Direct Capitalization: Rate Derivation & Application

Chapter: Direct Capitalization: Rate Derivation & Application

Introduction

Direct capitalization is a valuation technique used to convert an estimate of a single year’s net operating income (NOI) into an indication of value. This method is primarily applied to properties exhibiting stable income streams and predictable expenses. It relies on the principle that the value of an income-producing property is directly related to its capacity to generate income. It is expressed by the IRV Formula: Income = Rate * Value

Core Principles of Direct Capitalization

The foundation of direct capitalization rests upon the following principles:
* Stability of Income: The method assumes a relatively stable income stream in the near term. Significant fluctuations in income, due to factors like rapidly changing market conditions or lease terms, can reduce the reliability of the direct capitalization method.
* Single-Year Income Analysis: Direct capitalization focuses on a single year’s NOI. While this simplifies the analysis, it overlooks potential changes in income and expenses over time.
* Market Extraction of Rates: Capitalization rates are typically derived from comparable sales in the market, reflecting prevailing investor expectations and risk profiles.
* Ratio-Based Approach: Direct capitalization fundamentally relies on ratios, specifically the capitalization rate, which represents the relationship between income and value.

Derivation of Overall Capitalization Rate (RO)

The overall capitalization rate (RO) is a crucial component of direct capitalization. It reflects the overall rate of return an investor expects to receive from a property, considering both income and potential appreciation.

1. Direct Extraction from Comparable Sales

The most direct method of deriving RO involves analyzing recent sales of comparable properties. The formula is straightforward:
RO = NOI / Sale Price

Where:

• RO is the overall capitalization rate
• NOI is the net operating income of the comparable property for the year following the sale
• Sale Price is the price at which the comparable property was sold

Example:
A comparable property sold for $1,000,000 and had an estimated NOI of $80,000 for the following year. The RO would be:

RO = $80,000 / $1,000,000 = 0.08 or 8%

Challenges:

• Data Availability: Obtaining reliable NOI data for comparable sales can be challenging. Sales prices are public record, but NOI information is often private.
• Comparability Issues: Ensuring that the comparable properties are truly comparable to the subject property is critical. Differences in location, age, condition, lease terms, and other factors can skew the extracted RO. The subject’s and comparable properties should have very similar potential income. If the subject’s income changes by 4% per year and a comparable’s income stays the same due to a lease, without an adjustment, the properties are not comparable.

2. Derivation using Effective Gross Income Multiplier (EGIM) and Net Income Ratio (NIR)

An alternative approach involves utilizing the EGIM and NIR, which are market-derived ratios. The formula is:

RO = NIR / EGIM

Where:

• NIR is the net income ratio (NOI / Effective Gross Income)
• EGIM is the effective gross income multiplier (Sale Price / Effective Gross Income)

Example:
A property has an EGIM of 6.0 and an expense ratio of 40%. This means the NIR is 1 - 0.40 = 0.60. Therefore:

RO = 0.60 / 6.0 = 0.10 or 10%

3. Band of Investment Technique: Mortgage and Equity Components

This method partitions the RO into its mortgage and equity components, reflecting the capital structure of the investment. The formula is:

RO = (M * RM) + ((1 - M) * RE)

Where:

• M is the loan-to-value ratio (LTV)
• RM is the mortgage capitalization rate (mortgage constant)
• RE is the equity capitalization rate

The mortgage capitalization rate (RM) can be calculated by dividing the annual debt service (ADS) by the initial mortgage amount. It can also be calculated via financial calculator.

Example:
Assume a property has a loan-to-value ratio of 70%, a mortgage constant of 0.09 (9%), and an equity capitalization rate of 0.12 (12%). Then:
RO = (0.70 * 0.09) + (0.30 * 0.12) = 0.063 + 0.036 = 0.099 or 9.9%

Determining RM:

• Consult with lenders to determine current mortgage rates and terms.

• Use financial calculators to determine the annual mortgage constant (RM) based on the loan amount, interest rate, and loan term. If the lender quotes 10% annual rate with monthly payments for 25 years:

  Keystrokes Output

  25 g n 300.000000
  10 g i 0.833333
  1 PV 1.000000
  0 FV 0.000000
  PMT -0.009087

  RM = PMT × 12: Þ 12 = 0.10904

Determining RE:

• Requires careful market research. Look at equity dividend rates of comparable properties.
• It is affected significantly if there are substantial changes in the future.

