Capital market theory and real estate valuation: a case study in choosing an `appropriate' discount rate.
In a typical police action by a state property commission in a condemnation, property owners and their attorneys enlist the services of state licensed real estate appraisers for valuation analysis. In cases where an entire tract or parcel of land is condemned, the appraiser's primary purpose is to estimate the market value of the complete taking at the time of the condemnation. When only a fraction of a tract or parcel of land is condemned, the appraiser must not only estimate the market value of the taking at the time of the condemnation, but must also estimate the consequential damages to the remaining part of the tract or parcel, less any benefits to the remaining part of the tract or parcel. As such, positive and negative externalities are given due consideration in determining a final estimate of the value of the taking.
Although property appraisers undergo extensive training for certification purposes and routinely complete continuing education courses to meet state licensing requirements, variation can and does exist for estimates of market value on condemned property for which certain facts are not in dispute. In addition, when condemned property has previously supported an on-going business, there may be even greater variation in estimates of market value resulting from differences of opinion concerning relevant cash flows, timing and longevity of cash flows and appropriate discount rates used to value those cash flows. But, when condemned property has existing lease arrangements in place, one would expect that differences of opinion concerning value would be much less variable than in those circumstances where cash flows have to be estimated. In such circumstances, when there are differences of opinion concerning market value, the differences in the estimates lie primarily in the choice of an `appropriate' discount rate.
This paper focuses on the construction of, and relationship between, discount rates and capitalization rates and then illustrates their proper application and construction in the context of a recent valuation assignment in a property condemnation.
II. The Relationship Between Discount Rates and Capitalization Rates
Discount rates and capitalization rates are often used interchangeably, which is incorrect. While the two concepts are similar, they are not identical. The use of a discount rate to determine the present value of an income stream captures all of the expected future cash flows generated from an investment while the use of a capitalization rate, or cap rate, assumes that an income stream is nominally constant in perpetuity, and only takes into account the initial periodic cash flow in determining a present value for the investment. To illustrate these concepts we define the following variables
V present value of the investment CF periodic cash flow from the investment (annually-end of period) k total or required rate of return from the investment g annual growth rate of the investment's cash flows
When the cash flows from an investment are expected to occur in perpetuity, and to grow at a constant rate, the relationship between these variables can be expressed as (1):
(1) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
Equation (1) can be further reduced to the following form (2):
(2) V = C[F.sub.1] / k - g
Assuming that the cash flows are received in perpetuity, and that the growth rate is constant, the present value of an investment is found by dividing the cash flow received in period I by the required rate of return minus the growth rate. Obviously, if the cash flows are not received in perpetuity, equation (2) cannot be utilized to find the present value of the investment. (3) Used in the context of equations (1) and (2), k can also be referred to as a discount rate. (4)
In circumstances where the cash flows received from an investment are expected to remain nominally constant in perpetuity, i.e., the growth rate is equal to zero; equation (2) can be expressed as:
(3) V = C[F.sub.1] / k
Only in this particular circumstance can k, the discount rate, also be referred to as the capitalization rate. (5) However, in circumstances where the cash flows from an investment are expected to grow in perpetuity at a constant rate, the capitalization rate is equal to the discount rate, k, minus the growth rate, g.
From the preceding discussion of discount rates and capitalization rates it is apparent that capitalization rates can be thought of as a subset of discount rates and therefore can only be used in certain circumstances to determine the present value of an investment. The use of a discount rate to determine present value offers the user the flexibility of considering cash flows of finite time periods as well as a variation in the growth rate of those cash flows. Despite the wealth of literature on the appropriate use of discount rates and capitalization rates there continues to exist some perplexity regarding their application by professional appraisers. As Boice (1999) points out, "some confusion appears to exist in the minds of some appraisers regarding how best to approach these valuation (discounted cash flow and income capitalization) problems." (pg. 154)
III. Construction of Discount Rates
As pointed out in the previous section, the discount rate and the required rate of return are synonyms. Pratt, Reilly & Schweihs (1996) point out what has long been realized by investors when they state, "the discount rate is a market-driven rate. It represents the expected yield rate--or rate of return--necessary to induce investors to commit funds to the subject investment, given its level of risk." (pg. 161) Determining the level of risk associated with an investment is one of the most critical components necessary to construct an appropriate discount rate for use in determining value. A well-developed measure of the risk associated with holding an asset, or portfolio of assets, is the standard deviation. (6) This measure of risk takes into account all the risk associated with holding an asset regardless of the source of the risk. (7) The figures in Table 1 illustrate the historical positive relationship between risk and return in six U.S. capital markets over the period 1926-1996. Although these figures are ex-post, they do provide investors with some guidance regarding the risk-return trade-off of various types of investments. In addition they provide appraisers, when valuing a cash flow or income stream, a starting point for choosing an appropriate discount rate. (8)
For publicly traded securities (stock and bonds) information on risk and return, ex-post, is readily obtained. For privately held securities, which include stock in privately held companies, leasing arrangements on property, etc., information on risk and return, ex-post, is much harder to obtain. (9) Nevertheless, cash flows from these privately held assets can be estimated, and adjustments in risk can be approximated to reflect their unique characteristics. For instance, the value to minority interest shareholders of a small privately held company would differ from the value to minority interest shareholders of the exact same (now) publicly traded company because of a lack of marketability of the ownership rights. (10) The starting point, however, for determining the value of a minority shareholder's interest in a private company would be in the publicly traded market.
