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Partitioning capitalization rates: operating leases in unitary valuation.


Appraisers recognize that the overall capitalization rate must satisfy the market return requirements of all investment positions when using direct capitalization techniques. A common practice in the unitary method of property assessment valuation is to modify the income stream for operating leases without similarly adjusting the capitalization rate. This article argues that a corresponding adjustment to the capitalization rate must accompany the income adjustment to ensure the resulting market value estimate is unaffected by this procedural deviation and to preclude gross overvaluation resulting in payment of excess property taxes.


The unit valuation process is used primarily when valuing income-producing properties, such as railroads, airlines, utilities, and telecommunication companies, for ad valorem tax purposes. Unit valuation is "an appraisal of an integrated property as a whole without any reference to the value of its component parts." It can be distinguished from a fractional appraisal, which values one of the parts without reference to the value of the whole, and from a summation appraisal, where a valuation of the whole is derived by adding two or more fractional appraisals. (1)

The Committee on Unit Valuation of the National Association of Tax Administrators states that unit appraisals are usually preferable to summation appraisals when valuing multijurisdictional, integrated properties, such as railroads and utilities.
 [Unit appraisals] are markedly superior where there is considerable
 obsolescence or considerable going-concern value because there is
 no good method by which to measure obsolescence or going-concern
 value as such. Unit appraisals are preferable to summation
 appraisals in utility valuation work for the added reason that the
 evidences of unit value are more readily available for utility
 properties than the evidences of fractional values." (2)

Others, such as Supreme Court Justice Oliver Wendell Holmes, have asserted that the unit valuation process is valid because firms valued by such methods are comprised of assets that "are part of an organic system of wide extent." (3)

An operating enterprise subject to the unitary method of valuation is viewed as a single asset. This simplifies some aspects of the valuation exercise but creates problems in others. For example, market indicators of value under the unitary method often include information from the financial marketplace. Since the financial marketplace is considered efficient and fairly transparent, the value of an organic operating concern can be proxied by the value of that firm's securities. This is called the stock and debt approach to value in the unitary method.

Rates of return from various capital sources are obtained in the financial marketplace to derive the cost of capital components used in establishing capitalization rates. Furthermore, audited financial statements from firms subject to unitary valuation are widely available. These income and capitalization components, taken directly from the marketplace, are conveniently combined to develop income indicators of value for the unitary method.

However, the nature of these large, multijurisdictional and often regulated firms requires some deviation from standard fee appraisal practice.

For example, depreciation and income taxes are included in the financial statements of these firms as ordinary expenses and, as such, reduce the reported operating income that is capitalized into value. The principal argument for allowing these expenses to be included in the valuation procedure is that the financial marketplace already recognizes the inclusion of depreciation and income taxes in determining the observed market value of securities (stock and debt approach) and in the observed market rates of return of these securities (direct capitalization approach). To disallow these expenses would require an alteration of the already-available market information and is viewed as an unnecessary step in the valuation process.

The thrust of this article is to examine currently accepted adjustments for leased assets as they apply to the unit method of valuation for ad valorem taxation and to see if they are internally consistent with appraisal and financial valuation theory and practice. (4) Examples used in this discussion include depreciation and income taxes to be consistent with long-established, accepted, and currently applied unit valuation procedures.

Basic Financial Valuation: The Principle of Consistency

A primary valuation principle from the perspective of financial economists is the principle of consistency between cash flows and capitalization rates. It means that both the cash flows paid to investors (items found in the numerator of direct capitalization) and the rates of return required by investors (items found in the denominator of direct capitalization) must be consistent with each other. (5) It is also understood that all investor groups have a particular required rate of return that they believe compensates them for their level of financial risk. (6) Violations of this consistency principle result in biased valuations.

For instance, to estimate the value of stock, debt, or leases, it is important to realize that the equity holders have a residual claim on the cash flows of the firm. This means that equity holders own the cash flow that is available after all the other contractual obligations have been honored.

