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The theory, assumptions, and limitations of direct capitalization.

Historically, real estate investments have been motivated by a combination of three investment benefits: 1) cash flow, 2) appreciation, and 3) tax shelter. During the 1970s, most of the investment interest in real estate was caused by real estate's inflation hedge qualities, making the appreciation of real estate an important benefit. The rise and fall of real estate syndications during the 1980s was predicated on real estate tax shelter benefits (or lack thereof). According to a recent Forbe's article by Stephen E. Roulac, cash flow will be the primary source of value in real estate investments in the 1990s as overbuilt markets continue to depress value appreciation and as the Tax Reform Act of 1986 continues to reduce real estate tax shelter benefits.(1)

Over the past three decades the combination of real estate benefits has changed. Valuation models used for real estate should explicitly address the subtleties of each of these three benefits (i.e., cash flow, appreciation, tax shelter). Only cash flow benefits, however, are explicitly included in the direct capitalization valuation model. Some would argue that real estate investment benefits other than cash flow are peripheral in nature and thus the implicit inclusion of real estate appreciation and tax benefits in the capitalization rate is sufficient. This is not the case, however.

It is the duty of an appraiser to include all influences on value when appraising real estate. Further, because virtually all investors in commercial real estate consider more than current cash flow in their investment analyses, it is incumbent on an appraiser to assess these influences on value in the income approach.

The motivation for this article arises from the common and misguided perception that both property appreciation and tax benefits are explicitly included in the capitalization rate--they are not. Direct capitalization measures the current return of a real estate asset based on the anticipated net operating income (NOI). In addition, direct capitalization rate valuation does not include any explicit provisions for measuring below-line costs in the valuation of real property.(2) To disregard property appreciation, tax benefits, and below-line costs in the valuation of real estate is similar to assuming that a single-family homeowner purchases a house solely as a place to live without considering the deductibility of mortgage interest payments, the anticipated appreciation, and the maintenance costs of home ownership. Similarly, commercial property investors are more sophisticated in their analyses of income-producing properties than to simply apply a capitalization rate to a NOI.

In the past several years, The Appraisal Journal has published numerous insightful articles describing the relationship between the internal rate of return and the capitalization rate in the income valuation of real estate. A recent article by David Bradley, "The Capitalization Rate, the Discount Rate, and Inflation,"(3) delineates how the internal rate of return (IRR) equals the capitalization rate plus an income growth rate (i.e., Y = R + g, where Y is the IRR, R is the capitalization rate, and g is the income growth factor).(4) In 1990 two other articles appeared in The Appraisal Journal that apply Bradley's insights to appraisal problems.(5) Both articles primarily discuss the results of applying a higher reversion capitalization rate than the going-in capitalization rate in a discounted cash flow (DCF) analysis. Although increasing the reversion capitalization rate does reduce the IRR of an investment, it is only one of several factors that prevents the equation Y = R + g from being maintained.

The purpose of this article is to extend and broaden the implications of these three articles by further analyzing the limitations of the direct capitalization approach to value. First the financial theory that underlies the equation--internal rate equals capitalization rate plus growth rate--is reviewed. The financial theory is then applied to real estate, the assumptions and limitations of the theory are reviewed, and exceptions to the equation are applied to several real estate cash flow examples.

FINANCIAL THEORY

Financial assets are valued based on the stream of expected cash flows an asset produces over its lifetime. For stock market investments, the stream of income is the annual dividends. Dividends are taken out of a firm's net income. Net income is both after tax and after interest payments; therefore, the dividend is paid out of the residual profits after all corporate obligations have been met. Assuming that a share of stock is purchased from a company that pays all its net income out as dividends, that the dividend amount remains constant over time, and that the share of stock is held forever, the value of this security could then be valued as follows:

|V.sub.0~ = D/|(1 + |k.sub.s~).sup.1~ + D/|(1 + |k.sub.s~).sup.2~ + ... + D/|(1 + |k.sub.s~).sup.a~ + ... + D/|(1 + |k.sub.s~).sup.|infinity~~ (1)

where |V.sub.0~ is the value today, D is the annual dividend rate, and |k.sub.s~ is the discount rate and both D and |k.sub.s~ are constant over time. As the dividend and the discount rate are both constant, equation 1 can be reduced to:

|Mathematical Expression Omitted~

Because the holding period for the stock investment is infinity (i.e., there is no sale), cash flows in the distant future will approach a zero value as the compounded discount rate, |k.sub.s~, grows over time and D remains constant. Therefore, equation 2 can be further simplified:

|V.sub.0~ = D/|k.sub.s~ (3)

