A leasehold interest is income plus the return of its own capital. The dual rate method prices both, and the single rate needs a much higher yield to agree.
Multiply the profit rent by a dual rate years' purchase: one over the sum of the remunerative yield and an annual sinking fund instalment, grossed up for tax, that rebuilds the capital before the lease runs out. An illustrative profit rent of 90,000 for 15 years, at 8.00 per cent remunerative and a 2.50 per cent sinking fund with tax at 25 per cent, gives a YP of 6.4786 and a value of 583,070. A single rate YP at the same 8.00 per cent says 770,353, 24.3 per cent more, and the difference is the cost of rebuilding the capital at a safe, taxed rate instead of at 8.00 per cent.
Worked in full in Commercial Real Estate Investing by Julian R. Sterling, with every figure reproduced in a free workbook.See the book on Amazon →
A leasehold interest with a fixed head rent below market value is a wasting asset. The head lessee collects the market rent, pays the head rent and keeps the difference, the profit rent, until the lease ends; then the interest is worth nothing. The traditional UK method values that income with a dual rate YP, and it remains a staple of valuation exams and of APC questions, while many practitioners now prefer a single rate at a higher yield. Both are shown below, because the useful thing is to see what each one assumes.
| Input | Value |
|---|---|
| Market rent received from the occupier | 150,000 |
| Fixed head rent paid to the freeholder, no reviews | 60,000 |
| Profit rent | 90,000 |
| Unexpired term of the head lease | 15 years |
| Freehold all-risks yield for the same building | 6.00% |
| Remunerative rate: freehold yield plus 2 points for the leasehold | 8.00% |
| Accumulative (sinking fund) rate | 2.50% |
| Tax rate on the sinking fund instalment | 25% |
Annual sinking fund (ASF) at 2.50% for 15 years = 0.025 ÷ (1.02515 − 1) = 0.025 ÷ (1.448298 − 1) = 0.055766
Grossed up for tax = 0.055766 ÷ (1 − 25%) = 0.074355
Dual rate YP, tax adjusted = 1 ÷ (0.08 + 0.074355) = 6.4786
Value = 90,000 × 6.4786 = 583,070
In Excel: =B1/(B2+(B3/((1+B3)^B4-1))/(1-B5)) with the profit rent in B1, the remunerative rate in B2, the accumulative rate in B3, the term in B4 and the tax rate in B5.
The proof is that the profit rent covers both returns exactly. At a price of 583,070, an 8.00 per cent return on capital is 46,646 a year. The net sinking fund instalment is 583,070 × 0.055766 = 32,516, which needs 43,354 before tax at 25 per cent, and which, invested at 2.50 per cent for 15 years, grows back to 583,070. 46,646 plus 43,354 is the 90,000 of profit rent. Nothing is left over and the capital is whole when the lease expires.
| Method | YP | Value | Below single rate |
|---|---|---|---|
| Single rate at 8.00% | 8.5595 | 770,353 | |
| Dual rate, 8.00% and 2.50%, no tax | 7.3656 | 662,903 | 13.9% |
| Dual rate, tax adjusted at 25% | 6.4786 | 583,070 | 24.3% |
The single rate assumes the buyer can reinvest the capital it recovers each year at 8.00 per cent; the dual rate assumes only a safe 2.50 per cent, after tax. That is why the dual rate value is lower. Turned into an internal rate of return, the tax-adjusted value of 583,070 is a single rate of 12.95 per cent on the 90,000 for 15 years, and the untaxed dual rate value a single rate of 10.57 per cent. A valuer who prefers a single rate is not getting a different answer by magic: to reach the same value, the single rate has to sit almost 5 points above the remunerative rate.
| Unexpired term, years | Single rate YP | Value | Dual rate YP, tax adjusted | Value | Gap |
|---|---|---|---|---|---|
| 5 | 3.9927 | 359,344 | 2.9970 | 269,734 | 24.9% |
| 10 | 6.7101 | 603,907 | 5.0248 | 452,235 | 25.1% |
| 15 | 8.5595 | 770,353 | 6.4786 | 583,070 | 24.3% |
| 25 | 10.6748 | 960,730 | 8.4009 | 756,083 | 21.3% |
| 40 | 11.9246 | 1,073,215 | 10.0219 | 901,970 | 16.0% |
| Accumulative rate | YP, tax adjusted | Value |
|---|---|---|
| 0.00% | 5.9211 | 532,895 |
| 1.00% | 6.1413 | 552,718 |
| 2.50% | 6.4786 | 583,070 |
| 4.00% | 6.8218 | 613,965 |
The gap is widest on short and medium terms, where recovering the capital is most of the annual cash flow, and narrows on long leases, where the income behaves more like a freehold. The accumulative rate matters less than the tax adjustment: moving it from 1.00 to 4.00 per cent changes the value by 61,247, less than the 79,833 the tax adjustment takes off at 2.50.
Valuing the leasehold at the freehold yield, as if it carried freehold risk. A single rate YP for 15 years at 6.00 per cent is 9.7122, which gives 874,102, 49.9 per cent more than the tax-adjusted dual rate value of 583,070, or 291,032 overpaid. The leasehold carries more risk than the freehold, because the head rent is paid whatever happens to the occupier, and it ends. Both have to be in the rate or in the YP.
Two further errors are common. One is applying the tax adjustment when the buyer does not pay tax, such as a pension fund, which overstates the discount by 79,833 here. The other is using a dual rate YP on a profit rent that will change: if the head lease or the sublease has rent reviews, the profit rent is not level and the term has to be split into periods or modelled as a cash flow. The single rate building block is in how to calculate years' purchase, and the freeholder's side of the same lease in how to value a commercial ground rent.
A leasehold profit rent is income plus the return of capital, and the valuation has to say at what rate the capital comes back. The tax-adjusted dual rate puts 90,000 for 15 years at 583,070; the single rate at the same yield at 770,353. If you prefer a single rate, use a yield that prices the wasting asset, here 12.95 per cent, and state it. The income account, yields and attribution behind the book's case are in the free workbook for this case.
A single rate YP discounts the income at one yield and implicitly reinvests recovered capital at that same yield. A dual rate YP splits the return into a remunerative rate on capital and a lower, safe accumulative rate for a sinking fund that rebuilds the capital. For 90,000 a year over 15 years at 8.00 per cent, the single rate YP is 8.5595 and the tax-adjusted dual rate YP with a 2.50 per cent sinking fund is 6.4786.
The instalment set aside to recover capital comes out of taxed income, so the buyer needs more profit rent before tax to save the same net amount. With tax at 25 per cent, a net annual sinking fund of 0.055766 becomes 0.074355 gross. On a 90,000 profit rent for 15 years, the tax adjustment cuts the value from 662,903 to 583,070.
Solve for the internal rate of return of the price against the profit rent. In the illustrative case, a tax-adjusted dual rate value of 583,070 for 90,000 a year over 15 years is equivalent to a single rate of 12.95 per cent, almost 5 points above the 8.00 per cent remunerative rate. Without the tax adjustment the equivalent single rate is 10.57 per cent.
This article is one calculation from Commercial Real Estate Investing. The book takes the same case from first principles to the decision, chapter by chapter, and every figure it prints is a live formula in the free companion workbooks.
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