Income Stream Patterns and Reversion Valuation

Chapter: Income Stream Patterns and Reversion Valuation

Introduction

In the context of yield capitalization, understanding income stream patterns and reversion valuation is crucial for accurate property valuation. This chapter delves into the scientific principles underlying these concepts, providing a framework for analyzing various income stream patterns and estimating the reversion value of a property. Yield capitalization, at its core, relies on the principle of present value, where future income streams and the reversion are discounted back to their present worth using an appropriate discount rate (yield rate).

Different Rates

Discount rates are primarily a function of perceived risks. Different portions of forecast future income may have different levels of risk and therefore different yield rates. In lease valuation, for example, one rate might be applied to discount the series of net rental incomes stipulated in the lease, and a different rate might be applied to discount the reversion, which is known as the split-rate method or bifurcated method.

Income Stream Patterns

An appraiser should identify the pattern that the income stream is expected to follow during the projection period. These patterns may be grouped into the following basic categories:
* Variable annuity (irregular income pattern)
* Level annuity
* Increasing or decreasing annuity

1. Variable Annuity (Nonsystematic Change)

A variable annuity is characterized by payment amounts that vary in each period in a non-systematic way. This could be due to factors like fluctuating occupancy rates, unpredictable operating expenses, or market volatility.

• Valuation: To value a variable annuity, the present value of each individual income payment is calculated separately and then summed. This process is known as Discounted Cash Flow (DCF) analysis.

• Formula:

  PV = CF1 / (1 + r)^1 + CF2 / (1 + r)^2 + ... + CFn / (1 + r)^n

  Where:

  • PV = Present Value
  • CFt = Cash Flow in period t
  • r = Discount Rate
  • n = Number of periods
  • Practical Application: Consider a commercial property with fluctuating rental income due to lease expirations and renewals. The appraiser would project the specific rental income for each year of the projection period, considering potential vacancy and market rent changes, and then discount each year’s income back to its present value.

2. Level Annuity

A level annuity represents a stable income stream where the amount of each payment remains constant over time. This is often seen in properties with long-term leases and predictable operating expenses. There are two types of level annuities:
* Ordinary annuities
* Annuities payable in advance

• Formula (Ordinary Annuity):

  PV = PMT * [1 - (1 + r)^-n] / r

  Where:

  • PV = Present Value
  • PMT = periodic payment❓❓
  • r = Discount Rate
  • n = Number of periods

• Formula (Annuity Payable in Advance):

  PV = PMT * [1 - (1 + r)^-n] / r * (1 + r)
  Annuity Payable in Advance = Ordinary Annuity * (1 + r)
  Where:

  • PV = Present Value
  • PMT = Periodic Payment
  • r = Discount Rate
  • n = Number of periods

• Practical Application: A property leased to a national retailer under a long-term, triple-net lease with a fixed rental rate would generate a level annuity.

3. Increasing or Decreasing Annuity

An increasing or decreasing annuity involves an income stream that changes systematically over time. There are three basic patterns:

• Step-Up and Step-Down Annuities
• Straight-Line (Constant-Amount) Change per Period Annuities
• Exponential-Curve (Constant-Ratio) Change per Period Annuities

3.1. Step-Up and Step-Down Annuities

These annuities feature a series of level annuities of differing amounts paid across different periods within the lease term.

• Valuation: The present value of each level annuity segment is calculated separately using the level annuity formula and then summed to find the total present value.
• Practical Application: A lease agreement stipulating rent increases every few years (e.g., $500 for the first three years, $750 for the next four years, and $1,200 for the next six years).

3.2. Straight-Line (Constant-Amount) Change per Period Annuity

This pattern reflects an income stream that increases or decreases by a fixed amount each period.

• Formula:

  PV = (d + hn)anl - h(n - anl)/i

  where:

  • PV = Present value of the increasing/decreasing annuity
  • d = First payment
  • h = Constant periodic change in payment amount (positive for increasing, negative for decreasing)
  • n = Number of periods
  • i = Discount rate per period
  • anl = Present value of an annuity of $1 per period at rate i for n periods.

• Practical Application: An office building with a lease agreement specifying annual rent increases of $5,000.