Equation 3 shows that if the dividend of a stock has a zero growth, the value of a share of stock equals the dividend divided by the discount rate. In finance terms equation 3 is referred to as a perpetuity, because the dividend is expected to continue forever, or into perpetuity. The direct capitalization is based on the same premises as the perpetuity.

Relaxing the no-growth assumption, a model estimating the value of future dividends when g |is not equal to~ 0 yields:(6)

|V.sub.0~ = |D.sub.0~(1 + g)/|k.sub.s~ - g = |D.sub.1~/|k.sub.s~ - g (4)

Equation 4 states that the value of an asset is equal to the expected dividend over the next 12 months (i.e., the dividend at the end of period one) divided by the total yield minus the expected growth rate. Because the investor expects to realize part of the return from the growth of the dividend, which ultimately increases the stock price, the investor reduces the expected dividend return requirements by the expected dividend growth rate, g. Equation 4 can be solved for |k.sub.s~, which yields:

|k.sub.s~ = |D.sub.1~/|V.sub.0~ + g (5)

Because |D.sub.1~/|V.sub.0~ is the expected annual dividend return of a share of stock and g is the expected growth in value of a share of stock, the combination of these two is the total return of a constant growth stock. Understanding these stock valuation principles is helpful in applying financial theory to real estate valuation models.

CONVERTING FINANCIAL THEORY INTO REAL ESTATE PRACTICE

Progressing from equation 1 through equation 3, it is interesting to note that the value of a stream of cash flows can be reduced to a single-period valuation model. Although there are some simplifying assumptions (e.g., zero income growth, the security assumed to be held forever), it is instructive to conceptualize the relationship between a stream of dynamic cash flows and a static equation.

Substituting the terminology used in The Appraisal of Real Estate, tenth edition, to the stock valuation equation 3, annual dividends (D) can be replaced by the property's NOI; k, or the total expected return of the stock, can be replaced by Y, or the expected IRR of a real estate investment; and |V.sub.0~ remains as the value of the underlying asset. Thus equation 3 becomes the direct capitalization formula:

|V.sub.0~ = NOI/Y (6)

where the NOI of a property is divided by the expected IRR (Y) to derive the property value. It should be noted that the NOI is divided by the expected IRR, or, when the NOI has a zero growth rate the IRR equals the direct capitalization rate. In equation 6, real estate terms can be directly replaced by finance terms with one significant limitation: stock dividends come from the net income of the corporation, which is the after-tax, after-interest residual income of the corporation. On the other hand, the NOI of a real estate investment does not include below-line costs, interest, or income taxes, and therefore is not equivalent to the net income of a corporation.

Relaxing the no-growth assumption, as was done in equation 4, equation 6 becomes:

|V.sub.0~ = NO|I.sub.0~(1 + g)/Y - g = NO|I.sub.1~/Y - g

Solving for Y results in:

Y = NO|I.sub.1~/|V.sub.0~ + g (8)

Replacing NOI/|V.sub.0~ with R returns:

Y = R + g (9)

From equation 9 it can be seen that the overall capitalization rate R does not explicitly include an income growth component as g is separate from the capitalization rate, R. The fact that the capitalization rate does not include an income growth component is important for two reasons. First, as a result of the current oversupply of real estate and the expectation that the oversupply will reduce income growth rates for much of the remainder of this decade, direct capitalization rates need to be adjusted upward. Second, those who thought that the direct capitalization rate explicitly includes an inflation premium, like the authors of Modern Real Estate, fourth edition,(7) need to change the way capitalization rates are derived when using the built-up method of determining a capitalization rate.

