Solving the Functional Obsolescence Calculation Question?

abstract

There exists a question over the correct methodology to calculate functional obsolescence in the reproduction cost approach. This article postulates that adherence to the Principle of Substitution in the replacement and reproduction cost methods answers this question. Since the Principle of Substitution applies to both types of cost indicators, theoretically, both approaches should arrive at the same indication of market value. To achieve this result, the formulas for both approaches must be equivalent. Since there is a general agreement as to the replacement cost formula, whether a particular reproduction functional obsolescence formula is correct, is easily determined mathematically.

There exists a question in the appraisal profession over the correct methodology to calculate functional absolescence in the reproduction cost approach. As a result, proponents advocate conflicting formulas.  This article postulates that adherence to the Principle of Substitution answers this question. The Principle of Substitution, which defines the comparison substitute property contemplated by a hypothetical purchaser, applies equally to both the reproduction and replacement cost approaches. Therefore, theoretically, both cost approaches should indicate an identical market value for a subject property, even though, in application they sometimes differ. To conceptually achieve like indications of market value in both cost approaches, the formulas for both the reproduction and replacement cost approaches must be mathematically equivalent. Because the replacement cost formula is widely accepted as correct, the fundamental question is whether a particular reproduction cost functional obsolescence formula ca n be correct if it violates the Principle of Substitution by creating an inequality between the reproduction cost formula, of which it is a part, and the accepted correct replacement cost formula. The answer is no; the Principle of Substitution requires equivalence. This article explores the validity of the equivalency test and examines one reproduction cost functional obsolescence formula that passes the test.

Principle of Substitution

The Principle of Substitution typically states that "no prudent buyer would pay more for a property than the cost to acquire a similar site and construct improvements of equivalent desirability and utility without undue delay."  Thus, the Principle of Substitution makes clear that the substitute or comparison property contemplated by a hypothetical buyer that features design, materials, and equipment of desirability and utility equivalent to the subject property. The design, materials, and equipment are the most cost-effective, since the Principle of Substitution requires that the costs be based on what the typical rational buyer would spend in the marketplace. Cost-effective does not simply mean the least costly. The rational prudent behavior of a buyer in the marketplace dictates that the buyer will compare costs for a substitute property of equivalent utility and desirability consisting of a design, materials, and equipment which yields the highest anticipated net present value.  A cost indicator of market value, as calculated by either the reproduction or the replacement cost approach, is based on this Principle of Substitution. 

The significance of correctly applying this principle to both types of cost indicators is that the final costs in both cost indicators must reflect the costs of the same comparison property. While this conclusion appears, at first glance, to run contrary to the premise that the replacement cost approach is based on a modern replacement property while the reproduction cost approach is based on a replica of the subject property, it is, in fact, consistent. Buyers and sellers in the marketplace, following the same Principle of Substitution, envision only one substitute property for cost comparison purposes--market behavior is obviously not affected by which type of cost indicator an appraiser uses. Rather, both cost approaches must reflect market behavior. While the replacement cost approach begins with a modern replacement and the reproduction cost approach begins with a replica of the property, both ultimately must reflect the costs of the same comparison property. Therefore, any lack of mathematical equivale nce in the formulas used in the two cost approaches would mean that at least one of the approaches did not represent the most cost-effective property with like utility and desirability in violation of the Principle of Substitution.

Using a replacement cost approach, the development of costs for the comparison property are uncontroversial and straightforward. The manner in which the costs to reflect the comparison property are developed in a reproduction cost approach is more circuitous and subject to controversy. For this reason, we begin with an examination of the replacement cost approach formula as the first step in the process of developing a correct reproduction cost functional obsolescence formula.

Replacement Cost Approach Procedure

The first step in a replacement cost approach is to develop the costs new to build or acquire the most cost-effective property forecasted to achieve the highest net present value, with equivalent utility to the subject property and without any of its deficiencies or burdens. These costs reflect a new comparison property which, while possessing the equivalent utility, will not be a duplicate or replica of the subject property if more cost-effective equipment, materials, or design are available on the valuation date. Equivalent utility means a similar ability to meet the functional value-enhancing needs met by the subject property. This mean, for example, a similar value-adding square footage or capacity. Equivalent utility also contemplates a similar total useful life as the subject property.

