a "fair" developer profit) and developers will have an incentive to add to the existing stock. Ultimately, the expansion of supply causes real rents to decrease to the required or equilibrium level.(5) Thus, although inelastic in the short run, the supply of space is fairly elastic (i.e., price responsive) over longer time periods. Short-run equilibrium in the asset market requires only that the market clear; that is, that willing property sellers find willing buyers. Long-run equilibrium in the asset market, however, requires that market-clearing asset prices equal construction costs.

If current rental rates are below the required minimum, as is the case in an overbuilt market, construction will be cut back until market rents rise to the required level. Only then will developers be able to recover construction costs from the sale of new properties and thereby earn a rate of return comparable to what can be earned on alternative investments of similar risk. It should be noted that if the supply of space in a local market could be instantaneously adjusted to the current level of tenant demand (i.e., if even the short-run supply of space were highly elastic), current rental rates in a competitive market would always equal minimum required rents and properties would not sell at a discount to construction costs. The supply of space and therefore current rental rates, however, cannot adjust immediately to changing market conditions. Thus, a combination of reduced construction along with normal growth in demand for space and steady obsolescence of the existing stock are required before higher real rents can be generated for income-producing properties in overbuilt markets.(6)

A TYPICAL APPLICATION OF DCF ANALYSIS TO MARKET VALUATION

Until quite recently, professional appraisers of income-producing property have primarily employed simple income capitalization to estimate market value. With this approach, estimated first-year (or stabilized) net operating income (NOI) of the subject property is converted into an estimate of market value by dividing NOI by the appropriate capitalization rate. The appropriate cap rate in this exercise is typically "abstracted" from the market by calculating first-year NOI as a percent of selling price from recent transactions of properties thought to be comparable with the subject. The application of simple income capitalization does not require explicit estimates of cash flow streams beyond the first year. Implicit estimates of future cash flows, however, are reflected in the cap rates abstracted from the market in the comparable sales analysis.

This can be seen by noting that transaction prices in a competitive market reflect the investment valuations of willing buyers and sellers, which in turn reflect assumptions about future cash flows. More optimistic assessments of future cash flows in a local market increase the prices investors are willing to pay per dollar of current rental income. This increase in sale price multiples decreases cap rates and thereby increases the estimated value of the subject property. Thus, the use of simple income capitalization with cap rates abstracted from the market does not relieve an appraiser of the difficult task of projecting future market conditions and cash flows.

A multiperiod DCF approach to market valuation measures and values cash flows to the equity investor over time after all operating and sale expenses have been paid. Unlike simple income capitalization, DCF techniques require an appraiser to make explicit future cash flow projections. The cash inflows and outflows associated with the acquisition of an existing income property can be represented by the following expression:

|Mathematical Expression Omitted~.

|V.sub.o~ is the estimated market value of the subject property. Effective gross rents, |R.sub.0~, are expected to grow at the average annual nominal rate ||Pi~.sub.r~ where ||Pi~.sub.r~ is usually thought of as the expected rate of general inflation in the economy adjusted downward for economic depreciation. ||Delta~.sub.t~ is a rental adjustment factor intended to capture the effects of over- or under-building on future rent increases. OE represents first-year operating expenses (primarily maintenance and property tax expenditures) that are assumed to increase at the annual rate of ||Pi~.sub.o~. The final term in equation 1 represents the present value of the cash flow from the sale of the property at the end of the projected N-year holding period, at which time proportional selling costs equal to B will be incurred.

The mean or expected value of all future cash flows is converted to present (i.e., market) value by discounting at y, the appropriate yield.(7)

It is important to emphasize that a multiperiod DCF approach to income property valuation is an application of "mean/variance" analysis, a standard approach to incorporating risk into the valuation of many financial assets. Mean/variance analysis portrays investors as weighing the advantages of expected benefits from alternative courses of action against the disadvantages of the particular risks that apply. More specifically, mean/variance analysis explicitly recognizes that the expected variability as well as the expected amount of future cash flows are fundamental to the determination of market values in a competitive market. Other things being equal, mean/variance investors are assumed to prefer assets with higher mean returns (given comparable levels of risk) and to avoid assets whose cash flows and returns are expected to be more volatile than assets with the same expected return.

This risk/return tradeoff in the context of DCF analysis requires that an appraiser's best guess of future cash flows be plugged into the numerator of the DCF valuation equation. If an appraiser is relatively uncertain about these point estimates of expected future cash flows, perhaps because the subject property is located in an overbuilt market that is difficult to analyze, the appraiser should penalize the subject by discounting the point estimates with a higher yield rate than that which would be applied to a similar but less risky property. In short, an internally consistent application of DCF analysis requires that adjustments for properties perceived to be relatively risky be made in the discount rate rather than by incorporating overly conservative or "worst-case" cash flow forecasts.

It is important to note that risk is defined as the range of potential variation between actual future cash flows and the projected mean cash flows used in calculating value. Thus, income properties located in overbuilt markets are not necessarily riskier investments just because current values are below construction costs; that is, risk does not depend on the current level of rents or values. Rather, risk is a function of the degree of certainty market participants place on their estimates of future cash flows.

In many applications of the multiperiod valuation model, the rental adjustment factor in equation 1, ||Delta~.sub.t~, is set equal to zero. That is, effective gross rental income is expected to grow at the rate of expected general inflation minus the effects of economic deterioration or aging. It should be emphasized that this pattern of projected rental income invokes the rather strong assumption that the real estate market of interest has obtained long-run equilibrium. In other words, market values are assumed to equal construction costs and current and expected rents are forecasted to be just sufficient to provide investors with a competitive (i.e., risk-adjusted) rate of return.

