land valuation❓❓ Methods: Extraction, Allocation, and Capitalization

Introduction

This chapter delves into three fundamental land valuation methods: extraction, allocation, and capitalization. These techniques are employed when direct sales comparison, the preferred method, is challenging due to limited vacant land sales data. Each method relies on different principles and market information to derive an estimate of land value. understanding❓ the strengths and weaknesses of each approach is crucial for accurate land valuation.

1. Market Extraction

1.1. Principle and Theory

The extraction method, also known as abstraction, estimates land value by deducting the depreciated cost of improvements from the overall sale price of an improved property. The underlying principle is that the residual value represents the land’s contribution to the total property value. This method assumes that the improvements contribute a measurable amount to the overall value. The accuracy hinges on accurately estimating the cost and depreciation of the improvements.

1.2. Mathematical Formulation

The extraction method can be represented by the following equation:

V_L = V_O - V_I

Where:

• V_L = Estimated Land Value
• V_O = Overall Sale Price of the Improved Property
• V_I = Depreciated Value of the Improvements (Building and Site Improvements)

The depreciated value of the improvements (V_I) is calculated as:

V_I = Cost_Building + Cost_{Site Improvements} - Depreciation

Depreciation encompasses all forms of loss in value, including physical deterioration, functional obsolescence, and external obsolescence. Depreciation can be estimated using various methods, such as the age-life method, cost-to-cure method, or market extraction itself (bootstrapping).

1.3. Practical Application and Example

Consider an improved property that recently sold for $351,000. To estimate the land value using extraction, we need to determine the depreciated value of the improvements. Assume the following:

• Cost of Residence: 2,800 sq ft * $75/sq ft = $210,000
• Cost of Basement: 500 sq ft * $25/sq ft = $12,500
• Cost of Porches, etc.: 500 sq ft * $25/sq ft = $12,500
• Cost of Garage: 750 sq ft * $25/sq ft = $18,750
• Total Cost of Building Improvements: $210,000 + $12,500 + $12,500 + $18,750 = $253,750
• Total Depreciation (all causes): 12% of $253,750 = $30,450
• Depreciated Value of Building Improvements: $253,750 - $30,450 = $223,300
• Depreciated Value of Site Improvements: $12,500

Therefore:

V_L = $351,000 - $223,300 - $12,500 = $115,200

The estimated land value is $115,200.

Another example from the provided text:

Overall value: $140,000
Less value of the building: $110,000
Less value of the site improvements: $5,000
Land value: $25,000

1.4. Limitations

The extraction method is most reliable when:

• Improvements are relatively new and depreciation is minimal.
• Cost data for improvements are readily available and reliable.
• The highest and best use of the property is its current use.

The method becomes unreliable when:

• Significant depreciation exists, making accurate depreciation estimates challenging.
• consistent use issues arise❓❓ (i.e., the improvements do not represent the highest and best use of the land).
• The improvements have a negative impact on value (e.g., a dilapidated building). In such cases, the method can produce inaccurate results. The provided text shows an example where “The house does not contribute the same amount of value on both sites, so this extracted land value is incorrect. In fact, this house is very close to meeting the wrecking ball and the value is much lower. This technique is unreliable when consistent use issues must be addressed.”

2. Allocation

2.1. Principle and Theory

The allocation method estimates land value by determining the typical ratio of land value to total property value in a comparable area and applying this ratio to the subject property’s value. It is based on the theory that land value is a function of the entire property value. The success of this method depends on finding sufficient sales data of improved properties and vacant land in areas that compete with the subject property. It is crucial that both the subject and comparable properties are improved to their highest and best use.

2.2. Mathematical Formulation

The allocation method involves the following steps:

1. Calculate the Land-to-Property Value Ratio (VL/VO) for comparable sales:

VL/VO = Land Value / Overall Property Value

2. Apply the Ratio to the Subject Property’s Value:

Estimated Land Value = (VL/VO) * Subject Property Value

2.3. Practical Application and Example

The provided text contains an example of the allocation method.

Exhibit 17.5 summarizes the characteristics of four sales of improved properties in areas where land value can easily be estimated. The property in Sale 1 sold for $400,000 and the land is valued at $80,000. The ratio of land value to property value (VL/VO) is 20%. This ratio can then be applied to the subject’s area to estimate a value range there. If property values in the subject’s neighborhood range from $425,000 to $475,000, a reasonable value estimate for the subject’s land would be $85,000 to $95,000.

• VL/VO = $80,000 / $400,000 = 20%
• Subject area low estimate: 20% * $425,000 = $85,000
• Subject area high estimate: 20% * $475,000 = $95,000

2.4. Limitations

• Finding persuasive, reliable support for the ratio of land value to property value is difficult.
• Skewed analyses can occur if the subject is improved to its highest and best use and the comparable is not.
• The method’s accuracy is limited by the availability of data. The ratio of land value to building value using assessor’s records can be used, but can contain innacuracies due to lag.
• Properties must be improved to their highest and best use to prevent loss in value due to inconsistent use.
• It may not be as accurate as sales comparison analysis.

