Direct Capitalization Rate Derivation

Chapter: Direct Capitalization Rate Derivation

Introduction

Direct capitalization is a valuation technique used to convert a single year’s income expectancy into an estimate of value. This chapter will delve into the methods used to derive the capitalization rate (cap rate), a critical component of direct capitalization. We will explore various techniques, including extraction from comparable sales, the band of investment method, and the debt coverage formula, examining the scientific principles and mathematical relationships underpinning each approach.

1. Derivation of R_O from Comparable Sales

1.1 The Concept of Direct Extraction

The most straightforward method for deriving the overall capitalization rate (R_O) is to analyze comparable sales. This involves identifying properties similar to the subject property that have recently sold and for which reliable income and expense data are available.

1.2 The IRV Formula

The foundation of this method lies in the fundamental IRV formula:

I = R x V

Where:
I = Net Operating Income (NOI) for the following year of sale
R = Capitalization Rate (R_O)
V = Sale Price of the Comparable Property

Rearranging the formula to solve for R:

R_O = I / V

This formula states that the capitalization rate is simply the ratio of the property’s net operating income to its sale price.

1.3 Steps in Derivation

1. Identify Comparable Sales: Select properties that are similar to the subject in terms of location, property type, size, age, condition, and use.
2. Gather Data: Collect verified sale prices and detailed income and expense statements for the comparable properties. It’s crucial to obtain data for the year following the sale date to reflect the income stream a new investor would expect.
3. Calculate NOI: Carefully calculate the Net Operating Income (NOI) for each comparable by subtracting total operating expenses from total revenue. Ensure consistent expense categories across all comparables and the subject property. This is especially important when considering reserves for replacement or tenant improvements.
4. Calculate R_O: Divide the NOI of each comparable by its sale price to determine its capitalization rate.
5. Reconcile and Select Rate: Analyze the range of R_O values obtained from the comparables. Consider factors such as property characteristics, market conditions, and data reliability to reconcile the differences and select the most appropriate R_O for the subject property. Weight the R_O based on the comparables’ similarities to the subject.

1.4 Potential Issues and Adjustments

• Differences in Income Potential: If comparable properties have significantly different income growth potential compared to the subject, the extracted R_O may be skewed. For example, if the subject property has a lease with built-in rent increases while the comparables have level rents, an adjustment is needed.
• Expense Ratio Discrepancies: Ensure the expense ratio (Total Expenses / Total Income) is considered. While the R_O calculation is based on NOI, differing expense ratios can indicate varying management efficiencies or deferred maintenance, requiring further investigation.
• Data Verification: Always verify the accuracy of the data obtained from comparable sales. Inaccurate or incomplete information can lead to a misleading R_O.

1.5 Practical Application

Suppose three comparable properties sold recently with the following data:
| Property | Sale Price (V) | NOI (I) | R_O (I/V) |
|—|—|—|—|
| Comp 1 | $1,000,000 | $80,000 | 8.0% |
| Comp 2 | $1,200,000 | $90,000 | 7.5% |
| Comp 3 | $900,000 | $75,000 | 8.3% |

The R_O range is 7.5% to 8.3%. After analyzing the properties, you determine that Comp 3 is most similar to the subject. You might select an R_O of 8.2% for the subject property, slightly lower than Comp 3’s to account for market changes.

2. Derivation of R_O Using the Effective Gross Income Multiplier (EGIM) and Net Income Ratio (NIR)

2.1. Relationship between EGIM, NIR, and R_O

An alternative to direct extraction is using the Effective Gross Income Multiplier (EGIM) and the Net Income Ratio (NIR). The relationship is expressed as:

R_O = NIR / EGIM

2.2. Explanation of EGIM and NIR

• EGIM: The Effective Gross Income Multiplier is the ratio of the sale price to the effective gross income (EGI). EGI is the potential gross income less vacancy and collection losses.
• NIR: The Net Income Ratio is the ratio of the Net Operating Income (NOI) to the Effective Gross Income (EGI). It reflects the proportion of gross income remaining after operating expenses are paid.

2.3. Calculation Example

Assume a comparable property has an EGIM of 6 and an expense ratio of 40%.