At this point in the appraisal process, the replacement costs new fully account for the first two elements of the comparison property namely the most cost-effective, and the equivalent utility of the subject property. Superadequacy, one type of functional obsolescence, has been addressed at this stage of the process, since the design, materials, and equipment selected are the most cost-effective. But the costs do not account for the remaining element of the comparison property, which is equivalent desirability to the subject property. Desirability of the subject property is a reflection of two features: first, the remaining useful life of the subject property; and second, any deficiencies or burdens affecting market value (which accounts for any remaining functional obsolescence and external obsolescence).

The remaining useful life of the subject property is accounted for by a depreciation charge to the replacement costs new. Deficiency the other component in the element of desirability, must also be measured. This cost is accounted for by deducting the cost to correct the internal deficiencies or defects at the subject property, if curable (cost to cure),  or for incurable internal deficiencies or defects, the value of the loss is deducted. Finally, a deduction is made for economic obsolescence to adjust for external deficiencies.

Thus, the market value of the subject property using the replacement cost approach is simply the replacement cost new (to achieve equivalent utility in the most cost-effective manner)--minus an age-life depreciation charge and minus the lesser of the cost to cure or value of loss to the subject property (to achieve equivalent internal desirability of the subject property)--minus external obsolescence (to achieve equivalent external desirability of the subject property).

This widely accepted formula can be written as follows:

Step 1

RPLCMV = RPLCN - RPLCD - CC(VL) - EO

Where:

RPLCMV = Replacement Cost Indicator of Market Value of subject property;

RPLCN = Replacement Cost New,

RPLCD = total Replacement Cost Depreciation charged,

CC(VL)= the Cost to Cure (or Value of Loss if less), and

EO = the adjustment for External Obsolescence

As is apparent in this formula, functional obsolescence is not captured in a separate variable. It is accounted for in the replacement costs new, replacement cost depreciation, and in the cost to cure or value of the loss if less.

Reproduction Cost Approach Procedure

A reproduction cost approach formula should arrive at the same indication of market value of the subject property since it too is based on the Principle of Substitution, which defines a single comparison property. The reproduction cost approach, like the replacement cost approach, develops costs that would reflect a substitute comparison property with equivalent utility and desirability, as required by the Principle of Substitution. The reproduction cost approach, however, requires more steps than the replacement cost indicator to arrive at the costs of the substitute comparison property.

The reproduction cost approach first develops the costs new to create a duplicate or replica of the subject property. The costs new of the duplicate property are typically different from the costs new of the substitute comparison property. These costs new must then be reduced to reflect the remaining useful life of the subject property by deducting for physical depreciation. The next step is to deduct for functional obsolescence. (It is the manner of calculating this deduction for which there is question in the appraisal community.) The last step is to deduct for external obsolescence.

This widely accepted reproduction cost approach can be expressed algebraically as follows:

Step 1

RPROMV = RPROCN - RPROD - RPROFO - EO

Where:

RPROMV = Reproduction Cost Indicator of Market Value of subject property,

RPROCN = Reproduction Cost New,

RPROD = Reproduction Cost Depreciation,

RPROFO = Reproduction Functional Obsolescence, and

EO = the adjustment for External Obsolescence

Here, unlike the replacement cost formula, functional obsolescence is accounted for in a single variable. This difference necessitates precision in the use of the term functional obsolescence. While the replacement cost approach fully accounts for functional obsolescence, it can only be measured directly as a single variable in the reproduction cost method. This is why the use of the term reproduction cost functional obsolescence helps avoid confusion when referring to a single amount to be deducted in the reproduction cost approach.

Reproduction Cost Functional Obsolescence Procedure

Based on these two accepted equations for the replacement and reproduction cost approaches, a correct formula for calculating reproduction functional obsolescence is easily derived since the two formulations must be equivalent under the Principle of Substitution. A correct formulation for reproduction functional obsolescence is derived as follows:

Step 1

Where: RPROCNLD is Reproduction Cost New Less Depreciation (Depreciated Reproduction Cost);

RPLCNLD is Replacement Cost New Less Depreciation (Depreciated Replacement Cost);

and the previous variables apply as set forth above.