Although the figures provided in Table 1 clearly illustrate the dichotomy that exists between the risks and return associated with an investment in publicly traded stocks versus bonds, an overlap does occur once other asset categories, or sub-divisions of these asset categories, are included. For instance, if long-term corporate "junk" bonds were included as an asset category in Table 1, it is reasonable to assume that the risk and return associated with holding those bonds would be greater than that of long-term corporate bonds. (11) In addition, if publicly held small-company stocks, even smaller than those listed in Table 1, were included as an asset category in Table 1, the risk and return associated with holding those stocks would be greater than that of those small-company stocks listed. (12)
The choice of an appropriate discount rate, or capitalization rate if applicable, used for valuing a particular asset or security involves an estimation of the risks involved. The greater the chance that the actual return from an asset differs from the expected return, the greater the risk, and therefore the greater the discount rate used to determine the present value of the asset. The first step for valuation professionals must be a thorough understanding of the historical long-term risk-return relationship that exists in publicly traded securities. Jones (1999) states, "There is no reason to assume that (these) relative relationships (based on the historical record) will differ significantly in the future." (pg. 138) It is only with this understanding that valuation professionals can make the appropriate adjustments necessary to the discount rate, which depend on the specific risk characteristics of the asset involved, to properly estimate the value of privately traded assets.
IV. Case Study
A recent valuation assignment in which we were engaged required an application of the concepts discussed in sections II and III. The assignment involved a particular circumstance in which a state property commission, in late 1999, invoked its power of condemnation over a small commercial parcel of land in a metropolitan area in the southeastern United States. As is typical in these matters, the property owner and his attorneys contacted a local real estate appraiser to determine the value of the taking. (13) However, the property owner, who was an experienced real estate investor, was skeptical of his appraiser's valuation, as well as the valuation of the state's appraiser. Therefore, economic expertise was needed, because of the somewhat unique circumstances associated with a lease agreement, to see if the property merited a higher valuation. Given that the state's appraiser valued the property considerably lower than the property owner's appraiser, we focused our analysis on the higher of the two valuations, that of the property owner's appraiser (hereinafter referred to as APPRAISER), to see if a reasonable determination of value had been obtained. (14)
V. Facts Relevant to the Property
According to information provided by our client's attorney, the subject property, located at the corner of a very heavily traveled four-lane intersection less than one mile from a major mall, contained, before the condemnation, approximately .71 acres of land. The state department of transportation condemned approximately 3241 square feet of the right-of-way (slightly more than 10% of the property) and beyond that an additional 980 square feet (approximately 3% of the property) of permanent easement for purposes of improved traffic flow resulting from an added turn lane. Prior to the condemnation, the property owner enjoyed access to both streets from three curb cuts on the property. After the condemnation, the state department of transportation allowed the property owner access to both streets via two curb cuts.
Real estate appraisers typically use three separate, but interrelated, approaches to determine value. It is not uncommon for these approaches, which include the cost, income, and market data approaches, to correlate well with one another. The APPRAISER used the market data approach and the income approach in determining a value for the subject property. (15) As a result of his analysis, he concluded that the before the "take" market value of the property was $1,045,000, relying on an almost identical conclusion based on the market data approach and the income approach. The state's appraiser concentrated on the market data, or comparable sales, approach and provided an estimate of value before the "take" that was substantially lower than that of the APPRAISER'S income approach. (16)
VI. Facts Relevant to the "Take"
For several years preceding the DOT condemnation, the subject property had been leased to a car dealer and used as a used-car lot. The only improvements on the property, other than paving, included a renovated gas station. Approximately two months prior to the DOT condemnation notification, the car dealer vacated the subject property and the property owner entered into negotiations with a convenience store operator/gas jobber (operator). The property owner and operator, prior to DOT condemnation notification, reached an agreement in principle concerning what was in effect a ground-lease as the renovated gas station was in no condition to serve as a modern convenience store. The operator agreed to tear down the existing building and make all necessary site improvements, which included building a new building and canopy, installing five multi-product gasoline dispensers and paving the parking lot, at his complete expense, which was estimated to be in excess of $1,000,000. To effect such improvements the operator borrowed approximately one-third of the amount from a regional financial institution. (17) It is important to note that the property owner did not subordinate the ground lease to the loan. The lease was to run for a term of 25 years with monthly lease payments in the amount of $7500. In addition to lease payments that were to be adjusted annually by the percentage increase in the consumer price index (CPI), the operator agreed to pay all taxes and assessments, maintenance and repairs, and insurance on the property during the lease term.