In short, applying standard assumptions of rental income growth to overbuilt markets ignores the increases in the level of real rents that will occur as the excess supply of space is worked off. In fact, because many overbuilt markets are also currently perceived as relatively risky, numerous appraisers (and their clients) seem reluctant to incorporate anything but flat projections of nominal future rental income. Such an approach does not necessarily understate the current value of an existing property if an appraiser is simultaneously using a discount rate that is too low. In effect, an appraiser may derive a reasonable estimate of market value for a property in an overbuilt market by adjusting for the relative riskiness of the cash flows in the numerator, rather than in the denominator, of the DCF equation. In addition to being inconsistent with basic principles of microeconomics, however, using projections of rental income that are less than the expected (or mean) levels does a disservice to a client because it masks the true determinants of market value. Overly pessimistic rent projections (which decrease values) are offset by overly optimistic risk assessment (which decreases required yields and increases values).(8)

An example property

To facilitate discussion of these concepts, consider the following simple numerical example, which is summarized in Table 1. The subject property is a newly constructed office building with 55,500 leasable square feet. Based on current supply-and-demand conditions, effective gross income (EGI) for the next year is projected to be $1,000,000, or $18 per square foot. The rate of general inflation (minus economic depreciation) is expected to be 4% per year over the projected 10-year holding period (|Pi~ = 0.04). Operating expenses will consume 15% of first-year income and thereafter grow at an annual rate of 5% (||Pi~.sub.o~ = 0.05). The market value of the property at the end of any year is set equal to NOI in the subsequent year capitalized at 9%. Selling expenses are assumed to be 4% (B = 0.04). The projected stream of NOI, including the selling price net of expenses, is converted into an estimate of current market value using a (constant) 12% discount rate (y = 0.12).(9)

The cost of constructing or reproducing the subject property, including land and developer profit, is estimated at $11,721,700. If an appraiser assumes that the current year EGI of $1,000,000 will increase at the rate of general inflation, or 4% per year, the estimated value of the subject property is $9,768,085, or $1,953,615 below reproduction costs. Clearly, this office market has not obtained long-run equilibrium. The market-clearing rental rate of $18 per square foot in the space market produces value estimates that are substantially below construction costs when rental income is projected to grow at the rate of general inflation.

Using the assumptions in Table 1, an appraiser can calculate that first-year EGI of $1,200,000 or $21.6 per square foot is required to equate market value with reproduction costs of $11,721,700 when rental income is projected to grow at the rate of general inflation. Thus, current rents in this overbuilt market are 20% below (i.e., $18 versus $21.6) required, or long-run equilibrium, rental rates.

The loss in rental income caused by the excess supply of office space is depicted graphically in Figure 1 under the assumption that the current excess supply (or disequilibrium) persists over the expected 10-year holding period. As noted previously, first-year EGI of $1,200,000 is required to restore long-run equilibrium in the asset market. The slope of the line defined by points (RR, A) reflects nominal income growth of 4% per year. If current rental income (CR) of $1,000,000 is TABULAR DATA OMITTED also expected to increase at 4% per year, then the amount of lost income from the excess supply is represented by the shaded area (RR, A, B, CR), which has a present value of $1,953,615.(10)

THE RENT ADJUSTMENT VALUATION MODEL

Is it reasonable for an appraiser to assume that increases in effective rental income will merely keep pace with inflation in this overbuilt market? The answer is clearly no. Because current rents are below minimum required rents, builders will sharply reduce if not eliminate the amount of new product that they bring to the market. The combination of reduced new construction along with normal growth in the demand for space and steady obsolescence of the existing stock will reduce, over time, the excess supply of space. As supply falls relative to demand, higher effective rents will be generated for the existing stock. Market participants understand that this process will continue until effective rents "catch up" with required rents, because only then will developers have an incentive to bring new product to the market. Higher effective rents can be generated by higher contract (or stated) rents or by reduced vacancies. In overbuilt markets it is unlikely that higher contract rents will be observed until vacancies fall to normal levels.

How quickly will effective gross rents rise from current to required levels? The rise in real rents will occur at the most rapid rate in fast-growing markets with higher absorption rates, and the smaller the difference between current market and required rents the sooner the asset market will obtain long-run equilibrium. Markets with slower economic growth may not allow any significant increases in real rents for a number of years, even if there is a near cessation of new construction.

Because effective rents will not rise instantaneously to required levels, existing properties in overbuilt markets will sell at a discount to reproduction costs. The magnitude of the discount will depend on how slowly investors think rents will rise to equilibrium levels. The longer the expected adjustment period, the greater the present value of expected below-equilibrium rents, and the greater the discount from reproduction costs. Investor expectations should vary with both the expected growth rate of the area and the extent of the initial disequilibrium.(11) Even in slow-growing overbuilt markets, however, market participants expect that real increases in effective rental income will eventually occur. That is, they expect that ||Delta~.sub.t~ in equation 1 will become positive in some future year.

How should an appraiser incorporate future increases in real rental income into his or her cash flow forecast? First, an assumption must be made about the length of the recovery time period. Second, the pattern of real effective rent increases over the expected recovery period must be forecasted. In terms of equation 1, an appraiser must specify ||Delta~.sub.t~ for each year of the expected recovery period.

One possibility is to assume that real rents do not adjust until the end of the forecasted recovery period at which time they "spike" to their required level. The pattern of expected rental income generated by this assumption is depicted in Figure 2, and assumes that the excess supply of space will persist for seven years. Current market value estimates with this assumption will exceed those from the "no-recovery" scenario because the amount of projected lost income from below-equilibrium rents is less. In terms of the example property, ||Delta~.sub.t~ is set to zero for t = 1 - 6 and set to 0.20 for t = 7. The assumed spike in effective rental income in year 7 (from point D to point C) increases the estimate of current market value from $9,768,085 to $11,195,958. Thus, the discount from reproduction costs is reduced from $1,953,615 to $525,715 relative to the no-recovery assumption.