Net operating cash flow of the firm - Cash flow to debt holders - Cash flow to leaseholders/ Cash flow to equity holders

When performing financial calculations, it is important to comply with the principle of consistency in the following ways:

* Cash flow that belongs only to the equity holders must be capitalized at the required market rate of return of the equity holders to determine the market value of the equity holders' investment in the firm's employed assets ([V.sub.E]).

* Cash flow that belongs only to the debt holders must be capitalized at the required market rate of return of the debt holders to determine the market value of the debt holders' investment in the firm's employed assets ([V.sub.D]).

* Cash flow that belongs only to the leaseholders must be capitalized at the required market rate of return of the leaseholders to determine the market value of the leaseholders' investment in the firm's employed assets ([V.sub.L]).

The total value of a firm ([V.sub.F])--the purpose of a unitary valuation for property assessment--is simply the simultaneous sum of the value of all the investment positions supplying capital. If there are three types of investors (equity holders, debt holders, and leaseholders), then

[V.sub.F] = [V.sub.E] + [V.sub.D] + [V.sub.L] = [V.sub.Capital Supplied] (1)

The components of the total value of the firm ([V.sub.E], [V.sub.D], and [V.sub.L]) are cointegrated and codependent because the marketplace from which market-based capitalization rates are determined already acknowledges and prices the interrelationship between the capital providers when pricing these capital sources. In other words, the marketplace for the equity of the firm does not ignore the fact that the firm uses debt and/or lease financing when pricing the firm's equity. Rather, the marketplace incorporates the fact that the firm uses these other forms of capital to leverage or otherwise maximize the value of the firm's equity. As such, any positive benefits received by equity holders from using fixed costs of capital (e.g., debt and lease payments) will be positively priced in the firm's equity. This positive benefit already exists in the market capitalization of the firm's equity.

Obviously, if the principle of consistency is violated between the cash flows to the capital sources and the associated component capitalization rates, then the resulting valuation estimates will be incorrect when summed. For instance, if to estimate the value of the equity holder's position in the firm the valuer starts with the total cash flow of the firm but does not subtract out both the cash flow to the debt holders and the leaseholders first, then the cash flow to equity holders will be overestimated, as will the resulting equity valuation.

One way to visualize this principle of consistency is to assume that there is no growth in any cash flow (i.e., the cash flows are perpetuities). Valuations are then simple ratios, where the numerator is the amount of annual cash flow belonging to a particular investor group, and the denominator is the capitalization rate, or required rate of return, for each particular investor group.

[V.sub.E] = Cash flow received by equity holders/ Required market rate of return to equity holders = [CF.sub.E]/[R.sub.E]

[V.sub.D] = Cash flow received by debt holders/ Required market rate of return to debt holders = [CF.sub.D]/[R.sub.D]

[V.sub.L] = Cash flow received by leaseholders/ Required market rate of return to leaseholders = [CF.sub.L]/[R.sub.L]

This would indicate that the value of the firm is [rewriting Equation (1)]

[V.sub.F] = ([CF.sub.E]/[R.sub.E]) + [CF.sub.D]/[R.sub.D]) + ([CF.sub.L]/[R.sub.L]) = [CF.sub.F]/[R.sub.F] (2)

In other words,

[V.sub.F] = Total cash flow generated to be distributed to all investors/ Weighted average required return of capital contributors (3)

This is identical to the traditional, direct capitalization process in appraisal practice, where value is equal to net operating income (NOI) divided by the overall capitalization rate (V = NOI/[R.sub.o]).

Mixing and matching cash flows with the wrong capitalization rate obviously generates incorrect estimations if the numerator (cash flow to one investor group) represents two or more investor groups and the denominator reflects only one (or the wrong) investor group. Likewise, valuations will be underestimated if the numerator reflects only one or two investor groups but the denominator reflects all three investor groups, and so on.

The only way to correctly value the firm is to accurately determine (1) the total actual cash flows generated, (2) the proportional amount of cash flow distributed to each group, (3) each capital source's market-based rate of return, and (4) the associated proportions of each group's capital contribution to the firm.