After receiving DOT condemnation notification, the property owner immediately notified the operator to apprise him of the change in circumstances on the subject property. As a result of the "take", approximately 10% of the subject property, the operator was forced to re-configure the pump island layout and reduce the number of multi-product gasoline dispensers from five to four. This reduction in the number of multi-product dispensers would naturally result in a reduced volume of gasoline, as well as in-store items, sold by the operator. Consequently, the operator offered the property owner $1800 per month less, for a total lease payment of $5700 per month, than he had offered previously, with all other terms and conditions of the original lease remaining the same.
VII. The APPRAISER'S Estimate of Loss
The APPRAISER'S $352,850 estimate of loss, as provided to us by our client's attorney, after the "take" was comprised of $226,000 for consequential damages and $126,850 for the required right-of-way and required easement. To arrive at consequential damages of $226,000 the APPRAISER used the loss in income associated with the "take" of $1800 per month for 25 years. In his analysis he aggregated the monthly losses to arrive at a yearly loss of $21,600. (18) The APPRAISER made several assumptions prior to discounting the yearly cash flows. First, he assumed that an operating management fee of 5% would apply to the cash flows and accordingly deducted this figure from the yearly total gross cash flows for the entire 25 years. Second, in accordance with the lease agreement, he applied a CPI adjustment factor to the gross cash flows for each of the 25 years. His estimate of average inflation over the lease period was 3.5% and he adjusted each yearly cash flow accordingly. Third, a discount rate was necessary to determine the present value of the yearly-adjusted cash flows and the APPRAISER chose 11%, yielding a present value of $226,000. (19)
VIII. The APPRAISER'S Estimate of Consequential Damages
Our analysis of loss to the property owner as a result of the "take" focused on validating or rejecting the APPRAISER'S estimate of consequential damages, as we had no experience or expertise concerning the $126,850 estimate for the required right-of-way and required easement. (20) An unusual aspect of this case concerned the fact that the monthly lease reduction resulting from the "take" was never in dispute as the property owner had clear evidence of what the operator was willing to pay before and after the condemnation notification. Therefore, the APPRAISER used a non-disputable figure, $21,600 per year, in arriving at his estimate of consequential damages. However, the APPRAISER did make three assumptions, as outlined previously, in arriving at his estimate of consequential damages. Whether our estimate of consequential damages coincided with the APPRAISER'S estimate hinged on the extent to which we accepted those assumptions.
The APPRAISER'S three assumptions were: 1) 5% operating maintenance fee deducted yearly; 2) 3.5% per year lease adjustment based on expected CPI changes; and 3) 11% nominal interest rate used to discount cash flows. While those three assumptions were incongruous with our understanding of the actual risk characteristics of the income stream, we were in agreement with the APPRAISER'S choice of using a discount rate versus a capitalization rate to arrive at an estimate of consequential damages. As we have shown in section II, a capitalization rate can only be used when an income stream is expected to continue in perpetuity. (21)
Regarding the APPRAISER'S assumptions, a 5% operating maintenance fee deducted yearly was not appropriate in the context of this particular situation. The property owner negotiated a triple net lease with the operator for a period of 25 years just one month prior to the condemnation notification, therefore, there would be no need to include a "fee" for any management company or other entity. The property owner essentially had the lease structured so as to mimic an annuity. No action on the property owner's part was necessary except that of cashing the monthly check. Assumptions two and three are actually inter-related and need to be addressed together. When simultaneously "inflating" and then "discounting" a cash flow stream that grows at a constant rate, the same result can be obtained by calculating a "net" discount rate. In this situation, the APPRAISER was actually discounting the cash flow stream of $21,600 per year by the difference between the nominal interest rate of 11% and the CPI adjustment of 3.5%. This "net" discount rate of 7.5% seemed unreasonably high to us considering what we knew about returns from various asset classes over the last 75 years (Table 1). Therefore, we did not challenge the APPRAISER'S assumptions on inflation and the nominal discount rate individually, what we focused on was the magnitude of the difference between the two figures or the "net" discount rate that the APPRAISER used in his analysis.