As is shown here, the IRR equals the capitalization rate plus an income growth rate. Why is it, however, that the IRR is usually less than the capitalization rate plus the growth rate in most cash flow analyses? To answer this question it is necessary to assess the following assumptions that underlie the Y = R + g model:

1. The going-in capitalization rate equals the going-out capitalization rate and there are no selling costs at reversion.

2. The income and the expenses grow at the same rate, and that rate is unchanged from year to year. Further, the vacancy rate is a constant percentage of income.

3. There are no below-line cost items. In other words, the NOI from the property equals the cash throw-off of the property.

4. The investor is a tax-exempt entity. Therefore the benefits or costs of income taxes are not included.

5. There is no leverage. The purchase is assumed to be all cash.

Therefore, for the equation Y = R + g to hold, all of these assumptions must be maintained. If these assumptions hold, a DCF analysis can be reduced to a capitalization rate analysis. The problem with maintaining these assumptions is that they do not reflect reality in the valuation of real estate assets. In the next section, assumptions 1 through 3 are relaxed and the effects on the IRR are assessed.

APPLYING FINANCIAL THEORY TO REAL ESTATE CASH FLOWS

Five separate cash flow examples will be reviewed in this section. The first cash flow analysis reveals that the equation Y = R + g is maintained if all five previously stated assumptions are maintained. The first three assumptions are then relaxed in separate examples, revealing that under each scenario the IRR is less than the direct capitalization rate plus an income growth rate. Finally, in Figure 5, the first three assumptions are combined in a single cash flow analysis. Assumptions 4 and 5 are not explicitly addressed using DCF analyses because most appraisers assess the value of a property on a before-tax, before-debt basis. If the most probable purchaser of a property is tax oriented and uses leverage, however, an appraiser should also take that into consideration in a DCF analysis.

In Figure 1, each of the five valuation assumptions is assumed to hold. Given an after-vacancy income of $10,000, expenses of $3,000, and an annual income and expense growth rate of 4%, the 1992 NOI is $7,000. Capitalizing the first-year NOI of $7,000 using a 9% capitalization rate returns a property value of $77,778. Using an investment value of $77,778 and a reversion capitalization rate of 9%, the IRR of the property is 13%, maintaining the equation Y = R + g (i.e., 13% = 9% + 4%). Restated, a capitalization rate of 9% returns the same $77,778 value of the property as discounting the cash flows at 13%. Notice that the NOI from year 2002 incorporates the expectations of the next buyer, who will be purchasing the property based on the expected NOI for the year after the last year of the 10-year holding period.

As most appraisers realize, changing one or more of the five assumptions previously mentioned can dramatically change the expected IRR of a property. What many appraisers do not recognize, however, is that direct capitalization rate valuations do not explicitly account for these assumptions. For instance, most real TABULAR DATA OMITTED estate investments endure some obsolescence over a ten-year holding period. One example of such functional obsolescence is the increased clear height in warehouse buildings built in year 2002 that may result from new forklift technology. While an existing building may have an 18-foot clear height, a clear height of 24 feet is expected in comparable buildings in year 2002 (i.e., it is expected that it will be possible to stack four pallets in a new building in 2002 as a result of new forklift technology). The reversion capitalization rate must increase by 1% to 10% to account for this functional obsolescence. Increasing the reversion capitalization rate by 1% reduces the IRR by 72 basis points to 12.28% from the base-case IRR of 13%.(8)

Continuing to relax other of the five assumptions, Figure 3 assumes that rental step-ups occur in years 3, 7, and 11, or that the tenant has a 4-year lease and releases the space using a 4% compounded rental growth rate without annual escalations. In this scenario, the IRR falls from 13% to 12.44%, a reduction of 56 basis points. Although not shown here, several other income and expense growth scenarios could be presented that would also reduce the IRR. For example, growing the expenses faster than income--using the base case and growing expenses by 5%--reduces the IRR by 25 basis points to 12.75%. Another scenario that prevents the equation from holding is to use a vacancy lag or free-rent period of six months after each four-year lease, which reduces the IRR by 132 basis points to 11.68%. One other possibility is to have no income growth for three years, after which income grows at the expense growth rate of 4%. This lowers the IRR to 11.41%.