Example of the Principle of Financial Consistency

A simple example of the unitary valuation process shows how this process is employed in practice and how current practice results in biased valuations when operating leases are incorporated.

Assume that the stabilized net operating income of a firm subject to unitary valuation is $1,000,000, and the market value of the same firm is $10,000,000. This firm has only one asset (one property) generating revenue for it. The market value of debt represents 75% of the capital contributed to this firm, and the market value of equity represents the remaining 25% of the capital contributed to this firm.

Assume also that the market land-to-building value ratio is 1:3, which means that the land has a market value of $2,500,000 (1/4 of the total $10,000,000 value), and the building has a market value of $7,500,000 (3/4 of the total $10,000,000 value).

Finally, assume that the firm uses bonded debt to simplify the calculation of the valuation effects. Bonded debt is a common source of debt financing in place of traditional mortgages for firms subject to unitary valuation methods. (7)

Suppose the firm's debt has a market return of 8%. This means that the firm's annual debt payment is $600,000 (8% of the $7,500,000 debt outstanding). This debt payment is paid out of the $1,000,000 of net operating income, leaving the firm with $400,000 to pay equity holders. If equity has a market return of 16%, the equity contributor's value in the investment property is $2,500,000 ($400,000 divided by 16%). Together, the debt position ($7,500,000) plus the equity position ($2,500,000) in the property equal $10,000,000, the market value of the firm.

As proof of this example, Equation (1) can be used to calculate the value of the firm:

[V.sub.F] = [V.sub.E] + [V.sub.D] + [V.sub.L] = [V.sub.Capital Supplied]

[V.sub.F] = $2,500,000 + $7,500,000 + 0 = $10,000,000

Another method is to value the firm by capitalizing the total, stabilized NOI directly, using a weighted average of the component costs of capital. The band of investment overall capitalization rate (i.e., the weighted average cost of capital, or WACC) is 75% of 8% (i.e., 6%), plus 25% of 16% (i.e., 4%), or 10%. Capitalizing the stabilized NOI of $1,000,000 at this 10% overall capitalization rate also yields a value indication of $10,000,000. This is the same value achieved by partitioning NOI into its debt and equity payments and capitalizing each component at its appropriate capitalization rate, as shown previously. This result is exactly what is expected if both NOI and the component costs of capital have been estimated correctly, and it is the basis of the stock and debt approach. However, if the component costs of capital, their individual weights, or the component rates of return to investors are inaccurately determined, then the valuation estimate is very likely going to be wrong.

Adding Leased Assets to the Capital Structure

Another example of the unitary valuation process illustrates what happens when leased assets are incorporated into the capital mix.

Assume a competing firm is situated immediately adjacent to the owned property in the previous example. This competing firm owns the land where it operates, but it leases the structure on the site from a third party. This leased structure is identical to the structure on the adjacent, owned property and has a market value of $7,500,000. The competing firm's land parcel is a mirror image of the adjacent parcel. Since the two adjacent parcels of land are identical, the market value of both firms' land parcels is $2,500,000.

Suppose the operating income and operating expenses for both firms, exclusive of the lease payments for the structure, are also identical. The only difference between the two adjacent parcels is that one firm owns its structure and the other firm leases its structure. Therefore, according to current unitary valuation practice, the firm with the leased structure has lease payments that need to be identified and priced into the unitary valuation model to ensure that the unitary value of the firm is accurately established.

Now assume that the lease payment (on this long-term operating lease of the structure) is stabilized at $750,000. Normally in the unitary valuation process, the firm leasing the property would deduct this lease expense as an ordinary operating expense, thus reducing the estimate of NOI by the amount of the lease payment. This results in $250,000 of NOI, after the lease, for this competing firm ($1,000,000 of NOI, as in the earlier example, less the $750,000 lease payment).

Since this is leased property, the debt and equity capital requirements of the competing firm are now significantly lower because the firm does not have to acquire the structure with debt and equity capital. However, the capital structure for this firm is now a combination of debt, equity, and lease capital. At this point, two questions are raised: Are the market values of the two adjacent properties (basically) the same? Does market value diminish, or is there a market value gain caused by a financing choice (leasing versus owning the structure)?

