Capitalization & Discounting: Yield Analysis

Chapter: Capitalization & Discounting: Yield Analysis

Introduction

This chapter delves into the crucial aspect of yield analysis within real estate valuation, focusing on how capitalization rates and discounted cash flow (DCF) techniques are employed to derive meaningful insights into investment returns. We will explore the scientific theories and principles underpinning these methodologies, along with practical applications and illustrative examples.

1. Fundamentals of Yield Analysis

1.1 Defining Yield:

Yield, in the context of real estate, represents the return on investment (ROI) expressed as a percentage of the property’s value or cost. It reflects the income-generating capacity of a property relative to its price. Yield analysis is paramount to informed decision-making in real estate investments.

1.2 Core Principles:

• Time Value of Money: This foundational concept dictates that money received today is worth more than the same amount received in the future due to its potential earning capacity.

• Risk and Return: Higher perceived risk typically necessitates a higher required yield to compensate investors for the increased uncertainty.

• Opportunity Cost: The yield should exceed the returns available from alternative investments with similar risk profiles.

2. Capitalization Rate (Cap Rate) Analysis

2.1 Definition and Formula:

The capitalization rate (R) is a ratio that expresses the relationship between a property’s net operating income (NOI) and its value (V):

R = NOI / V

Where:
NOI = Gross Operating Income - Operating Expenses
V = Property Value

2.2 Components of the Capitalization Rate:

The cap rate can be deconstructed into its fundamental components: yield rate (Y) and capital recovery rate (Recapture Rate). In simplest terms with straight-line capital recovery, the formula is:

R = Y + Recapture Rate

• Yield Rate (Y): Represents the investor’s required rate of return on their invested capital. It reflects the opportunity cost of capital and the perceived risk associated with the investment.

• Capital Recovery (Recapture) Rate: Accounts for the return of capital, reflecting the decrease in the asset’s value over time due to depreciation or obsolescence. This component represents the annual amount that must be earned to recover the initial investment.

2.3 Straight-Line Capitalization:

• Concept: Assumes a constant periodic decline in the value of the property over its economic life.

• Calculation: If the property has an original value of $50,000 and is expected to depreciate to $0 over 10 years, the annual recapture is $5,000.

  • Periodic Rate of Change in Value = Original Value * Periodic Rate of Change
  • Periodic Change in Income = Periodic Change in Value * Yield Rate

2.4 Limitations of Straight-Line Capitalization:

• Unrealistic Assumption: Rarely accurately reflects actual market behavior, where income and value changes are seldom linear.

• Overly Simplistic: Fails to account for factors like fluctuating market conditions, changing demand, and variable operating expenses.

2.5 Expanding the Straight-Line Concept:

The traditional concept of straight-line recapture can be expanded to remove some of its theoretical constraints and facilitate a broader range of practical applications. The expectation of a predictable decline in income can be expanded to include any predictable change, which allows an appraiser to consider growing assets as well as wasting assets. A predictable rate of change within the foreseeable future can also eliminate the need to consider the full economic life of a property. Although there are significant theoretical differences, the expanded straight-line concept corresponds mathematically to classic straight-line recapture.

Under both the expanded and classic straight-line concepts, changes in value and income are presumed to occur on a straight-line basis. The basic requirements for a satisfactory return on, and complete recovery of, invested capital are also preserved. However, the expanded concept does not require that capital be recaptured in annual installments throughout the economic life of a property. Rather, the property could be resold for a predictable amount at some point during its economic life, thereby providing for partial or complete return of the invested capital at the time of resale.

R = Y - (A/n)
Where:
R = Capitalization Rate
Y = Yield Rate
A = Relative change in value in ‘n’ periods
n = Number of periods

Example:
A leased fee interest that will produce income to the leased fee (Ilf) of $19,000 the first year. This income stream is expected to decline thereafter in the standard straight-line pattern and value is expected to fall 25% in 10 years. The anticipated income pattern must match up with the lease contract. To appraise the leased fee to yield 12%, the formula Rlf = Ylf — Alf /n is used, where the subscript LF denotes the leased fee.
R = 0.12 — (-0.25 x 0.1) = 0.145
Value = 19,000 / 0.145 = 131,034

2.6 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. Thus, A a can be replaced with the periodic compound rate of change (CR). The formula then becomes 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 If both income and value are expected to change at the same compound rate, the
capitalization rate is expected to remain constant. Therefore, this pattern of growth or decline is sometimes referred to as the frozen cap rate pattern.

R = Y - CR
Where:
R = Capitalization Rate
Y = Yield Rate
CR = Periodic compound rate of change

Example:
An income-producing property is expected to produce net operating income of $50,000 for the first year. Thereafter both net operating income and value are expected to grow at a constant ratio of 2% per year. In other words, 2% is the expected ratio of the increase in income for any year to the income for the previous year. The ratio of the increase in value for any year to the value for the previous year is also 2%. To appraise the property to yield 11%, the formula is
R =Y,- CR=0.11 — 0.02 = 0.09
Value = 50,000 / 0.09 = 555,556

3. Discounted Cash Flow (DCF) Analysis

3.1 Principles of DCF:

DCF analysis involves projecting future cash flows associated with a property and discounting them back to their present value using a specified discount rate. It explicitly accounts for the timing and magnitude of cash inflows and outflows.

