Introduction

Land Values and External Obsolescence

Stanley D. Longhofer

†

July 2018

Abstract

External obsolescence is perhaps one of the trickiest aspects of implementing the cost approach

in appraisal. Because it is driven by factors outside the property, it is important for appraisers to

make sure that these factors do not also impact the land value estimate used to derive a final

indication of value. In other words, external obsolescence is prone to double counting. This

paper argues that the external obsolescence can only arise when the existing structure is not the

site’s highest and best use. As a result, external factors that affect the property’s value are

attributable to the land if the current use is its highest and best use, and are external obsolescence

of the building otherwise.

†

Stephen L. Clark Chair of Real Estate and Finance, and Director, Center for Real Estate, Barton

School of Business, Wichita State University. The ideas in this paper are the byproduct of

research supported by a David C. Lincoln Fellowship from the Lincoln Institute of Land Policy,

to which I am grateful for financial support.

1. Introduction

Estimating the external obsolescence of a structure is perhaps one of the trickiest aspects

of implementing the cost approach in appraisal. Because it is driven by factors outside the

property, it is difficult to distinguish external obsolescence from reductions in land value. If the

appraiser is not careful, it would be easy to accidentally double count these outside influences,

with their effects showing up both in the land value estimate and the estimated value of the

structures.

In this article, I show that external obsolescence arises when and only when the existing

structure is not the site’s highest and best use. As a result, external factors that affect the

property’s value are attributable to the land when the current use optimal and to external

obsolescence of the building otherwise. By paying careful attention to the highest and best use of

the site, therefore, the appraiser can more accurately allocate the impact of external factors to the

land and building value estimates.

This has several important implications for practicing appraisers. First, it provides the

analyst a simple and theoretically rigorous test for determining whether external obsolescence

should be applied in the cost approach: Is the current use – both in terms of property type and

scale – the property’s highest and best use? If the answer is “yes,” then no external obsolescence

of the structure is present, and all value change due to the external factor is attributable to the

land.

Second, this analysis can help validate the magnitude of estimated external obsolescence

if it is present. As shown below, external obsolescence is simply the difference between the

value of the land in its optimal use and its value in the current use. When an appraiser uses

traditional methods to estimate external obsolescence, the resulting figure can be compared with

this benchmark to verify its reasonableness.

Finally, this analysis provides external confirmation of the land value estimate that may

have been derived from another source. If the property’s current use is its highest and best use

and a large estimate of external obsolescence is required in the cost approach, it may imply that

the external land value estimate needs to be reevaluated.

2. Defining and Measuring External Obsolescence

The Dictionary of Real Estate Appraisal defines external obsolescence as “An element of

depreciation; a defect, usually incurable, caused by negative influences outside a site and

generally incurable on the part of the owner, landlord, or tenant.”

Williams discuss three

sources of external obsolescence: locational (e.g., a neighborhood whose values are transitioning

into a new HBU), environmental (a noxious nearby use) and economic (e.g., the rents a location

can command change due to changing economic conditions such as oversupply).

Because each

of these factors can also affect land values, it can be challenging to determine how much they

actually affect structure values, as opposed to the land itself.

The Appraisal of Real Estate suggests three methods for estimating external

obsolescence.

First, it can be measured as the residual of market-extracted depreciation once

estimates of physical deterioration and functional obsolescence have been subtracted.

Alternatively, the appraiser might use paired data analysis to directly estimate the impact of an

Appraisal Institute, The Dictionary of Real Estate Appraisal, 4

ed. (Chicago: Appraisal Institute, 2002), 86.

Thomas P. Williams, “Estimating Economic Obsolescence in Supply-Saturated Office Markets,” The Appraisal

Journal (April 1996): 148-154.

Appraisal Institute, The Appraisal of Real Estate, 12

ed. (Chicago: Appraisal Institute, 2001), 412-414.

external factor on the property’s value. Finally, one might estimate external obsolescence by

capitalizing the income loss due to the external factor.

Some authors have proposed more specific methodologies for estimating external

obsolescence due to special influences such as over-supply within a market

or market-wide

downturns.

At the end of the day, however, each of these methods essentially involve estimating

the total value loss due to the external factor and then allocating it between the land and the

building in a relatively arbitrary way. The purpose of this article is to provide guidance as to

when this value loss is attributable to the land and when it is attributable to the structure.

Perhaps the most practically relevant and theoretically satisfying treatment of external

obsolescence can be found in In Defense of the Cost Approach: A Journey into Commercial

Depreciation.

In this excellent book, the author provides straightforward techniques for

estimating external obsolescence and clearly demonstrates that it is inappropriate to simply

allocate the impact of external factors based on a land-to-cost or other arbitrary ratios. All of the

book’s examples, however, are developed assuming an accurate external land value estimate. As

discussed above, the present analysis provides a benchmark for validating that this external land

value estimate is reasonable, given the parcel’s highest and best use.

