Contribution, Returns, and Highest & Best Use

Chapter: Contribution, Returns, and Highest & Best Use

I. Introduction
This chapter explores the fundamental economic principles of contribution, returns (increasing and decreasing), and highest and best use. These principles are crucial for understanding how various factors influence real estate value❓ and for making informed decisions in appraisal and investment. We will delve into the underlying scientific theories, practical applications, and relevant examples to illustrate these concepts.

II. Principle of Contribution
A. Definition
The principle of contribution states that the value of a component of a property❓ is determined by the amount it contributes to the value of the entire property, regardless of its cost. This contribution is also known as its marginal productivity.
B. Marginal Productivity and Marginal Cost
The marginal productivity of a component is the increase in value it adds to the property (or the decrease its absence would cause).
Marginal Cost is the actual cost of the component.
C. Mathematical Representation
Let:
V_total = Total value of the property
V_component = Value contributed by the component
Then:
V_component = V_total (with component) - V_total (without component)

D. Practical Application
1. Sales Comparison Approach: The principle of contribution is particularly useful in the sales comparison approach to value. It helps appraisers adjust comparable property values❓ based on differences in features.
For example, consider two similar houses:
House A (with garage): Sale Price = $300,000
House B (without garage): Sale Price = $280,000
The contribution of the garage is $300,000 - $280,000 = $20,000. Therefore, an appraiser would adjust the comparable sales price by $20,000 for the presence or absence of a garage.
2. Renovation Decisions: The principle guides renovation decisions. If adding a feature costs more than its contribution to value, the renovation may not be economically justified.

E. Experiments/Case Studies
1. Market Surveys: Conduct surveys in specific neighborhoods to determine the price differences between houses with and without certain features (e.g., a finished basement, a deck). Analyze the data to quantify the marginal productivity of each feature.
2. Before-and-After Studies: Analyze the sale prices of properties before and after renovations. Control for market fluctuations to isolate the value added by the specific improvement.
F. Example
Consider installing new siding on a house. The siding costs $7,000. After installation, the house’s value increases by $5,000. In this case, the marginal productivity of the siding is $5,000. Since the marginal cost ($7,000) exceeds the marginal productivity ($5,000), the investment was not financially optimal from a pure value-addition perspective.

III. Principle of Increasing and decreasing returns❓❓
A. Definition
The principle of increasing and decreasing returns states that as additional units of one factor of production (e.g., capital) are added to a fixed amount of other factors (e.g., land), the marginal returns will initially increase, then reach a point of maximum❓ return, and eventually decrease.
B. Stages of Returns
1. Increasing Returns: The rate of return on investment increases at an increasing rate. Each additional unit of input generates a progressively larger increase in output.
2. Constant Returns: The rate of return increases, but at a decreasing rate. Each additional unit of input generates a smaller increase in output than the previous unit.
3. Decreasing Returns: The rate of return begins to decrease. Each additional unit of input generates a smaller and smaller increase in output, eventually leading to a decrease in total output.

C. Mathematical Representation
This can be modeled using production functions. A simplified version is:
Q = f(L, K)
Where:
Q = Output (e.g., property value)
L = Land (fixed)
K = Capital (variable investment)
The principle of increasing and decreasing returns is reflected in the shape of the production function and its derivatives.
1. Increasing Returns: ∂²Q/∂K² > 0
2. Decreasing Returns: ∂²Q/∂K² < 0
3. Optimal Investment: Point where marginal return equals marginal cost.

D. Practical Application
1. Property Development: A developer decides how much to invest in a property improvement. Investing too little may result in lower-than-optimal returns, while investing too much will yield diminishing returns.
2. Agricultural Land: A farmer decides how much fertilizer to apply to a field. Initially, each unit of fertilizer increases crop yield significantly (increasing returns). However, beyond a certain point, additional fertilizer leads to smaller yield increases (decreasing returns), and may even damage the crop (negative returns).