Investment Value vs. Market Value

Financial theory supports appraisal's claim that the market value of an asset is independent of the financing choices made to acquire the use of an asset. Financial theory also claims that leasing is simply an alternative to conventional debt Financing. These statements do not say that the investment value of an asset might (and often can) be enhanced by a specific financing choice. Investment value enhancements resulting from specific financing choices are definitely possible, just as superior management of a particular property can enhance its investment value by lowering operating expenses and increasing cash flows.

As is customary in appraising the market value of a property, appraisers do not consider special financing or income tax considerations for particular investors. Financial literature strongly acknowledges that leasing is simply a special case of financing that must be properly addressed in an investment valuation model since favorable financing terms can give certain equity investors positive arbitrage profits when using such capital sources. It is an inarguable fact that the choice of financing used to acquire and use a property neither enhances nor encumbers the market value of the property, even when the investment value of the property can potentially be enhanced or encumbered.

Any difference between the firm's unit market value and the firm's unit investment value to security holders needs to be acknowledged in the appraisal assignment and then correctly accounted for in the final unitary value determination. In the examples used here, each property's market value is constructed to be $10,000,000. How then is this market value estimate obtained when the operating statement is encumbered with a lease payment?

Consideration of Lease Payments

Before considering the effect of lease payments on market value, first, the competing firm's component costs of capital and their relative proportions in the valuation assignment are needed.

In the present leasing example, the component costs of capital are as follows: (1) debt on the site with the leased structure is 18.75% of the total capital contributed; (2) equity on the same site is 6.25% of the total capital contributed; and (3) the lease obligation is 75% of the total capital contributed. This is true because the land-to-building value ratio is 1:3, which means that 25% of the firm's total capital is attributed to land owned and financed from traditional sources--18.75% debt (3/4 of 25%) and 6.25% equity (1/4 of 25%)--and 75% of the firm's total capital is the structure financed through the long-term lease.

Since the market cost of debt is 8% (from the previous example) and the firm's operations are financed with 18.75% debt, the component cost of the debt is 1.5% (18.75% times 8%). Similarly, the market cost of equity is 16% and the firm's operations are financed with 6.25% equity, resulting in a component cost of equity of 10% (6.25% times 16%). Together, debt and equity capital contributors receive a weighted average return of 2.5%. Therefore, if the return to debt and equity participants is 2.5%, and this return is capitalized into its respective NOI components of $250,000 (after deducting for the lease payment), then the market value of the whole property (both leased and owned assets) is $10,000,000.

[V.sub.F] = [NOI.sub.Including Lease Payment]/[WACC.sub.Debt & Equity] (4)

[V.sub.F] = $250,000 / 2.5% = $10,000,000 (5)

This simple example shows that when lease payments are included in an operating statement, all that is necessary is to ensure that only income payments made to the capital contributors at their proportional and correct capitalization rate are capitalized into value. In other words, the chosen market capitalization rate must match the income--and the proportion of income--that is capitalized. This is the principle of consistency in practice.

If appraisers know the market costs of debt and equity along with their relative proportions to the entire firm investment, they just need to proportionally capitalize the debt and equity contributions into the NOI (assuming that the lease payments are included as expenses). There is no need to modify the income statement or make assumptions about converting leased assets to owned equivalents. If there is a modification to the income statement (as supported by many unitary valuation practitioners), then the appraiser must make similar adjustments to the capitalization process to accurately reflect the changes in the capital structure implied by the change in the income statement.

Current Approach to Modifying NOI for Leases

Some practitioners view leases as a form of capital and believe that the income statement must therefore reflect that fact. (8) The common method used by utility appraisers for ad valorem taxation purposes is to remove the fractional ownership influences caused by lease payments, move the bulk of the expense below the NOI line, and then make further adjustments to treat the leased asset as if it were owned.