Is it reasonable to assume that no adjustment in real effective rents will occur until the end of the projected recovery period? Reduced new construction along with growth in the demand for space and steady obsolescence of the existing stock will reduce the excess supply of space over time. As the supply of space falls relative to demand, higher effective rents for the existing stock will gradually be generated by higher contract rents or decreased vacancies (barring, of course, any unforeseen "shocks" to future supply and demand).

A more plausible pattern of rental income over the recovery period is depicted in Figure 3. This pattern of real rent increases can be incorporated into a valuation model (spreadsheet or otherwise) by adding two required inputs to the standard DCF model. First, define d as the total percentage difference between current market rents (CR) and long-run equilibrium rents (RR). Second, define y as the number of years over which the total required adjustment in rents is expected to occur. The annual rent adjustment parameter in year t is equal to

||Delta~.sup.t~ = {|(1 + d).sup.(1/y-1))~ - 1 if t |is less than or equal to~ y (2)

{0 if t |is greater than~ y.

For the example property, d = 0.20 and y = 7. Thus, ||Delta~.sub.t~ = 0.03085 for all t |is less than or equal to~ 7. Note that |1.03085.sup.6~ = 1.20. One is subtracted from y in the calculation of ||Delta~.sub.t~ because it is assumed that rents are fixed in year 1. Thus, for rents to fully recover by the end of year 7, the 20% required increase is actually spread over 6 years.(12)

A gradual increase in real rents over the assumed recovery period increases the estimate of market value relative to the rent spike assumption because the amount of below-equilibrium rent over the assumed holding period is reduced. The estimated market value of the example property increases to $11,524,940, a discount of $196,760 (or 2%) from reproduction costs.

It should be noted that this $11,524,940 estimate of value is $1,757,855 greater than the estimate obtained when it is assumed that real rents do not recover from the current overbuilding. Assume, for the moment, that 12% is the appropriate risk-adjusted discount rate and that $11,524,940 is the correct estimate of market value because it incorporates a gradual increase in real rents over time. One could arrive at the same value estimate assuming no increase in real rents (scenario 1) if cash flows are discounted at a rate of 9.47% instead of 12%. My contention is that appraisers in overbuilt markets may be backing into reasonable value estimates in this fashion: overly conservative rent projections are offset by the use of discount rates that understate the perceived riskiness of the projected cash flows.

An important advantage of the rental adjustment valuation model is that changes in effective rental income over time attributable to the current excess supply of space can be separated from income increases as a result of other causes such as general inflation. The rental adjustment valuation model requires just two additional variable inputs: 1) the percentage difference between current market and required effective gross income; and 2) the number of years required to absorb the excess space. While it is difficult to project the number of years that a local market will require to recover, such projections cannot be avoided and should be clearly visible in an appraisal report. The sensitivity of market value estimates to different recovery period assumptions can be quickly determined. For example, the appraiser of the example property could show the client that a 4-year recovery period assumption would produce (from equation 1) a ||Delta~.sub.t~ of 0.0627 (for all t |is less than or equal to~ 4) and a value estimate of $11,746,420, versus $11,524,940 with a 7-year recovery. A more pessimistic recovery period assumption of 10 years would produce a ||Delta~.sub.t~ of 0.0205 (for all t |is less than or equal to~ 10) and a value estimate of $11,333,585.(13)

CONCLUSION

Nationally, commercial real estate markets were substantially overbuilt during the last half of the 1980s. This excess supply of real estate, especially office space, still exists in many markets with the recent economic recession undoubtedly contributing to the persistence of the real estate downturn. Evidence of the excess supply can be found in downtown commercial vacancy rates that exceed 15% in most major markets (rates in non-central business districts are higher) and transaction prices below what it would cost to reproduce the properties new.

Projecting the future pattern of rental income for properties in overbuilt markets is a difficult task that appraisers cannot avoid. Cash flow projections should depend on how quickly investors think the excess supply of space will be absorbed. The estimated recovery period should in turn depend on current supply and demand conditions and on the expected rate of economic growth in the local economy. This article discusses the effects of current and projected local market conditions on market rents and values and develops a variant of the standard DCF model--the rent adjustment valuation model--that allows appraisers to explicitly incorporate these anticipated effects into their market value estimates. Any uncertainties concerning the (point) estimates of cash flows in overbuilt markets should be reflected in higher discount (yield) rates rather than by incorporating overly pessimistic cash flow forecasts.

1. Hendershott and Kane report that 300 billion real dollars (1991) were invested in commercial real estate during the 1970s. In the 1980s, this investment increased 57% to 470 billion real dollars. Patric H. Hendershott and Edward J. Kane, "Causes and Consequences of the 1980s Commercial Construction Boom," Journal of Applied Corporate Finance (May 1992): 61.

2. See David Shulman and Therese E. Byrne, "The U.S. Office Market: Hitting Bottom with a Thud," United States Real Estate Research (Salomon Brothers, June 13, 1991).

3. See David Shulman, "Shopping Centers: The Next Office Market?" United States Real Estate Research (Salomon Brothers, September 24, 1990).

4. Shulman and Byrne, 1.

5. Discounted cash flow analyses contain estimates of future "nominal" cash flows. Even if basic demand and supply relationships in the local space market are not expected to change (i.e., the asset market has obtained long-run equilibrium), nominal cash flows may be expected to change over time simply as a result of general inflation in the economy. A decrease in "real," or inflation-adjusted, rental income occurs when increases in nominal rents do not keep pace with general inflation. Real increases occur only when percentage changes in rental income exceed the general inflation rate.

