When applying the residual method, what is the effect of uncertainty in input variables, such as income or costs, on the resulting land value estimate?

Chapter Title:

From Residual Value to Business Value: Allocation and Appraisal Methods

Introduction:

Real estate valuation often begins with isolating residual values, such as land value in development scenarios or the component values within a complex property. However, the ultimate goal is to determine the overall business value of a property or enterprise. Bridging this gap requires a systematic approach to allocation and appraisal. This chapter explores the methodologies used to transition from residual value calculations to comprehensive business value assessments, emphasizing accuracy and transparency in the valuation process.

Overview

This chapter delves into the methods employed to allocate value to different components of a property or business and the appraisal techniques used to determine its overall worth. We will examine how residual valuation methods contribute to a broader understanding of value and how these methods can be integrated with other appraisal approaches. The chapter highlights the scientific and practical implications of choosing appropriate allocation and appraisal methods, particularly in complex real estate scenarios. The scientific importance lies in the application of economic principles and statistical analysis to derive defensible and reliable value estimates.

Key concepts covered in this chapter include:

• Residual Value Methods: Understanding the strengths and limitations of residual value calculations, particularly in land valuation and development appraisals.
• Apportionment Techniques: Exploring different approaches to allocate value to various components of a property, such as land and improvements, leasehold interests, and tangible versus intangible assets.
• Business Value Allocation: Methods for allocating the total business value of an operating property (e.g., gasoline station, hotel) to its various assets, including real estate, goodwill, and other intangibles.
• Sales Comparison Approach: Applying the sales comparison approach, including adjustments for property characteristics.
• Income Capitalization Approach: Utilizing income capitalization techniques, including ratio models (e.g., Gross Income Multiplier) and Discounted Cash Flow (DCF) analysis, to derive property values based on income potential.
• Cost Approach: Employing the cost approach, considering reproduction or replacement costs, accrued depreciation, and land value, to estimate property value.
• Reconciliation of Value Indicators: Comparing and reconciling value estimates derived from different appraisal approaches to arrive at a final, well-supported value conclusion.
• Goodwill: Distinguishing between goodwill attached to the property versus the user and its impact on valuation.

Topic:

From Residual Value to Business Value: Allocation and Appraisal Methods

Body:

From Residual Value to Business Value: Allocation and Appraisal Methods

1. From Land Residual to Market Value: The Residual Method

The residual method is a valuation technique used to determine the value of a component of a property (typically land) by deducting the development costs (including construction costs, developer's costs, and entrepreneurial profit) from the expected income generated by the completed development. The underlying premise is:

Land Value = Development Income - Total Development Costs

The estimated development income relies on the expected demand of the market and legal permissions.

Limitations of the Residual Method:

The residual method is highly sensitive to the accuracy of its inputs. Small errors in the estimation of income or costs can result in significant changes in the residual value. This sensitivity stems from the fact that any uncertainties are disproportionately reflected in the residual value.

For example:

Assume:
* Potential Income from lots = 100 lots × 300,000 FU/lot = 30,000,000 FU
* Total Development Costs = 100 lots × 200,000 FU/lot = 20,000,000 FU
* Entrepreneurial Profit = 10% of Total Development Costs = 2,000,000 FU

Land Residual Value = 30,000,000 - 20,000,000 - 2,000,000 = 8,000,000 FU

Now, consider a 5% decrease in income and a 5% increase in costs:

• Potential Income = 100 lots × (300,000 * 0.95) FU/lot = 28,500,000 FU
• Total Development Costs = 100 lots × (200,000 * 1.05) FU/lot = 21,000,000 FU
• Entrepreneurial Profit = 10% of Total Development Costs = 2,100,000 FU

Land Residual Value = 28,500,000 - 21,000,000 - 2,100,000 = 5,400,000 FU

In this scenario, a small 5% change in input variables lead to a 32.5% change in Land Residual Value.