3.3. Exponential-Curve (Constant-Ratio) Change per Period Annuity

This annuity exhibits income that increases or decreases at a constant ratio, leading to compounding increases or decreases. Also referred to as Exponential annuity

• Formula
  The formula for valuing a stream of income that increases or decreases at a constant rate “g” per period where g is the growth rate:
  PV = CF1 / (1+r) + CF1*(1+g)/(1+r)^2 + CF1*(1+g)^2/(1+r)^3 + ... + CF1*(1+g)^(n-1) / (1+r)^n
  If “g” is constant:
  PV = CF1 * [1 - ((1+g)/(1+r))^n] / (r-g)
  Where:

  • PV = Present Value
  • CF1 = Cash Flow in the first period
  • r = Discount Rate
  • g = Constant growth rate per period
  • n = Number of periods

• Practical Application: An apartment building in a rapidly growing area where rents are projected to increase by 5% annually.

Reversion Valuation

The reversion represents the anticipated return of capital at the end of the investment’s projection period. It’s essentially the future value of the property when it is sold. The length of the projection period and the discount rate are interactive. Generally, the longer the projection period, the greater the risk and the higher the discount rate.

Methods for Estimating Reversion Value

1. Terminal Capitalization Rate (Going-Out Cap Rate): Apply a capitalization rate (RN) to the projected net operating income (NOI) for the year following the end of the forecast period.

   • Formula:

     Reversion Value = NOI(n+1) / RN

     Where:

     • NOI(n+1) = Net Operating Income in the year after the projection period
     • RN = Terminal Capitalization Rate
       2. Projected Sales Price: Estimate the future sales price based on comparable sales data, market trends, and anticipated appreciation or depreciation.
       3. Constant Value: Assume the property value remains constant over the projection period. This is a conservative approach.

Factors Influencing Reversion Value

• Market Conditions: Supply and demand dynamics, interest rates, and economic growth all impact property values.
• Property Condition: The physical condition of the property and any deferred maintenance will affect its resale value.
• Lease Terms: The terms of existing leases, including rental rates and expiration dates, influence investor interest.
• Economic Life: The remaining economic life of the property impacts its long-term income-generating potential.
• Investor Expectations: Understanding market expectations for property value changes in the specific locale is crucial.
• Net Proceeds of Resale: An appraiser considers the net proceeds of resale refers to the net difference between a transaction price and the selling expenses, which may include brokerage commissions, legal fees, closing costs, transfer taxes.

Reversion and Yield

The reversion represents a significant❓ portion of the total return on investment. The effective rate of return on the investment will be negative if the investor’s capital is not recaptured through some combination of cash flow and reversion proceeds. For certain investments, all capital recapture is accomplished through the reversion, generally indicating higher risk. For other investment properties, part of the recapture is provided by the reversion and part is provided by the investment’s income stream.

Discounting Models

Specific valuation models or formulas, categorized as either income models or property models, have been developed for application to corresponding patterns of projected benefits.
Income models can be applied only to a stream of income. The present value of an expected reversion or any other benefit not already included in the income stream must be added to obtain the investment’s total present value. When a property model is used, an income stream and a reversion are valued in one operation.

Income Models

Valuation models can be applied to the following patterns of income:
* Variable or irregular income
* Level income
* Straight-line (constant-amount) change per period income
* Exponential-curve (constant-ratio) change per period income (i.e., the K factor)
* Level-equivalent income

Variable or Irregular Income

As mentioned previously, a discounting process or formula can be used to solve any present value problem. The present value of an uneven stream of income is the sum of the discounted benefits treated as a series of separate payments or reversions. This model simply totals all present values using the standard discounting formula.

Level Income

When a lease provides for a level stream of income or when income can be projected at a stabilized level, one or more capitalization procedures may be appropriate depending on the investor’s capital recovery expectations. Capitalization can be accomplished using what is known as capitalization in perpetuity. No income stream is perpetual, but the classic conception of an income stream capitalized in perpetuity is based on the assumption of an infinite level income stream.

Conclusion

Analyzing income stream patterns and accurately estimating the reversion value are critical components of yield capitalization. By understanding the underlying scientific principles, considering market dynamics, and applying appropriate valuation techniques, appraisers can arrive at reliable property valuations. The choice of which method is the best for a particular appraisal is based on the specific characteristics of the property, the nature of the income stream, and the available market data.