This process of undoing the firm's lease financing decision must account for not only adjustments to the income that is capitalized into value, but also changes to the firm's component market capitalization rates affected by undoing the firm's capital structure. The income statements in Tables 1, 2, and 3 relate to the previous example of the firm with the leased structure. (9)

Remember that, in the unitary valuation process, income taxes and depreciation are valid expenses in determining NOI. If the modified NOI is used, as is commonly prescribed by some unitary valuation appraisers, $1,205,500 would be capitalized at the weighted average cost of only debt and equity to arrive at a value for the property with the leased structure. But, what is the correct capitalization rate? If the prescribed method of many Western U.S. utility appraisers is followed by using the firm's WACC (band of investment debt and equity rate) on this modified NOI, the $1,205,500 would be capitalized at the firm's market cost of only debt and equity capital (10%) to achieve a property market value of $12,055,000.

But how can this figure be possible? The market value of the property by direct sales comparison (and by construction of this example) is only $10,000,000 (e.g., the identical property adjacent to this one has a market value of $10,000,000). Furthermore, when the capital sources for the adjacent property are directly valued and summed, the result is also $10,000,000. (10) Where does the extra $2,055,000 of market value arise? The simple answer is that this extra value does not exist, and the law of one price (11) must be maintained. It is merely an overestimation due to the bias inherent in current valuation practice.

This process, prescribed the Western States Association of Tax Administrators (WSATA), and supported by many utility appraisers, illustrates the reason that when an adjustment is made to the numerator of the direct capitalization approach, a similar adjustment is needed in the denominator of the valuation process to maintain consistency. If an adjustment to the capitalization rate is not made, it is considered a violation of the principle of consistency.

Modifying the Capitalization Rate

The WSATA acknowledges that modifying the capitalization rate is an acceptable practice and directly addresses this issue in its appraisal manual: "The most critical judgment an appraiser must make is to select a capitalization rate that is consistent with the income to be capitalized." (12) In an example describing when adjusting the capitalization rate is necessary, the WSATA manual states, "if a capitalization rate derived with an income stream that excludes [an expense] is to be applied to an income stream that includes (an expense), then components for [that expense] must be added to the capitalization rate." This process of adding to the capitalization rate when expenses are excluded in the income statement will be explored next, keeping in mind that the law of one price still holds.

Whenever an expense item is removed from NOI to obtain a (larger) modified NOI figure, the capitalization rate applied to the modified NOI must always be higher than the firm's weighted average cost of equity and debt. This concept is known as loading in the assessment appraisal profession. (13)

One way to rationalize the need to modify NOI is to say that by using a leased asset, the firm is actually overcapitalized relative to the net income generated by the firm and to be paid to capital contributors (debt and equity). As such, the implied cost (or benefit) of overcapitalization needs to be added to the firm's costs of debt and equity. In the example, the amount to add to the capitalization rate for this overcapitalization is 2.055% and is calculated by the process described next based on Tables 1, 2, and 3.

Capitalization Rate Adjustment Examples

The cost of converting an asset from being leased to being an owned equivalent must appear in the costs to the existing capital contributors if there is a change to the cash flow they receive. For consistency sake, a hypothetical change to income requires a hypothetical change to the capitalization rate. If the property hypothetically became an owned asset of the firm, then the cash flows to the capital contributors would also need to hypothetically change.

Based on the market value of comparable properties, such as the firm with the owned structure immediately adjacent to the one in this example, the change to the cash flows to capital contributors that would arise represents 2.055% of that comparable property's value ($205,500 divided by $10,000,000). Because NOI is used to pay all of the capital contributors and because debt and equity holders' actual market contributions of capital are unaffected by the change caused by the modification that the appraiser imposed, the return to the equity holder group would hypothetically increase by $205,500. Therefore, that capital cost component would be added to the capitalization rate (the firm's WACC) to account for these additional market returns in the modified NOI statement. Adding 2.055% to the WACC of 10% yields the capitalization rate necessary to pay the debt holders for their investment (this is unchanged) and to pay the equity holders for their investment (this increases).