1. Calculate NIR:
   Since Expense Ratio = (Total Expenses / Effective Gross Income), then:

   NIR = 1 - Expense Ratio
   NIR = 1 - 0.40 = 0.60

2. Calculate R_O:

   R_O = NIR / EGIM
   *R_O = 0.60 / 6 = 0.10 or 10%

2.4 Limitations

While this technique is valid, it’s less commonly used because if you have the EGIM and expense data to calculate the NIR, you likely already have enough information to directly calculate the NOI and extract the R_O as described in Section 1.

3. Derivation of R_O by Band of Investment - Mortgage and Equity

3.1 The Band of Investment Concept

The band of investment technique is based on the premise that the overall capitalization rate is a weighted average of the capitalization rates required by the different components of capital invested in the property – typically the mortgage and equity.

3.2 The Formula

R_O = (M x R_M) + ((1 - M) x R_E)

Where:
M = Loan-to-Value Ratio (LTV) - the proportion of the property value financed by a mortgage.
R_M = Mortgage Constant - the ratio of annual debt service to the original loan amount.
R_E = Equity Capitalization Rate (Equity Dividend Rate) - the ratio of pre-tax cash flow to equity invested.

3.3 Calculation of R_M

The mortgage constant (R_M) can be calculated using a financial calculator or a spreadsheet program using the following steps. Given, i the periodic interest rate and n the number of periods:
R_M = i / (1-(1+i)^-n)
Often, the periodic interest rate is the monthly interest rate and the number of periods is the number of months in the mortgage period. R_M is the mortgage constant, which represents the annual debt service divided by the initial loan amount.

3.4 Steps in Derivation

1. Determine LTV (M): Obtain the typical loan-to-value ratio for similar properties in the market. This information can be gathered from lenders, brokers, or market surveys.
2. Determine Mortgage Constant (R_M): Obtain the prevailing mortgage interest rate and loan term (amortization period) from lenders. Calculate the mortgage constant (R_M) using the formula above.
3. Determine Equity Capitalization Rate (R_E): This is the most subjective part of the process. R_E represents the rate of return an investor expects on their equity investment. It’s influenced by factors such as the perceived risk of the investment, alternative investment opportunities, and investor preferences. R_E can be estimated through market surveys, interviews with investors, or analysis of comparable sales.
4. Calculate R_O: Plug the values for M, R_M, and R_E into the formula to calculate the overall capitalization rate.

3.5 Example

Assume the following:
* LTV (M) = 70%
* Mortgage Interest Rate = 6% per year, compounded monthly
* Loan Term = 25 years (300 months)
* Equity Capitalization Rate (R_E) = 12%

1. Calculate Mortgage Constant:

   Using the formula R_M = i / (1-(1+i)^-n) where i = 0.06/12 = 0.005 and n=300. R_M = 0.005 / (1- (1.005)^-300 ) = 0.006443. Multiplying by 12 yields the annual R_M = 0.0773.

2. Calculate R_O:
   R_O = (0.70 x 0.0773) + (0.30 x 0.12)
   *R_O = 0.0541 + 0.036 = 0.0901, or 9.01%

3.6 Limitations

• Subjectivity of R_E: Estimating the equity capitalization rate (R_E) can be challenging, as it is influenced by various subjective factors. A small change in R_E can have a significant impact on the calculated R_O.
• Market Fluctuations: Interest rates and investor expectations can change over time, affecting the mortgage constant and equity capitalization rate, thus influencing the derived R_O.

4. Derivation of R_O by Band of Investment - Land and Building (Residual Techniques)

4.1 Theoretical Basis

This approach divides the property into its land and building components and assigns separate capitalization rates to each. It’s based on the idea that land and buildings have different risk profiles and therefore require different rates of return.

4.2 The Formula

R_O = (L x R_L) + (B x R_B)

Where:
L = Land Ratio (Value of Land / Total Property Value)
R_L = Land Capitalization Rate
B = Building Ratio (Value of Building / Total Property Value) = 1 - L
R_B = Building Capitalization Rate

4.3 Steps in Derivation

1. Determine Land Ratio (L) and Building Ratio (B): Estimate the relative value of the land and building components. This can be done through cost approach analysis, market extraction, or allocation methods.
2. Determine Land Capitalization Rate (R_L): Estimate the appropriate capitalization rate for the land. This can be derived from comparable land sales or based on the return required for alternative land investments.
3. Determine Building Capitalization Rate (R_B): Estimate the appropriate capitalization rate for the building. This can be derived from comparable building sales or based on the return required for similar building investments. Typically, R_B is higher than R_L due to the depreciating nature of the building.
4. Calculate R_O: Plug the values into the formula to calculate the overall capitalization rate.