IX. Our Critique of the APPRAISER'S "Net" Discount Rate
Having narrowed our job down to focusing on an "appropriate" "net" discount rate, we first had to show why the APPRAISER'S "net" discount rate was inappropriate under these circumstances. As is commonly known about any investment, past returns are no guarantee of future returns, but past returns, and the risk associated with earning those returns are a good starting point to view differences in risk and return of various asset classes. (22) It is fairly easy to find information for various asset classes, excluding real estate, for any period of time over the last 75 years, as we previously discussed in section III (Table 1). However, when you include real estate, the task is a little more difficult.
A number of investment companies routinely calculate the return and risk associated with holding various classes of assets. Table 2 provides Morgan Stanley Capital International's calculations of the return and risk on various asset classes for the years 1945-1992 (Jones, 1998). We think this period of time is long enough, and contemporary enough, to give a fair representation of the differences that one might expect in relative return and risk for these investments. The assets classes are listed from high to low according to their return during this time period. The second column shows inflation-adjusted returns while the third column shows the risk, as measured by the standard deviation of returns, of the various asset classes. The last column shows a risk index for the various asset classes, which is simply the standard deviation of returns divided by the return of the asset multiplied by 10. (23) This index provides a more meaningful basis for comparison when the returns on two asset classes are not the same and the standard deviation of returns for those assets are different.
The results of risk and return over this time period are especially instructive when we compare them to the "net" discount rate that the APPRAISER used in calculating consequential damages for the subject property. From Table 2, commercial real estate generated an average annual inflation-adjusted return of 3.1% over the time period. This return was achieved with a relatively modest amount of risk as measured by the standard deviation, 4.3%. The S&P 500 Index, in contrast, returned a much higher average annual inflation-adjusted return over the time period, 7.2%. The S&P 500's return, however, was achieved by accepting a much higher level of risk, 19.3%. Of course with what we knew about the relationship between risk and return as set forth in the Capital Asset Pricing Model's (CAPM) Capital Market Line (CML), this came as no surprise to us. (24) The surprise, however, came from looking at the "net" discount rate that the APPRAISER utilized in calculating consequential damages on the subject property. The APPRAISER used a "net" or "inflation-adjusted" discount rate of 7.5%, which was greater than the average annual return of the S&P 500 Index from 1945-1992. In addition, the S&P 500 Index had a standard deviation of returns almost five times that of commercial real estate over this same time period. Therefore, we advocated using a "net" discount rate more appropriate for the level of risk associated with holding commercial real estate, approximately 3.1%.
X. Our Estimate of the "Net" Discount Rate
We felt it necessary to calculate an "appropriate" "net" discount rate in more than one way as a sort of "reality check". Several facts arose out of conversations with the property owner and his attorneys that helped us construct an "appropriate" "net" discount rate. The relevant facts were: 1) the lease was not subordinated to the loan taken out by the operator; 2) the operator's (lessee's) lender was a super-regional bank whose bonds were rated A by Standard and Poor's; 3) the yield to maturity on an A-rated bond with a 25-year term at the time was 7.63%; 4) the operator was spending over $1,000,000 on improvements to the property. Therefore, we concluded that the property owner had an implicit guarantee from the bank, as well as from the sheer dollar amount of the improvements, which made the "character" of the lease payments more like those of an A-rated bond. (25) This suggested that we de-compose the nominal rate on a 25-year A-rated bond into its appropriate parts.
Following Brigham, Gapenski and Ehrhardt (1999) we can express the nominal rate of interest, K, as equal to K*+IP+MRP+DRP+LP, where K* equals the real risk free rate, IP the average expected inflation over the time period, MRP the maturity risk premium, DRP the default risk premium and LP the liquidity premium for the security in question. (26) The characteristics of the lease payment on the subject property suggest that the nominal rate of interest, 7.63%, needs adjustment. The lease called for annual adjustments in the lease payments equal to the percentage increase in the CPI, which means that K=7.63% is an overstatement of the appropriate rate by which the cash flows should be discounted. This CPI adjustment actually has an impact on two of the five components of the nominal rate of interest, the most obvious being the inflation premium, IP. In addition, since over long time periods the level of inflation strongly influences interest rates, a CPI adjustment tends to minimize the maturity risk premium of a fixed income security. (27) Over the last 70 years, the maturity risk premium for long-term bonds has averaged 1.5% (Brigham, Gapenski & Ehrhardt, 1999). Therefore, 7.63% could reasonably be adjusted downward by the average inflation rate expected over the next 25 years as well as by an estimate of the maturity risk premium. (28)
Estimates of inflation over long time periods are varied, but a reasonable range for the next 25 years is in the 3%-4% range. (29) As such, to be conservative, we chose to use 3% for the average expected rate of inflation over this time period. (30) Combining our average expected annual rate of inflation of 3%, with the historical maturity risk premium for long-term bonds of 1.5%, allows us to adjust K by 4.5 percentage points. This allows us to re-write the equation as K-IP-MRP=K*+DRP+LP or 7.63%-3%-1.5%= 3.13%=K*+DRP+LP. At this point there is no need for us to estimate K*, the real risk free rate of interest or DRP, the default risk premium. We have assumed that the risk of default on the lease payments, because of an implicit guarantee by the bank and the dollar amount of improvements made by the operator, are essentially the same as the risk faced by the holder of a 25-year A-rated bond. (31) However the liquidity premium must be addressed before we proceed further with our analysis.
