Capitalization & Discounting: Rate Selection & Application

Chapter 4: Capitalization & Discounting: Rate Selection & Application

Introduction

This chapter delves into the critical aspects of capitalization and discounting in real estate valuation, focusing on rate selection and application. We will explore the theoretical underpinnings and practical implications of these techniques, providing a comprehensive understanding of how to derive and utilize appropriate rates for accurate valuation.

4.1 Fundamental Principles of Capitalization and Discounting

Capitalization and discounting are fundamental techniques used to convert future income streams into a present value. Both rely on the principle that money has a time value, meaning that a dollar received today is worth more than a dollar received in the future.

• Capitalization: This process converts a single year’s income or an average income into value using a capitalization rate.
• Discounting: This process converts a series of future income streams and a reversion value into a present value using a discount rate. Discounting is the central component of Discounted Cash Flow (DCF) analysis.

4.2 Understanding Yield, Discount, and Capitalization Rates

Key to both methods is an understanding of Yield, Discount, and Capitalization rates and how they relate to the time value of money.

• Yield Rate (Y): The required rate of return on an investment, reflecting the investor’s opportunity cost❓ and perceived risk. It can also be described as an investors ‘Internal Rate of Return’ (IRR).
• Discount Rate (r): Used in DCF analysis to reflect the time value of money and risk associated with future cash flows. The difference between the yield rate and discount rate can be subtle, but it’s essential to understand how the market❓ perceives these rates.
• Capitalization Rate (R): A rate used to convert a single year’s income expectancy into an opinion of value. It is a function of the yield rate and expectations of future income patterns.

4.3 The Relationship Between Cap Rate, Yield Rate, and Growth

Capitalization rates are inversely related to property values and are affected by yield rates and growth expectations. Understanding the components of a capitalization rate helps to improve the accuracy of valuation. The most basic relation is:

• R = Y - g

Where:
* R is the Capitalization Rate
* Y is the Yield Rate
* g is the expected Growth Rate

4.4 Rate Selection Considerations

Selecting the appropriate capitalization or discount rate is crucial for accurate valuation. Factors to consider include:

1. Risk: Higher-risk investments require higher rates to compensate for the increased uncertainty. Sources of risk can be further be divided into:
   • Financial Risk - Leverage, refinancing risk, etc.
   • Liquidity Risk - Inability to quickly convert to cash
   • Management Risk - Competence of management to operate the property.
   • Business Risk - External factors affecting the specific property’s income stream.
2. Opportunity Cost: The return that could be earned on alternative investments.
3. Inflation: Expectations of future inflation can impact required rates of return.
4. Market Conditions: Prevailing interest rates, economic growth, and investor sentiment all influence rate levels.
5. Property-Specific Factors: Characteristics such as location, property type, tenant quality, and lease terms affect perceived risk and required returns.

4.5 Methods for Extracting Capitalization and Discount Rates

Several methods can be used to extract capitalization and discount rates from market data:

1. Market Extraction: Analyzing sales of comparable properties to derive implied rates.
   • Example: If a property with a Net Operating Income (NOI) of $100,000 sells for $1,000,000, the implied capitalization rate is $100,000/$1,000,000 = 10%.
2. Band of Investment: A technique that weighs the required returns of debt and equity to arrive at an overall rate.
   • Formula: R = (LTV * Mortgage Rate) + ((1 - LTV) * Equity Dividend Rate)
     • Where:
       • R = overall capitalization rate❓❓
       • LTV = Loan-to-Value Ratio
       • Mortgage Rate = Interest Rate on Debt Financing
       • Equity Dividend Rate = Required Return on Equity
   • Example: If LTV = 70%, Mortgage Rate = 6%, and Equity Dividend Rate = 10%, then R = (0.70 * 0.06) + (0.30 * 0.10) = 0.042 + 0.03 = 0.072 or 7.2%.
3. Surveys and Publications: Consulting industry surveys and publications that report market-derived rates.
4. Direct Comparison: Interviewing market participants such as investors and brokers.

4.6 Application of Capitalization Rates

The most common ways to apply capitalization rates are as follows:

1. Direct Capitalization:
   • Formula: Value = NOI / R
   • Where:
     • NOI = Net Operating Income
     • R = Capitalization Rate
   • Example: If a property has an NOI of $150,000 and a capitalization rate of 8%, the estimated value is $150,000 / 0.08 = $1,875,000.

4.7 Straight-Line Capitalization (Linear Projection)

This method assumes that income either declines (wasting asset) or grows (growing asset) at a constant rate over time. The method also assumes a constant recapture of capital. The text example uses the formula:

• R = Y - Aa

Where:

• A is the relative change in value in n periods
• a is 1/n

The text gives the example of a leased fee interest that will produce income (I_LF) of $19,000 the first year and decline. To appraise the leased fee to yield 12%, the formula is used, where the subscript LF denotes the leased fee.

R = 0.12 – (-0.25 x 0.1) = 0.145

Value = I_LF / R = $19,000 / 0.145 = $131,034

4.8 Exponential-Curve (Constant-Ratio) Changes in Income and Value

When both income and value are expected to change at a constant ratio, the capitalization rate can be determined without tables using the general formula R=Y—Aa where A a is the relative change in value and income for one period. The periodic compound rate of change (CR) can be used to replace A a in the following:

• R=Y-CR

Where Y is the yield rate per period and CR is the rate of change per period. An expected loss is treated as a negative rate of change, and the formula becomes:

• R=Y-(-CR) or R=Y+ CR

4.9 Discounted Cash Flow (DCF) Analysis

Discounted cash flow (DCF) analysis is an appropriate tool for valuing any pattern of regular or irregular income. The text examples give the formula:

• NPV = Σ CFt / (1 + r)^t

Where:

• NPV = net present value❓❓
• CFt = Cash Flow in Period t
• r = Discount Rate
• t = Time Period

4.10 Investment Analysis

In addition to developing an opinion of value or extracting a yield rate from comparable sales, discounted cash flow analysis techniques are often used to test the performance of real estate investments at a desired rate of return. Measures of investment performance include:

• Net present value
• Internal rate of return
• Payback period
• Profitability index (or benefit/cost ratio)
• Time-weighted rate

4.11 Challenges and Considerations

• Data Quality: Accurate income and expense data are essential for reliable rate derivation and application.
• Market Volatility: Rapidly changing market conditions can render rates obsolete quickly.
• Subjectivity: Rate selection involves a degree of professional judgment and can vary among appraisers.
• Terminal Value: Choosing an appropriate terminal value calculation for the last year of the DCF is critical. Typically this will be a straight capitalization formula: V = NOI / R

Conclusion

Selecting and applying appropriate capitalization and discount rates are fundamental to accurate real estate valuation. By understanding the theoretical principles, market dynamics, and methodological approaches discussed in this chapter, appraisers can develop well-supported and reliable value opinions. Continued education and awareness of market trends are essential for staying current in this critical area of valuation.