Practical Applications:

• Feasibility studies for proposed developments.
• Land valuation in situations where comparable sales data is scarce.
• Supporting evidence for other valuation methods, providing transparency in cash flows.

Equation:

Land Value (LV) = Expected Income (EI) - Total Development Costs (TDC) - Entrepreneurial Profit (EP)

2. Apportionment: Dividing the Whole into Parts

When valuing real estate, the objective is often to value all interests, benefits and rights associated with ownership. Fee interest is the most complete form of ownership. However, interests can also be partial, (e.g. the right to use, occupy or lease a property).

Marketable minority interests can be valued by direct comparison. Unmarketable partial interests, relative to the total bundle of rights, are valued via apportionment.

Common Apportionment Issues:

• Land and improvements.
• Leasehold and leased fee interests.
• Equity and debt.
• Tangible (property, plant, equipment) and intangible (business value) assets.

The Concept of the Marketable Entity:

The market value must relate to a coherent economic and legal entity fit to be sold. The valuer's role is to identify this marketable entity. For residential real estate, this is often the inseparable combination of land and buildings under full ownership.

The market value of the 'marketable whole' is then allocated to its components. This allocation is not necessarily market-based but driven by logic and consistency.

Premise: The sum of the parts equals the market value of the whole.

Methods of Apportionment:

Because there is no market conformity to rely on, various methods of apportionment can be valid, as long as they are logical and consistent.

Example: Apportionment of a Residential Property

Consider a residential property with the following characteristics:

• Market Value: 1,000,000
• Building Cost (New): 900,000
• Obsolescence (Accrued Depreciation of Improvements): 20%
• Market Price of Vacant Parcel (Comparable Sales): 250,000

Several apportionment methods can be used:

• Building Residual:
  • Building Value = Market Value - Parcel Value = 1,000,000 - 250,000 = 750,000
• Land Residual:
  • Depreciated Replacement Cost (DRC) of Building = 900,000 × (1 - 0.20) = 720,000
  • Land Value = Market Value - DRC Building = 1,000,000 - 720,000 = 280,000
• Land Value by % Land in New Development:
  1. Total Cost = Vacant parcel price + building cost = 250,000 + 900,000 = 1,150,000
  2. % Land in new property = 250,000 / 1,150,000 = 21.74%
  3. Land Value = Market Value * % Land in new property = 1,000,000 * 0.2174 = 217,391
  4. Building Value = 1,000,000 - 217,391 = 782,609
• Land Value by % Land in DRC:
  1. DRC property = DRC building + Vacant parcel value = (900,000 * 0.8) + 250,000 = 970,000
  2. % land in DRC = 250,000 / 970,000 = 25.77%
  3. Land value = Market Value total * % land in DRC = 1,000,000 * 0.2577 = 257,732

3. Business Value and Allocation

Market value is always assigned to a clearly defined entity that is optimally marketable (economically and legally). RICS uses the term 'operational entity' while IFRS uses 'cash generating unit'.

Consider a gasoline station. The operating unit encompasses real estate, inventory, branding, and personnel. This whole represents an optimally marketable and valuable entity.

When valuing components (e.g., the real estate portion for financing), allocation is necessary. If the business value cannot be allocated to tangible/intangible assets, a 'floating surplus' or goodwill exists.

Goodwill and allocation are interlinked.

Both the RICS and IVSC consider the appraisal of trading properties (gas stations, hotels, etc.) to be the domain of the property valuer, because:

1. The allocation problem is manageable, with the majority of value allocated to real property.
2. Trading properties are often marketable, enabling the use of comparison methods.

Goodwill: Attached to the Property or the User?

If the business value cannot be fully allocated to tangible assets, the question of goodwill arises. Crucially, is the goodwill attached to the property or the user?

Example: A gasoline station previously branded with "AAA" being valued vacant. The goodwill associated with the "AAA" brand is excluded from the market value, while the goodwill linked to the location is included.

