Capitalization Rates & Income Patterns

Chapter X: Capitalization Rates & Income Patterns

This chapter delves into the intricate relationship between capitalization rates and income patterns in real estate valuation. We’ll explore various income pattern models and their impact on capitalization rate selection and application. Understanding these concepts is crucial for accurate property valuation, especially when employing income capitalization techniques.

1.0 Introduction to Income Patterns

Real estate income rarely follows a perfectly stable trajectory. Understanding the anticipated income pattern is vital for selecting the appropriate valuation method and interpreting capitalization rates.

1. 1 Types of Income Patterns

   1. 1. 1 Level Income: This assumes a constant net operating income (NOI) throughout the projection period. It’s simplest but rarely reflects real-world scenarios.
   2. 1. 2 Straight-Line Income Change: Income increases or decreases by a fixed amount each period. This linear progression simplifies calculations but might not capture market dynamics accurately.
   3. 1. 3 Exponential Curv❓❓e (Constant-Ratio) Income Change: Income changes by a constant percentage each period, reflecting growth or decline. This is often a more realistic assumption than straight-line changes.
   4. 1. 4 Variable or Irregular Income: Income fluctuates unpredictably, demanding detailed period-by-period analysis using Discounted Cash Flow (DCF) techniques.

2.0 Capitalization Rates and Straight-Line Income Patterns

Straight-line capitalization assumes a linear change in income and, often, value. This approach simplifies valuation but has limitations.

1. 1 Straight-Line Recapture:

   The Appraisal of Real Estate provides us with valuable insights in straight-line capitalization. The text states, “the straight-line capitalization procedure reflects some useful mathematical relationships: First Period Return on Investment = Original Value x Yield Rate Periodic Change in Value = Original Value x Periodic Rate of Change Periodic Change in Income = Periodic Change in Value x Yield Rate When the decline in income and value reflects these relationships, the periodic rate of change is the recapture rate and the reciprocal of the recapture rate is the economic life.” This means, that the investor receives a return on capital as well as a return of capital. We can see from the PDF provided, that the straight-line capitalization rate is simply a combination of the yield rate and the straight-line rate of change.
   2. 2 Mathematical Formulation:

   The capitalization rate (R) can be expressed as:

   R = Y − Aₐ

   Where:

   Y is the yield rate (discount rate).
   A is the total relative change in value over n periods (e.g., a 25% decline would be A = -0.25).
   a = 1/n is the periodic rate of change (the straight-line recapture rate).
   3. 3 Example:

   Suppose a property generates a first-year NOI of $19,000. The income and value are expected to decline linearly, with the property’s value decreasing by 25% over 10 years. An investor requires a 12% yield.

   A = -0.25
   a = 1/10 = 0.1
   Y = 0.12

   R = 0.12 - (-0.25 * 0.1) = 0.12 + 0.025 = 0.145 or 14.5%

   Value = NOI / R = $19,000 / 0.145 = $131,034.48
   4. 4 Limitations:

   Straight-line assumptions are rarely realistic reflections of market behavior. Investors often anticipate non-linear income changes and value fluctuations.

3.0 Exponential Curve (Constant-Ratio) Income Patterns

This model assumes income and value change at a constant percentage rate.

1. 1 Formula:

   The capitalization rate (R) is calculated as:

   R = Y − CR

   Where:

   Y is the yield rate.
   CR is the compound rate of change (growth or decline) per period.
   If CR is positive (growth), R is lower. If CR is negative (decline), R is higher.
   2. 2 Frozen Cap Rate:

   When income and value change at the same compound rate, the capitalization rate remains constant, leading to the term “frozen cap rate.”
   3. 3 Example:

   A property generates a first-year NOI of $50,000. Income and value are expected to grow at a constant rate of 2% per year. An investor demands an 11% yield.

   Y = 0.11
   CR = 0.02

   R = 0.11 - 0.02 = 0.09 or 9%

   Value = NOI / R = $50,000 / 0.09 = $555,555.56
   4. 4 Rearranging the formula:

   Y = R + CR

   This shows that the yield rate equals the capitalization rate plus the periodic change rate.

4.0 Variable or Irregular Income Patterns

When income streams are unpredictable, DCF analysis is crucial.