Replacement cost indication of market value

= Reproduction cost indication of market value

substituting the appropriate variables

RPLCMV = RPROMV

Step 2

substituting the accepted formulas

RPLCMV = RPROMV

RPLCN - RPLCD - CC(VL) - EO

= RPROCN - RPROD - RPROFO - EO

Step 3

by canceling out EO on both sides...

RPLCN - RPLCD - CC(VL) - EO

= RPROCN - RPROD - RPROFO - EO

equals

RPLCN - RPLCD - CC(VL)

= RPROCN - RPROD - RPROFO

Step 4

by moving RPROFO to the left side of the equation...

RPLCN - RPLCD - CC(VL) = RPROCN

- RPROD - RPROFO

equals

RPROFO + RPLCN - RPLCD - CC(VL)

= RPROCN - RPROD

Step 5

moving the replacement cost formula to the right side of the equation...

RPROFO + RPLCN - RPLCD - CC(VL)

= RPROCN - RPROD

equals

RPROFO = RPROCN - RPROD

- RPLCN + RPLCD + CC(VL)

Step 6

this reduces as follows...

RPROFO = (RPROCN - RPROD)

- (RPLCN - RPLCD)

+ CC(VL)

equals

RPROFO = RPROCNLD - RPLCNLD + CC(VL)

or interpreted,

Functional obsolescence in the reproduction cost approach is equal to the depreciated reproduction cost minus the depreciated replacement cost plus the cost to cure, (or value of loss, if less). 

This six-step reproduction cost functional obsolescence formula correctly applies the Principle of Substitution, because the reproduction and replacement cost indicators are mathematically equal. 

Calculating Replacement Cost Depreciation

Even when using a correct reproduction functional obsolescence formula, a common mistake in applying the replacement cost formula can prevent the two cost approach indications from being equal as conceptually required. This common mistake is miscalculating the depreciation for remaining useful life.

The remaining useful life of the subject property is accounted for by a step that deducts a depreciation charge from the replacement costs new of the comparison property, which has none of the deficiencies of the subject. Therefore, the depreciation deduction must reflect the remaining useful life of the subject, as if the cost to cure had been spent removing all curable deficiencies in order to match the comparison plant to the subject property. Simply using the existing remaining useful life of the subject, without the cure, is conceptually incorrect. It is a mismatch to depreciate the replacement costs new by the existing useful life of the subject property and then deduct for a cost to cure, which, when applied to the subject property, would have changed the remaining useful life of the subject property. Whatever remaining useful life is embedded in the specific costs to cure must be accounted for in the comparison property. For example, if the costs to cure are based on the addition of a used component, the remaining useful life of the used component must be appropriately reflected in the depredation charged to the replacement costs new prior to the deduction of the cost to cure. Likewise, if the cost to cure is based on a cure which adds a brand new item, then no depreciation would be deducted from that portion of the replacement cost new that reflects the cured components. 

Examples

The calculation of reproduction cost functional obsolescence and replacement cost depreciation is illustrated through a series of hypothetical examples. In these examples the cost indicator is presumed to be the sole indicator of market value and is, thus, presumed to equal market value. Of course, if other indicators of market value are available, a reconciliation process would be necessary. There is no external obsolescence.

Hypothetical 1. In this scenario a wood-products plant was constructed 10 years ago. Since it lacks an automated sorter, which a modern plant would use, the owner has relied on manual labor to do the sorting. This is an example of a deficiency requiring an addition. The replacement cost new of the subject plant without the automated sorter is \$2 million. This is also the cost to reproduce a replica of the subject property. The remaining useful life of the subject property is at 50%, as it exists uncured without the sorter. The cost to install a new automated sorter at the subject property is \$500,000. This is the same cost to install the sorter in a newly constructed building on the valuation date, indicating no excess capital costs, such as retrofit costs. If the buyer spent the \$500,000 cost to cure, the subject property would have a new sorter with a 100% useful life, which is assumed less than the remaining useful life of the building, and the rest of the property would have a 50% useful life. For this re ason, the costs of the comparison property in the replacement cost approach, after deducting physical depreciation and just prior to the deduction for the cost to cure, must represent a comparison plant that has an equivalent useful life for the new sorter, which the cost to cure would provide, and for the remainder of the plant. Since the present worth of the excess operating costs for sorting the wood manually of \$1.1 million is more than the cost to cure, the deficiency is curable. This is sufficient information to perform a replacement cost approach, shown in Table 1.

