Leasehold Valuation: Traditional Methods and the Rise of DCF

Chapter: Leasehold Valuation: Traditional Methods and the Rise of DCF

Introduction

Leasehold valuation presents unique challenges compared to freehold valuation due to the finite nature of the lease term. This chapter will explore traditional methods used to value leasehold interests, focusing on the years purchase dual rate approach. We will then critically analyze the limitations of these methods and demonstrate the advantages of utilizing Discounted Cash Flow (DCF) analysis, a modern technique better suited for capturing the complexities of leasehold cash flows and risk.

6.1 Traditional Leasehold Valuation: An Overview

Historically, leasehold valuation relied on simplified models that primarily considered the profit rent (the difference between the rent received and the rent paid) and the remaining lease term. These methods aimed to provide a straightforward way to determine the capital value of the leasehold interest. A key aspect was the recognition that a leasehold is a wasting asset, whose value decreases over time as the lease term shortens.

6.2 The Years Purchase (YP) Dual Rate Method

The YP dual rate method was a dominant approach in traditional leasehold valuation. It recognizes that the investor requires both a return on their capital and a mechanism for the return of their capital at the end of the lease term. This is achieved by splitting the profit rent into two components: spendable income and a sinking fund contribution❓❓.

6.2.1 Principles and Rationale

The underlying principle is that the leasehold investor should be able to earn a competitive return on their investment while simultaneously accumulating funds to replace the capital invested at the end of the lease. This allows the investor, in theory, to reinvest in another leasehold interest of similar value, effectively maintaining their capital base. This approach was particularly relevant when rental growth❓ was considered minimal and reinvestment opportunities were readily available.

6.2.2 Mathematical Formulation

The YP dual rate formula is:

YP = 1 / (i + (SF_i))

Where:

• i = Remunerative rate (the desired rate of return on the investment, typically derived from the freehold all risks yield with an adjustment for the higher perceived risk of leasehold).
• SF_i = Annual sinking fund factor, calculated to accumulate to £1 at the end of the lease term at a safe, low-risk interest rate.

The annual sinking fund factor is calculated as:

SF_i = i / ((1 + i)ⁿ - 1)

Where:

• i = Sinking fund interest rate (typically a low, safe rate).
• n = Number of years remaining on the lease.

6.2.3 Derivation of the Annual Sinking Fund and Amount of £1 per Annum

Before delving into its application, it’s essential to understand the formula for the annual sinking fund (ASF) and its relationship with the “amount of £1 per annum” formula.

1. Amount of £1 per annum:
   This calculates the future value of investing £1 at the end of each year for n years, accumulating compound interest at a rate i. The formula is:

   Amount of £1 per annum = ((1 + i)ⁿ - 1) / i

   This formula essentially sums up the compound growth of each £1 invested over the respective years.
   For example, to calculate the future accumulations from investing £1 at the end of every year accumulating at compound interest of 5% for 10 years:

   ((1 + 0.05)¹⁰ - 1) / 0.05 = 12.578

2. Annual Sinking Fund (ASF):
   This calculates the annual sum needed to be invested at the end of each year to accumulate to £1 after n years at an interest rate i. It is the reciprocal of the “amount of £1 per annum”. The formula is:

   ASF = i / ((1 + i)ⁿ - 1)

   It determines the necessary savings amount per year to achieve a target future sum. This is crucial for the traditional leasehold valuation as it represents the portion of profit rent set aside to replace the original purchase price.

6.2.4 Practical Application and Example

Consider a leasehold property with a profit rent of £10,000 per annum and 15 years remaining on the lease. Assume a remunerative rate of 8% and a sinking fund rate of 3%.

1. Calculate the Annual Sinking Fund Factor (SF_i):

   SF_i = 0.03 / ((1 + 0.03)¹⁵ - 1) = 0.03 / (1.55797 - 1) = 0.0536

2. Calculate the Years Purchase (YP) Factor:

   YP = 1 / (0.08 + 0.0536) = 1 / 0.1336 = 7.485

3. Calculate the Capital Value:

   Capital Value = Profit Rent x YP = £10,000 x 7.485 = £74,850

In this example, the capital value of the leasehold interest is estimated at £74,850. This value reflects both the return on the investment (8% of £74,850) and the annual sinking fund contribution designed to recover the initial investment over the 15-year lease term.

