Sales Comparison and Income Approaches: Foundations of Value

I. Introduction

Real estate appraisal relies on several methodologies to estimate the value of a property. Two fundamental approaches, the sales comparison approach and the income approach, form the bedrock of valuation. This chapter delves into the scientific foundations of these approaches, providing a comprehensive understanding of their principles, methodologies, and applications.

II. Sales Comparison Approach: Leveraging Market Data

A. Core Principle: Substitution

The sales comparison approach is rooted in the economic principle of substitution. This principle posits that a rational buyer will pay no more for a property than the cost of acquiring an equally desirable substitute. In essence, the value of a property is directly related to the prices of comparable properties in the market.

B. Methodology: A Systematic Comparison

The sales comparison approach involves a systematic process:

1. Data Collection and Verification: The appraiser gathers detailed information on recent sales of comparable properties. This data encompasses various aspects, including:
   • Sale Price (SP): The actual transaction price.
   • Property Characteristics: Physical attributes (size, features, condition), location, and legal rights.
   • Transaction Details: Financing terms, conditions of sale (arm’s length transaction), and date of sale.
   • Verification: Data sources are verified to ensure accuracy and reliability. Verification helps the appraiser form an opinion as to the reliability of the data, and may also yield additional information about the comparable sale.
2. Selection of Comparable Properties:
   • Similarity: Comparables should share similar characteristics with the subject property, minimizing the need for significant adjustments.
   • Proximity: Located in the same or similar neighborhood as the subject property.
   • Recency: Recent sales are preferred, as changing market conditions affect values.
   • For a sale to be considered comparable for purposes of the sales comparison approach to value, it must be competitive with the subject property.
3. Identification of Elements of Comparison: The appraiser identifies key elements that influence property value, such as:
   • Real Property Rights Conveyed: Differences or restrictions as to the real property rights conveyed in a transaction must be accounted for.
   • Financing Terms: If financing terms are not typical of those available in the market, the financing is not cash equivalent, and may require an adjustment based on market data. Financing on terms that are typical of the market is called cash equivalent financing.
   • Conditions of Sale: Motivation of buyer and seller should indicate an arm’s length transaction.
   • Expenditures Immediately After Sale: Expenditures immediately after sale are expenditures that would have to be made upon purchase of the property and that a knowledgeable buyer may negotiate into the purchase price.
   • Market Conditions (Date of Sale): Recent sales are preferred, because changing market conditions affect values.
   • Location: Comparables located in the same neighborhood as the subject are the most reliable.
   • Physical Characteristics: The majority of adjustments in residential appraisals are for differences in physical characteristics.
   • Economic Characteristics: Economic characteristics such as income, operating expenses, lease provisions, management, and tenant mix are used to analyse income-producing properties.
   • Other Characteristics: The appraiser must be alert to any other characteristics of the subject or a comparable that could influence value, and make whatever adjustments are necessary.
4. Comparative Analysis and Adjustments:
   • Quantitative Adjustments: Dollar amount or percentage adjustments based on market data (paired data analysis).
   • Qualitative Adjustments: Superior, inferior, or equal ratings based on relative comparison analysis.
   • Adjustments are made to the prices of the comparables.
   • The formula for converting percentage adjustments into dollar amounts depends on how the percentage relationship is defined.
   • The sequence of adjustments depends on the appraiser’s analysis of the market, but adjustments for transactional elements of comparison are usually made before adjustments for physical elements of comparison.
   • When the subject property is superior to a comparable in some characteristic, the comparable’s price is adjusted upward.
5. Reconciliation and Value Indication:
   • The adjusted sales prices of the comparables are reconciled to arrive at a single indicated value or a range of values for the subject property. The appraiser must reconcile the various adjusted comparable sales prices, and estimate a value or range of values for the subject that is indicated by the sales comparison approach.
   • The subject property’s value should fall within the range indicated by the adjusted prices of the comparables.