Asset classes vary in the liquidity premium applicable to them. Organized markets for securities ensure that the liquidity premium for exchange listed securities remain very low, usually less than one-half of one percent (Brigham, Gapenski and Ehrhardt, 1999). For real estate, the liquidity premium is higher as property typically cannot be liquidated within the time frame as an exchange listed security. However, the characteristics of the property owner must be considered when evaluating an appropriate liquidity premium to place on this investment. In this case, the property owner owed nothing on the property and had owned the property for 12 years. In addition the property owner owned four other pieces of commercial property either directly adjacent to the subject property or within one-eighth of a mile of the subject property that he had owned for 30 years. Clearly, this property owner was a buy-and-hold investor whose holding period for commercial real estate far exceeded that of an average investor. As such we determined that an appropriate liquidity premium to use in this case was approximated by the liquidity premium inherent in the 25-year A-rated bond. (32) Therefore, we determined that there was no need to adjust the nominal rate of interest further and were satisfied that a discount rate of 3.13% was appropriate to use in this particular instance. Our calculated rate of 3.13% is nearly identical to the 3.1% inflation-adjusted return of commercial real estate from 1945-1992, and therefore serves as our "reality check." (33)
XI. Our Estimate of Loss and Why It Is Conservative
As can be seen in Table 3, which reports a comparison of our assumptions and conclusions versus that of the APPRAISER'S, using a "net" discount rate of 3.13% to calculate a value for consequential damages associated with the condemnation yields a figure of $360,119. Adding this figure to the APPRAISER'S estimate of $126,850 for the required right-of-way and required easement yields a total estimate of loss associated with the condemnation of $486,969, compared with the APPRAISER'S total estimate of loss of $352,850. We felt that this figure was a conservative estimate of loss for several reasons. First, using the data from Table 2 and assuming that the CML is an accurate depiction of the risk/return tradeoff, we estimated the return of the various asset classes using simple linear regression. Table 4 reports the actual return as well as our regression-based estimates of return. (34) The estimated return for commercial real estate was 6%, which indicates that the actual return "plots" above the CML. As a result, commercial real estate appears to have been undervalued over this time period relative to other asset classes. The implications for the subject property, therefore, suggest that real estate investors would be inclined to accept returns less than those earned given the risk associated with earning those returns. Second, the returns for commercial real estate reported in Table 2 are average returns for all commercial real estate in the United States over the time period. The subject property is located in a county whose GDP per capita mirrors that of the state's GDP per capita. (35) In addition, the state where the subject property is located has experienced a growth rate in real per capita GDP in excess of the national growth rate in real per capita GDP, from 1982-1997. (36) If past trends continue regarding growth, then the subject property is likely to experience a real increase in value which suggests that a lease renewal at the end of 25 years would reflect this. (37) Third, since the returns reported in Table 2 are averages, we felt that the location of the subject property warranted some consideration concerning "average returns." As conveyed to us by our client's attorney and by the APPRAISER, the subject property is located in the best retail section of the city due to past and present development activity. As a business moves further and further away from the center of economic activity, rents have a predictable pattern of decline, which can be depicted as rent gradients (Nourse, 1967). In the earlier part of this century, this might have meant that rents decline with distance from the city center. But with improvements in transportation and reductions in transportation cost, today centers of economic activity could as easily be "k" miles from the city center as at the center. Suburban centers may well claim higher rents than downtown. In the case at hand, the subject property is uniquely centric so that movement away from it in any direction is likely to lower the rent per square foot. Thus, using "average return" figures could considerably understate its value. All of these factors combined tend to make our estimates somewhat conservative. (38)
Valuation of assets is inherently subjective. In addition, the particular approach used to determine value, whether it is the income, cost or market data approach, or combinations thereof, is subject to professional judgment. In this particular case, where we have unchallenged and irrefutable evidence on the magnitude of the lease income loss due to the "take," the income approach must be superior to the market data approach if for no other reason than the arbitrariness inherent in selecting comparable properties.