6.2.5 Example with data from included PDF

(a) Value the head lessee’s interest for sale in the open market assuming comparable evidence indicates a freehold all risks yield of 6%.
(b) Show how both a return on and return of capital are achieved.
To reflect the additional risks of a leasehold interest a remunerative yield of 7% is adopted and a sinking fund of 4% (Table 6.7).

YP for 10 years at 7 + 4% = 1/(0.07+(0.04/((1+0.04)^10 -1))) = 6.5235

Net income received £12 000
Less ground rent payable £ 2 000
Profit rent £ 10 000
YP for 10 years at 7 + 4% × 6.5235
Capital value £65 235

Profit rent £10 000

Return on capital Return of capital
(spendable income) (sinking fund)
= £65 235 × 0.07 = £65 235 × ASF ten years at 4%
= £4 566.45 p.a. = £65 235 × 0.08329
= £5 433.42 p.a.

Annual sinking fund × amount of £1 p.a. 10 years at 4% £5433.42 p.a. × 12.006
Capital recouped £65 234*

6.3 Limitations of Traditional Methods

Despite its historical prevalence, the YP dual rate method suffers from several critical limitations, making it increasingly unsuitable for modern leasehold valuation:

1. Static Rental Growth Assumption: The most significant flaw is the assumption of constant rental values and yields throughout the lease term. This is rarely the case in reality, particularly with the prevalence of rent reviews and fluctuating market conditions. Inflation and rental growth significantly erode the real value of the sinking fund, meaning the investor will not be able to purchase an equivalent investment at the end of the lease.
2. Unrealistic Sinking Fund Rate: The low sinking fund rates used in the past (e.g., 2-4%) are often unrealistic in today’s investment climate. Investors typically seek higher returns, and borrowing costs are likely to exceed the sinking fund rate, making this strategy financially inefficient.
3. Ignores Investment Behavior: The model assumes that investors diligently set aside a portion of the profit rent into a sinking fund. In practice, investors are more likely to reinvest profits in other property ventures or use the income for other purposes, rendering the sinking fund concept irrelevant. Furthermore, the model fails to acknowledge investors typically hold a mixed portfolio of leasehold and freehold investments, and a dedicated sinking fund for each leasehold may not be a rational investment strategy.
4. Comparable Evidence Issues: Finding comparable leasehold transactions with similar characteristics (location, size, remaining term, rent levels) can be challenging, making it difficult to derive accurate remunerative rates. A simple 1-2% uplift on the freehold all-risks yield might not fully capture the specific risks associated with a particular leasehold.
5. Oversimplification of Cash Flows: The YP dual rate method treats the profit rent as a single, unchanging stream. It fails to account for potential rent reviews, lease extensions, or other events that could significantly alter the cash flow profile of the leasehold interest. This simplification can lead to inaccurate valuations, especially for leases with complex rent review patterns or significant growth potential.
6. Timing and Frequency of Payments: The traditional YP dual rate approach assumes annual payments in arrears. Modern leases often involve quarterly payments in advance, which can introduce discrepancies if not properly accounted for.
7. Occupier Perspective: The traditional method is inappropriate for owner-occupiers because they consider the purchase price to be a rental paid in advance which is tax deductible.

6.4 The Rise of Discounted Cash Flow (DCF) Analysis

Recognizing the shortcomings of traditional methods, DCF analysis has emerged as the preferred approach for leasehold valuation. DCF offers a more flexible and comprehensive framework for capturing the intricacies of leasehold cash flows and risk.

6.4.1 Principles of DCF

DCF analysis is grounded in the fundamental principle of finance: the value of an asset is equal to the present value of its expected future cash flows. This involves projecting all future cash inflows and outflows associated with the leasehold interest and discounting them back to the present using an appropriate discount rate.