C. Mathematical Representation: Adjustment Process

The adjustment process can be represented mathematically:

• V_subject ≈ SP_comp ± A₁ ± A₂ ± … ± A_n

Where:

• V_subject is the indicated value of the subject property.
• SP_comp is the sale price of the comparable property.
• A_i is the adjustment for the i-th element of comparison.

D. Paired Data Analysis: Quantifying Adjustments

Paired data analysis is a technique used to isolate the value of a specific property characteristic. By comparing the sale prices of two properties that are identical except for the characteristic in question, the appraiser can estimate the market value of that feature.

• Example:

  Property A: 3 bedrooms, 2 baths, Sale Price = $300,000
  Property B: 3 bedrooms, 3 baths, Sale Price = $310,000

  The market value of the additional bath is estimated to be $10,000 ($310,000 - $300,000).

E. Practical Application: Case Study

Imagine appraising a 3-bedroom, 2-bath house. Three comparable properties have sold recently:

• Comparable 1: 3 bedrooms, 2 baths, no garage, Sale Price = $280,000
• Comparable 2: 3 bedrooms, 3 baths, 1-car garage, Sale Price = $320,000
• Comparable 3: 4 bedrooms, 2 baths, 2-car garage, Sale Price = $350,000

Market data indicates:

• Garage: $15,000 per car space.
• Additional bath: $10,000
• Additional bedroom: $20,000

Adjustments:

• Comparable 1: +$15,000 (garage) -> Adjusted Price = $295,000
• Comparable 2: -$10,000 (bath), -$15,000 (garage) -> Adjusted Price = $295,000
• Comparable 3: -$20,000 (bedroom), -$30,000 (garage) -> Adjusted Price = $300,000

Reconciliation: The adjusted prices suggest a value range of $295,000 to $300,000. The appraiser would then reconcile these figures, considering the reliability of each comparable, to arrive at a final value opinion.

F. Limitations: Market Dependency and Subjectivity

The sales comparison approach heavily relies on the availability of sufficient and reliable market data. In markets with limited sales activity or significant heterogeneity, the approach may become less reliable. Moreover, the selection of comparable properties and the estimation of adjustments involve a degree of subjectivity, which can influence the final value opinion.

G. Reliability: Gross Adjustment, Net Adjustment, and Percentage Adjustment

A comparable is usually considered more reliable when it requires the least gross adjustment, net adjustment and percentage adjustment.

III. Income Approach: Capitalizing Income Streams

A. Core Principle: Present Value of Future Benefits

The income approach is based on the premise that the value of an income-producing property is equal to the present value of its expected future income stream. This approach is particularly relevant for commercial properties, rental apartments, and other investments where income generation is a primary driver of value.

B. Key Concepts: Income Capitalization

Income capitalization involves converting an estimated income stream into a present value estimate. Two primary methods are employed:

1. Direct Capitalization: Applying a capitalization rate to a single year’s stabilized income.
2. Yield Capitalization (Discounted Cash Flow Analysis): Projecting future cash flows and discounting them back to their present value.

C. Direct Capitalization: A Simplified Approach

1. Net Operating Income (NOI): The cornerstone of direct capitalization is the NOI, calculated as:

   NOI = Effective Gross Income (EGI) – Operating Expenses (OE)

   • EGI = Potential Gross Income (PGI) – Vacancy and Collection Losses
   • Operating Expenses: Expenses that do not vary depending on the occupancy of the property are fixed expenses. Variable expenses are operating expenses that do vary depending on occupancy. Reserves for replacement are funds that are set aside for replacing short-lived components of the property. A short-lived component is an item that has a life span that is less than the expected life of the building, such as carpeting, paint, roofing, or mechanical equipment.
   • Mortgage principal and interest, depreciation (book depreciation), and income taxes are not included as operating expenses when calculating net operating income.