The replacement cost formula indicates a market value for the subject property of \$1 million. This means that the reproduction cost formula, to be correct, should also indicate a market value of \$1 million. Table 2 indicates this equality.

Both cost indicators show a market value for the subject property of \$1 million. The amount of reproduction functional obsolescence is zero. A zero reproduction cost functional obsolescence does not mean that the subject property has no deficiency; it does. But the cost to cure the deficiency is offset by additional capital costs in the comparison property that the subject property does not have. If additional costs above the \$500,000, such as retrofit costs, would be incurred for installing the sorter in the subject property that would not have been incurred if installed at the time of an original construction on the valuation date, then these excess costs would, of course, be a penalty. Simply deducting the cost to cure for functional obsolescence would indicate a market value of \$500,000. Common sense tells us that this is incorrect since, with the addition of a \$500,000 sorter, the subject property would be the same as the comparison plant which has a \$1.5 million market value.

Hypothetical 2. This scenario is the same as the previous one. It illustrates an alternative method of calculating the market value of the subject property by isolating the reproduction functional obsolescence calculation solely to the deficiency; rather than the whole plant costs. As shown in Table 3, this approach also gives a correct indication of market value for the subject property of \$1 million.

Hypothetical 3. This scenario is the same as the previous one, except the cost to cure of \$500,000 represents the addition of a used automated sorter with a 50% remaining life. This scenario can be calculated correctly in two ways, using the same formulas. The first method depreciates the capital costs associated with the sorter in the replacement method by 50% and uses \$500,000 as the cost to cure. The alternative is not to depreciate the capital costs related to the sorter and make the cost to cure \$1,000,000, rather than \$500,000. Either method is correct because a matching depreciation is reflected in the cost to cure and the capital costs associated with the cured item. The first replacement cost approach method is as shown in Table 4.

The second method, using the same formulas, also gives an answer of \$1,000,000 when the cure is not depreciated in the capital costs or cost to cure, as illustrated in Table 5.

The replacement cost formula indicates a market value of the subject property of \$1 million. This means that the reproduction cost formula, to be correct, should also indicate a market value of \$1 million. Table 6 indicates this equality.

Hypothetical 4. This scenario is the same as the previous one, except that steel walls at the comparison plant are more cost-effective than the concrete walls at the subject property because they provide the same utility as the subject's concrete walls, at less capital cost. This is an example of an incurable deficiency. As in the previous example, the subject property lacks an automated sorter that a modern plant would use. The replacement cost new of the plant, with steel walls and without the automated sorter, is \$1.6 million. The reproduction cost new of the subject plant with concrete walls is \$2 million. There is a 50% remaining useful life of the subject property as it exists uncured. The cost to install a new automated sorter at the subject property is \$600,000. This is the more than the \$500,000 cost to install the sorter if a new building were constructed on the valuation date, indicating excess capital costs such as retrofit costs. Since the cure is based on a new automated sorter, the replacement costs of the comparison property, just prior to the deduction for the cost to cure, must represent a plant that has a 50% remaining life with the addition of a new automated sorter that has a 100% remaining useful life. That is what the buyer would end up with if they cured the subject property with a new sorter. The present worth of the excess operating costs is \$1.1 million. This is sufficient information to perform a replacement cost approach is shown in Table 7.

The replacement cost approach indicates a market value of \$700,000. The reproduction cost formula should indicate the same market value if it is correct (Table 8).

The reproduction cost approach confirms the \$700,000 market value with a reproduction cost functional obsolescence of \$300,000, of which \$200,000 is the excess capital cost of the concrete walls (depreciated) and the other \$100,000 is the excess cost to cure (retrofit cost, \$600,000 - \$500,000).