At the heart of this analysis is the residual theory of land values, wherein the value of a

parcel is the difference between its market value and fair compensation to the other factors of

production. A direct implication of this theory is that the sources of external obsolescence all, in

MacKenzie S. Bottum, “Estimating Economic Obsolescence in Supply-Saturated Office Markets,” The Appraisal

Journal (October 1988): 451-455. See also MacKenzie S. Bottum and Scott D. Evans, “Supply-Saturation-Induced

External Obsolescence: Two techniques for Quantifying Value Loss,” The Appraisal Journal (October 1993): 545-

552.

Mark Galleshaw, “Market-Wide External Obsolescence,” The Appraisal Journal (October 1991): 519-525.

E. Nelson Bowes, In Defense of the Cost Approach: A Journey into Commercial Depreciation (Chicago: Appraisal

Institute, 2011).

the first instance, affect land values, with structure values affected only as a byproduct. Indeed,

the urban economic theory that underlies much of appraisal practice is built on the primacy of

land values. Thus, to understand external obsolescence, we must first understand how these

outside factors affect land values.

3. Land Values and Highest and Best Use

Appraisers and others involved in real estate are generally quite familiar with the dictum

that a parcel’s land value is determined by its value under its highest and best use as though

vacant, regardless of its current use. An important implication of this idea, however, is less well

understood: if the building/structure present on the parcel maximizes the land’s value – that is, if

the current use is the parcel’s highest and best use – then any loss in value due to external factors

is attributable to the land, not the building. In other words, structural external obsolescence

arises if and only if that building is the wrong building for the site.

To see this, consider a vacant parcel of land with two potential uses: office and retail. The

details of these uses are summarized in the first column of Table 1. If the property is developed

as an office building, it’s annual net operating income (NOI) would be $360,000. Assuming a

market capitalization rate of 8 percent, the office’s total market value would be V

= $4.5 million

($360,000 ÷ 0.08). If it costs C

= $2.5 million to build the office building (and assuming it

would be built without any physical deterioration or functional obsolescence), this implies that

the land is worth $2 million if it is developed as on office building (L

= V

– C

= $4.5 – $2.5 =

$2). This breakdown of land and building values is depicted in Figure 1.

Alternatively, the owner could develop the site as a retail building. This use would

generate annual NOI of $280,000 and assuming the same 8 percent market cap rate, the

property’s total market value as a retail building would be V

= $3.5 million ($280,000 ÷ 0.08).

Assuming it would cost C

= $1 million to construct the building, the land’s value in a retail use

would be L

= $2.5 million (L

= V

– C

= $3.5 − $1 = $2.5). Because a retail use brings the

highest total economic return to the land’s owner, the parcel’s highest and best use is retail.

Indeed, if these two uses were proposed by different developers, the land would be sold to the

retail developer because of her willingness to pay more for the parcel.

Suppose that the owner develops the land for retail as outlined above and consider what

happens when factors external to the property change. The question we want to address is when

such factors will be captured in the land value and when an adjustment for external obsolescence

should be applied to the estimated value of the structure.

For example, suppose a change in retail demand at this location causes rents (and hence

NOI) to fall by 10 percent. This scenario is depicted in in the second column of Table 1, where

we see that the property is now worth V

= $252,000 ÷ 0.08 = $3.15 million. In other words,

market conditions have caused the property’s value to drop by $350,000.

In this case, all of the lost value is attributable to the land. To see this, note that the cost

of constructing the retail building has not changed (it is still $1 million), so if the land were

vacant it would be worth $2.15 million ($3.15 – $1) to a retail developer. This is still more than

what the land is worth as an office (which we assume has not changed), so the property’s highest

and best use remains retail. Since the land’s value is, by definition, its value under its highest and

best use as though vacant, the land value is $2.15 million, or $350,000 less than it was before

rents fell, as shown in Figure 2. Thus, the entire value loss is attributable to the land, and the

“external” factors affecting the property do not result in any external obsolescence to the

building.

This will be true as long as retail remains the property’s highest and best use. Suppose,

however, that retail rents fall even more dramatically, so that the property’s annual NOI falls to

$224,000; this scenario is summarized in the third column of Table 1 and illustrated in Figure 3.

In this case, property’s total value falls to $2.8 million ($224,000 ÷ 0.08), making the land worth

$1.8 million ($2.8 - $1) in a retail use if the property were vacant. This is now lower than what it

would be worth as an office (still $2 million). As a result, the parcel’s highest and best use is

now office, meaning that the land value is $2 million, its value under the parcel’s highest and

best use as though vacant. The remaining value loss, E

= $200,000, is attributable to the

building in the form of external obsolescence.