British terminology distinguishes:

• Cats-goodwill: Attached to the property ("stays home").
• Dogs-goodwill: Attached to the user ("moves out").

Property-Related Business Valuation:

This involves valuing REIT interests, (OTC)-derivatives, (mortgage-backed) securities, shared development-options, and participations in ventures like public-private partnerships.

Distinctive elements include valuing debt and issues like the degree of control.

4. Appraisal Methods: Sales Comparison, Income Capitalization and Cost Approach

Appraisal methods have evolved into three main approaches:

• Sales Comparison Approach (Direct Comparison)
• Income Capitalization Approach
• Cost Approach

In the US, all three methods are often used, followed by a reconciliation to arrive at an opinion of value. In Europe, one method may be chosen based on the appraisal's scope.

4.1 Sales Comparison Approach

This approach uses prices paid for similar properties to estimate the market value of the subject property.

Assumptions:

1. Sale prices are a reliable indicator of market value.
2. Equal/similar properties should sell for equal/similar prices.

Process:

1. Find transactions involving property rights comparable to the subject property.
2. Adjust the comparable property prices for differences from the subject property (location, age, size, building characteristics, etc.).

• Beware of non-linear relationships. For instance, the marginal contribution of an additional square foot may decrease as the property size increases.

Number of Comparables:

• Quantity is a function of quality. Higher quality comparables require fewer observations.
• In homogeneous markets (housing), three comparables may suffice.
• Using more than four comparables provides minimal increase in accuracy.
• Location is critical to accuracy.
• In distressed markets, you may need to look at different neighborhoods and time adjustment of value over time.

Mechanics of Direct Sales Comparison:

1. Gather information on sales of comparable properties.
2. Adjust selling prices for differences between the comparable properties and the subject property, resulting in adjusted selling prices.
3. Estimate the value of the subject property using weighted average of the adjusted selling prices of the comparable properties, based on appraiser's judgment.

Table 15.2: Direct Sales Comparison Approach (Example)

Feature	Subject	Comparable 1	Comparable 2	Comparable 3	Comparable 4
Transaction Price		105,000	115,000	122,000	100,000
Transaction Date	Current	6 months ago	9 months ago	10 days ago	1 year ago
Time Adjustment		2,625	4,313	0	5,000
Condition	Similar	Similar	Similar	Similar	Similar
Location	Similar	Similar	Similar	Similar	Similar
Age (years)	15	22	12	8	20
Age Adjustment		2,800	-1,200	-2,800	2,000
Living Area (sq ft)	2,200	2,100	2,350	2,400	2,000
Area Adjustment		-3,000	-4,500	-6,000	6,000
Adjusted Price		116,425	109,113	113,200	119,000
Average Estimate	113,000

Time adjustment is crucial to reflect value changes between the transaction date and the valuation date. Paired data analysis can refine adjustments.

4.2 Income Capitalization Approach

The value of a property is a function of the income it is expected to produce. It can be calculated using a ratio model or a discounted cash-flow (DCF) model.

Ratio Model

The gross income multiplier (GIM) compares a property's market value to its gross income. Although simple, it is often an oversimplification as the contract rent will very rarely be equal to the market rent at any point in time. It is therefore better to calculate based on net rental income.

Process of Direct Income Capitalization:

1. Determine market rent based on recent comparables.
2. Calculate gross rental income using net rentable space.
3. Deduct average operating costs from gross rental income to arrive at net rental income (essential to calculate average maintenance costs).
4. Calculate capital value by dividing net rental income by the market yield for similar properties or other investments, adjusted for the real estate risk premium.

Other adjustments might include:
* The difference between contract rent and market rent.
* Vacancy allowance.
* Renewal of a short leasehold.
* A major renovation in the near future.
* Purchase costs

After adjustments, the appraised value is determined to meet the required yield.

Table 15.3: Direct Income Capitalization (Example)

(Example table would be inserted here. The provided document references ROZ Real Estate Council.)