The extra NOI that exists after developing the modified NOI statement is the ratio of modified NOI to NOI including lease payment, or in this example $1,205,500 divided by $1,000,000 or 1.2055. This indicates that the process of modifying the NOI statement to treat the leased assets as owned assets increases the cost of capital to 12.055% (10% WACC multiplied by the overcapitalization factor of 1.2055). It is not, as some practitioners say, equal to the existing firm capital because the debt and equity holders are now sharing a different proportion of return from NOI.

Another way to look at this situation is with the following example. If there were no change in the NOI after modifying the income statement, the debt and equity holders would receive 100% of the NOI. However, in the previous example, the debt and equity holders actually receive 82.953% ($1,000,000) of the $1,205,500 modified NOI. The difference between what capital contributors actually receive and what the appraiser hypothetically estimates as NOI is 17.047% of the modified NOI. So 17.047% divided by 82.953%, or 20.55%, of the modified NOI is hypothetically paid to equity holders. This means that the capitalization rate needs to be increased by 20.55% to account for the change in the percentage return to debt and equity holders. A 20.55% increase of the existing 10% capitalization rate is also 12.055%.

Now assume that the 12.055% capitalization rate is correct and is partitioned into the returns due each capital contributor (further assuming that the actual capital structure is still 75% debt and 25% equity on $10,000,000 of total assets purchased). Debt holders are still receiving 8% on their $7,500,000 contribution, which is $600,000. Equity capital holders are still receiving 16% on their $2,500,000 contribution, which is $400,000. Taken together, the actual total returns to capital are distributed correctly. However, there is this extra hypothetical income, or overage, to distribute. The overage must go to equity holders as residual claimants, increasing their return that would appear in their cost of capital component and in the weighted average cost of capital.

Suppose there were the hypothetical $1,205,500 of modified NOI. Debt receives an 8% return on the $7,500,000 of debt outstanding, or $600,000 from this modified NOI. Subtracting the debt payment from this hypothetical income results in $605,500, equity's hypothetical return. Compared to an actual market value of equity of $2,500,000, the equity rate of return is now 24.22% ($605,500 divided by $2,500,000). If the new 24.22% cost of (return to) equity is used at its 25% contribution to the WACC, that component becomes 6.055% (25% of 24.22%), and the new capitalization rate becomes 12.055% (6% weighted cost of debt and 6.055% new weighted cost of equity). If the capitalization rate is not increased, consistency is violated, and the parcel's value is artificially increased above market value. This is akin to financial alchemy: creating value from nothing. Capitalizing the hypothetical income ($1,205,500) at the hypothetical capitalization rate (12.055%) yields a market value of $10,000,000 and not $12,055,000.

Therefore, the additional $2,055,000 of value established using mismatched income and capitalization rates is a deviation from the real market value of the firm. Also, appraisers who modify the NOI used to determine the value of property with leased assets are inconsistent in their determination of capitalization rates unless they similarly modify their capitalization rates to account for the additional income that they capitalize into value. The WSATA has a mechanism in its procedural documents to prevent this potential inconsistency, but this step is often ignored. The process of artificially increasing NOI to capitalize in a market valuation assignment without similarly raising the capitalization rate, will establish value estimates that are always inflated, are not representative of market conditions, and are significantly above actual market value.

In financial valuation, it is often presumed that a firm is maximizing shareholder wealth. A corollary to this is that, in so doing, the firm is minimizing its cost of capital. Therefore, to alter a firm's capital structure decision would require an acknowledgement that the modified capital structure is at some point other than the minimum. This means that any change in undoing a firm's capital decisions would require finding a capitalization rate higher than what is observed in the marketplace. This is consistent with the analysis here that shows it is necessary to raise the capitalization rate in this example to 12.055%.

An Alternative Approach: Removing Lease Payments

As previously mentioned, some practitioners believe leases are a form of capital and that the income statement must therefore reflect that fact. Their principal argument stems from the concept that the lessor of the property has a profit motive, and therefore the value of the leased asset needs to be included in the analysis to prevent the lessor's value in the leased property from escaping taxation. If that is true, then the lease needs to be viewed simply as an alternative form of investment in the firm that is not unlike other capital providers.