6.4.2 DCF Formula

The basic DCF formula is:

PV = ∑ (CF_t / (1 + r)^t)

Where:

• PV = Present Value (the estimated value of the leasehold interest)
• CF_t = Cash Flow in period t (e.g., annual profit rent, reversionary rent)
• r = Discount rate (reflecting the risk associated with the leasehold interest)
• t = Time period (e.g., year 1, year 2, etc.)
• ∑ = Summation over the entire forecast period

6.4.3 Advantages of DCF in Leasehold Valuation

1. Explicit Cash Flow Projections: DCF requires explicit projections of all future cash flows, allowing for the incorporation of rent reviews, lease extensions, variable operating expenses, and any other relevant factors. These projections can be based on market research, historical data, and reasonable assumptions about future market conditions.
2. Flexible Discount Rate: The discount rate can be tailored to reflect the specific risks associated with the leasehold interest, including factors such as the creditworthiness of the tenant, the volatility of the rental market, and the length of the lease term. This allows for a more nuanced assessment of risk compared to the fixed remunerative rates used in traditional methods.
3. Consideration of Reversionary Value: DCF can explicitly model the reversionary value of the property at the end of the lease term, reflecting the potential for future income generation. This is particularly important for leases with significant reversionary potential, as it allows for a more complete assessment of the long-term value of the leasehold interest.
4. Sensitivity Analysis: DCF facilitates sensitivity analysis, allowing valuers to assess the impact of changes in key assumptions (e.g., rental growth rates, discount rates) on the estimated value. This provides a valuable tool for understanding the range of possible outcomes and identifying the key drivers of value.
5. Transparency and Auditability: DCF models provide a clear and transparent framework for valuation, making it easier to understand the assumptions and calculations that underpin the final value estimate. This enhances the auditability and defensibility of the valuation.
6. Ability to model complex rental growth scenarios: DCF analysis is well suited for modelling scenarios where rent reviews on head and subleases do not coincide.
7. Reflects High Gearing: DCF analysis can be used to correctly reflect the nature of gearing for highly geared investments.

6.4.4 DCF Example with data from included PDF

Here’s an example illustrating how a simplified DCF approach can value leasehold investments, drawing from the provided PDF data. This showcases how DCF can differentiate between investments A and B based on varying rental growth potential, something traditional YP methods struggle with.

We’ll use the “shortcut DCF approach” presented in the document. This isn’t a full-blown DCF (missing operating expenses, terminal value calculations) but serves to highlight the concept.

Assumptions:

• Equated yield (discount rate) = 16%
• Annual rental growth rate = 5%
• Lease term = 10 years, with a rent review after 5 years

Investment A:

• Current MRV (Market Rental Value): £50,000
• Head rent: £5,000
• Profit rent (Year 1-5): £45,000

Investment B:

• Current MRV: £250,000
• Head rent: £205,000
• Profit rent (Year 1-5): £45,000

DCF Calculation:

Investment A

Term I (Years 1-5):
Rent receivable = £50,000
Less head rent = £5,000
Profit rent = £45,000
YP for five years at 16% = 3.2743
CV of term = £147,344
Term II (Years 6-10):
MRV today = £50,000
× amount £1 five years at 5% = 1.2763
Expected MRV = £63,814
Less head rent = £5,000
Profit rent = £58,814
YP for five years at 16% = 3.2743
PV five years at 16% = 0.4761
CV term II = £91,685
CV of leasehold = £239,029 Say £240,000

Investment B

Term I (Years 1-5):
Rent receivable = £250,000
Less head rent = £205,000
Profit rent = £45,000
YP for five years at 16% = 3.2743
CV of term = £147,344
Term II (Years 6-10):
MRV today = £250,000
× amount £1 five years at 5% = 1.2763
Expected MRV = £319,075
Less head rent = £205,000
Profit rent = £114,075
YP for five years at 16% = 3.2743
PV five years at 16% = 0.4761
CV term II = £177,831
CV of leasehold = £325,175 Say £325,000

Interpretation:

The DCF approach results in a value of £240,000 for Investment A and a value of £325,000 for Investment B. This is in contrast to the YP method where each leasehold was valued at £232,808.

The DCF model highlights the significant impact of rental growth and gearing. Investment B, with its higher MRV and potential for greater profit rent increase post-review, is deemed more valuable despite having the same initial profit rent as Investment A. This distinction, missed by the traditional YP approach, underlines the strength of DCF in capturing the dynamic nature of leasehold investments.

6.5 Conclusion

While traditional methods like the YP dual rate provided a simplified approach to leasehold valuation, their reliance on static assumptions and inability to capture the complexities of modern leasehold cash flows render them increasingly obsolete. DCF analysis, with its flexibility, transparency, and ability to incorporate dynamic factors, has emerged as the superior method for leasehold valuation, providing a more accurate and reliable assessment of value in today’s dynamic real estate market.