3. Income Capitalization

Income capitalization techniques are most applicable for valuing leased land, especially under long-term leases. These methods convert the expected future income stream generated by the land into a present value estimate.

3.1. Direct Capitalization: Land Residual Method

3.1.1. Principle and Theory

The land residual method separates the net operating income (NOI) of a property into two components: income attributable to the building and income attributable to the land. It requires knowing the building value, the building capitalization rate (R_B), the NOI of the property (I_O), and the capitalization rate for the land (R_L).

3.1.2. Mathematical Formulation

1. Calculate Income to the Building (I_B):

I_B = V_B * R_B

Where:

• V_B = Value of the Building
• R_B = Capitalization Rate for the Building

2. Calculate Income to the Land (I_L):

I_L = I_O - I_B

Where:

• I_O = Net Operating Income of the Property

3. Calculate Land Value (V_L):

V_L = I_L / R_L

Where:

• R_L = Capitalization Rate for the Land

3.1.3. Practical Application and Example

The net operating income for the property is $125,000. The capitalization rate for the land is 10%. The value of the building is $800,000. The capitalization rate to the building is 12%.

1. Income to the building: I_B = $800,000 * 0.12 = $96,000
2. Income to the land: I_L = $125,000 - $96,000 = $29,000
3. Value of the land: V_L = $29,000 / 0.10 = $290,000

3.1.4. Limitations

• Requires data that can be almost impossible to find in many markets.
• Complicated by differences in risk associated with some leases.
• This is a theoretical division of real estate because the leased fee and leasehold interests are the actual rights transferred.

3.2. Direct Capitalization: Ground Rent Capitalization

3.2.1. Principle and Theory

Ground rent capitalization directly capitalizes the ground rent income stream to arrive at a land value estimate. It’s useful in land lease situations and requires few subjective inputs, assuming data is available.

3.2.2. Mathematical Formulation

V_L = I_L / R_L

Where:

• V_L = Estimated Land Value
• I_L = Income to the Land (Ground Rent)
• R_L = Capitalization Rate for the Land

3.2.3. Practical Application and Example

Income to the land (IL): $12,000
Capitalization rate for the land (RL): 0.12

VL = $12,000 / 0.12 = $100,000

3.2.4. Limitations

• Comparable land sales with similar lease rates and terms are usually difficult to find.
• Combining data sources to establish a capitalization rate is less desirable than extracting data directly from the market, but it can be an effective tool in markets where data is limited.
• Combining data sources should only be done when there is no other way of obtaining the capitalization rate, and it should be checked using other methods to ensure its accuracy.

3.3. Yield Capitalization: Subdivision Development Method (Discounted Cash Flow Analysis)

3.3.1. Principle and Theory

The subdivision development method, a discounted cash flow (DCF) model, is employed to value land for potential subdivision development. It forecasts the expected cash flows from lot sales, subtracts development costs, and discounts the net cash flows back to a present value, representing the land value. This technique is complex, making it less preferable when vacant land sales data are available.

3.3.2. Mathematical Formulation

The general formula for present value is:

PV = CF₁ / (1 + r)¹ + CF₂ / (1 + r)² + … + CF_n / (1 + r)ⁿ

Where:

• PV = Present Value (Land Value)
• CF_i = Net Cash Flow in Period i
• r = Discount Rate (reflecting risk and required return)
• n = Number of Periods (Holding Period)

Each CF is derived as:

CF = (Number of Lots Sold * Sale Price per Lot) - Development Costs - Operating Expenses

Development costs may include engineering, surveying, permitting, infrastructure installation (roads, utilities), and marketing. Operating expenses include real estate taxes, sales commissions, advertising, and an entrepreneurial incentive (developer’s profit).

3.3.3. Practical Application and Example

The provided text presents a table of values, where PGI stands for Potential Gross Income.

Assume a 40-acre parcel has a highest and best use as a 60-lot residential subdivision. The average lot price is $147,500, the typical buyer is a home builder, and the projection period is over the next 24 months. The discount rate is 12%.

The table of values from the document show that the total estimated present value of the land is $3,927,561

3.3.4. Limitations

• It is complex.
• It requires a large number of calculations, which makes it more cumbersome and less persuasive than direct sales comparison analysis.
• Applicability is limited in many markets.
• Comparable sales of development land sometimes have to be analyzed carefully because topographical issues limit the number of lots that can be platted on parcels of the same size. For example, one 100-acre parcel may allow for 50 lots to be built, but another 100-acre parcel that is more level could be developed with 100 lots.

Conclusion

Extraction, allocation, and capitalization offer alternative approaches to land valuation when direct sales comparison data is scarce. Extraction relies on deducting the depreciated value of improvements, while allocation uses land-to-value ratios. Capitalization methods, including the land residual technique, and the subdivision development method convert future income streams into present value estimates. The choice of method depends on data availability, market conditions, and the specific characteristics of the subject property.