4. Band of Investment Technique: Land and Building Components

This approach divides the RO into land and building components, reflecting the different risk and return characteristics of each asset. The formula is:

RO = (Land Ratio * RL) + (Building Ratio * RB)

Where:

• Land Ratio is the proportion of the property’s value attributable to the land
• RL is the land capitalization rate
• Building Ratio is the proportion of the property’s value attributable to the building
• RB is the building capitalization rate

Example:
A property has a land ratio of 20%, a land capitalization rate of 8%, and a building capitalization rate of 11%. The building ratio is 1 - 0.20 = 0.80. Therefore:

RO = (0.20 * 0.08) + (0.80 * 0.11) = 0.016 + 0.088 = 0.104 or 10.4%

5. Debt Coverage Ratio (DCR) Formula (Mortgage Underwriters Method)

This method, also known as the mortgage underwriters method, derives the RO based on mortgage lending criteria. The formula is:

RO = M * RM * DCR

Where:

• M is the loan-to-value ratio
• RM is the mortgage capitalization rate (mortgage constant)
• DCR is the debt coverage ratio (NOI / ADS)

Example:
A lender quotes a 75% loan-to-value ratio with a 9% mortgage and a DCR of 1.2. The annual mortgage constant is 0.10797. Therefore:

RO = 0.75 * 0.10797 * 1.2 = 0.09717 or 9.717%

Application of Direct Capitalization

Once the RO has been determined, it can be applied to the subject property’s NOI to estimate its value. The formula is:

Value = NOI / RO

Example:
A property has an estimated NOI of $90,000, and the derived RO is 0.09 (9%). The estimated value would be:

Value = $90,000 / 0.09 = $1,000,000

Considerations and Challenges

• Accuracy of NOI Estimate: The accuracy of the direct capitalization method is highly dependent on the accuracy of the NOI estimate. Thorough due diligence and market research are essential.
• Accounting for Reserves: Accounting for reserves for replacement and tenant improvement expenses is a common problem in the application of direct capitalization. If the list of expenses for the comparables includes line items for reserves and tenant improvement expenses, the same items should be included in the calculation of the subject property’s expenses. The reverse is also true.
• Market Conditions: Direct capitalization assumes a relatively stable market. Rapidly changing interest rates, vacancy rates, or rent levels can impact the accuracy of the valuation.
• Reconciling Multiple Rates: Appraisers are usually required to reconcile various capitalization rates found in the market.

Practical Applications and Related Experiments

1. Sensitivity Analysis:

• Purpose: To assess the impact of changes in NOI and RO on the estimated value.
• Method: Vary the NOI and RO within a reasonable range (e.g., +/- 5%) and observe the resulting changes in value.
• Expected Outcome: Demonstrates the sensitivity of the direct capitalization method to key variables.

2. Comparative Analysis of Different RO Derivation Methods:

• Purpose: To compare the ROs derived using different methods (e.g., direct extraction, band of investment).
• Method: Apply each method to the same set of comparable data and compare the resulting ROs.
• Expected Outcome: Provides insights into the strengths and weaknesses of each method and helps in selecting the most appropriate method for a given situation.

3. Case Study: Applying Direct Capitalization to a Small Apartment Building:

• Scenario: Evaluate a 20-unit apartment building with historical income and expense data.
• Steps:
  1. Gather market data on comparable apartment building sales.
  2. Extract ROs from the comparable sales.
  3. Derive RO using the band of investment technique (mortgage and equity).
  4. Reconcile the derived ROs and select the most appropriate rate.
  5. Estimate the subject property’s NOI.
  6. Apply the selected RO to the NOI to estimate the property’s value.
• Expected Outcome: A comprehensive valuation of the apartment building using the direct capitalization method.

Conclusion

Direct capitalization is a valuable tool for valuing income-producing properties. However, it is essential to understand its limitations and to use it in conjunction with other valuation methods, such as discounted cash flow analysis, to arrive at a well-supported value conclusion. The accurate derivation of the capitalization rate and a realistic estimate of the NOI are critical for the reliability of the method.