Leasehold Valuation: Dual Rate to DCF Transition

Leasehold Valuation: Dual Rate to DCF Transition

This chapter explores the transition from the traditional dual-rate method to the more sophisticated Discounted Cash Flow (DCF) analysis for leasehold valuation. We will delve into the underlying principles of the dual-rate approach, analyze its shortcomings, and demonstrate how DCF overcomes these limitations by incorporating a time value of money perspective and considering dynamic cash flow projections.

1. Introduction: The Evolution of Leasehold Valuation

Leasehold valuation aims to determine the present worth of a property interest held under a lease agreement. Historically, the dual-rate method was a prevalent technique, particularly in periods of relatively stable rental markets. However, the rise of inflation, rent reviews, and a more complex investment landscape necessitated a shift towards DCF analysis, which offers a more flexible and accurate framework.

2. The Dual-Rate Method: Principles and Mechanics

The dual-rate method acknowledges that a leasehold interest is a wasting asset, meaning its value diminishes over time as the lease term expires. It separates the investor’s return into two components:

• Remunerative Rate (i): This represents the rate of return the investor expects on the capital invested in the leasehold, comparable to the yield on a freehold investment, but often adjusted upward to reflect the higher risk associated with leaseholds. It represents the “spendable income.”

• Sinking Fund Rate (SFi): This is a lower, risk-free rate used to calculate the annual contribution to a sinking fund. The sinking fund is theoretically intended to accumulate enough capital by the end of the lease term to replace the original investment, effectively allowing the investor to purchase another similar leasehold interest. Historically, this rate was based on low-yield insurance policies.

2.1. Key Formulas within the Dual-Rate Method

2.1.1. Amount of £1 Per Annum:

This formula calculates the future value of investing £1 at the end of each year for ‘n’ years, compounded at a rate ‘i’.

Amount of £1 per annum = ( (1 + i)^n - 1 ) / i or (A - 1)/i where A = (1+i)^n

2.1.2. Annual Sinking Fund (ASF):

This calculates the annual amount needed to be invested to accumulate to £1 at the end of ‘n’ years, compounded at a rate ‘i’. It is the reciprocal of the “amount of £1 per annum” formula.

Annual Sinking Fund (ASF) = 1 / ( Amount of £1 per annum ) = i / ( (1 + i)^n - 1 ) or i / (A-1)

2.1.3. Years’ Purchase Dual Rate (YP Dual Rate):

This is the core formula for the dual-rate method. It calculates the Years’ Purchase (YP) multiplier, which is then multiplied by the profit rent❓❓ to determine the capital value.

YP Dual Rate = 1 / ( i + [SFi / ((1 + SFi)^n - 1)] )

Where:

• i = Remunerative Rate
• SFi = Sinking Fund Rate
• n = Lease Term (in years)

2.2. Example of Dual-Rate Application (Based on the provided PDF)

A shop is let on a head lease with 10 years remaining at a ground rent of £2,000 p.a. The head lessee sublets the premises for £12,000 p.a. A freehold all-risks yield of 6% is observed. A remunerative yield of 7% and a sinking fund rate of 4% are adopted.

1. Profit Rent: £12,000 (Sublease Rent) - £2,000 (Head Lease Rent) = £10,000
2. YP Dual Rate: Using the formula with i=0.07, SFi=0.04, and n=10:

YP Dual Rate = 1 / ( 0.07 + [0.04 / ((1 + 0.04)^10 - 1)] ) ≈ 6.5235

3. Capital Value: £10,000 (Profit Rent) * 6.5235 (YP Dual Rate) = £65,235

4. Analysis of Return On and Return Of Capital:

   • Return on Capital (Spendable Income): £65,235 * 0.07 = £4,566.45

   • Return of Capital (Sinking Fund): £65,235 * (ASF for 10 years at 4%) = £65,235 * (0.04 / ((1.04)^10 - 1)) ≈ £5,433.42

   • Total Profit Rent: £4,566.45 + £5,433.42 = £10,000 (The Profit Rent)

5. Sinking Fund Accumulation Verification:

   • £5,433.42 (Annual Sinking Fund) * (( (1 + 0.04)^10 - 1 ) / 0.04) ≈ £65,234
   • This demonstrates that at the end of the lease term the accumulated sinking fund will equal the original purchase price.

3. Limitations of the Dual-Rate Method

Despite its historical significance, the dual-rate method suffers from several critical drawbacks, rendering it less suitable for modern valuation practices:

• Static Rental Value Assumption: The method assumes that rental values remain constant throughout the lease term, ignoring the impact of inflation and rent reviews. This is an unrealistic assumption in dynamic property markets.

• Unrealistic Sinking Fund Rate: The use of a low, risk-free rate for the sinking fund is often unrealistic. investors typically❓ seek higher returns and may reinvest profits in other property ventures rather than setting aside funds at such low rates. Also, the low rate does not reflect real rates of return for a typical investor.

• Inflation Neglect: The sinking fund only replaces the nominal purchase price, not the real value adjusted for inflation. This means the accumulated fund may be insufficient to purchase a comparable leasehold interest at the end of the lease term.

• Ignoring Gearing Effects: The dual-rate method struggles to account for the gearing effect, where profit rents are disproportionately affected by changes in the overall rental value, especially when the sub-lease has review dates that do not coincide with the head lease. A small rise in the overall rental value may create a larger increase in profit rent which is not captured by the dual rate.

• Payment Frequency Discrepancies: The formula assumes annual payments, while most leases involve quarterly or monthly payments, leading to inaccuracies.