6. During the second half of the 1980s, resources were poured into unproductive real estate that could have been invested productively in other assets. Giliberto estimates that nearly 1 billion square feet of excess commercial space was constructed in the last half of the 1980s at a direct cost of $48 billion. (S. Michael Giliberto, "Commercial Flows and Construction: A Note," mimeo, Salomon Brothers, 1992). A measure of the total economic cost of misallocated resources is the current value of past and future reduced cash flows caused by the overbuilding. Hendershott and Kane estimate this economic cost to be $120 billion to $140 billion (Hendershott and Kane, 168).

7. Mortgage debt inflows and outflows are not typically included in the projected cash flows. Rather, all before-debt (and before-tax) payments are discounted by the required yield rate. Debt flows include the net loan proceeds disbursed by the lender at closing, periodic interest and principal payments, and the loan balance remaining at the time of the sale. If an appraiser is valuing the property subject to the existing debt financing, the debt flows should be explicitly incorporated into the analysis. See the American Inst. of Real Estate Appraisers, The Appraisal of Real Estate, 9th ed. (Chicago: American Inst. of Real Estate Appraisers, 1987), 541-548. It should be noted that if the debt flows are incorporated into the DCF valuation model, projected after-debt cash flows to the equity investor should be discounted by the investor's before-debt return on both debt and equity. For an expanded discussion of discount rates in multiperiod DCF models, see David C. Ling, "Implementing Discounted Cash Flow Valuation Models: What is the Correct Discount Rate?" The Appraisal Journal, (April 1992): 267-274.

8. Using pessimistic rent forecasts and discount rates that understate the expected variation of the subject's future cash flows is a confusing half-step toward the use of "certainty equivalent" valuation. In a certainty equivalent valuation model, expected (or risky) cash flows in the numerator are replaced by the amount that the investor would accept with certainty in lieu of the risky cash flows. These certainty equivalents are then discounted at the risk-free rate of interest. See chapter 19 in Gaylon Greer and Michael Farrell, Investment Analysis for Real Estate Decisions (Longman Publishing, 1988).

9. The cash flow model represented by equation 1 and the numerical example is quite simplistic. For example, it is more difficult to project average rental rate increases for properties encumbered by long-term leases. Also, operating expenses actually contain both fixed and variable components and therefore may be expected not to increase at a fixed rate over time, especially if real adjustments in rental income are projected. The proposed rental adjustment valuation model that is developed in this article can be used to value more complex cash flow streams. The purpose of this article, however, is to present the basic method and underlying economics of the proposed model.

10. It should be noted that CR reflects the effects of competition for tenants at the individual property level. Property owners set rents in such a way as to maximize net income of vacancies and expenses. Thus, the marginal property owner has considered the effects of decreasing rents to increase occupancy and has concluded that a lower rental rate will decrease net income. The level of effective gross rents that maximizes net rental income depends on the perceived price elasticity of demand for space.

11. A useful analogy can be drawn from the pricing of discount bonds. Bonds sell at a discount when they are earning a below-market coupon (i.e., rent). The more the coupon is below market and the longer the bonds are expected to earn the below-market coupon (i.e., the longer the bond's maturity), the lower is the market value of the bond relative to par or book value.

12. Other adjustments to rental income, such as step functions, could be used if an appraiser thought them to be more appropriate for a subject property.

13. Addition of the rental adjustment variables to a standard DCF spreadsheet requires the following modifications. First, add input "cells" for d (the total percentage difference between current and required rents) and y (recovery period in years). Second, calculate ||Delta~.sub.t~ for each year of the assumed holding period using the input values for d and y. If your cash flow forecasts for each year are developed in columnms, then a row of corresponding ||Delta~.sub.t~s must be calculated for each year. The row of ||Delta~.sub.t~s are calculated with " @IF" statements: If year is |is less than or equal to~ y (which can be determined by the column number of the spreadsheet cell), then ||Delta~.sub.t~ is calculated per the first line in equation 2. If year is |is greater than~ y, then ||Delta~.sub.o~ is set equal to zero. Finally, for each year, add ||Delta~.sub.t~ to rental income increases caused by such factors as general inflation.

David C. Ling, PhD, is a professor in the graduate school of business administration at the University of Florida. He received an MBA in finance and a PhD in real estate economics from Ohio State University, and has previously published in The Appraisal Journal.

Rental rates in overbuilt markets are below the levels required to stimulate new construction. Because rents cannot immediately rise to required levels, many existing properties are selling at discounts to reproduction costs. The magnitude of the discount depends on how slowly investors think rent will rise to required or equilibrium levels. The longer the expected adjustment period, the greater the discount from reproduction costs. Appraisers' expectations of future cash flows should therefore vary with both the expected growth rate of the local market and the extent of the initial disequilibrium. In this article, the effects of current and projected local market conditions on market rents and values are discussed and a variant of the standard discounted cash flow (DCF) valuation model--the rent adjustment valuation model--is developed that allows (forces) appraisers to explicitly incorporate these anticipated effects into their market value estimates.

VALUATION AND THE IMPORTANCE OF LOCAL MARKET CONDITIONS

It is important to distinguish between the "space" market and the "asset" market when analyzing local markets for income-producing real estate. Equilibrium in the former is determined by the interaction between tenant demand for, and the available supply of, leasable space. The supply of rental space is relatively unresponsive to changes in rental prices (i.e., inelastic) in the short run. Thus, competitively determined rental rates in the space market are primarily determined by the current level of effective tenant demand. A primary determinant of the pace of future construction is the relationship between current rental rates in the local market and "required" (or equilibrium) rental rates. The required level of effective rental income in the first year of operations is that which equates the net present value of the income property investment to zero for typical investors, employing a typical set of assumptions about future rental rates, operating expenses, and resale values. This required first-year effective gross rent per dollar of investment serves as a hurdle rate for prospective developers and investors in income-producing property. If current supply and demand conditions in the market are such that properties generally earn rents greater than the required minimum rent, investors will add new construction to the existing stock in an attempt to capture these "excess" rents.