Competent appraisers can and do have differences of opinion concerning the estimation of cash flows (both amount and length) for income producing property when leases are short term in nature. In addition, differences of opinion do exist concerning appropriate discount rates utilized in valuing cash flows. However, when faced with factual data concerning the magnitude and duration of the lease income loss due to a property condemnation, the only real issue to be debated concerns the discount rate. We have provided evidence here, based on our opinion of the actual character of the income stream, the characteristics of the subject property and the holding period profile of the property owner, that suggests that the "net" discount rate utilized by the APPRAISER was inordinately high. (39)
Table 1 Annual Rates of Return (US), 1926-1996 * Average Inflation Standard Return Adjusted Return Deviation Small-company stocks 17.7% 14.5% 34.1% Large-company stocks 12.7% 9.5% 20.3% Long-term corporate bonds 6.0% 2.8% 8.7% Long term government bonds 5.4% 2.2% 9.2% Intermediate-term government bonds 5.4% 2.2% 5.8% U.S. Treasury bills 3.8% .6% 3.3% Inflation 3.2% 4.5% Source: Stocks, Bonds, Bills, and Inflation: 1997 Yearbook (Chicago: Ibbotson Associates, 1997), as reported in Brigham, Gapenski & Ehrhardt (1999). Small-company stocks, as represented by the smallest 20% of stocks (by market value) listed on the New York Stock Exchange. Large-company stocks, as represented by the Standard and Poor's 500 Composite Index (S&P 500). Long-term corporate bonds, as represented by the Salomon Brothers long-term high-grade corporate bond total return index. Long-term government bonds, as represented by a U.S. Treasury bond with a 20-year maturity. Intermediate-term government bonds, as represented by a U.S. Treasury bond with a five-year maturity. U.S. Treasury bills, as represented by a bill with a maturity of approximately 30 days. Table 2 Annual Rates of Return (US), 1945-1992 * Return Inflation Standard Risk Adjusted Deviation Index Return S&P 500 Index 11.7% 7.2% 19.3% 16.5 Commercial Real Estate 7.6% 3.1% 4.3% 5.7 Corporate Bonds 5.4% 0.9% 3.3% 6.2 Long term T-bonds 4.9% 0.4% 4.7% 9.7 T-bills 4.8% 0.3% 1.5% 3.2 Inflation 4.5% * Source: Morgan Stanley Capital International as reported in Jones (1998). Table 3 Assumptions and Conclusions APPRAISER'S OUR'S 1) Number of years cash flows discounted 25 25 2) Yearly operating maintenance deducted from lease payments 5.0% 0% 3) Nominal interest rate 11.0% 7.63% 4) Yearly CPI lease adjustment 3.5% 3.0% 5) Maturity risk premium adjustment N/A 1.5% 6) Net discount rate (3 minus 4 minus 5) 7.5% 3.13% * Estimate of consequential damages $226,000 $360,119 Estimate of the required right-of-way and required easement (we used the APPRAISER'S figure) $126,850 $126,850 Total Estimate of Damages $352,850 $486,969 * We chose to use this figure for the net discount rate instead of the inflation-adjusted return for commercial real estate, from Table 2, of 3.1%. Table 4 Regression Based Estimates of Return * Actual Return Estimated Return S&P 500 Index 11.7% 11.7% Commercial Real Estate 7.6% 6.0% Corporate Bonds 5.4% 5.6% Long term T-bonds 4.9% 6.1% T-bills 4.8% 4.9% * The model is specified as follows: Asset Category Return = [alpha] + [beta] Market Return + Asset Category Specific Risk
(1) For a more in-depth treatment of the relationships discussed in this section see Brigham, Gapenski & Ehrhardt (1999) and Pratt, Reilly and Schweihs (1996).
(2) Equation (2) is generally referred to as the Gordon Growth Model. For a derivation of this equation see Brigham and Gapenski (1996).
(3) However, as the number of years that cash flows are received increases, the discounted present value of the cash flows converges to what one would obtain using equation (2). Assuming a reasonable value of k and g, for instance 10% and 4% respectively, after 100 years, the present value obtained from discounting each cash flow individually very closely approximates the present value obtained using equation (2). The greater the percentage point differential between k and g, the fewer the number of years necessary for the two values to converge and vice versa.
(4) Our use of a discount rate implies using a discounted cash flow analysis to determine the present value of an investment.
(5) Our use of a capitalization rate implies the use of income capitalization to determine the present value of an investment.
(6) Another measure of risk, Beta, is also well developed in the finance literature. Beta is a measure of relative risk and its proper use assumes that the asset in question is part of a well-diversified portfolio of assets. For a discussion of the construction and use of Beta, see Jones (1998).
