Cost Estimation and Depreciation in Valuation

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Chapter: Cost Estimation and Depreciation in Valuation

Introduction

In leasehold valuation, understanding the underlying cost of an asset and how that value diminishes over time (depreciates) is paramount. This chapter delves into the scientific principles and practical methodologies for estimating costs and accounting for depreciation. We will explore various approaches, from basic market analysis to detailed quantity surveys, and examine how depreciation is categorized and measured using different models. The cost approach to valuation is based on the principle of substitution, which posits that a rational investor will pay no more for an asset than the cost to acquire or construct an equivalent substitute.

I. Cost Estimation: Principles and Methodologies

Accurately estimating the cost of an asset, particularly a building or improvement on a leasehold property, is the first critical step in the cost approach to valuation. Several methods exist, each with its own level of detail and applicability. These methods are used to estimate either the reproduction cost (the cost of creating an exact replica) or the replacement cost (the cost of creating an asset of equal utility, using modern materials and techniques).

A. Comparative Unit Method (Square Foot Method)

This is a widely used and relatively simple method, particularly suitable for residential properties. It relies on calculating the cost per unit area (typically square feet or square meters) and multiplying it by the total area of the asset.

1. Principle: The core principle is that similar assets (e.g., houses) tend to have similar costs per unit area, assuming comparable quality and design.
2. Procedure:
   • Determine Area: Accurately measure the total area of the asset being valued.
     Example: A house with a living area of 1280 sq. ft. and an attached garage of 576 sq. ft.
   • Establish Unit Costs: Obtain unit costs from market analysis of comparable new construction, cost estimating manuals, or costing services. Unit costs may be derived in two ways: by market analysis or by use of cost estimating manuals or services.
     Example: Living area cost: $60 per sq. ft.; Garage cost: $25 per sq. ft.
   • Calculate Total Cost: Multiply the area of each component by its respective unit cost and sum the results. The total cost of building can be calculated by
     Cost_total= Area_living * UnitCost_living + Area_garage * UnitCost_garage
     Example:
     Cost of living area = 1280 sq. ft. * $60/sq. ft. = $76,800
     Cost of garage = 576 sq. ft. * $25/sq. ft. = $14,400
     Total Cost of Building = $76,800 + $14,400 = $91,200
   • Add Site Value and Other Improvements: Include the value of the land (site) and other site improvements (e.g., landscaping, driveway) to arrive at the total property value.
     Total cost of improvements = $91,200 (building) + $8,500 (other improvements) = $99,700 (indicated improvement value)
     Total value of the property = $99,700 + $35,000 (site value) = $134,700
3. Mathematical Representation:
   • Let C represent the total cost of the asset.
   • Let A_i represent the area of component i (e.g., living area, garage).
   • Let U_i represent the unit cost of component i.
   • Then, C = Σ (A_i * U_i) + Site Value + Site Improvements.

4. Market Analysis to find Unit Cost by Market Analysis:
   To establish UNIT COST BY MARKET ANALYSIS, the appraiser gathers data on the sales of comparable new homes. The comparables must be similar to the subject property in both size and quality of construction, and the appraiser must be able to determine the site values for the comparables. The appraiser subtracts the site value from the sales price, and then divides the result by the square footage of the comparable. The result is a unit cost.
   UNIT COST = (sales price - site value)/square footage of the comparable

   Example: A new 1,500 square foot rambler sold recently for $120,000. Market data support the appraiser’s estimate of the site value for this property of $30,000, so the building value is $90,000 ($120,000 sales price, $30,000 site value). Assuming the home does not suffer from any depreciation, its value should be equivalent to its cost. So the appraiser takes $90,000 (the building value or cost) and divides that by 1,500 (the size in square feet). The result, $60 per square foot, becomes the unit cost.
   5. Factors Affecting Unit Costs:
   * Size: Unit costs are generally higher for smaller buildings due to fixed costs (e.g., kitchen, bathroom) being spread over a smaller area.
   * Complexity: Buildings with complex designs (e.g., L-shaped structures) have larger perimeter walls and higher unit costs than simple, square buildings.

B. Unit-In-Place Method

This method involves estimating the cost of individual building components (e.g., foundation, walls, roof) and summing them to arrive at the total cost.

1. Principle: Buildings are constructed from discrete components, and each component has a defined unit cost for material and installation.
2. Procedure:
   • Identify Components: Break down the building into its major components.
   • Quantify Components: Measure the quantity of each component (e.g., square feet of flooring, linear feet of walls).
   • Determine Unit Costs: Obtain unit costs for each component from cost manuals or local contractors.
   • Calculate Total Cost: Multiply the quantity of each component by its respective unit cost and sum the results.
     Total = sum( quantity of each item * unit cost )
3. Mathematical Representation:
   • Let C represent the total cost of the asset.
   • Let Q_j represent the quantity of component j.
   • Let U_j represent the unit cost of component j.
   • Then, C = Σ (Q_j * U_j).