• Occupier-Specific Considerations: The method is less relevant for owner-occupiers, who typically view the purchase price as a business investment rather than a property investment and may not establish a sinking fund. “Key money” and other factors influencing occupier decisions are difficult to incorporate.

• Limited Comparable Evidence: Finding suitable leasehold comparables with similar characteristics (location, term, rent ratio) is often challenging. Simply adding a premium to the freehold yield may not adequately capture the unique risks and opportunities of a leasehold investment.

4. DCF Analysis: A Modern Approach

DCF analysis provides a more comprehensive and flexible approach to leasehold valuation by explicitly considering the time value of money and projecting future cash flows.

4.1. Fundamental Principle: Present Value

The core principle of DCF is that a pound received today is worth more than a pound received in the future due to the potential to earn interest or returns on the money today. DCF calculates the present value (PV) of each expected future cash flow and then sums these present values to arrive at the property’s total value.

4.2. Key Components of DCF Analysis for Leaseholds

• Projected Cash Flows: Estimating the expected rental income (or profit rent in the case of a sublease), operating expenses, and any other relevant cash inflows and outflows over the lease term. This includes considering rent reviews, potential vacancy periods, and any capital expenditures.
• Discount Rate: Selecting an appropriate discount rate (r) that reflects the riskiness of the investment. This rate represents the required rate of return for the investor and is used to discount future cash flows back to their present value. The discount rate used in the DCF should consider many factors that contribute to the risk of the investment such as location, tenant quality, remaining lease term and potential obsolescence.
• Terminal Value: Estimating the value of the leasehold interest at the end of the projection period (i.e., at the end of the lease term). The terminal value is the present value of all cash flows beyond the explicit projection period. Often it is assumed that at the end of the lease term there is no additional value.

4.3. The DCF Formula

The basic DCF formula is:

PV = ∑ [CFt / (1 + r)^t]

Where:

• PV = Present Value (i.e., the value of the leasehold)
• CFt = Cash Flow in period t
• r = Discount Rate
• t = Time period (e.g., year)
• ∑ = Summation (adding up all the present values)

4.4. Applying DCF to Leasehold Valuation: An Example (Building on the PDF)

Consider the example from the PDF where two leasehold investments (A and B) each currently produce a profit rent of £45,000 p.a. and are held on ten-year head leases. Both are sublet for ten years at Market Rental Value (MRV), with a rent review on the sublease in five years’ time. Investment A has a current MRV of £50,000, while Investment B’s MRV is £250,000.

Assume a discount rate of 16% and a rental growth rate of 5% p.a.

Steps:

1. Project Cash Flows for Each Investment: Project the MRV and profit rent for each investment for the first 5 years (Term 1) and after the rent review (Term 2).
2. Calculate Present Value of Term 1 Cash Flows: Discount each year’s profit rent back to the present using the 16% discount rate.
3. Estimate Profit Rent at Review: Calculate the MRV at the review date (5 years from now) by growing the current MRV by 5% per year.
4. Calculate Present Value of Term 2 Cash Flows: Discount the profit rent after the rent review back to the present value.
5. Sum the Present Values: Add the present values of Term 1 and Term 2 cash flows to arrive at the total value of each leasehold investment.

Based on the results provided in the PDF (using a simplified DCF approach), Investment A would be valued at approximately £239,029 and Investment B at £325,175.

4.5. Advantages of DCF over Dual-Rate

• Flexibility: DCF can accommodate complex cash flow patterns, including varying rental growth rates, rent reviews, and irregular expenses.
• Time Value of Money: It explicitly accounts for the time value of money, providing a more accurate representation of value.
• Risk Adjustment: The discount rate can be adjusted to reflect the specific risks associated with a particular leasehold investment.
• Transparency: DCF provides a transparent and easily understandable framework for valuing leaseholds, allowing for sensitivity analysis and scenario planning.
• Gearing Considerations: DCF allows the valuer to explicitly model the impact of gearing, or the relationship between head rent and sublease rent, on the overall profitability and risk profile of the investment.
• Market-Driven Discount Rates: Modern valuation uses market derived yields to determine the relevant discount rate for the investment. This is in contrast to the static and artificial sink fund rate of the dual-rate method.

5. Practical Applications and Related Experiments

• Sensitivity Analysis: Conduct sensitivity analysis by varying the discount rate and rental growth rates to assess the impact on the leasehold value. This helps understand the potential upside and downside risks of the investment.

  • Experiment: Model the impact of a 1% increase or decrease in the discount rate on the calculated present value. Observe how sensitive the valuation is to changes in the discount rate.

• Scenario Planning: Develop different scenarios for future rental growth (e.g., optimistic, pessimistic, base case) and calculate the leasehold value under each scenario.

  • Experiment: Simulate a scenario where rental growth slows to 2% per year due to a recession. Compare the resulting value to the base case scenario.

• Comparison of Dual-Rate and DCF: Valuate the same leasehold interest using both the dual-rate method and DCF analysis. Compare the results and analyze the reasons for any differences.

  • Experiment: Valuate an identical leasehold using both dual-rate and DCF using varying rates of rental growth, and observe how the difference in valuations change across the different growth rates.

6. Conclusion

The transition from the dual-rate method to DCF analysis represents a significant advancement in leasehold valuation. While the dual-rate method provided a basic framework, its limitations, particularly the static assumptions and neglect of the time value of money, make it unsuitable for today’s dynamic property markets. DCF analysis offers a more flexible, accurate, and transparent approach, allowing valuers to make better-informed investment decisions. By considering future cash flows, risk, and the time value of money, DCF provides a robust framework for assessing the true worth of a leasehold interest.