Land Valuation Techniques: Extraction, allocation❓, and Capitalization

Introduction

Land valuation is a crucial aspect of real estate appraisal. Accurately determining land value is essential for various purposes, including property taxation, investment analysis, and lending decisions. This chapter focuses on three fundamental land valuation techniques: extraction, allocation, and capitalization. These methods provide different approaches to isolating and estimating the value of land.

1. Extraction Method

1.1. Concept and Principles

The extraction method, also known as the abstraction method, estimates land value by subtracting the depreciated cost of improvements❓ from the overall sale price of an improved property. The underlying principle is that the difference between the total property value and the value of the improvements represents the land’s contribution.

1.2. Mathematical Representation

Let:

• V_O = Overall value (sale price) of the improved property
• V_B = Depreciated value of building improvements
• V_S = Depreciated value of site improvements
• V_L = Estimated land value

Then, the formula for extraction is:

V_L = V_O - V_B - V_S

1.3. Steps Involved

1. Determine the overall sale price of the improved property (V_O). This data comes from recent comparable sales.
2. Estimate the cost of replacing the existing improvements new. This involves calculating the cost of labor and materials needed to reconstruct the building and site improvements.
3. Estimate accrued depreciation of the improvements. Depreciation accounts for the physical deterioration, functional obsolescence, and external obsolescence affecting the improvements. This can be calculated using various depreciation methods (e.g., straight-line, cost-to-cure).
4. Calculate the depreciated value of the building improvements (V_B) and site improvements (V_S). This is the difference between the replacement cost and the accrued depreciation.
5. Subtract the depreciated value of the improvements from the overall sale price to arrive at the estimated land value (V_L).

1.4. Example

As per the provided file, we can illustrate the Extraction Method with the following details:

Gross sale price (V_O): $351,000

Cost of residence: $210,000 (2,800 square feet @ $75/sqft)

Cost of basement: $12,500 (500 square feet @ $25/sqft)

Cost of porches, etc: $12,500 (500 square feet @ $25/sqft)

Cost of garage: $18,750 (750 square feet @ $25/sqft)

Total Cost of building Improvements = $253,750

Total depreciation (all causes) = 12% = $30,450

Depreciated value of building improvements (V_B) = $253,750 - $30,450 = $223,300

Depreciated value of site improvements (V_S) = $12,500

Estimated land value:

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

V_L = $115,200

Alternative calculation:

Overall Value (V_O): $140,000

Less value of building: $110,000

Less value of site improvements: $5,000

Land value (V_L): $25,000

1.5. Limitations

• Reliability depends on accurate cost and depreciation estimates. Inaccurate assessments can significantly skew the resulting land value.
• Suitable only when improvements contribute positively to the property value. When improvements are obsolete or nearing the end of their economic life (as indicated in the PDF, “house is very close to meeting the wrecking ball”), the extraction method becomes less reliable.
• Assumes consistent use and highest and best use. The method is less accurate if the subject and comparable properties do not have similar uses or are not improved to their highest and best use.
• Difficulty in accurately estimating depreciation: Depreciation is not always a linear or easily quantifiable factor.

2. Allocation Method

2.1. Concept and Principles

The allocation method estimates land value by determining the typical ratio of land value to overall property value in a comparable area. This ratio is then applied to the subject property’s value to estimate its land value. The allocation method is particularly useful when vacant land sales data is scarce. It is based on the theory that land value is a function of the entire property value.

2.2. Mathematical Representation

Let:

• V_L = Land value of the comparable property
• V_O = Overall value (sale price) of the comparable property
• Ratio = Land value to overall property value ratio
• V_L(Subject) = Estimated land value of the subject property
• V_O(Subject) = Overall value of the subject property

Then:

Ratio = V_L / V_O

V_L(Subject) = Ratio V_O(Subject)

2.3. Steps Involved

1. Research recent sales of improved properties in the subject’s competitive market area. Gather data on overall sale prices (V_O) and estimated land values (V_L) for these properties. Land values can be estimated through extraction or other methods.
2. Calculate the land-to-property value ratio for each comparable sale. Divide the land value by the overall sale price to obtain the ratio.
3. Analyze the ratios and select a representative ratio or a range of ratios applicable to the subject property. Consider factors such as location, zoning, and property characteristics.
4. Estimate the overall value of the subject property (V_O(Subject)). This may involve using sales comparison or income capitalization approaches.
5. Apply the selected ratio to the overall value of the subject property to estimate its land value (V_L(Subject)).

2.4. Example

The file provides the example of the Allocation Method. Sales 1-4 are improved properties with various sale prices and estimated land values:

Sale 1: V_O = $400,000, V_L = $80,000, Ratio = 20.00%
Sale 2: V_O = $400,000, V_L = $80,000, Ratio = 20.00%
Sale 3: V_O = $420,000, V_L = $84,000, Ratio = 20.00%
Sale 4: V_O = $440,000, V_L = $88,000, Ratio = 20.00%

If property values in the subject’s neighborhood range from $425,000 to $475,000, and a reasonable ratio is 20%, then the estimated land value range for the subject property would be:

Lower Bound: 0.20 * $425,000 = $85,000

Upper Bound: 0.20 * $475,000 = $95,000

2.5. Limitations

• Accuracy depends on the reliability of the ratio and the comparability of the properties. The ratios can be skewed if there are inconsistencies in the characteristics of the comparable properties.
• Assumes similar highest and best use for all properties. If the subject or comparable properties are not improved to their highest and best use, the ratio may be inaccurate.
• Market conditions can affect the ratio. Changes in supply and demand can alter the relationship between land and overall property values.
• Difficulty in finding persuasive, reliable support for the ratio: This makes it harder to find persuasive, reliable support for the ratio of land value to property value.