1. 1 Discounted Cash Flow (DCF) Analysis:

   Each projected benefit (income and reversion value) is individually discounted back to its present value. This method allows for irregular income patterns and varying discount rates.
   2. 2 Formula:

   Present Value (PV) = Σ [CFt / (1 + r)t] + [RV / (1 + r)n]

   Where:

   CFt is the cash flow in period t.
   r is the discount rate.
   t is the period number.
   RV is the reversion value (sale price) at the end of the holding period (n).
   n is the total number of periods in the projection.
   Σ denotes the sum of all periods.

5.0 Level-Equivalent Income

Any income pattern can be converted to a level-equivalent income for simplified valuation.

1. 1 Process:

   1. Calculate the present value of the actual cash flows.
   2. Calculate the level payment (annuity) that has the same present value over the same period.
   3. 2 Example:

   A property has NOI growing at 4% per year, starting at $200,000. The value is expected to increase by 15% over a five-year period. The yield rate is 12%.

   1. Projected NOIs: $200,000, $208,000, $216,320, $224,973, $233,972.

   2. Present Value of Cash Flows (at 12%): $774,096.

   3. Level-Equivalent Income: $774,096 * (installment to amortize one factor, 0.277410) = $214,742

   4. Capitalization Rate:

      R = Y − Aₐ = 0.12 − 0.15 * (sinking fund factor, 0.157410) = 0.096389

   5. Value = $214,742 / 0.096389 = $2,227,879

   6. 3 Financial Calculator Use:

   Financial calculators can streamline level-equivalent income calculations. The provided text mentions specific keystrokes for HP calculators to calculate NPV and then solve for PMT (payment), which represents the level equivalent income.

6.0 Discounted Cash Flow (DCF) Analysis and Investment Analysis

DCF analysis is a powerful tool for valuing properties with any income pattern, particularly complex or irregular ones.

1. 1 Applicability:

   • Determines present value given a rate of return.
   • Extracts a yield or discount rate from comparable sales.
     2. 2 Process:
   1. Develop detailed spreadsheets projecting incomes, expenses, and cash flows over the ownership period.
   2. Discount cash flows (including the net resale price) at an appropriate rate to derive present value.
   3. 3 Considerations:
   • Consistency: Data on cash flows, compounding, and discounting must be consistent with market practices.
   • Frequency: Discounting frequency (annual, monthly, etc.) should reflect investor behavior.

2. 4 Investor Expectations:

   DCF analysis should identify and incorporate investors’ expectations on the appraisal date.

7.0 Investment Analysis

DCF techniques are also used to evaluate real estate investment performance.

1. 1 Key Measures:

   • Net Present Value (NPV)
   • Internal Rate of Return (IRR)
   • Payback Period
   • Profitability Index (Benefit/Cost Ratio)
   • Time-Weighted Rate of Return
     2. 2 Forecasting:

   Forecasting is a crucial part of Investment Analysis and DCF analysis. The provided text discusses forecasting categories to be addressed in DCF analysis which include, current market rental rates, lease expiration dates, and expected rental rate changes, Lease concessions and their effect on market rent, Existing base rents and contractual base rent adjustments, Lease extensions and renewal options, Existing and anticipated expense recovery (escalation) provisions, Tenant turnover, Vacancy loss and collection allowance, Operating expenses and changes over the projection period, Net operating income, Capital items including leasing commissions and tenant improvement allowances, Reversion and any selling or transaction costs and a discount or yield rate (or rates).

8.0 Net Present Value (NPV) and Internal Rate of Return (IRR)

These are two key DCF models for measuring investment performance.

1. 1 Net Present Value (NPV):

   NPV = PV of Positive Cash Flows − PV of Negative Cash Flows (Capital Outlays)
   If NPV > 0: Investment exceeds return requirements.
   If NPV < 0: Investment does not meet return requirements.
   If NPV = 0: Investment meets return requirements exactly.
   2. 2 Internal Rate of Return (IRR):

   The discount rate that makes NPV equal to zero. It represents the actual rate of return generated by the investment.

9.0 Conclusion

Understanding the relationship between capitalization rates and income patterns is paramount for accurate real estate valuation. While simplified models like straight-line capitalization have their place, DCF analysis offers greater flexibility and realism when dealing with variable or complex income streams. By carefully considering income patterns and utilizing appropriate valuation techniques, appraisers can provide well-supported and credible value opinions.