Discount Rate Application in Valuation Methodologies

Chapter 5: Discount Rate Application in Valuation Methodologies

Introduction

This chapter delves into the practical application of discount rates within various real estate valuation methodologies. A solid understanding of discount rate theory is crucial, but its effective implementation determines the accuracy and reliability of the final valuation. We will explore common techniques, their underlying principles, limitations, and relevant mathematical formulations.

5.1 Risk-Adjusted Discount Rate (RADR) Method

The Risk-Adjusted Discount Rate (RADR) is perhaps the most widely used method for incorporating risk into valuation. It adjusts the discount rate to reflect the perceived riskiness of the investment.

5.1.1 Principles of RADR

The core idea behind the RADR is that investors require a higher rate of return for investments with higher risk. This increased return compensates them for the potential of lower-than-expected cash flows or even total loss of investment.

Mathematically, the present value (PV) of a future cash flow (CF) is calculated as:

PV = CF / (1 + r)^n

where ‘r’ is the risk-adjusted discount rate, and ‘n’ is the number of periods in the future when the cash flow will be received.

A higher ‘r’ results in a lower PV, reflecting the increased risk associated with that future cash flow.

5.1.2 Components of the RADR

The RADR is typically composed of two main components:

• Risk-free rate (r_f): This represents the theoretical return on an investment with zero risk, usually proxied by the yield on government bonds with a similar maturity to the investment’s expected holding period.

• Risk premium (RP): This is the additional return required to compensate the investor for the specific risks associated with the real estate investment.

RADR = r_f + RP

The risk premium is determined based on a number of factors, including:

• property❓ type
• Location
• Tenant quality
• Lease terms
• Market conditions
• Economic outlook

5.1.3 Advantages and Disadvantages of RADR

Advantages:

• Simplicity: Relatively easy to understand and implement.
• Market Acceptance: Widely used and accepted by practitioners.
• Reflects Risk Aversion: Directly incorporates risk into the valuation process.

Disadvantages:

• Subjectivity: Determining the appropriate risk premium is highly subjective.
• Risk-Time Relationship: Assumes a constant risk premium over time, which may not be realistic. The impact of the discount rate exponentially decreases the weight of distant cash flows, while risk may not grow at an exponential rate.
• Potential for Double Counting: Risks already factored into cash flow projections❓❓ should not be double-counted by increasing the discount rate. For example, vacancy risk.
• Fails to properly flag risky elements: A single discount rate does not differentiate between the risk profiles of individual cash flows.

5.1.4 Practical Application and Experiment

Imagine two similar properties. Property A, leased to a credit-worthy tenant with a long-term lease, is assigned a risk premium of 2%. Property B, leased to a startup company with a short-term lease, is assigned a risk premium of 5%. If the risk-free rate is 3%, the discount rates would be 5% and 8% respectively.

Experiment: A sensitivity analysis could be performed. Varying the risk premium for Property B by +/- 1% and observing the impact on the present value provides insights into the sensitivity of the valuation to perceived risk.

5.2 Sliced Income Approach

The Sliced Income Approach addresses some of the limitations of the RADR by disaggregating the net cash flows into sets with different risk profiles and discounting them at different rates.

5.2.1 Principles of Sliced Income Approach

This approach acknowledges that not all cash flows associated with a real estate investment carry the same level of risk. For example, rental income secured by a long-term lease is generally considered less risky than the projected exit value, which is subject to market fluctuations.

5.2.2 Implementation

The cash flows are divided into “slices” based on their risk characteristics. For example:

1. Core Income Slice: Rental income during the initial lease term. Discounted at a lower rate (e.g., risk-free rate + small premium).
2. Reversionary Income Slice: Rental income after lease expiry and the exit value. Discounted at a higher rate reflecting market risk and re-leasing uncertainties.

The present value of each slice is calculated separately, and then summed to arrive at the total property value.

5.2.3 Advantages and Disadvantages

Advantages:

• More granular risk assessment.
• Allows for varying discount rates over time.
• Addresses the risk-time relationship more effectively than the single RADR.

Disadvantages:

• More complex to implement.
• Requires careful analysis to determine appropriate discount rates for each slice.
• Less commonly used in the property investment market, making it harder to compare valuations against market transactions.

5.2.4 Practical Application

Consider a property with a lease expiring in 5 years. The current rent is \$100,000 per year, and the projected exit value in 5 years is \$1,500,000.

1. Core Income Slice: Discount the \$100,000 annual rent for 5 years at a 6% discount rate.
2. Reversionary Income Slice: Discount the \$1,500,000 exit value at a 10% discount rate.

Summing the present values of both slices provides the total property value.

5.3 Certainty Equivalent (CE) Approach

The Certainty Equivalent approach directly adjusts the expected cash flows to reflect risk, rather than adjusting the discount rate.

5.3.1 Principles of Certainty Equivalent

The CE method asks: “What certain cash flow would an investor be willing to accept in lieu of a risky future cash flow?” This certain cash flow is the certainty equivalent. It aims to determine the investment’s prospective secure net cash flows. Standard deviations of the variable inputs to the DCF model are used to adjust the expected cash flows to a certain certainty level (e.g., 95%).