Put another way, prices or values in the asset market are multiples of the rental rates competitively determined in the space market. If current rents exceed required minimum rents, market values will exceed construction costs (that includes the price of land and a "fair" developer profit) and developers will have an incentive to add to the existing stock. Ultimately, the expansion of supply causes real rents to decrease to the required or equilibrium level.(5) Thus, although inelastic in the short run, the supply of space is fairly elastic (i.e., price responsive) over longer time periods. Short-run equilibrium in the asset market requires only that the market clear; that is, that willing property sellers find willing buyers. Long-run equilibrium in the asset market, however, requires that market-clearing asset prices equal construction costs.

If current rental rates are below the required minimum, as is the case in an overbuilt market, construction will be cut back until market rents rise to the required level. Only then will developers be able to recover construction costs from the sale of new properties and thereby earn a rate of return comparable to what can be earned on alternative investments of similar risk. It should be noted that if the supply of space in a local market could be instantaneously adjusted to the current level of tenant demand (i.e., if even the short-run supply of space were highly elastic), current rental rates in a competitive market would always equal minimum required rents and properties would not sell at a discount to construction costs. The supply of space and therefore current rental rates, however, cannot adjust immediately to changing market conditions. Thus, a combination of reduced construction along with normal growth in demand for space and steady obsolescence of the existing stock are required before higher real rents can be generated for income-producing properties in overbuilt markets.(6)

A TYPICAL APPLICATION OF DCF ANALYSIS TO MARKET VALUATION

Until quite recently, professional appraisers of income-producing property have primarily employed simple income capitalization to estimate market value. With this approach, estimated first-year (or stabilized) net operating income (NOI) of the subject property is converted into an estimate of market value by dividing NOI by the appropriate capitalization rate. The appropriate cap rate in this exercise is typically "abstracted" from the market by calculating first-year NOI as a percent of selling price from recent transactions of properties thought to be comparable with the subject. The application of simple income capitalization does not require explicit estimates of cash flow streams beyond the first year. Implicit estimates of future cash flows, however, are reflected in the cap rates abstracted from the market in the comparable sales analysis.

This can be seen by noting that transaction prices in a competitive market reflect the investment valuations of willing buyers and sellers, which in turn reflect assumptions about future cash flows. More optimistic assessments of future cash flows in a local market increase the prices investors are willing to pay per dollar of current rental income. This increase in sale price multiples decreases cap rates and thereby increases the estimated value of the subject property. Thus, the use of simple income capitalization with cap rates abstracted from the market does not relieve an appraiser of the difficult task of projecting future market conditions and cash flows.

A multiperiod DCF approach to market valuation measures and values cash flows to the equity investor over time after all operating and sale expenses have been paid. Unlike simple income capitalization, DCF techniques require an appraiser to make explicit future cash flow projections. The cash inflows and outflows associated with the acquisition of an existing income property can be represented by the following expression:

|Mathematical Expression Omitted~.

|V.sub.o~ is the estimated market value of the subject property. Effective gross rents, |R.sub.0~, are expected to grow at the average annual nominal rate ||Pi~.sub.r~ where ||Pi~.sub.r~ is usually thought of as the expected rate of general inflation in the economy adjusted downward for economic depreciation. ||Delta~.sub.t~ is a rental adjustment factor intended to capture the effects of over- or under-building on future rent increases. OE represents first-year operating expenses (primarily maintenance and property tax expenditures) that are assumed to increase at the annual rate of ||Pi~.sub.o~. The final term in equation 1 represents the present value of the cash flow from the sale of the property at the end of the projected N-year holding period, at which time proportional selling costs equal to B will be incurred.

The mean or expected value of all future cash flows is converted to present (i.e., market) value by discounting at y, the appropriate yield.(7)

It is important to emphasize that a multiperiod DCF approach to income property valuation is an application of "mean/variance" analysis, a standard approach to incorporating risk into the valuation of many financial assets. Mean/variance analysis portrays investors as weighing the advantages of expected benefits from alternative courses of action against the disadvantages of the particular risks that apply. More specifically, mean/variance analysis explicitly recognizes that the expected variability as well as the expected amount of future cash flows are fundamental to the determination of market values in a competitive market. Other things being equal, mean/variance investors are assumed to prefer assets with higher mean returns (given comparable levels of risk) and to avoid assets whose cash flows and returns are expected to be more volatile than assets with the same expected return.

This risk/return tradeoff in the context of DCF analysis requires that an appraiser's best guess of future cash flows be plugged into the numerator of the DCF valuation equation. If an appraiser is relatively uncertain about these point estimates of expected future cash flows, perhaps because the subject property is located in an overbuilt market that is difficult to analyze, the appraiser should penalize the subject by discounting the point estimates with a higher yield rate than that which would be applied to a similar but less risky property. In short, an internally consistent application of DCF analysis requires that adjustments for properties perceived to be relatively risky be made in the discount rate rather than by incorporating overly conservative or "worst-case" cash flow forecasts.

It is important to note that risk is defined as the range of potential variation between actual future cash flows and the projected mean cash flows used in calculating value. Thus, income properties located in overbuilt markets are not necessarily riskier investments just because current values are below construction costs; that is, risk does not depend on the current level of rents or values. Rather, risk is a function of the degree of certainty market participants place on their estimates of future cash flows.

In many applications of the multiperiod valuation model, the rental adjustment factor in equation 1, ||Delta~.sub.t~, is set equal to zero. That is, effective gross rental income is expected to grow at the rate of expected general inflation minus the effects of economic deterioration or aging. It should be emphasized that this pattern of projected rental income invokes the rather strong assumption that the real estate market of interest has obtained long-run equilibrium. In other words, market values are assumed to equal construction costs and current and expected rents are forecasted to be just sufficient to provide investors with a competitive (i.e., risk-adjusted) rate of return.

