Discount Rate Adjustments & Valuation Methodologies

1. Introduction

This chapter delves into the complexities of discount rate adjustments and their implications for real estate valuation methodologies. The selection and adjustment of discount rates are critical steps in discounted cash flow (DCF) analysis, which is a cornerstone of modern real estate valuation. We will explore the underlying scientific principles, practical applications, and potential pitfalls associated with different approaches.

2. The Risk-Adjusted Discount Rate (RADR) Approach

2.1. Overview

The Risk-Adjusted Discount Rate (RADR) approach is a widely used method that incorporates risk into the valuation process by increasing the discount rate applied to future cash flows. The premise is that riskier investments require a higher rate of return to compensate investors for the increased uncertainty.

2.2. Formula

The basic DCF formula using RADR is:

PV = Σ [CFt / (1 + r)^t]

Where:

• PV = Present Value
• CFt = Expected Cash Flow in period t
• r = Risk-Adjusted Discount Rate
• t = Time period

2.3. Determining the Risk Premium

The RADR is typically calculated by adding a risk premium to a risk-free rate:

r = rf + RP

Where:

• rf = Risk-free rate (e.g., yield on government bonds)
• RP = Risk premium

The risk premium reflects the incremental risk associated with the specific real estate investment compared to a risk-free investment. This premium considers factors such as:

• Market Risk: General economic conditions, interest rate fluctuations, and changes in investor sentiment.
• Property-Specific Risk: Location, tenant quality, lease terms, property condition, and potential for obsolescence.
• Liquidity Risk: The difficulty and potential cost of selling the property quickly.
• Management Risk: The competence and effectiveness of property management.

2.4. Limitations of the RADR Approach

• Subjectivity: Determining the appropriate risk premium is subjective and relies heavily on market data, comparable transactions, and the valuer’s judgment.
• Myopic Time Horizon: The RADR approach assumes that risk increases linearly with time. While distant cash flows are generally riskier, the exponential growth inherent in the discount rate may not accurately reflect the true pattern of risk. For example, a long-term lease to a creditworthy tenant may have low risk even for distant cash flows.
• Double Counting: A crucial pitfall is “double-counting” risk. If potential risks, such as vacancy periods or rent concessions, are already explicitly factored into the projected cash flows, the RADR should not be further increased to account for these same risks. This leads to an artificially depressed valuation.
• Mathematical complexities with unequal project lengths: Comparing projects with similar types of risks but unequal lengths is mathematically complex.

2.5. Example: RADR Calculation

Assume a risk-free rate of 3% (government bond yield) and a risk premium of 4% is deemed appropriate for a specific property.

r = 3% + 4% = 7%

Using this 7% discount rate, future cash flows are discounted to arrive at the present value of the property.

2.6. Experiment: Sensitivity Analysis of RADR

Conduct a sensitivity analysis by varying the risk premium within a plausible range (e.g., 3% to 5%) and observing the impact on the present value. This demonstrates the significant influence of the discount rate on the valuation outcome. Document the percentage change in value for each 0.5% change in the risk premium.

3. Sliced Income Approach

3.1. Overview

The sliced income approach addresses some limitations of the RADR by disaggregating the net cash flows into components with different risk profiles and applying different discount rates to each. This allows for a more nuanced assessment of risk.

3.2. Application

A common application is separating rental income from the terminal value (reversion). Rental income, particularly from long-term leases to strong tenants, may be considered relatively low-risk and discounted at a lower rate. The terminal value, which depends on future market conditions and may be subject to cyclical fluctuations, is considered higher risk and discounted at a higher rate.

3.3. Formula

The present value is calculated as the sum of the present values of each income slice:

PV = PV(Rental Income) + PV(Terminal Value)

Where:

PV(Rental Income) = Σ [Rental Income_t / (1 + r1)^t]
PV(Terminal Value) = [Sale Price / (1 + r2)^n]

• r1 = Discount rate for rental income
• r2 = Discount rate for terminal value
• n = Number of years in the projection period

3.4. Advantages

• Greater Accuracy: Better reflects the true risk profile of different cash flow components.
• Transparency: Clearly identifies the discount rates applied to each income stream.
• Flexibility: Adaptable to complex property situations with varying risk factors.