4. Measurements: The appraiser must be sure that the measurements used for the different building components are the same as the measurements for which the costs are stated.
   Example: Wall framing costs may be stated as so much per lineal foot of wall, while the cost for painting the walls may be quoted as a cost per square foot of wall surface. Other costs, such as unit costs for plumbing or electrical systems, may be given as costs per square foot of building area.

5. Adjustments: The cost calculated by the unit-in-place method must be adjusted to account for differences in time (current cost) and location (local cost), and also for any cost items that are not included in the unit cost figures (such as indirect costs and entrepreneurial profit).

C. quantity survey method❓❓

This is the most detailed and accurate cost estimation method, often used by contractors for bidding on projects.

1. Principle: A comprehensive accounting of all materials, labor, equipment, and overhead required for construction.
2. Procedure:
   • Bill of Materials: Create a detailed list of all materials required.
   • Labor Estimates: Estimate the labor hours and costs for each task.
   • Equipment Costs: Account for equipment rental or usage costs.
   • Overhead Allocation: Allocate indirect costs (e.g., permits, insurance, supervision).
   • Summation: Sum all costs to arrive at the total estimated cost.
3. Measurements: In the unit-in-place method, a single unit cost is used to calculate the cost of exterior wall framing, including the cost for the framing lumber, sheathing, carpentry labor, scaffolding, etc. In the quantity survey method, the quantities of each of these items would be estimated separately, and each would be multiplied by its own unit cost (cost per board foot of framing lumber, cost per square foot of sheathing, cost per hour of carpentry labor, etc.).
4. Mathematical Representation: This involves a highly detailed summation of numerous individual costs.
5. Complexity: Requires specialized knowledge of construction practices and cost accounting.

D. Cost Index Trending

This method updates historical costs using construction cost indexes.

1. Principle: Construction costs change over time, and cost indexes track these changes.
2. Procedure:
   • Obtain Original Cost: Determine the original construction cost of the asset.
   • Identify Cost Indexes: Find a relevant construction cost index for the original construction date and the current date.
   • Calculate Index Ratio: Divide the current index value by the original index value.
   • Apply Ratio to Original Cost: Multiply the original cost by the index ratio to estimate the current cost.
     CurrentCost = OriginalCost * (CurrentIndex/OriginalIndex)
3. Mathematical Representation:
   • Let C_current represent the current cost.
   • Let C_original represent the original cost.
   • Let I_current represent the current index value.
   • Let I_original represent the original index value.
   • Then, C_current = C_original * (I_current / I_original).
4. Limitations: Cost index trending is NOT considered very reliable. There is no guarantee that the actual cost was typical for similar improvements that were built at the same time.

II. Depreciation: Principles and Assessment

Depreciation represents the loss in value of an asset over time due to various factors. Understanding the types of depreciation and how to measure them is crucial for accurate valuation. Depreciation is the difference between the market value of the improvement and its cost.

A. Types of Depreciation

1. Physical Deterioration:
   • Definition: Loss in value due to wear and tear, damage, or aging of physical components.
   • Causes: Weathering, corrosion, lack of maintenance, accidents.
   • Examples: Broken windows, leaky roofs, peeling paint, termite damage or worn carpeting.
   • Curable vs. Incurable:
     • Curable: Cost to correct is less than the resulting increase in value. Example: Repainting a house.
     • Incurable: Cost to correct exceeds the resulting increase in value, or correction is physically impossible. Example: Repairing a severely cracked foundation.
   • Long-Lived vs. Short-Lived Items:
     • Long-Lived: Components expected to last the entire economic life of the asset (e.g., foundation).
     • Short-Lived: Components that require replacement during the asset’s economic life (e.g., paint, carpeting, roof covering).
2. Functional Obsolescence:
   • Definition: Loss in value due to design inadequacies, outdated features, or inefficiencies that make the asset less desirable compared to modern alternatives.
   • Causes: Poor layout, inadequate amenities, technological advancements, code changes.
     Example: At one time homes were frequently built without bedroom closets. Clothing was stored in chests or wardrobe cabinets. At the time, people owned limited clothing. This design would not be adequate for modern needs.
   • Deficiencies vs. Superadequacies:
     • Deficiencies: Lacking essential features or having inadequate levels of features (e.g., inadequate insulation).
     • Superadequacies: Over-improvement; features whose cost exceeds their contribution to value (e.g., using excessively expensive materials).
   • Curable vs. Incurable: Similar criteria as physical deterioration.
3. External (Economic) Obsolescence:
   • Definition: Loss in value due to factors external to the property itself, arising from the surrounding environment or broader economic conditions.
   • Causes: Proximity to undesirable land uses, economic downturns, changes in zoning regulations, high crime rates.
   • Examples: A residence located in an industrial area. Also, if a community’s sole employer (such as the mill owner in a logging community) goes out of business or closes its operations in the community.
   • Generally Incurable: Property owners have little or no control over these external factors.