These two scenarios demonstrate a simple but important fact: external obsolescence only

occurs when the property is not in its highest and best use. As long as the current use is the

highest and best use, any external factors that change the property’s value will affect the land

value, not the structure value.

4. External Obsolescence and Development Scale

On the surface, it might seem that this concept would suggest that external obsolescence

rarely occurs given that many if not most appraisal assignments involve parcels that are already

in their highest and best uses. It’s important to note, however, being developed to the wrong

scale can also be a form of sub-optimal use. That is, if the current structure is not the same size

as the one that would be built if the property were vacant, external obsolescence will occur as

well.

To see this, consider the residential example outlined in in the first column of Table 2. In

this example, the subject property is an older 1,000 square foot single-family home. The home’s

effective age is 30 years out of an economic life of 50 years. Based on its condition and age, the

house would rent for $1.10 per square foot per month. Assuming a gross rent multiplier (GRM)

of 100, the property’s market value using the income approach is $110,000 ($1.10 psf × 1,000 sf

× 100).

Suppose that the cost of new construction is $150 per square foot. In this case, the

existing house would cost $150,000 to construct new. Using the age-life method, we can

estimate the property’s physical deterioration to be $90,000 ($150,000 × 30 ÷ 50), so that the

property’s remaining physical value is $60,000. Assuming no functional obsolescence, what

remains to be estimated in order to apply the cost approach is (1) the value of the land and (2)

any functional obsolescence of the building.

The land value is determined by the parcel’s highest and best use as though vacant.

Suppose that if this were a vacant lot, the optimal structure would be a 1,500 square foot house

that would rent for $2.00 per square foot per month.

This structure would cost $225,000 to build

($150 psf × 1,500 sf) and the property’s market value would be $300,000 ($2.00 psf × 1,500 sf ×

100). Given this, the implied value of the land under its highest and best use as though vacant –

and hence in its current use – is $75,000.

An astute reader will wonder how this relates to the rent on the existing structure. For internal consistency, I have

assumed that the existing structure’s rent is the HBU rent reduced to account for the property’s effective age.

Specifically, Current Rent = HBU Rent × [1 – (Effective Age ÷ Economic Life) × (Cost New of HBU ÷ Value of

HBU)] = $2.00 psf × [1 – (30 ÷ 50) × ($225,000 ÷ $300,000)] = $1.10 psf.

From this it is straightforward to determine the structure’s external obsolescence. The

remaining physical value of the existing building is its $150,000 construction cost less the

physical deterioration of $90,000, or $60,000.

Subtracting this from the total market value of the

parcel gives the land value under the current use or $110,000 – $60,000 = $50,000. But as we

saw above the actual land value is $75,000, its value under the highest and best use. The

difference, $25,000, is therefore attributable to the structure in the form of external obsolescence.

Once again, the external obsolescence exists only because the current use is different from the

property’s highest and best use. In this example, however, the suboptimal use is due to the size of

the structure, not its intended purpose.

It is worth noting that when the “sub-optimality” of the existing structure is due to the

wrong scale of the building, higher market rents actually serve to increase the structure’s

external obsolescence. To see this, consider what happens in the example above if market rents

for a new structure were to rise by 20 percent to $2.40 per square foot; this situation is depicted

in the second column of Table 2. In this case, the optimal structure (HBU as Vacant) will be

worth $360,000 ($2.40 psf × 1,500 sf × 100). The increase in rents has no impact on construction

costs, so the entire value increase is attributable to the land, raising the parcel’s land value to

$135,000.

Of course, the parcel is not vacant; it has an existing structure. The increase in rent causes

the market value the property in its existing use to rise to $150,000 ($1.50 psf × 1,000 sf ×

For simplicity, I have assumed that the structure has no functional obsolescence. If it did, this would be subtracted

here as well.

Notice that the parcel’s land value rises by more than 20 percent. This is because the overall value increase is

magnified into its land value because of the of the property’s “land leverage;” see Raphael W. Bostic, Stanley D.

Longhofer and Christian Redfearn, “Land Leverage: Decomposing Home Price Dynamics,” Real Estate Economics

(Summer 2007), 183-208.

100).

Given the remaining physical value of the structure (which remains unchanged at

$60,000), the value of the land under its current use would be $90,000. Nevertheless, the land’s

true value is $135,000, its value under its highest and best use as though vacant. The difference

between these two values, $135,000 – $90,000 = $45,000, is the structure’s external

obsolescence, or its value loss due to having the “wrong” structure on the site.

It may seem unusual to have external obsolescence increase when market rents rise. This

is because the existing structure is not the structure that would be built if the land were vacant.