3.5. Disadvantages

• Complexity: Requires more detailed analysis and judgment to determine appropriate discount rates for each slice.
• Potential for Inconsistency: Ensuring consistency in the application of different discount rates across properties can be challenging.

3.6. Example: Sliced Income Valuation

Consider a property with annual rental income of $100,000 for the next 10 years and a projected sale price of $1,500,000 at the end of year 10. Assume a discount rate of 6% for rental income and 9% for the terminal value.

PV(Rental Income) = $100,000 * [1 - (1 + 0.06)^-10] / 0.06 = $736,009
PV(Terminal Value) = $1,500,000 / (1 + 0.09)^10 = $633,745

PV = $736,009 + $633,745 = $1,369,754

3.7. Hardcore Top Slice (Split Income)

This approach is used when the risk profile of the net rental income changes significantly at a future date, for instance, after the expiry of a lease for an older property. The rental income is then sliced into a “hardcore” stable portion and a “top slice” reflecting the higher risk associated with re-letting or repositioning the property.

4. Unbundling the Valuation Yield to Derive Implied Rental Growth

4.1. Concept

The overall valuation yield used in a direct capitalization approach implicitly incorporates expectations about future rental growth. It’s possible to “unbundle” this yield to estimate the market’s implied rate of rental growth.

4.2. Formula

In its simplest form (perpetuity with constant growth):

Yield = (NOI1 / Value) = r - g

Where:

• Yield = Capitalization Rate
• NOI1 = Net Operating Income in the first year
• Value = Property Value
• r = Discount Rate
• g = Implied Rental Growth Rate

Rearranging the formula to solve for g:

g = r - Yield

4.3. Example

If a property is valued using a capitalization rate (Yield) of 6% and the appropriate discount rate (r) is 8%, the implied rental growth rate is:

g = 8% - 6% = 2%

This suggests the market expects rents to grow at an average annual rate of 2% in perpetuity.

4.4. Considerations

This simple formula assumes constant growth to perpetuity. In reality, rental growth patterns are more complex, often involving periods of higher growth followed by stabilization. More sophisticated models are needed to account for these variations. The rent review pattern and required rate of return influence the rate of growth.

5. Individual Investor’s Required Rate of Return

Different investors have varying risk appetites, investment objectives, and access to capital, leading to diverse approaches in determining the appropriate discount rate.

• Institutions (Life Insurance Companies, Pension Funds): These entities often use the concept of opportunity cost. They compare the risk/return profile of real estate to alternative investments, particularly government bonds (gilts). They add a risk premium to the gilt yield, considering factors like illiquidity, tenant default risk, and potential for inflation hedging.
  • Prime property investments typically have a risk premium of 2% above gilt yields.
  • Institutions are careful to avoid double-counting risks if they are already explicitly accounted for in the net cash flows.
• Open-End Funds and Property Unit Trusts: These funds primarily attract investments from private investors. Fund managers often focus on initial yields that exceed short-term interest rates to remain competitive. They prioritize sustainable incomes (properties with strong tenants and long leases) and easily saleable properties. Some managers may not utilize DCF approaches, relying instead on initial yield comparisons.
• Core-Plus Investors: These investors target higher returns (10-14%) by combining gearing (leverage) with value-add strategies, such as re-letting or refurbishment. They are willing to accept higher risks, such as re-letting risk, to achieve their target returns. Again, double-counting of risks should be avoided.
• Property Companies: The objective of property companies is to maximize shareholder wealth. They often use the weighted average cost of capital (WACC) as their discount rate, reflecting the cost of both debt and equity. Some companies may erroneously use the marginal cost of debt or set target rates of return based on perceived achievable levels.
• Corporate Occupiers: Larger corporate occupiers tend to assess the value of property assets based on their contribution to the business, using a weighted average cost of capital approach. Flexibility is a crucial factor. Smaller corporate occupiers may see property as a safe haven for surplus cash or as collateral for future borrowing.