DCF Model

The DCF model estimates value based on explicit forecasts of income and costs over a defined holding period (typically ten years).

Key Assumptions and Estimates:

• Rent and rental growth/decline.
• Operating costs and their increase/decrease.
• Vacancy allowances.
• Incentives.
• Renovation and refurbishment costs.
• Terminal value (property value at the end of the forecast period).

Since cash flows occur in the future, a discount rate must be applied.

Methods for Determining the Discount Rate:

• Summation approach (estimates expected returns for individual parts of the DCF model).
• Observed capitalization rates and forecasts of income and value.
• Historical relationships of real estate yield to other investment yields.
• Surveys of investor expectations.

Transparency in assumptions is the strength of a DCF model. However, unrealistic assumptions can become its weakness.

Analysis of Income-Capitalization Methods:

Characteristic	Detail DCF	Ratio Models (GIM)
Transparency	Explicit	Implicit
Testability on Market	More Complex	Easier "Mark to Market"
Business Valuation	Free cash-flows model	Gross operating profit and turnover capitalization

4.3 Cost Approach

The cost approach determines the value by adding the reproduction (or replacement) cost of the property's improvements (as if new) to the accrued depreciation of the improvements and the land value.

Value = Reproduction/Replacement cost - accrued depreciation + land value

The cost approach has its limitations because it does not consider the effect of:
* Loss of utility.
* Change in tenant requirements.
* Depreciation of older properties.
* Friction between technical and economic lifespan.

5. Comparison of Valuation Methods

Factor	Income Capitalization Methods	Business Valuation Related Methods	Residual (Land) Valuation	Cost-Based Methods
Detail	DCF Model	DCF Models (future value-basis)		Explicit DRC (components)
Transparency	Ratio Models (GIM)	Gross operating profit and turnover capitalization	Land residual (nominal basis)	Implicit DRC (comparative units)
Testable on Market Conformity			Sales comparison

6. Challenges Ahead

Principles of real estate appraisal are relatively constant, but applications change. For example:

Green Buildings: Dealing with split incentives between landlords and tenants regarding energy efficiency and the impact of longer economic life in different locations.

Declining demand for office space: Due to budget cuts and remote working.

These challenges require appraisers to stay updated with market developments.

ملخص:

Summary

This chapter explores the transition from determining the residual value of land to understanding the broader concept of business value within real estate valuation. It delves into various allocation and appraisal methods necessary for this transition, highlighting their strengths, weaknesses, and appropriate applications.

• The residual method, used to derive land value, is highly sensitive to input uncertainties. Small changes in income or cost assumptions can lead to disproportionately large fluctuations in the residual value.
• Apportionment is crucial for allocating value among different components of a property or business, such as land and improvements, leasehold and leased fee interests, or tangible and intangible assets. It emphasizes the importance of defining the marketable entity for valuation.
• The chapter demonstrates that different logical and consistent apportionment methods can be valid, even without direct market validation, as long as the sum of the parts equals the market value of the whole.
• Business value goes beyond the physical property and includes operational aspects like brand, personnel, and stock. Valuing the business enterprise necessitates allocation of value to different assets, leading to the concept of goodwill, which can be attached to the property or the user.
• The chapter differentiates between property valuation and business valuation, noting that property valuers typically handle trading properties due to the significant portion of value attributable to real estate and the applicability of the comparison method.
• The three traditional appraisal approaches - sales comparison, income capitalization, and cost approach - are discussed. The sales comparison approach relies on finding comparable properties and adjusting for differences. The income capitalization approach relates value to the income it is expected to generate, whereas the cost approach depends on the replacement costs of the property as if new accrued depreciation of the improvements plus land value
• The income capitalization approach consists of a ratio model and a discounted cash-flow (DCF) model. The DCF model bases the value estimate on explicit forecasts of income and costs over the entire holding period of a property.