Hypothetical 5. This scenario involves a chemical plant rather than the previous wood-products plant. In this example, hightech ceramic coated steel walls at the comparison substitute plant are more cost-effective than the uncoated steel walls at the subject property. This is not because they cost less than the uncoated walls of the subject property, but because their high resistance to corrosion reduces maintenance costs sufficiently to justify the extra capital costs. This is an example of a curable deficiency requiring substitution or modernization (defect). The replacement cost new of the plant is \$2.2 million. The reproduction cost new of the plant is \$2 million. There is a 50% remaining useful life of the subject property as it exists uncured which does not change when cured. The cost to coat the subject walls with ceramic material is \$300,000. The present worth of the excess operating costs to maintain the uncoated walls in the corrosive environment is \$400,000. This is sufficient information to perfor m a replacement cost approach (Table 9).

The replacement cost approach indicates a market value of \$800,000. The reproduction formula should indicate the same market value if it is correct (Table 10.)

The reproduction cost approach confirms the \$800,000 market value with a reproduction cost functional obsolescence of \$200,000. The \$300,000 cost to cure is not the amount of reproduction functional obsolescence. A buyer would only achieve a net savings of \$200,000 in the comparison property because the cost to cure the defect is offset by necessary higher capital costs required to achieve the savings in the excess operating costs. Since the buyer would not save \$300,000 in the comparison property; the subject property is not penalized by that amount in the reproduction cost method.

Hypothetical 6. In this scenario a building has a substandard electrical system. The costs new of the existing substandard system is \$5,000. It has a 50% remaining useful life. The cost to install an adequate system new on the valuation date would have been \$6,000. The cost to cure the old system is \$9,000. If the system is updated, the present worth of the increased rents is \$2,000. This defect is incurable since the value of the loss is less than the cost to cure. This is sufficient information to perform a replacement cost approach (Table 11.)

The replacement cost formula indicates a market value for the substandard electrical system of \$1,000. This means that the reproduction cost formula, to be correct, should also indicate a market value of \$1,000. Table 12 indicates this equality.

Other Functional Obsolescence Models

There are at least three other functional obsolescence models used by some proponents. One is the functional obsolescence five-step formula.  In contrast with the six-step formula proposed in this article, it deducts the replacement cost new rather than the depreciated replacement cost. This five-step formula indicates the correct result only when the replacement cost depreciation deduction related to the functional obsolescence is appropriately zero. For example, its use in Hypothetical 6, which requires a deduction for depreciation in the replacement model related to the defective item, fails to indicate the correct result. It shows a reproduction cost indication of market value of \$4,000, compared to the correct replacement cost indication of market value of \$1,000 (\$5,000 - \$2,500 - [\$5,000 - \$2,500 + \$2,000 - \$6,000] = \$4,000). Adding a sixth step, deducting any appropriate replacement cost depreciation charge, to the five-step functional obsolescence formula corrects the formula and makes it universa lly applicable. In this example, adding the replacement depreciation charge of \$3,000 as a sixth step in the five-step functional obsolescence formula results in a correct market value of \$1,000.

Another reproduction functional obsolescence approach, a two-step method which simply deducts the cost to cure (or value of the loss, if less), has little applicability. Where the depreciated replacement costs are less than the depreciated reproduction costs, simply deducting the cost to cure fails to recognize the additional cost savings in the cost-effective comparison property. Also when the depreciated replacement costs are more than the depreciated reproduction costs, which occurs when the anticipated net present value increase in cash flow justifies the added capital costs, simply deducting the cost to cure fails to recognize that the buyer of the comparison property only benefits from the net between the additional capital costs and the cost to cure (or value of the loss, if less). When the buyer increases anticipated profitability at the comparison property for an added cost, that additional investment must be accounted for when calculating reproduction functional obsolescence.