As market rents increase, the “penalty” or value loss from having the wrong structure on the site

increases as well. Because this value loss has nothing to do with the land, it is rightly attributed

to the structure in the form of external obsolescence.

This phenomenon is directly related to “teardowns.” If rents continued to rise, the land

value would rise and external obsolescence would increase until the structure value became

negative. Eventually, the structure’s external obsolescence would become sufficiently large that

it would pay the owner to tear it down and replace it with a new, correctly sized, home (in this

case, one that is 1,500 square feet).

5. Practical Implications and Conclusions

The purpose of this article has been to highlight the underlying source of external

obsolescence. A structure suffers from external obsolescence if and only if the current use is not

the property’s highest and best use, whether this is based on the functional use or the scale of the

building within a given use.

Once again, the new rent of the property is related to its highest and best use rent as outlined note 7 above.

This simple fact can help practicing appraisers in three ways. First, it allows an appraiser

to quickly and simply determine whether external factors are affecting the structure value and,

hence, whether an estimate external obsolescence will be needed. If the current use is the

property’s highest and best use in both type and scale, no external obsolescence can be present.

All external factors will be captured in the estimated value of the land.

Second, if external obsolescence is present, this analysis provides a reference point for

the magnitude of the estimated external obsolescence. In theory, external obsolescence must be

equal to the difference between the value of the land in its optimal use and its value under the

current use. When an appraiser uses traditional methods to estimate external obsolescence, the

resulting figure can be compared to this benchmark to help validate the reasonableness of the

estimate.

Finally, the ideas here can help the appraiser determine whether the independent land

value estimate derived by other means is internally consistent. If the property’s current use is its

highest and best use and the appraiser cannot reconcile the cost approach without applying

significant external obsolescence to the structure, this raises the question of whether the land

value estimate is correct, since all external influences in this instance must be attributable the

land.

6. Exhibits

Table 1

Potential Uses

Scenario 1

Scenario 2

Office

Retail

Office

Retail

Office

Retail

Net Operating Income (NOI)

$360,000

$280,000

$360,000

$252,000

$360,000

$224,000

Cap Rate

8.00%

Market Value (V = NOI / R)

$4,500,000

$3,500,000

$4,500,000

$3,150,000

$4,500,000

$2,800,000

- Construction Cost (C)

$2,500,000

$1,000,000

$2,500,000

$1,000,000

$2,500,000

$1,000,000

= Land Value in Use if Vacant (L

)

$2,000,000

$2,500,000

$2,000,000

$2,150,000

$2,000,000

$1,800,000

Total Value (V)

$3,500,000

$3,150,000

$2,800,000

- Land Value (L)

$2,500,000

$2,150,000

$2,000,000

= Structure Value (S)

$1,000,000

$800,000

External Obsolescence (E = L - L

) when the Current Use is not the Highest and Best Use

$200,000

Table 2

Baseline Scenario

Market Rents Rise

Current

Structure

HBU as

Vacant

Current

Structure

HBU as

Vacant

Size

1,000 sf

1,500 sf

1,000 sf

1,500 sf

Effective Age

30 years

0 years

30 years

0 years

Economic Life

50 years

Rent PSF

$1.10 psf

$2.00 psf

$1.50 psf

$2.40 psf

Monthly Rent

$1,100

$3,000

$1,500

$3,600

Gross Rent Multiplier (GRM)

100

Total Value (V = Rent × GRM)

$110,000

$300,000

$150,000

$360,000

Construction Costs

$150 psf

Cost New (C = SF × Cost PSF)

$150,000

$225,000

$150,000

$225,000

- Physical Deterioration (PD)

$90,000

= Remaining Physical Value (PV)

$60,000

$225,000

$60,000

$225,000

- External Obsolescence (EO = PV - S)

$25,000

$45,000

= Structure Value (S)

$35,000

$225,000

$15,000

$225,000

Land Value under Current Use (L

= V - PV)

$50,000

$75,000

$90,000

$135,000

Total Value (V)

$110,000

$300,000

$150,000

$360,000

- Land Value (L)

$75,000

$135,000

= Structure Value (S)

$35,000

$225,000

$15,000

$225,000

= 2

= 2.5

= 1.0

1.5

2.5

3.5

4.5

5.5

1.5

2.5

3.5

4.5

5.5

Retail is the Property's Highest and Best Use

Figure 1

= 2

= 2.5

= 2.15

= 1.0

1.5

2.5

3.5

4.5

5.5

0 .5 1 1.5 2 2.5 3 3.5 4 4.5

5.5 6

Retail Rents Fall without Changing HBU

Figure 2

= 2

= 2.5

= 2

= 0.8

= 0.2

1.5

2.5

3.5

4.5

5.5

.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6

Retail Rents Fall Changing HBU to Office

Figure 3