In short, applying standard assumptions of rental income growth to overbuilt markets ignores the increases in the level of real rents that will occur as the excess supply of space is worked off. In fact, because many overbuilt markets are also currently perceived as relatively risky, numerous appraisers (and their clients) seem reluctant to incorporate anything but flat projections of nominal future rental income. Such an approach does not necessarily understate the current value of an existing property if an appraiser is simultaneously using a discount rate that is too low. In effect, an appraiser may derive a reasonable estimate of market value for a property in an overbuilt market by adjusting for the relative riskiness of the cash flows in the numerator, rather than in the denominator, of the DCF equation. In addition to being inconsistent with basic principles of microeconomics, however, using projections of rental income that are less than the expected (or mean) levels does a disservice to a client because it masks the true determinants of market value. Overly pessimistic rent projections (which decrease values) are offset by overly optimistic risk assessment (which decreases required yields and increases values).(8)

An example property

To facilitate discussion of these concepts, consider the following simple numerical example, which is summarized in Table 1. The subject property is a newly constructed office building with 55,500 leasable square feet. Based on current supply-and-demand conditions, effective gross income (EGI) for the next year is projected to be $1,000,000, or $18 per square foot. The rate of general inflation (minus economic depreciation) is expected to be 4% per year over the projected 10-year holding period (|Pi~ = 0.04). Operating expenses will consume 15% of first-year income and thereafter grow at an annual rate of 5% (||Pi~.sub.o~ = 0.05). The market value of the property at the end of any year is set equal to NOI in the subsequent year capitalized at 9%. Selling expenses are assumed to be 4% (B = 0.04). The projected stream of NOI, including the selling price net of expenses, is converted into an estimate of current market value using a (constant) 12% discount rate (y = 0.12).(9)

TABLE 1 Discounted Cash Flow (DCF) Summary Example Property Assumptions: $ 1,000,000 Current effective gross income (EGI) $11,721,702 Construction costs including a fair profit for developer 20% Difference between required (equilibrium) rents and current EGI 4% Expected general inflation rate (net of economic depreciation (||Pi~.sub.r~)) 15% Operating expenses as a percent of EGI in first year 5% Expected growth rate in operating expenses beyond first year (||Pi~.sub.o~) 9% Terminal capitalization rate 4% Selling expenses (B) 12% Required yield on all equity acquisitions (y) 10% Expected holding period in years (N) Indicated Market Value Under Four Alternative Scenarios: $ 9,768,085 Assuming current rental income increases at the rate of general inflation $11,721,702 Assuming current year EGI of $1,200,000 and subsequent increases at rate of general inflation $11,195,958 Assuming current rental income grows at the rate of general inflation for 6 years then "spikes" 20% in year 7 $11,524,940 Assuming rental income grows at rate of general inflation plus 3.09% per year over the 7-year recovery period

The cost of constructing or reproducing the subject property, including land and developer profit, is estimated at $11,721,700. If an appraiser assumes that the current year EGI of $1,000,000 will increase at the rate of general inflation, or 4% per year, the estimated value of the subject property is $9,768,085, or $1,953,615 below reproduction costs. Clearly, this office market has not obtained long-run equilibrium. The market-clearing rental rate of $18 per square foot in the space market produces value estimates that are substantially below construction costs when rental income is projected to grow at the rate of general inflation.

Using the assumptions in Table 1, an appraiser can calculate that first-year EGI of $1,200,000 or $21.6 per square foot is required to equate market value with reproduction costs of $11,721,700 when rental income is projected to grow at the rate of general inflation. Thus, current rents in this overbuilt market are 20% below (i.e., $18 versus $21.6) required, or long-run equilibrium, rental rates.

The loss in rental income caused by the excess supply of office space is depicted graphically in Figure 1 under the assumption that the current excess supply (or disequilibrium) persists over the expected 10-year holding period. As noted previously, first-year EGI of $1,200,000 is required to restore long-run equilibrium in the asset market. The slope of the line defined by points (RR, A) reflects nominal income growth of 4% per year. If current rental income (CR) of $1,000,000 is TABULAR DATA OMITTED also expected to increase at 4% per year, then the amount of lost income from the excess supply is represented by the shaded area (RR, A, B, CR), which has a present value of $1,953,615.(10)

THE RENT ADJUSTMENT VALUATION MODEL

Is it reasonable for an appraiser to assume that increases in effective rental income will merely keep pace with inflation in this overbuilt market? The answer is clearly no. Because current rents are below minimum required rents, builders will sharply reduce if not eliminate the amount of new product that they bring to the market. The combination of reduced new construction along with normal growth in the demand for space and steady obsolescence of the existing stock will reduce, over time, the excess supply of space. As supply falls relative to demand, higher effective rents will be generated for the existing stock. Market participants understand that this process will continue until effective rents "catch up" with required rents, because only then will developers have an incentive to bring new product to the market. Higher effective rents can be generated by higher contract (or stated) rents or by reduced vacancies. In overbuilt markets it is unlikely that higher contract rents will be observed until vacancies fall to normal levels.

How quickly will effective gross rents rise from current to required levels? The rise in real rents will occur at the most rapid rate in fast-growing markets with higher absorption rates, and the smaller the difference between current market and required rents the sooner the asset market will obtain long-run equilibrium. Markets with slower economic growth may not allow any significant increases in real rents for a number of years, even if there is a near cessation of new construction.