An alternative approach, supported by the WSATA but rarely used, is to remove the lease payment from the calculation of NOI. (14) This causes the lease payment to become a return stream to the lessor that must be capitalized. Therefore, a lease component must be incorporated in the cost of capital calculation. The operating statements and capitalization rate process can be modified using the method shown in Table 4.

In this method, there is no need to adjust depreciation or income taxes because that would require further modification to the capitalization components of the market returns on debt and equity.

The next step is to modify the calculation process for capitalization rate to be consistent with the distribution of income. The market cost of equity is still 16% (and 6.25% of firm capitalization) and the market cost of debt is still 8% (and 18.75% of firm capitalization). The market cost of the lease is 10% (as constructed in these examples--$750,000 lease payment divided by the $7,500,000 market value of the structure) and the leased structure represents 75% of firm capitalization. Using these proportions of firm capital and their associated market costs yields a weighted average cost of capital equal to 10%, as shown in Table 5.

Removing the lease payment as an allowable expense (and accounting for it as a rate of return for the leased property owner) requires adding the component cost of lease capital to the process used in determining the overall capitalization rate. Adding this to the valuation model yields an income stream of $1,000,000 to capitalize. When that income is then capitalized at the correct overall capitalization rate of 10%, the result is a property valued at $10,000,000. This value is the same as those derived from all of the methods presented here and further demonstrates that the partial process used by some practitioners in the assessment community is incorrect.


Partitioning capitalization rates and the NOI used to determine value in a direct capitalization approach improve the understanding of how value is determined in the marketplace. Unitary valuation professionals can make adjustments to NOI provided that the appraiser consistently adjusts the capitalization rate to account for the additional distribution of return to the appropriate capital contributors. Current practice is often deficient in completing the process necessary to achieve a market value standard. Typically, only the first step (to increase NOI) is taken without fully comprehending and recognizing that this step then requires an adjustment (typically, an increase) in the costs of capital that reflects the new distribution allocation of income. This article shows that the process of making an adjustment for leased property should result in the same market valuation estimate as when no adjustment is made, provided the proper cost of capital--one that does not violate the principle of consistency--is employed in the valuation assignment.

Any unit valuation assignment for a firm that employs leased assets that is completed without ensuring consistency between the income that is capitalized into value and the income's capitalization rate will result in an incorrect estimate of market value. The inconsistent methods used in many unitary valuations today result in overvaluation and resultant excess property taxes because of a flawed, incomplete process.

by Thomas W. Hamilton, PhD, and David O. Vang, PhD

(1.) National Association of Tax Administrators (U.S.) and C. M. Chapman, Appraisal of Railroad and Other Public Utility Property for Ad Valorem Tax Purposes (Chicago: Federation of Tax Administrators, 1954), 2.

(2.) Ibid.

(3.) Wallace v. Hines, 253 U.S. 66, 69 (1920).

(4.) This analysis also expands on articles appearing in the Journal of Property Tax Management and Valuation between 1994 and 2000 (although these articles do not focus on the capitalization process). See Joseph M. Davis and John R. Cesta, "The Valuation of Operating Lease Property in the Unitary Method," Valuation 39, no. 1 O

(5.) Franco Modigliani and Merton H. Miller, "The Cost of Capital, Corporation Finance and the Theory of Investment," American Economic Review (June 1958): 261-297.

(6.) William F. Sharpe, "Capital Asset Prices: A Theory of Market Equilibrium Under Conditions of Risk," Journal of Finance (September 1964): 425-442.

(7.) Amortizing debt would basically result in a similar outcome, with only a slightly different result that has no effect on the issue of consistency between cash flows and the capitalization function.

(8.) Western States Association of Tax Administrators and Committee on Centrally Assessed Property, Appraisal Handbook: Valuation of Utility and Railroad Property (Wichita: Western States Association of Tax Administrators, 1989), 59-72.