(7) For a very good introductory treatment of this subject see Brigham, Gapenski & Ehrhardt (1999) or Jones (1998).
(8) Obviously the list of asset categories in Table 1 is not exhaustive, it is meant primarily as a starting point for understanding the risk/return relationship and for getting a "feel" for the returns that investors expect from certain asset categories.
(9) While we realize that a lease is not formally a security, it does exhibit many of the same characteristics that a security exhibits. A lease obligates a tenant to a financial commitment in exchange for certain rights to an asset.
(10) In addition, a discount for owning a non-controlling interest would also apply. For a more complete discussion of a discount for lack of marketability when valuing ownership interests in limited partnerships and limited liability companies, see Bowles and Lewis (1999).
(11) Depending on the appetite for risk of the investor, it is certainly possible for a "junk" bond, or "junk" bond portfolio, to exhibit a level of return, and risk, in excess of large-company stocks.
(12) These stocks would likely be those small company stocks listed on other exchanges such as the NASDAQ or any of the regional exchanges.
(13) The state employed its own real estate appraiser to determine the value of the taking as is customary.
(14) Initial discussions with the property owner revealed that he was extremely displeased with the state's estimate of value and even somewhat displeased with his own appraiser's estimate of value. Therefore, our attention was focused on the valuation as determined by the property owner's appraiser.
(15) The cost approach was deemed inappropriate as the subject property was vacant approximately two months prior to the condemnation notification and contained one building, a renovated gas station, which was scheduled to be razed by the new tenant to construct a convenience store.
(16) As will be seen later, the valuation hinged on facts most appropriate to the income approach.
(17) The financial institution was actually a super-regional bank whose bonds carry an S&P credit rating of A.
(18) The APPRAISER used end of year discounting. Of course if the APPRAISER had discounted the losses on a monthly basis rather than on a yearly basis then the resulting net present value would have been lower.
(19) The appraiser, during preparation for the mediation hearing, said that an 11% discount rate was widely used in the area for real estate valuation purposes.
(20) The appraiser said that this figure was estimated using recent sales figures of comparable commercial property in the vicinity of the subject property.
(21) The APPRAISER only considered lease payments for 25 years in his analysis. We took the same approach as the lease was for a specified time period of 25 years.
(22) Of course we realize that short-term Treasuries have essentially no risk associated with them, but longer term Treasuries bear a maturity risk and inflation risk.
(23) This risk index, when calculated as the standard deviation divided by the return, is known as the coefficient of variation, which measures the risk per unit of return.
(24) Jones (1998) points out that "The CAPM is an equilibrium model that encompasses two important relationships. The first, the Capital Market Line, specifies the equilibrium relationship between expected return and total risk for efficiently diversified portfolios." (pg. 230) In this case, because of limited information, we have assumed that the property owner holds a diversified portfolio of real estate investments and that the standard deviation is the correct measure of risk.
(25) The operator borrowed approximately $360,000 on the project and if he defaulted on the lease payments, the bank, to protect their position, would have to step in and make the lease payments. In addition, the total investment by the operator exceeded $1,000,000, which became part of the "real property." It is highly unlikely, given the actual location of the property, that the property owner could not re-lease the property (land, building, canopy and pumps) in the case of default, to another convenience store operator for at least what the original operator was willing to pay, $7500 per month, for a ground lease only.
(26) Most finance texts use this structure to explain how nominal rates are determined.
(27) Maturity risk can arise from two sources: 1) changing market conditions affecting the supply and demand for the security, and 2) inflationary expectations to the extent they affect relative security prices. For this reason, accounting for inflationary risk basically leaves only one source, changing market conditions, and therefore minimizes maturity risk, ceteris paribus. As Jones (1998) points out, "this risk (inflation premium) is related to interest rate risk (maturity risk premium), since interest rates generally rise as inflation increases, because lenders demand additional inflation premiums to compensate for the loss in purchasing power." (pg. 141)
(28) Because the lease payments are CPI adjusted, we have chosen to use Brigham, Gapenski & Ehrhardt's (1999) full estimate of the maturity risk premium, 1.5%, to adjust the nominal rate of interest. We realize that this adjustment is likely to "understate" the "net" discount rate utilized in our analysis, and, as such, have compensated for this by using a conservative estimate of inflation, which tends to "overstate" the "net" discount rate. However, the extent to which we have compensated for this is unknown.
(29) From Table 1, U.S. inflation, as reported by Ibbotson, for the years 1926-1996 averaged 3.2% (Brigham, Gapenski & Ehrhardt).