E. Examples & Experiments
1. Residential Construction:
Consider a builder developing a house on a fixed-size lot. They can choose different levels of finish, landscaping, and amenities.
Initially, adding better finishes increases the sales price significantly (increasing returns).
As the finishes become extremely luxurious, the incremental increase in sales price diminishes (decreasing returns).
2. Commercial Property Renovation:
A property owner decides how much to invest in renovating an office building.
A basic renovation attracts more tenants and increases rental income❓ (increasing returns).
An extravagant renovation with excessively high-end features may not justify the increased costs (decreasing returns) and might not attract significantly more tenants.

F. Case Study: Builder Example (as presented in document)
The table provided illustrates the principle of increasing and decreasing returns. Note that initially, each additional 100 sq. ft. added to the house substantially increased the estimated sales price (increasing returns). However, after a certain point (around 2,100 sq. ft.), the increase in sales price became smaller, and the marginal return began to decline (decreasing returns). The builder should aim for the square footage where the marginal return is greatest relative to the marginal cost.

IV. Highest and Best Use
A. Definition
The highest and best use of a property is the most probable and legal use of that property that is physically possible, appropriately supported, financially feasible, and results in the highest value.

B. Four Criteria
1. Legally Permissible: The use must be allowed under current zoning regulations or have a reasonable probability of obtaining the necessary approvals (e.g., a variance).
2. Physically Possible: The site must be suitable for the proposed use given its size, shape, topography, soil conditions, and other physical attributes.
3. Financially Feasible: The use must generate sufficient income or utility to justify the costs of development and operation. The present value of the expected cash flows must exceed the cost of the investment.
4. Maximally Productive: Among the legally permissible, physically possible, and financially feasible uses, the one that results in the highest value for the property.

C. Mathematical Representation
The concept can be formalized as:
HBU = Argmax [PV(Net Income_i) - Cost_i]
Where:
HBU = Highest and best use
Net Income_i = Expected net income from use ‘i’
Cost_i = Cost of developing and operating use ‘i’
PV = Present Value operator (discounting future income)
Argmax = The use ‘i’ that maximizes the expression.

D. Highest and Best Use as Vacant vs. Improved
1. As Vacant: Determines the optimal use of the land if it were vacant and available for development.
2. As Improved: Determines whether the existing improvements should be retained, renovated, or demolished. The decision depends on whether the value of the property in its current use exceeds the value of the land vacant for a different use (less demolition costs).

E. Practical Applications
1. Appraisal: The highest and best use analysis is crucial for determining the appropriate valuation approach and selecting comparable properties.
2. Investment: Investors use highest and best use analysis to identify properties with potential for value appreciation through redevelopment or change of use.
3. Land Use Planning: Planners consider highest and best use when making zoning decisions and allocating land resources.

F. Examples
1. Residential Property:
A property is currently used as a single-family home. However, the surrounding area has been rezoned for multi-family development. An appraiser needs to determine if the highest and best use is still single-family residential or if it is multi-family residential. The appraiser would evaluate the value of the land as if vacant for multi-family development, compare it to the value of the property as currently improved, and factor in the cost of demolition and redevelopment.
2. Commercial Property:
A vacant lot is located in a growing commercial area. Possible uses include a retail store, an office building, or a parking garage. The appraiser would analyze the potential income, costs, and risks associated with each use to determine which use would generate the highest value.

G. Consistent Use Principle
The principle of consistent use requires that both the land and improvements be valued for the same use, even if they are being valued separately. It is improper to value the land for one use and the improvements for a different use. The goal is to ensure that value determination is consistent in the assumption of how the property is used, either in its present form, or if the underlying land would be put to better use if it were vacant.

H. Conformity, Progression, and Regression Principles
1. Principle of Conformity: Property values are enhanced when the uses of surrounding properties conform to the use of the subject property. This is the rationale behind zoning regulations.
2. Principle of Progression: The value of a less desirable property is increased by its proximity to more desirable properties.
3. Principle of Regression: The value of a more desirable property is decreased by its proximity to less desirable properties.

V. Conclusion
Understanding the principles of contribution, returns, and highest and best use is essential for accurate real estate valuation and informed decision-making. These principles provide a framework for analyzing the factors that influence property value, optimizing investment strategies, and making sound land use decisions. Applying these concepts effectively requires careful analysis, market research, and a thorough understanding of the specific characteristics of the property and its surrounding environment.