Because effective rents will not rise instantaneously to required levels, existing properties in overbuilt markets will sell at a discount to reproduction costs. The magnitude of the discount will depend on how slowly investors think rents will rise to equilibrium levels. The longer the expected adjustment period, the greater the present value of expected below-equilibrium rents, and the greater the discount from reproduction costs. Investor expectations should vary with both the expected growth rate of the area and the extent of the initial disequilibrium.(11) Even in slow-growing overbuilt markets, however, market participants expect that real increases in effective rental income will eventually occur. That is, they expect that ||Delta~.sub.t~ in equation 1 will become positive in some future year.

How should an appraiser incorporate future increases in real rental income into his or her cash flow forecast? First, an assumption must be made about the length of the recovery time period. Second, the pattern of real effective rent increases over the expected recovery period must be forecasted. In terms of equation 1, an appraiser must specify ||Delta~.sub.t~ for each year of the expected recovery period.

One possibility is to assume that real rents do not adjust until the end of the forecasted recovery period at which time they "spike" to their required level. The pattern of expected rental income generated by this assumption is depicted in Figure 2, and assumes that the excess supply of space will persist for seven years. Current market value estimates with this assumption will exceed those from the "no-recovery" scenario because the amount of projected lost income from below-equilibrium rents is less. In terms of the example property, ||Delta~.sub.t~ is set to zero for t = 1 - 6 and set to 0.20 for t = 7. The assumed spike in effective rental income in year 7 (from point D to point C) increases the estimate of current market value from $9,768,085 to $11,195,958. Thus, the discount from reproduction costs is reduced from $1,953,615 to $525,715 relative to the no-recovery assumption.

Is it reasonable to assume that no adjustment in real effective rents will occur until the end of the projected recovery period? Reduced new construction along with growth in the demand for space and steady obsolescence of the existing stock will reduce the excess supply of space over time. As the supply of space falls relative to demand, higher effective rents for the existing stock will gradually be generated by higher contract rents or decreased vacancies (barring, of course, any unforeseen "shocks" to future supply and demand).

A more plausible pattern of rental income over the recovery period is depicted in Figure 3. This pattern of real rent increases can be incorporated into a valuation model (spreadsheet or otherwise) by adding two required inputs to the standard DCF model. First, define d as the total percentage difference between current market rents (CR) and long-run equilibrium rents (RR). Second, define y as the number of years over which the total required adjustment in rents is expected to occur. The annual rent adjustment parameter in year t is equal to

||Delta~.sup.t~ = {|(1 + d).sup.(1/y-1))~ - 1 if t |is less than or equal to~ y (2)

{0 if t |is greater than~ y.

For the example property, d = 0.20 and y = 7. Thus, ||Delta~.sub.t~ = 0.03085 for all t |is less than or equal to~ 7. Note that |1.03085.sup.6~ = 1.20. One is subtracted from y in the calculation of ||Delta~.sub.t~ because it is assumed that rents are fixed in year 1. Thus, for rents to fully recover by the end of year 7, the 20% required increase is actually spread over 6 years.(12)

A gradual increase in real rents over the assumed recovery period increases the estimate of market value relative to the rent spike assumption because the amount of below-equilibrium rent over the assumed holding period is reduced. The estimated market value of the example property increases to $11,524,940, a discount of $196,760 (or 2%) from reproduction costs.

It should be noted that this $11,524,940 estimate of value is $1,757,855 greater than the estimate obtained when it is assumed that real rents do not recover from the current overbuilding. Assume, for the moment, that 12% is the appropriate risk-adjusted discount rate and that $11,524,940 is the correct estimate of market value because it incorporates a gradual increase in real rents over time. One could arrive at the same value estimate assuming no increase in real rents (scenario 1) if cash flows are discounted at a rate of 9.47% instead of 12%. My contention is that appraisers in overbuilt markets may be backing into reasonable value estimates in this fashion: overly conservative rent projections are offset by the use of discount rates that understate the perceived riskiness of the projected cash flows.

An important advantage of the rental adjustment valuation model is that changes in effective rental income over time attributable to the current excess supply of space can be separated from income increases as a result of other causes such as general inflation. The rental adjustment valuation model requires just two additional variable inputs: 1) the percentage difference between current market and required effective gross income; and 2) the number of years required to absorb the excess space. While it is difficult to project the number of years that a local market will require to recover, such projections cannot be avoided and should be clearly visible in an appraisal report. The sensitivity of market value estimates to different recovery period assumptions can be quickly determined. For example, the appraiser of the example property could show the client that a 4-year recovery period assumption would produce (from equation 1) a ||Delta~.sub.t~ of 0.0627 (for all t |is less than or equal to~ 4) and a value estimate of $11,746,420, versus $11,524,940 with a 7-year recovery. A more pessimistic recovery period assumption of 10 years would produce a ||Delta~.sub.t~ of 0.0205 (for all t |is less than or equal to~ 10) and a value estimate of $11,333,585.(13)

CONCLUSION

Nationally, commercial real estate markets were substantially overbuilt during the last half of the 1980s. This excess supply of real estate, especially office space, still exists in many markets with the recent economic recession undoubtedly contributing to the persistence of the real estate downturn. Evidence of the excess supply can be found in downtown commercial vacancy rates that exceed 15% in most major markets (rates in non-central business districts are higher) and transaction prices below what it would cost to reproduce the properties new.

Projecting the future pattern of rental income for properties in overbuilt markets is a difficult task that appraisers cannot avoid. Cash flow projections should depend on how quickly investors think the excess supply of space will be absorbed. The estimated recovery period should in turn depend on current supply and demand conditions and on the expected rate of economic growth in the local economy. This article discusses the effects of current and projected local market conditions on market rents and values and develops a variant of the standard DCF model--the rent adjustment valuation model--that allows appraisers to explicitly incorporate these anticipated effects into their market value estimates. Any uncertainties concerning the (point) estimates of cash flows in overbuilt markets should be reflected in higher discount (yield) rates rather than by incorporating overly pessimistic cash flow forecasts.