3. Capitalization Method

3.1. Concept and Principles

The capitalization method estimates land value by capitalizing the income attributable to the land. This method is most applicable for leased land, where the ground rent represents the income stream generated by the land. Capitalization involves converting an income stream into an estimate of value by dividing the income by an appropriate capitalization rate.

3.2. Direct Capitalization: Land Residual Method

The land residual method partitions the net operating income (NOI) into income attributable to the building and income attributable to the land.

3.2.1 Mathematical Representation

Let:

• I_O = Net operating income (NOI) of the property
• R_O = Overall capitalization rate
• V_B = Value of the building improvements
• R_B = Building capitalization rate
• I_B = Income attributable to the building
• I_L = Income attributable to the land
• R_L = Land capitalization rate
• V_L = Land value

Then:

I_B = V_B * R_B

I_L = I_O - I_B

V_L = I_L / R_L

3.2.2 Steps Involved

1. Estimate the net operating income (NOI) of the property (I_O).
2. Determine the value of the building improvements (V_B). This can be estimated using cost or sales comparison approaches.
3. Determine the appropriate building capitalization rate (R_B). This rate reflects the return on investment required for the building improvements.
4. Calculate the income attributable to the building (I_B) by multiplying the building value by the building capitalization rate.
5. Subtract the income attributable to the building from the overall NOI to arrive at the income attributable to the land (I_L).
6. Determine the appropriate land capitalization rate (R_L). This rate reflects the return on investment required for the land.
7. Capitalize the income attributable to the land by dividing it by the land capitalization rate to estimate the land value (V_L).

3.2.3 Example

The net operating income for the property is $125,000: I_O = $125,000

The capitalization rate for the land is 10%: R_L = 0.10

The value of the building is $800,000: V_B = $800,000

The capitalization rate to the building is 12%: R_B = 0.12

Therefore,

The value of the building multiplied by the capitalization rate to the building equals the income to the building: I_B = V_B * R_B = $800,000 * 0.12 = $96,000

The income to the building is subtracted from the income overall to determine the income to the land: I_L = I_O − I_B = $125,000 − $96,000 = $29,000

The income to the land is divided by the capitalization rate to the land to estimate land value: V_L = $29,000 / 0.10 = $290,000

3.2.4 Limitations

• Requires accurate estimates of both building value and capitalization rates. Errors in these estimates can significantly affect the land value.
• Difficult to apply in many markets due to data limitations. Obtaining reliable data on building capitalization rates and land capitalization rates can be challenging.
• Assumes a stable income stream and capitalization rate. Changes in these factors can impact the accuracy of the valuation.

3.3. Direct Capitalization: Ground Rent Capitalization

This is a simpler and more commonly used method for valuing leased land, particularly when comparable sales data is limited.

3.3.1 Mathematical Representation

Let:

• I_L = Income to the land (ground rent)
• R_L = Land capitalization rate
• V_L = Land value

Then:

V_L = I_L / R_L

3.3.2 Steps Involved

1. Determine the annual ground rent (income to the land) (I_L). This is the rent paid by the lessee to the lessor for the use of the land.
2. Select an appropriate land capitalization rate (R_L). This rate should reflect the risk and return characteristics of the leased land investment. Capitalization rates can be derived from market data, such as sales of comparable leased land or surveys of investor expectations.
3. Capitalize the ground rent by dividing it by the land capitalization rate to estimate the land value (V_L).

3.3.3 Example

Income to the land (I_L): $12,000

Capitalization rate for the land (R_L): 0.12

Land value (V_L): $12,000 / 0.12 = $100,000

3.3.4 Limitations

• Relies on the availability of reliable ground rent data and capitalization rates. Finding comparable land sales with similar lease rates and terms can be challenging.
• Assumes a stable lease agreement and rent payment. Changes in lease terms❓ or the lessee’s ability to pay rent can impact the accuracy of the valuation.
• May not be suitable for complex lease arrangements. The method is most applicable to simple ground leases with clear and consistent rent payments.

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

Subdivision development analysis is based on a discounted cash flow model.

3.4.1 Steps Involved

1. Estimate the total revenue from lot sales.
2. Project expenses:
   • Development Costs
   • Real Estate Taxes
   • Sales Commission
   • Advertising, etc.
   • Entrepreneurial incentive (Developer’s Profit)
3. Discount the net cash flow to its present value.

3.4.2 Example

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 example in the PDF outlines a quarterly analysis of lot sales, expenses, and discounted cash flow, ultimately arriving at an indicated land value of approximately $3,927,561.

3.4.3 Limitations

• Complex and requires a large number of calculations.
• Highly sensitive to assumptions about sales prices, absorption rates, expenses, and discount rates.
• Requires significant market research and feasibility analysis to support the assumptions.

Conclusion

The extraction, allocation, and capitalization methods offer valuable approaches to land valuation. Each technique has its strengths and limitations, and the selection of the appropriate method depends on the availability of data, the characteristics of the property, and the intended use of the appraisal. Appraisers must carefully consider these factors and apply sound judgment to arrive at a credible and reliable estimate of land value.