B. Age and Economic Life

1. Actual Age: The chronological age of the asset (time since construction).
2. Effective Age: The apparent age of the asset based on its condition and market perception. May be greater or less than actual age.
   Example: An exceptionally well maintained building might have a chronological age of 20 years❓❓ but an appraiser might use an effective age of 14 years to determine the depreciation. On the other extreme, the appraiser might determine that a poorly maintained 20-year-old property should have an effective age of 26 years.
3. Economic Life: The period during which the asset contributes value to the property.
4. Remaining Economic Life: The time from the appraisal date until the end of the asset’s economic life.
5. Relationship:
   • Economic Life = Effective Age + Remaining Economic Life
   • Effective Age = Economic Life - Remaining Economic Life
   • Remaining Economic Life = Economic Life - Effective Age
     Example: A house built in 1980 has an estimated economic life of 50 years. The house is appraised in 1994, when its actual age is 14 years. Because the house has been well maintained, and its design and layout are still popular in the market, the appraiser estimates that it has a remaining economic life of 40 years. In this case, the effective age of the house would be 10 years (50 - 40 = 10), as compared to the actual age of 14 years.

C. Methods of Estimating Depreciation

1. Economic Age-Life Method (Straight-Line Method):

   • Principle: Assumes depreciation occurs at a constant rate over the asset’s economic life.

   • Procedure:

     • Estimate effective age and economic life.
     • Calculate the accrued depreciation rate: DepreciationRate = EffectiveAge / EconomicLife.

     • Multiply the accrued depreciation rate by the estimated cost to determine the amount of depreciation.
       Depreciation = (Effective Age ÷ Economic Life) x Cost
       Example: An appraiser estimates the reproduction cost of a home at $220,000. The home has an economic life of 60 years, and an effective age of 15 years. Under the economic age-life method, depreciation would be calculated as follows:
       15 ÷ 60 = 0.25 (25%) accrued depreciation rate
       0.25 x $220,000 = $55,000 accrued depreciation
       $220,000 - $55,000 = $165,000 depreciated value of improvement

     • Subtract depreciation from cost to arrive at depreciated value.
       Value = Cost – Depreciation

       • Limitations: Simplistic and may not accurately reflect actual depreciation patterns.
         2. Sales Comparison Method:
       • Principle: Derives depreciation estimates by comparing sales prices of similar properties with and without the specific defect or condition causing depreciation (paired data analysis).
       • Procedure:
     • Identify comparable sales with and without the depreciation-causing factor.
     • Calculate the difference in sales prices, which represents the market’s perception of the depreciation amount.
       Example: A subject property suffers from functional obsolescence due to a poor floor plan. Market analysis reveals that comparable houses with similar floor plans sell for $110,000, while comparable houses with more functional floor plans sell for $120,000. This indicates that the functional obsolescence due to the poor floor plan causes depreciation of $10,000 ($120,000 - $110,000 = $10,000).
       • Data Requirements: Requires a sufficient number of comparable sales to isolate the impact of the depreciation factor.
         3. Capitalization Method:
       • Principle: Similar to the sales comparison method but focuses on income differences between comparable properties with and without the depreciation-causing factor.
       • Procedure:
     • Identify comparable rental properties with and without the defect.
     • Calculate the difference in net operating income (NOI) attributable to the defect.
     • Capitalize the income difference using an appropriate capitalization rate to estimate the depreciation amount.
     • Depreciation= IncomeDifference/capitalization rate
       Example: A subject property suffers from external obsolescence due to its location near a busy airport. Comparable properties in similar locations rent for $800 per month, while comparables in more favorable locations command monthly rents of $900. The $100 difference in monthly rent is multiplied by 12 (months) to give an annual difference. This difference is then divided by a capitalization rate. If the rate were eight percent, then $1,200 divided by .08 would mean the locational difference would be $15,000.
       • Application: Suitable for income-producing properties where income data is readily available.
         4. Cost to Cure Method:
       • Principle: Depreciation due to curable items is estimated based on the cost to repair or replace those items.
       • Procedure:
     • Identify curable physical deterioration and functional obsolescence items.
     • Estimate the cost to cure each item.
     • The total cost to cure represents the total depreciation due to curable items.
       • Verification: Ensure the repair or replacement is physically and legally possible, and the cost does not exceed the resulting increase in value.

2. Observed Condition Method (Breakdown Method):

   • Principle: Estimates each type of depreciation (physical deterioration, functional obsolescence, and external obsolescence) separately, using various techniques (straight-line, sales comparison, capitalization, cost to cure).
   • Procedure: Combines elements of other methods to provide a comprehensive assessment of depreciation.

III. Conclusion

Accurate cost estimation and depreciation assessment are critical to the cost approach to leasehold valuation. Understanding the underlying scientific principles and methodologies allows for a more robust and defensible valuation process. The choice of method depends on the nature of the asset, available data, and the appraiser’s expertise. It’s important to remember that the cost approach is often used in conjunction with other valuation approaches to arrive at a comprehensive and reliable estimate of value.