The last functional obsolescence method, sometimes proposed deducts for the cost to cure and the depreciated reproduction cost of the existing item when the deficiency requires substitution or modernization (defect). This four-step method always fails to reflect market realities since, while appropriately deducting a depreciated cost for the existing item, it recognizes only a zero value for the replacement item which has at least the same utility as the existing item and may produce even more cash flow. This method will always indicate a windfall to a buyer equal to the depreciated replacement cost of the curing replacement item. If the buyer paid the indicated price from that method and then spent the cost to cure, curing the property, the buyer would have obtained the subject property "as cured" while investing less than its market value. This windfall is evident by comparing the buyer's out-of-pocket investment with a separate cost indicator of the subject property as cured, represented by the depreciate d (age-life) replacement cost of the subject before a deduction for the cost to cure (or value of the loss, if less). The market does not allow systemic windfalls since the price of the subject property would be bid up until there is not a windfall and equilibrium is reached. Pairing this four-step method for a defect (an existing item needing modernization or substitution) with the five-step method for a deficiency (requiring an addition) is also illogical. Such a combination credits a cost indicator, in a five-step method, with the full replacement cost new of the curing item when an addition is required but inexplicably fails to recognize any value for the curing replacement item if the same property now has an existing item and a four-step method is used. Consider, for example, if the existing item could be removed at minimal cost. This combination of approaches would suddenly credit the property with the full replacement cost new of the curing item which would be contrary to market reality. 

Conclusion

While the appraisal process is an art as well as a science, its basic formulas and methodologies must be grounded in foundational appraisal principles and be able to withstand the associated critical mathematical proofs of that grounding. Customary use of a method can never be a substitute for this critical integrity. The formulation for calculating reproduction functional obsolescence is no exception. Any reproduction functional obsolescence formula that fails the equivalency test violates the Principle of Substitution, upon which both cost approaches rely, and is thus flawed.

Joseph A. Laronge has been an assistant attorney general for the Oregon Department of Justice since 1986. He handles complex property tax litigation involving utility, transportation, industrial, and commercial property in the Oregon supreme court and tax court. Previously he was a licensed appraiser and principal real estate broker.

He has taught college courses in real estate appraisal, real estate law, real estate principles, commercial property management, and was a former adjunct professor of law at Willamette University College of Law. He wrote "Property Tax Exemptions under Section 306 of the 4-R Act" for he Williamette Law Review, (26: 3, Summer 1990).

He earned a Juris Doctor degree from Cleveland Marshall Law School.

The author gratefully acknowledges the support of Douglas M. Adir and Dean Schmidt in discussing these topics.

(1.) For example, some proponents urge use of a reproduction cost functional obsolescence formula that consists solely of the cost to cure (or value of the loss when less), a two-step method. Other proponents advocate use of an adjustment that adds the difference between the depreciated reproduction cost of the existing item minus the replacement cost new of the curing item to the cost to cure (or value of the loss when less), a five step method, as propounded in The Appraisal of Real Estate, 11th ed. (third printing). While either of these formulas can work in certain circumstances, neither formula works under all circumstances since they do not pass the proposed equivalency test. Finally, some proponents advocate a functional obsolescence adjustment that adds the depreciated reproduction cost of the existing item to the cost to cure (or value of the loss if less). This four-step formula never works since, while it appropriately deducts the depreciated cost of the existing item, it illogically attributes zer o value to the replacement item which has at least equivalent utility and may also produce an incremental increase in cash flaw.

(2.) Appraisal Institute The Appraisal of Real Estate, 11th ed. (third printing) (Chicago, Illinois. Appraisal Institute, 1996): 336.

(3.) Brealey and Myers, "Net Present ValueuPresent Value of all Future Returns Minus Initial InvestmentuLeads to Better Investment Decisions Than Other Criteria." Principles of Corporate Finance, 4th ed., (1991): 73.

(4.) The Appraisal of Real Estate, 11th ed.: 336; Appmisin9 Machinery and Equipment, ASA, McGraw Hill ed.: 81.