(30) The parties, the state DOT and the property owner, agreed to try to settle their disagreement over valuation through mediation. During the mediation process, we presented our estimate of loss and used Brookshire and Slesnick's 1999 survey of NAFE members to support our estimate of inflation. We chose, however, to use the lower bound of the middle 50% of responses from that survey, 3%.
(31) This is a very conservative estimate of default risk for the property. The A-rated bond we have used is an unsecured corporate debenture while the property benefits from approximately $1,000,000 in capital improvements.
(32) As noted previously, we used the lower bound estimate for inflation of 3%, which made our adjustment of the nominal rate of interest conservative. Therefore, even if we have underestimated the liquidity premium, we feel that we have somewhat corrected for this by being conservative in our estimate of inflation.
(33) Rodgers (1989), concludes that the appropriate discount rate to use on a flat (fixed-payment) long-term ground lease should take into account the average Treasury bond rate for the remaining lease term. He provides an example using a discount rate that is 40 basis points over the relevant T-bond rate. Ceteris paribus, we would argue that it is reasonable to use an even lower discount for long-term leases that are subject to yearly CPI adjustments.
(34) We recognize the limitations of using such a small sample, however, our coefficient estimates are statistically significant at the .05 level. Our regression equation is: Return = 4.34 + .38 Risk and the [R.sup.2] = .88.
(35) The county's GDP per capita was 99% of the GDP per capita in the state in 1997.
(36) The real growth rate in US per capita GDP over the last 15 years was 1.75% while the real growth rate in the state's per capita GDP was 2.4%. In 1994 the per capita GDP for the state exceeded the per capita GDP nationally for the first time.
(37) We focused our analysis on discounting the 25 years of lease payments to the present. We made no attempt to forecast possible rental values after that time period. At this point we are simply pointing out that the potential for higher real rents is reasonable after 25 years based on economic trends.
(38) The extent to which our estimates are conservative, however, is unknown. In addition to the reasons we have cited concerning why we think our estimates are conservative, and as we have previously stated in footnote 21, we have made no allowance for any lease payments received after 25 years, based on instructions from our client's attorneys.
(39) Posatko and Mathis (1999) used a discount rate of 4.5% in determining the economic loss suffered by a professional practice in 1980. Their estimate, viewed in the context of the time period, gives us some reassurance as to the reasonableness of our "net" discount rate estimate.
Boice, R. Lane, "Discounted Cash Flow Analysis and Long-Term Leases," The Appraisal Journal, April 1999.
Bowles, Tyler J., and W. Cris Lewis, "The Economics of Ownership Rights in Valuing Minority Interests," Litigation Economics Digest, 1999, 4(1), 31-38.
Brigham, Eugene F., and Louis C. Gapenski, Intermediate Financial Management, Fort Worth, TX: The Dryden Press, 1996 (5th edition), Appendix 4A.
--, --, and Michael C. Ehrhardt, Financial Management: Theory and Practice, New York: The Dryden Press, 1999 (9th edition), 131-136, 171, 330-338, Chapters 5 and 6.
Brookshire, Michael and Frank Slesnick, "A 1999 Survey Study Of Forensic Economists: Their Methods And Their Estimates of Forecast Variables," Litigation Economics Digest, 1999, 4(2), 65-96.
Jones, Charles P., Investments: Analysis and Management, New York: John Wiley and Sons, 1998 (6th edition), 138,141,175,230, Chapters 6,7 and 9.
Nourse, Hugh O., Regional Economics, New York: McGraw-Hill, 1967, 93-126.
Posatko, Robert C., and Stephen A. Mathis, "Estimating Damages Due to the Loss of An Established Service Clientele: A Market Value Approach for Cases of Self-Employment," Journal of Forensic Economics, 1999, 12(2), 125-133.
Pratt, Shannon P., Robert F. Reilly and Robert P. Schweihs, Valuing a Business: The Analysis and Appraisal of Closely Held Companies, Chicago: IL: Richard D. Irwin, 1996 (3rd edition), 158-161.
Rodgers, Thomas, "Valuation of a Leased Fee Interest," The Appraisal Journal, January 1989, 36-50.
A. Frank Adams, III, John D. Jackson, and J. Philip Cook *
* A. Frank Adams, III, Ph.D., Economist, Department of Leadership & Professional Development, Kennesaw State University, Kennesaw, GA; John D. Jackson, Ph.D., Professor, Department of Economics, Auburn University, Auburn University, AL; J. Philip Cook, MAc, CPA, Assistant Dean, College of Business, Auburn University, Auburn University, AL.
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|Title Annotation:||condemned property|
|Author:||Adams, A. Frank, III; Jackson, John D.; Cook, J. Philip|
|Publication:||Journal of Forensic Economics|
|Date:||Mar 22, 2001|
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