3.2 Discount Rate Selection:

The discount rate is a critical input that reflects the investor’s required rate of return, taking into account the perceived risk of the investment and the opportunity cost of capital. The higher the perceived risk, the higher the discount rate.

3.3 DCF Formula:

The present value (PV) of a future cash flow (CF) is calculated as:

PV = CF / (1 + r)^n

Where:
r = Discount rate
n = Number of periods

The total present value of a stream of cash flows is the sum of the present values of each individual cash flow:

PV = ∑ [CFt / (1 + r)^t] (for t = 1 to n)

Where:
CFt = Cash flow in period t
r = Discount rate
t = Period number
n = Total number of periods

3.4 Application of DCF:

• Property Valuation: Estimating the present value of a property based on its projected future income stream and resale value (reversion).

• Investment Analysis: Evaluating the profitability of an investment by comparing the present value of its expected cash inflows to the initial investment cost.

4. DCF Analysis and 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

4.1 Net Present Value and the Internal Rate of Return
Net present value (NPV) and the internal rate of return (IRR) are two discounted cash flow models widely used to measure investment performance and develop decision-making criteria. Net present value (dollar reward) is the difference between the present value at a desired yield (discount) rate of all positive cash flows and the present value of all negative cash flows, or capital outlays. When the present value of the positive cash flows is greater than the present value of the negative cash flows or capital outlays, the investment exceeds the return requirements of the investor. If the reverse relationship exists (i.e., negative cash flows are greater than positive cash flows), the investment is not considered feasible at the desired yield, or at least not at the discount rate used to calculate present value. However, other investors may find the investment feasible.

A net present value of zero indicates that the present value of all positive cash flows equals the present value of all negative cash flows or capital outlays at the discount rate. The rate of discount that makes the net present value of an investment equal zero is the internal rate of return. In other words, the IRR is the rate that discounts all returns from an investment, including returns from its termination, to a present value that is equal to the original investment.

4.2 Calculating Level-Equivalent Income:
As noted previously, any pattern of income can be converted into a level-equivalent income. Therefore, the level income property model, R = Y — A Scan be used to solve for the value of any pattern of income once that income has been converted into its level equivalent.

4.2.1 Example:
An appraiser is valuing a property with net operating income of $200,000, growing at 4% per year. If the value is expected to increase 15% over a five-year projection period (A, = 15%) and the appropriate yield rate is 12%, the value can be calculated by first calculating the level-equivalent income and then dividing that income by an overall capitalization rate developed us- ing the level income property model.

• To calculate the level-equivalent income, first calculate the present value of the cash flows at the 12% yield rate:
  Year Net Income
  1 $200,000
  2 $208,000
  3 $216,320
  4 $224,973
  5 $233,972

• The net present value of the income stream at 12% is $774,096. This is easily converted to a level equivalent by multiplying it by the installment to amortize one factor, 0.277410.
  Level-Equivalent Income = $774,096 x 0.277410 = $214,742

• Next, the overall capitalization rate is developed using the level income property model.
  R, =Y, — Aa = 0.12 — 0.15(0.157410*) = 0.096389

• Sinking fund factor
• The value can then be obtained with the formula V = L as follows:
  y=$214.742
  ~ 0.096389 ~

5. Relationship between Cap Rate and DCF

Cap rates and DCF analysis are complementary techniques. The cap rate essentially represents a “snapshot” of yield at a specific point in time, while DCF provides a more comprehensive view of the investment’s performance over a longer period. A market-derived cap rate can be used to validate the terminal value assumption in a DCF model. The Gordon Growth Model is sometimes used to derive a terminal cap rate:

Cap Rate (Terminal) = Discount Rate - Terminal Growth Rate

6. Practical Considerations and Market Applications

6.1 Data Sources: Accurate and reliable data is essential for both cap rate and DCF analysis. Sources include market surveys, comparable sales data, appraisal reports, and financial statements.

6.2 Market Conditions: It’s crucial to consider prevailing market conditions, economic trends, and property-specific factors that can influence yields and discount rates.

6.3 Property Type: Different property types (e.g., office, retail, residential) typically exhibit varying risk profiles and, consequently, different yields.

6.4 Example Scenario:

Consider a commercial property with an NOI of $100,000 and a market cap rate of 8%. Using the cap rate formula (V = NOI / R), the estimated value is $1,250,000. A DCF analysis, projecting future cash flows and discounting them at a rate reflecting the property’s risk, can provide a more detailed valuation and assess the investment’s long-term profitability.

7. Common Mistakes and Pitfalls

7.1 Using Inappropriate Cap Rates: Applying cap rates from dissimilar properties or markets can lead to inaccurate valuations.

7.2 Overly Optimistic Projections: Making unrealistic assumptions about future income growth or expense reductions can inflate the results of a DCF analysis.

7.3 Ignoring Risk Factors: Failing to adequately account for risks associated with the property or market can result in an underestimation of the required yield or discount rate.

8. Conclusion

Yield analysis, through capitalization rates and discounted cash flow techniques, is a cornerstone of real estate valuation and investment decision-making. A thorough understanding of the underlying principles, appropriate application of the methodologies, and careful consideration of market conditions are essential for accurate and reliable results.