2. Capitalization Rate (Cap Rate): The cap rate represents the relationship between NOI and property value:

   Cap Rate (R) = NOI / Property Value (V)

   Rearranging the formula to solve for value:

   V = NOI / R

   The rate of return is the ratio between the amount of income and the amount of the investment. This rate is then applied to the property’s income to indicate its value.
   The rate of return on an investment is equal to the amount of income it produces divided by the amount the investor paid for the investment. Stated in mathematical terms:

   Rate of Return = Amount of Income divided by Amount of Investment
   The amount paid for the investment represents the investor’s idea of its value, so the formula for rate of return can also be stated as:
   Rate of Return = Amount of Income divided by Value

3. Cap Rate Derivation: Common methods for deriving cap rates include:

   • Market Extraction: Analyzing cap rates from comparable sales (NOI / Sale Price). The comparable sales method is considered the most reliable means for estimating a direct capitalization rate, assuming that adequate comparable sales data are available.
   • Band of Investment: Considering the weighted average of debt and equity returns. With the band of investment method, the appraiser calculates separate capitalization rates for the equity investor and for the lender(s). The weighted average of these rates is then used as the overall capitalization rate for the property.
   • Survey Data: Utilizing published surveys of investor expectations.
4. Comparable Sales Method (Preferred Method):
   • The comparable sales method is considered the most reliable means for estimating a direct capitalization rate, assuming that adequate comparable sales data are available. In the comparable sales method, the capitalization rate is derived by analyzing the sales prices and incomes of comparable income of properties that have sold recently. The appraiser divides the net income of the comparable by its sales price to obtain the capitalization rate.
   • In practice, the appraiser will analyze several comparables to determine a range of capitalization rates. The capitalization rate to be used for the subject property is then determined through reconciliation. This process is virtually identical to the process of obtaining a value indicator through the sales comparison approach to value
   • The sales price of the comparable may need to be adjusted to account for differences in market conditions or financing terms.
   • The calculation of income for the comparables must be made on the same basis as the calculation of income for the subject.
   • The comparables must be similar to the subject in terms of key investment criteria, including expected resale price, expected holding period for the investment, and tax consequences of the investment.

D. Yield Capitalization: Projecting and Discounting Future Cash Flows

1. Cash Flow Projections: Developing a forecast of future cash flows, considering factors such as:
   • Rental income growth
   • Vacancy rates
   • Operating expense inflation
   • Capital expenditures
   • Resale value
2. Discount Rate: Selecting an appropriate discount rate (yield rate) to reflect the time value of money and the risk associated with the investment. This rate is used to discount future cash flows back to their present value.

3. Present Value Calculation: Applying the discount rate to each projected cash flow:

   PV = Σ [CF_t / (1 + r)^t]

   Where:

   • PV is the present value of the property
   • CF_t is the cash flow in year t
   • r is the discount rate
   • t is the year of the cash flow

E. Practical Application: Case Study

A small office building generates an annual NOI of $50,000. Market data suggests a cap rate of 8%. Using direct capitalization, the value is:

V = $50,000 / 0.08 = $625,000

Alternatively, a discounted cash flow analysis might project the following:

Using a discount rate of 10%, the present value would be calculated for each year and then summed to obtain the property’s value.

F. Limitations: Forecasting Uncertainty and Rate Selection

The income approach is sensitive to the accuracy of income and expense projections, as well as the selection of an appropriate discount rate. These factors can be influenced by market volatility, economic conditions, and investor sentiment.

IV. Interrelationship and Reconciliation

In many appraisal assignments, both the sales comparison and income approaches are employed. The appraiser must then reconcile the value indications from each approach, considering their strengths and weaknesses in the context of the specific property and market.

• The sales comparison approach relies on market data to indicate the value of the subject property.
• Sales prices of comparable properties are adjusted to account for differences between the comparables and the subject.
• The appraiser analyzes sales of properties from the same market as the subject, because properties in the same market are subject to similar value influences.

V. Conclusion

The sales comparison and income approaches provide complementary perspectives on property value. Understanding the scientific foundations of these approaches is crucial for accurate and reliable real estate appraisal. By carefully analyzing market data, projecting income streams, and applying appropriate valuation techniques, appraisers can provide informed opinions that support sound investment decisions.