5.3.2 Implementation

1. Estimate Expected Cash Flows: Develop best-estimate cash flow projections.
2. Assess Risk: Identify the key risks affecting cash flows and quantify their potential impact (e.g., using sensitivity analysis or scenario planning).
3. Adjust Cash Flows: Reduce the expected cash flows to their certainty equivalents based on the assessed risk. This typically involves subtracting a risk premium from each cash flow.
4. Discount at the Risk-Free Rate: Discount the certainty equivalent cash flows at the risk-free rate.

PV = CE_CF / (1 + r_f)^n

5.3.3 Advantages and Disadvantages

Advantages:

• Forces explicit consideration of downside risks.
• May be more intuitive for some investors than adjusting the discount rate.

Disadvantages:

• Requires significant judgment in determining certainty equivalents.
• Less commonly used in real estate, which may limit its acceptance.
• Can be complex to implement, especially with multiple cash flows and risks.

5.3.4 Practical Application

Assume a project generates \$200,000 next year, but there is a 20% chance it will only generate \$100,000 due to economic uncertainty. An investor might determine that a guaranteed cash flow of \$170,000 is equally acceptable. The certainty equivalent is \$170,000. Using a risk-free rate of 3%, the present value is \$170,000 / (1.03)^1 = \$165,048.54

5.4 RADR vs. Certainty Equivalent

Both RADR and Certainty Equivalent methods aim to achieve the same goal: to account for risk in the valuation process. In theory, they should produce similar net present values (NPVs) if applied consistently.
Adjust discount rate for risk: RADR
Use net cash flows before risk adjustment: RADR
Use risk-free rate as discount rate: Certainty equivalent
Use net cash flows that are certain: Certainty equivalent

The choice between the two often depends on the investor’s preference and the nature of the investment. RADR is simpler and more widely used, while CE requires a more explicit assessment of risk and adjustment of cash flows.

5.5 Unbundling a Valuation Yield to Derive the Implied Rate of Rental Growth

It is possible to reverse engineer a valuation to find the implied rental growth rate within.

5.5.1 Perpetuity Method

If we assume a constant rental income stream into perpetuity, we can use the following formula to calculate the implied growth rate❓❓ (g):

g = r - (NOI / Value)

Where:
r = discount rate
NOI = Net Operating Income
Value = the property value

5.6 Individual Investor’s Required Rate of Return

Different players in the property investment market have different approaches for arriving at their discount rate or target rate of return.

5.6.1 Institutions

Institutions like life insurance companies and pension funds often use opportunity cost, benchmarked against risk/return profiles of other investments like gilts (government bonds). A risk premium is added to the gilt yield, reflecting the specific risks of property (illiquidity, tenant default, etc.), and adjusted for property’s hedge against unexpected inflation.

5.6.2 Open-End Funds and Property Unit Trusts

These funds, attracting investment from private investors, often focus on initial yields exceeding short-term interest rates, emphasizing sustainable incomes and readily saleable properties, potentially de-emphasizing DCF approaches.

5.6.3 Core-Plus Investors

Core-plus investors seek higher returns (10-14%) by employing strategies such as gearing (leverage) and adding value through active management (re-letting, refurbishment). Again, care must be taken to ensure risks aren’t double counted in both the discount rate and cash flows.

5.6.4 Property Companies

Property companies aim to maximize shareholder wealth by exceeding their weighted average cost of capital (WACC). However, some may use the marginal cost of debt or target rates of return set by the board.

5.6.5 Corporate Occupiers

Large corporate occupiers often consider the property’s role in supporting business activities, using a WACC approach. Flexibility is also a key factor. Smaller occupiers might view property as a safe haven for surplus cash.

5.7 Payback and Discounted Payback

The payback method calculates how long it will take for the net cash flows from the investment to recoup the initial capital outlay. In the discounted payback approach, the cash flows are discounted using a discount rate (e.g. 20% or more) to reflect their increasing uncertainty in the future. The discounted net cash flows are deducted from the initial outlay and the time taken to recoup this sum is calculated.

5.8 Freehold Valuation Approaches

Freehold valuations are typically divided into three categories:

1. Properties let at open market rental value.
2. Properties that are under-rented.
3. Properties that are over-rented.

Each category requires a slightly different valuation approach to account for the varying rental income profiles.

5.8.1 Rack-Rented Investments

A rack-rented property is one where the current rent equals the market rent. The basic valuation formula assumes a perpetual income stream:

Value = Net Rent / Discount Rate

However, the discount rate (or “yield”) must be adjusted to reflect the lease term. Shorter lease terms generally require higher yields to compensate for increased risk.

5.8.2 Under-Rented Investments

Under-rented properties (where the passing rent is below market) can be valued using two main methods:

1. Layer Method: This involves valuing the “core” income (passing rent) separately from the “uplift” (difference between market rent and passing rent). Each layer is discounted at an appropriate rate, and the results are summed.
2. Term and Reversion Method: This method treats the term income (passing rent) as a secure, non-growth income stream, discounted at a lower rate. The reversionary income (market rent) is viewed as riskier and is discounted at a higher rate.

5.8.3 Over-Rented Investments

When a property is over rented the approach will change again in order to reflect the risks associated with that property, a more extensive account of this is beyond the scope of this chapter.

Conclusion

The application of discount rates in real estate valuation is not a simple matter of plugging numbers into a formula. It requires careful consideration of the specific risks and characteristics of the investment, as well as a thorough understanding of the underlying economic principles. By mastering the different valuation methodologies and their associated discount rate techniques, practitioners can produce more accurate and reliable valuations that reflect the true value of real estate assets.