1. Hendershott and Kane report that 300 billion real dollars (1991) were invested in commercial real estate during the 1970s. In the 1980s, this investment increased 57% to 470 billion real dollars. Patric H. Hendershott and Edward J. Kane, "Causes and Consequences of the 1980s Commercial Construction Boom," Journal of Applied Corporate Finance (May 1992): 61.

2. See David Shulman and Therese E. Byrne, "The U.S. Office Market: Hitting Bottom with a Thud," United States Real Estate Research (Salomon Brothers, June 13, 1991).

3. See David Shulman, "Shopping Centers: The Next Office Market?" United States Real Estate Research (Salomon Brothers, September 24, 1990).

4. Shulman and Byrne, 1.

5. Discounted cash flow analyses contain estimates of future "nominal" cash flows. Even if basic demand and supply relationships in the local space market are not expected to change (i.e., the asset market has obtained long-run equilibrium), nominal cash flows may be expected to change over time simply as a result of general inflation in the economy. A decrease in "real," or inflation-adjusted, rental income occurs when increases in nominal rents do not keep pace with general inflation. Real increases occur only when percentage changes in rental income exceed the general inflation rate.

6. During the second half of the 1980s, resources were poured into unproductive real estate that could have been invested productively in other assets. Giliberto estimates that nearly 1 billion square feet of excess commercial space was constructed in the last half of the 1980s at a direct cost of $48 billion. (S. Michael Giliberto, "Commercial Flows and Construction: A Note," mimeo, Salomon Brothers, 1992). A measure of the total economic cost of misallocated resources is the current value of past and future reduced cash flows caused by the overbuilding. Hendershott and Kane estimate this economic cost to be $120 billion to $140 billion (Hendershott and Kane, 168).

7. Mortgage debt inflows and outflows are not typically included in the projected cash flows. Rather, all before-debt (and before-tax) payments are discounted by the required yield rate. Debt flows include the net loan proceeds disbursed by the lender at closing, periodic interest and principal payments, and the loan balance remaining at the time of the sale. If an appraiser is valuing the property subject to the existing debt financing, the debt flows should be explicitly incorporated into the analysis. See the American Inst. of Real Estate Appraisers, The Appraisal of Real Estate, 9th ed. (Chicago: American Inst. of Real Estate Appraisers, 1987), 541-548. It should be noted that if the debt flows are incorporated into the DCF valuation model, projected after-debt cash flows to the equity investor should be discounted by the investor's before-debt return on both debt and equity. For an expanded discussion of discount rates in multiperiod DCF models, see David C. Ling, "Implementing Discounted Cash Flow Valuation Models: What is the Correct Discount Rate?" The Appraisal Journal, (April 1992): 267-274.

8. Using pessimistic rent forecasts and discount rates that understate the expected variation of the subject's future cash flows is a confusing half-step toward the use of "certainty equivalent" valuation. In a certainty equivalent valuation model, expected (or risky) cash flows in the numerator are replaced by the amount that the investor would accept with certainty in lieu of the risky cash flows. These certainty equivalents are then discounted at the risk-free rate of interest. See chapter 19 in Gaylon Greer and Michael Farrell, Investment Analysis for Real Estate Decisions (Longman Publishing, 1988).

9. The cash flow model represented by equation 1 and the numerical example is quite simplistic. For example, it is more difficult to project average rental rate increases for properties encumbered by long-term leases. Also, operating expenses actually contain both fixed and variable components and therefore may be expected not to increase at a fixed rate over time, especially if real adjustments in rental income are projected. The proposed rental adjustment valuation model that is developed in this article can be used to value more complex cash flow streams. The purpose of this article, however, is to present the basic method and underlying economics of the proposed model.

10. It should be noted that CR reflects the effects of competition for tenants at the individual property level. Property owners set rents in such a way as to maximize net income of vacancies and expenses. Thus, the marginal property owner has considered the effects of decreasing rents to increase occupancy and has concluded that a lower rental rate will decrease net income. The level of effective gross rents that maximizes net rental income depends on the perceived price elasticity of demand for space.

11. A useful analogy can be drawn from the pricing of discount bonds. Bonds sell at a discount when they are earning a below-market coupon (i.e., rent). The more the coupon is below market and the longer the bonds are expected to earn the below-market coupon (i.e., the longer the bond's maturity), the lower is the market value of the bond relative to par or book value.

12. Other adjustments to rental income, such as step functions, could be used if an appraiser thought them to be more appropriate for a subject property.

13. Addition of the rental adjustment variables to a standard DCF spreadsheet requires the following modifications. First, add input "cells" for d (the total percentage difference between current and required rents) and y (recovery period in years). Second, calculate ||Delta~.sub.t~ for each year of the assumed holding period using the input values for d and y. If your cash flow forecasts for each year are developed in columnms, then a row of corresponding ||Delta~.sub.t~s must be calculated for each year. The row of ||Delta~.sub.t~s are calculated with " @IF" statements: If year is |is less than or equal to~ y (which can be determined by the column number of the spreadsheet cell), then ||Delta~.sub.t~ is calculated per the first line in equation 2. If year is |is greater than~ y, then ||Delta~.sub.o~ is set equal to zero. Finally, for each year, add ||Delta~.sub.t~ to rental income increases caused by such factors as general inflation.

David C. Ling, PhD, is a professor in the graduate school of business administration at the University of Florida. He received an MBA in finance and a PhD in real estate economics from Ohio State University, and has previously published in The Appraisal Journal.

Printer friendly Cite/link Email Feedback | |

Author: | Ling, David C. |
---|---|

Publication: | Appraisal Journal |

Date: | Jul 1, 1993 |

Words: | 5158 |

Previous Article: | Valuing sponsor shares in a cooperative apartment. |

Next Article: | The determination of hotel value components for ad valorem tax assessment. |

Topics: |