(9.) This process can be found in Goodwin, "Operating Leases: A New Controversy."

(10.) The leased structure has a market value of $7,500,000; debt and equity have a total market value of $2,500,000.

(11.) George J. Stigler, "The Economics of Information," Journal of Political Economy 69, no. 3 (June 1961): 215.

(12). Western States Association of Tax Administrators and Committee on Centrally Assessed Property, 59.

(13.) Dennis D. Kelsall, "Loading Capitalization Rates and Discount Rates for Property Taxes and Other Expense Items," The Appraisal Journal (April 1997): 171-178.

(14.) Western States Association of Tax Administrators and Committee on Centrally Assessed Property, 70-72.

Thomas W. Hamilton, PhD, is an associate professor of real estate at the University of St. Thomas in St. Paul, Minnesota. He earned his BS, MBA, and PhD in urban land economics from the University of Wisconsin--Madison. He also received an MS in finance from the University of Wyoming. Hamilton has published several articles on property tax assessment issues and regularly consults with energy and telecommunication companies. Contact: College of Business, University of St. Thomas-Minnesota, 2115 Summit Avenue, Mail # MCH 316, St. Paul, MN, 55105; T 651-962-5551; E-mail:

David O. Vang, PhD, is a professor of finance at the University of St. Thomas in St. Paul, Minnesota. He holds a BS from St. Cloud State University and a PhD in economics from Iowa State University. Vang has authored a textbook on entrepreneurial finance and has completed numerous financial consulting projects for multiple firms. Contact: College of Business, University of St. Thomas-Minnesota, 2115 Summit Avenue, Mail # MCH 316, St. Paul, MN, 55105; T 651-962-5127; E-mall:
Table 1 Original Net Operating Income Statement

NOI $1,000,000 (without lease payment, includes income taxes)
- Lease $750,000
NOI $250,000 (as reported, includes income taxes)

Table 2 Current Approach for Modifying Net
Operating Income Statement for Lease Payments

NOI $250,000 (as reported, includes income taxes)
+ Lease $750,000
NOI $1,000,000 (without lease payment,
 includes income taxes)
- Depreciation $15,000 (equivalent depreciation over 50 years)
+ Income Tax $220,500 (see Table 3 and explanation)
NOI $1,205,500 (modified NOI to capitalize)

Table 3 Income Tax Adjustment to Income Statement

Remove Lease

Lease $750,000
Tax Rate 30%
Tax Add-Back $225,000

Create Ownership

Depreciation $15,000
Tax Rate 30%
Tax Deduction $4,500

Note: Net effect on income taxes = $220,500 ($225,000 less $4,500).
Utility valuation [following the prescribed WSATA method) allows a
deduction for income taxes to be reflected in N01 along with
depreciation. Since the WSATA method is used in this example, the
taxes need to be accounted for in the statement.

Table 4 Alternative Approach for Modifying Net
Operating Income Statements for Lease Payments

Original Net Operating Income Statement

NOI $1,000,000 (without lease payment, includes income taxes)
- Lease $750,000
NOI $250,000 (as reported, includes income taxes)

Modified Net Operating Income Statement

NOI $250,000 (as reported, includes income taxes)
+ Lease $750,000
NOI $1,000,000 (without lease payment, includes income taxes)

Table 5 Weighted Average Cost of Capital

WACC = [W.sub.D] * [R.sub.D] + [W.sub.E] * [R.sub.E]
 + [W.sub.L] * [R.sub.L]
10% = 18.75% * 8% + 6.75% * 16% + 75% * 10%
10% = 1.5% + 1% + 7.5%


[W.sub.D] = percent of capital supplied by debt holders

[R.sub.D] = mortgage constant on debt

[W.sub.E] = percent of capital supplied by equity holders

[R.sub.E] = total return to equity holders

[W.sub.L] = percent of capital supplied by leaseholders

[R.sub.L] = lease payment rate of return
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Author:Hamilton, Thomas W.; Vang, David O.
Publication:Appraisal Journal
Date:Mar 22, 2007
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