It is not surprising that including below-line costs in the analysis also reduces the IRR, as can be seen in Figure 4. The below-line items included in Figure 4 include tenant improvements of $8.00 per square foot, and a 6% leasing commission on the base rent of $10 per square foot for a 1,000-square-foot building. Both tenant TABULAR DATA OMITTED TABULAR DATA OMITTED TABULAR DATA OMITTED improvements and leasing commissions are necessary to lease a building, and therefore need to be included as part of a DCF analysis. Also assumed is a 50% release provision, in which no tenant improvements or leasing commissions are incurred if the space is re-leased by the current tenant. The assumption of no cost upon re-lease of the space is somewhat simplistic, but does not reduce the effectiveness of the example. When tenant improvements and leasing commissions are included in the analysis, the IRR falls 137 basis points to 11.63%.

TABULAR DATA OMITTED

To reiterate the point that the direct capitalization rate does not explicitly include all investment benefits and costs, Figure 5 combines the cash flow effects of Figures 2 through 4 on the IRR of the property. Although the effects of different going-in and going-out capitalization rates, stepped-growth rates, and below-line costs items may be implicitly included in a subjective increase in the capitalization rate, none of these effects is explicitly included in a capitalization rate analysis. If an appraiser disregarded the effects shown in Figures 2 through 4, the appraiser would be overstating the IRR by 2.73%. Conversely, the going-in capitalization rate would have to be increased to 10.77% to maintain a 13% IRR (this assumes that the reversion capitalization rate remains at 10%). Finally, the effects of leverage and income taxes are not included in Figures 1 through 5. If taxes and leverage are included in the most probable purchaser's DCF analysis, however, an after-tax, after-leverage analysis should be completed by the appraiser.

CONCLUSION

Direct capitalization analysis often mis-states the value of real estate by neglecting to consider property appreciation, rental step-ups, and below-line costs as part of income valuation. In the current overbuilt real estate markets, below-line costs alone can reduce the IRR by 100 to 200 basis points or more, and can often be larger than the NOI in years of heavy tenant turnover. It is thus incumbent on an appraiser to value real estate based on the assumptions used in the marketplace--which include going-in capitalization rates that differ from going-out capitalization rates, fluctuating income and expense growth rates, and below-line item costs as well as tax and leverage implications on real estate investments. As demonstrated here, while each of these factors has a potentially large impact on the return of real estate assets and is included in the acquisitions analyses of most equity investors, it is not explicitly included in the direct capitalization analyses.

1. Stephen E. Roulac, "Bottom, Bottom, Where's the Bottom?" Forbes (March 16, 1992): 169.

2. Below-line costs are costs that are not included in the calculation of net operating income. These costs usually include tenant improvements, leasing commissions, and capital improvements. Although all of these items affect the cash flow of a property, they are not included in the net operating income calculations of most appraisers.

3. David M. Bradley, "The Capitalization Rate, the Discount Rate, and Inflation," The Appraisal Journal (April 1989): 237-243.

4. The internal rate of return (IRR) is defined as the discount rate at which an investment has a zero net present value.

5. Keith L. Honnold, "The Link Between Discount Rates and Capitalization Rates: Revisited," The Appraisal Journal (April 1990): 190-195; and Kelly D. Slay, "The Capitalization Rate, the Discount Rate, and Projected Growth in Value," The Appraisal Journal (July 1990): 324-327.

6. For a proof of equation 4, see page 238 of Eugene F. Brigham and Louis C. Gapenski, Financial Management, 6th ed. (Hinsdale, Illinois: The Dryden Press, 1991).

7. C. H. Wurtzebach and M. E. Miles, Modern Real Estate, 4th ed. (John Wiley and Sons, Inc., 1991), 217.

8. These results are consistent with Slay's article. See note 5.

Mark J. Eppli, PhD, is an assistant professor in the Graduate School of Business and Public Management at George Washington University, Washington, DC. He received a BBA and an MS in business administration as well as a PhD in business administration from the University of Wisconsin--Madison. Mr. Eppli has also served as a real estate financial analyst and consultant to several companies.
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Author:Eppli, Mark J.
Publication:Appraisal Journal
Date:Jul 1, 1993
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