6. Payback and Discounted Payback

6.1. Overview

In cases with high-risk investments or significant uncertainties making accurate cash flow modelling challenging, the payback method or discounted payback method can be used.

6.2. Payback Method

Calculates the time required for the estimated net cash flows to recoup the initial capital outlay.

6.3. Discounted Payback Method

Discounts the cash flows (often at a high discount rate of 20% or more) to reflect increasing uncertainty in the future. The discounted net cash flows are deducted from the initial outlay, and the time to recoup the sum is calculated.

6.4. Limitations

Payback methods do not consider the time value of money (except in the discounted version) and ignore cash flows beyond the payback period. They are simplistic measures of risk and profitability.

7. Certainty Equivalent

7.1. Overview

Instead of adjusting the discount rate for risk, the certainty equivalent approach focuses on adjusting the expected cash flows to reflect their uncertainty. This involves reducing the cash flows to a level considered equivalent to a certain outcome.

7.2. Application

The certainty equivalent adjusts the expected cash flows to, for example, a 95% certainty level (two standard deviations).

7.3. Calculation

Certainty Equivalent Cash Flow = Expected Cash Flow - Risk Adjustment

The risk adjustment is based on the standard deviation of the variable inputs to the DCF model.

7.4. Formula

PV = Σ [CECFt / (1 + rf)^t]

Where:

• CECFt = Certainty Equivalent Cash Flow in period t
• rf = Risk-free rate

7.5. Risk Adjusted Discount Rate vs. Certainty Equivalent

These two approaches should produce similar net present values if the figures have been adjusted appropriately. The risk adjusted discount rate adjusts the discount rate for risk while using net cash flows before risk adjustment. The certainty equivalent approach uses a risk-free rate as a discount rate and net cash flows that are certain.

7.6. Advantages and Disadvantages

• Focus on Downside Risks: Forces investors to consider the potential negative outcomes.
• Complexity: Requires statistical analysis to estimate the standard deviations of cash flow components.
• Limited Use: Not commonly used in the property investment market, making it difficult to apply consistently.

8. Freehold Valuation Approaches

Valuation methodologies differ based on the rental status of the property. In each case the assumption is that today’s passing rent and today’s estimate of the open market rental value are used. Thus, growth (and risk) is implicit in the valuation yield.

8.1. Rack-Rented Investments

8.1.1. Definition

A rack-rented property investment is one where the net rent equals the market rental value.

8.1.2. Valuation Approach

The valuation formula assumes that the rental income flows to perpetuity. The valuer will adjust the yield to reflect the length of the unexpired term on the lease.

8.1.3. Short Lease Term

In situations with short lease terms and limited comparable evidence, an increase in the yield is typically applied to reflect the increased risk.

8.1.4. Alternative Valuation

An alternative valuation method is appropriate to cross check the valuation.

8.2. Under-Rented Investments

8.2.1. Definition

The passing rent is less than the open market rental value.

8.2.2. Valuation Approaches

Two main methodologies:

• Layer method: In the investment marketplace the layer method using one equivalent yield tends to be the preferred method, the reason being that as only one valuation yield is used it makes the analysis of comparable evidence and other market transactions simpler.
• Term and reversion: The term and reversion method treats the rentals according to their risk and growth characteristics and is thus a preferred method.

8.3. Over-Rented Investments

The over-rented nature of the property introduces specific risks related to potential future rental declines.

9. Conclusion

Discount rate adjustments and valuation methodologies are intertwined and critical for accurate real estate valuation. While the RADR approach remains widely used, understanding its limitations and exploring alternative methods like the sliced income approach and certainty equivalent is essential. The selection of an appropriate discount rate and valuation methodology requires careful consideration of the specific property, market conditions, and investor objectives. Ignoring the potential for double-counting risk is a significant pitfall that must be actively avoided.