4.4 Example

Assume a property has a 20:80 land-to-building ratio.
* Land Ratio (L) = 0.20
* Building Ratio (B) = 0.80
* Land Capitalization Rate (R_L) = 7%
* Building Capitalization Rate (R_B) = 10%

R_O = (0.20 x 0.07) + (0.80 x 0.10)
R_O = 0.014 + 0.08 = 0.094, or 9.4%

4.5 Limitations

• Theoretical Nature: This method is theoretical since properties are sold and appraised as a whole, not as separate land and building components.
• Subjectivity of Allocation: Accurately allocating value between the land and building can be challenging.

5. Derivation of R_O Using the Debt Coverage Formula

5.1 The Lender’s Perspective

This method, also known as the mortgage underwriter’s method, derives the R_O based on the lender’s required debt coverage ratio (DCR) and loan terms. It reflects the lender’s risk assessment and financing criteria.

5.2 The Formula

R_O = M x R_M x DCR

Where:
M = Loan-to-Value Ratio (LTV)
R_M = Mortgage Constant
DCR = Debt Coverage Ratio (NOI / Annual Debt Service)

5.3 Understanding Debt Coverage Ratio (DCR)

The debt coverage ratio (DCR) is a critical metric for lenders. It indicates the extent to which the property’s NOI can cover the annual debt service payments. A higher DCR indicates a lower risk of default.
DCR = NOI / ADS

5.4 Steps in Derivation

1. Determine LTV (M): Obtain the loan-to-value ratio offered by lenders for similar properties.
2. Determine Mortgage Constant (R_M): Obtain the mortgage interest rate and loan term from lenders and calculate the mortgage constant.
3. Determine Required DCR: Find out the minimum debt coverage ratio required by lenders for the specific property type and market conditions.
4. Calculate R_O: Plug the values into the formula to calculate the overall capitalization rate.

5.5 Example

Assume the following:
* LTV (M) = 75%
* Mortgage Interest Rate = 8% per year, compounded monthly
* Loan Term = 20 years
* Required DCR = 1.25

1. Calculate Mortgage Constant: Using the formula R_M = i / (1-(1+i)^-n) where i = 0.08/12 = 0.006667 and n=240. R_M = 0.006667 / (1- (1.006667)^-240 ) = 0.008364. Multiplying by 12 yields the annual R_M = 0.1004

2. Calculate R_O:

R_O = 0.75 x 0.1004 x 1.25
R_O = 0.0941, or 9.41%

5.6 Limitations

• Lender’s Perspective Only: This method relies solely on the lender’s perspective and doesn’t directly incorporate the buyer’s or seller’s expectations.
• Market Inconsistencies: Debt coverage ratios can vary significantly between lenders, potentially leading to inconsistencies in the derived R_O.
• Favorable Lending Terms: If favorable lending terms are used, the equity investor must factor these into their decision to purchase, and the analysis should be liberal accordingly.

6. Surveys and Market Data

6.1 The Role of Market Surveys

Appraisers often rely on capitalization rate surveys published by real estate research firms and industry organizations. These surveys provide a snapshot of market trends and investor expectations, offering valuable support for R_O estimations.

6.2 Considerations When Using Survey Data

• Source Reliability: Evaluate the credibility and methodology of the survey provider.
• Data Relevance: Ensure the survey data is relevant to the specific property type, location, and market conditions.
• Derivation Methods: Understand the method used to derive the reported rates (e.g., average, median, weighted average).
• Local vs. National Data: Recognize the limitations of using national data in a local market analysis.

6.3 Gathering Information from Market Participants

Directly questioning real estate brokers about capitalization rates they observe in sales of income-producing properties in a specific market is another source of information.

Conclusion

Deriving an appropriate capitalization rate is a critical step in the direct capitalization process. This chapter has explored several methods, each with its own strengths and limitations. The most reliable approach involves a thorough analysis of comparable sales, combined with a careful consideration of market conditions, investor expectations, and financing parameters. Ultimately, the selected R_O should be well-supported and reflect a comprehensive understanding of the subject property and its market environment.