When a freeholder buys out a long head lease, the merged interest is worth more than the two parts. Here is how to measure the gain and price the deal around it.
Marriage value is the value of the merged, unencumbered interest minus the value of the freehold and the leasehold taken separately. On an illustrative office let on a head lease with 20 years left, the freehold is worth £3,745,365, the leasehold £3,927,259 and the merged freehold £8,333,333, so the marriage value is £660,710. Split equally, the freeholder should pay about £4,257,614 to buy the lease in, not the leasehold's stand-alone value.
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 →
The situation is common with older commercial property: a freeholder granted a long head lease at a fixed or low rent, the head lessee sublets the building at market rents and keeps the difference as a profit rent. When the freeholder wants control back, to refurbish, redevelop or simply sell a clean freehold, it has to buy the head lease. The question is what that lease is worth to the one buyer who can merge it.
| Input | Value |
|---|---|
| Market rent received from the occupational subtenants | £500,000 a year |
| Head rent paid by the head lessee to the freeholder, fixed | £100,000 a year |
| Unexpired term of the head lease | 20 years |
| Freehold yield (term, reversion and merged interest) | 6.0% |
| Leasehold yield on the profit rent, single rate | 8.0% |
| Share of marriage value to the head lessee | 50% |
Rents are treated as annual in arrears and held flat to keep the arithmetic visible. The leasehold is valued on a single-rate years' purchase at a higher yield; the dual-rate approach gives a lower leasehold value and therefore a larger marriage value. Purchaser's costs are ignored in all three valuations so that they cancel out.
1. Freehold subject to the head lease
Term: £100,000 × YP 20 years at 6% (11.4699) = £1,146,992
Reversion: £500,000 ÷ 6% = £8,333,333, deferred 20 years at 6% (× 0.3118) = £2,598,373
Freehold value = 1,146,992 + 2,598,373 = £3,745,365
2. Leasehold interest
Profit rent = 500,000 − 100,000 = £400,000 a year
Leasehold value = £400,000 × YP 20 years at 8% (9.8181) = £3,927,259
3. Merged freehold in possession of the full rent
£500,000 × YP perpetuity at 6% (16.6667) = £8,333,333
4. Marriage value = 8,333,333 − (3,745,365 + 3,927,259) = 8,333,333 − 7,672,624 = £660,710
Excel: =Rent/FHy - (HeadRent*PV(FHy,n,-1) + Rent/FHy/(1+FHy)^n + (Rent-HeadRent)*PV(LHy,n,-1))
The marriage value is 7.9 per cent of the merged value. It is real value, not an accounting artefact: the day after completion, the freeholder owns an interest the market would price at £8,333,333.
The head lessee will not sell for less than its stand-alone value of £3,927,259, which is what any other investor would pay for the profit rent. The freeholder will not pay more than £3,927,259 plus the whole £660,710, because above that the merger destroys value for it. Everything in between is negotiation. With an equal split, each side takes £330,355:
Price for the head lease = 3,927,259 + 50% × 660,710 = £4,257,614
Freeholder's gain = 8,333,333 − 3,745,365 − 4,257,614 = £330,355
The head lessee receives 8.4 per cent more than the open-market value of its lease. A freeholder with a redevelopment plan that only works once the lease is gone may have to concede more; a head lessee with no other buyer at a premium may accept less. At a 30 per cent share for the head lessee, the price is £4,125,472; at 70 per cent, £4,389,756.
Run the leasehold at the freehold yield of 6 per cent and its value is £400,000 × 11.4699 = £4,587,968. Add the freehold and the total is exactly £8,333,333: no marriage value at all. The gain is entirely the yield gap on the profit rent, the extra return the market demands for holding a wasting, less liquid leasehold interest, which disappears once the income sits inside a freehold.
| Leasehold yield | Leasehold value | Marriage value | As % of merged value | Price at 50:50 |
|---|---|---|---|---|
| 6.0% | 4,587,968 | 0 | 0.0% | 4,587,968 |
| 7.0% | 4,237,606 | 350,363 | 4.2% | 4,412,787 |
| 8.0% | 3,927,259 | 660,710 | 7.9% | 4,257,614 |
| 9.0% | 3,651,418 | 936,550 | 11.2% | 4,119,693 |
| 10.0% | 3,405,425 | 1,182,543 | 14.2% | 3,996,697 |
A higher leasehold yield raises the marriage value but lowers the price, because the head lessee's starting point falls faster than its half of the gain rises.
| Years unexpired | Freehold value | Leasehold value | Marriage value | As % of merged value |
|---|---|---|---|---|
| 5 | 6,648,388 | 1,597,084 | 87,861 | 1.1% |
| 10 | 5,389,299 | 2,684,033 | 260,002 | 3.1% |
| 20 | 3,745,365 | 3,927,259 | 660,710 | 7.9% |
| 40 | 2,314,815 | 4,769,845 | 1,248,673 | 15.0% |
Marriage value grows with the unexpired term because the yield gap applies to more years of profit rent. With five years left there is little to share, and a freeholder can often do better by waiting; with 40 years left the merger is worth 15.0 per cent of the building.
The common mistake is to offer the head lessee its open-market value and treat anything above it as overpaying. The leasehold's value to the freeholder is not £3,927,259; it is £3,927,259 plus whatever share of £660,710 the freeholder has to concede to unlock the merger. The opposite error is just as costly: a freeholder who pays a price based on the merged value less its own interest, £4,587,968, has handed the entire marriage value to the seller.
Value three interests, not two: the freehold subject to the lease, the leasehold on its own, and the merged freehold. The difference is the marriage value, £660,710 here, and the negotiation is about how it is split. Check the leasehold yield first, because it drives most of the answer. The free workbook for this case builds the rent roll and income account that valuations like these start from, and the ground rent article values the freeholder's side of a long lease at a low rent. Figures are illustrative and this is not valuation advice.
From the yield gap. A leasehold profit rent is valued at a higher yield than freehold income because it is a wasting, less liquid asset. Once merged, the same income is capitalised at the freehold yield. In the illustrative case, valuing the leasehold at 6 per cent instead of 8 per cent gives £4,587,968, exactly the amount that makes the two interests add up to £8,333,333, and the marriage value disappears.
No. Equal shares are the usual starting point in negotiation, not a rule. A party with a pressing need to merge, such as a freeholder planning a redevelopment, may concede more. On the illustrative £660,710, the freeholder pays £4,125,472 for the lease if the head lessee takes 30 per cent of the marriage value and £4,389,756 if it takes 70 per cent.
Residential enfranchisement and lease extensions follow their own statutory valuation rules, which have been the subject of reform in England and Wales, so check the current legislation. The arithmetic here is for a negotiated commercial merger, where marriage value is simply the value created by combining the interests, and the split is whatever the parties agree.
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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