(5.) The cost to cure equals the cost to acquire the replacement item, plus the cost to install the replacement item as if installed as part of new construction on the valuation date, plus any additional retrofit costs for installation, plus the cost of removal of the existing item, minus any salvage value of the existing item. The cost to cure does not include the depreciated reproduction cost of the existing item. Such inclusion results in a mismatch. The cost to cure is compared to the value of the loss to determine if the deficiency or defect is curable. The value of the loss represents the present worth of only the incremental increase in benefits attributable to the replacement item when compared to the existing item, and not the present worth of the original benefits that both the existing and also the replacement item will provide. Thus, there are two investment options, namely to retain the out-of-pocket dollars to cure and receive the cash flows from the subject uncured, or spend the out-of-pocket c osts and receive the cash flows from the subject cured. The present value of option 1 is the out-of-pocket costs to cure (retaining these dollars) plus the present value of the anticipated cash flows from the subject property uncured. The present value of option 2 is the present value of the anticipated cash flow from the subject property cured. The present value of the anticipated cash flow from the subject property cured equals the present value of the anticipated cash flow from the subject property uncured plus the value of the loss. When the present value of the anticipated cash flow from the subject property uncured is subtracted equally from both options, the remaining comparison is only the out-of-pocket cost to cure as compared to the value of the loss.

(6.) This equation works equally well for the whole property or just limited to the existing and replacement item.

(7.) This mathematical proof makes it evident that solely using the cost to cure (or value of loss if less) as a measure of reproduction cost functional obsolescence works only when the depreciated reproduction cost equals the depreciated replacement cost. Using the cost to cure (or value of loss if less) plus the depreciated reproduction cost never works since the depreciated replacement cost is never zero. The 11th ed. formula works only when the replacement cost depreciation deduction related to the functional obsolescence is appropriately zero.

(8.) Of course, if the life of the curing replacement item is greater than the actual anticipated remaining economic life of the core property in which it is placed, including consideration for ongoing replacement if typical, a depreciation adjustment is appropriate for the new item. Regardless, the same replacement depreciation for the new item must always be used in both the replacement cost approach and in the reproduction functional obsolescence calculation. The following hypothetical examples assume that the life of the curing item is less than or equal to the remaining economic life of the core property considering ongoing replacement, if typical.

(9.) The Appraisal of Real Estate, 1 1 th ed.: 388.

(10.) The mathematical reduction of the 11th ed. five-step and the proposed six-step formula for a curable deficiency and defect further makes clear the inappropriateness of the four-step method for a deficiency or a defect. Both the five and six-step formulas, when used for curable functional obsolescence, reduce to the following deductions: the depreciated reproduction cost of the existing item with a defect, if any, and the "excess" cost to cure. In the case of a deficiency, when there is no existing item, reproduction cost curable functional obsolescence is simply the excess cost to cure. These adjustments make intuitive sense. When there is a deficiency, the excess cost to cure is the only appropriate deduction since the reproduction costs should not be penalized for the cost of a replacement item which are not contained in the reproduction costs. A buyer would have to pay for the comparison substitute property any costs above the excess cost to cure. When there is an existing curable item with a defect, removing the depreciated costs of this existing item makes sense since the comparison substitute property would not have this asset. The four-step method when reduced, however, contains an additional deduction. Its formula reduces to the following deductions: the depreciated reproduction cost of the existing item with a defect, the excess cost to cure, and the replacement cost of the new item. This additional deduction, namely, the replacement cost of the new item, is illogical since the subject property does not have the new replacement item for which this costs is being deducted. This inappropriate additional deduction is the reason that the use of this method always results in a windfall to a buyer by exactly that amount. The

other important conclusion from the mathematical reduction of the 11th ed. and proposed six-step reproduction cost functional obsolescence formulas, for curable situations, is that the cost new and any depreciation of the replacement item as well as the economic life of the subject p roperty are irrelevant in the reproduction cost functional obsolescence calculation. This is evident because the replacement costs of the new item, whether depreciated or not, cancel out when these formula are mathematically reduced. The only requirement is that the same amount of age-life depreciation is consistently used for the new item in both the cost to cure and the replacement cost variable for the new item in the functional obsolescence formula. Note that since the cost to cure must be the most cost effective, the replacement "new" item may actually be a used item so that there is no value lost in the replacement cost indicator in those instances when the economic life of the core property, with typical replacements, is shorter than the remaining life of the replacement item.
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