ELMBIRCH PROPERTIES PLC [2017] UKUT 0314 (LC) re. 51 Humphrey Middlemore Drive
We start with bare facts:
“12. The long lease of No. 51 was granted on 20 June 1986 and is for a term of 99 years from 24 June 1985. The initial annual rent was £45, subject to a fixed increase on 24 June 2016 to £90, and a further increase on 24 June 2049 to £180. On 9 November 2015 the tenants … gave the appellant notice under section 42 of the 1993 Act claiming a new lease…“
We need to organise this data for the ground rent capitalisation calculations:
Ground rent increments: £45, £90, £180.
A 
Valuation date: 
09/11/2015 
← data entry 

B 
Lease start: 
24/06/1985 
← data entry 

C 
Original term yrs: 
99 
← data entry 

D 
Lease end: 
23/06/2084 
=(EDATE(B,C*12))1 

E 
Unexpired term: 
68.62 
=YEARFRAC(A,D) 

Years Unexpired 

F 
1^{st} increment 
24/06/1985 
0.62 
=YEARFRAC(A,G) 
G 
2^{nd} increment 
24/06/2016 
33.00 
=YEARFRAC(G,H) 
H 
3^{rd} increment 
24/06/2049 
35.00 
=YEARFRAC(H,J) 
I 
End of lease 
23/06/2084 
← data entry 
Online widgets provide only one ground rent, as does the LEASE example, whereas leases will tend to have a number of GR increments so to complete the full calculation you must have the above data.
1. Diminution in freeholder’s interest
We first need the ground rent yield. In this case it was decided at 5.5%.
(i) Value of existing freehold interest
We must calculate the present value of each of the three ground rent increments and then calculate the reversion to the future freehold vacant possession value (for the proposed extended lease).
(a) Present ground rent £45
Counting from the date of valuation, £45 is payable for 0.62 years. This is how it is recorded in the UT calculation:
Using a spreadsheet we don’t need to calculate the Years Purchase (YP) to get to the answer:
=PV(0.055,0.62,45)*1 = £26.71
But just to prove the YP:
=PV(0.055,0.62,1)*1 = 0.5936
(b) Reversion to future ground rent £90
Counting from the date of valuation, £90 is payable for 33 years, deferred 0.62 years. This is how it is recorded in the UT calculation:
Again, we don’t need to labour the calculation steps in a spreadsheet, but the formula is more complex to allow for the deferment period:
=PV(0.055,33,90)/(1+0.055)^0.62*1 = £1,312.46
Notice that the power N is the period of the previous increment (0.62 years).
Again, to prove the 33 year @ £90 YP:
=PV(0.055,33,1)*1 = 15.075
The next step needs care as it involves a Future Value. The UT decision records it like this:
This is the PV of a future value of £1 deferred 0.62 years @ 5.5%:
=PV(0.055,0.62,,1)*1 = 0.9673
Notice unlike calculating years purchase above, there is no value for Payment (PMT).
Or we could use the raw deferment formula:
PV deferment = (1+rate)^n^{def}
=(1+0.055)^0.62 = 0.9673
Now we have to multiply three elements:
= £90 * 15.075 * 0.9673 = £1,312.38
You can see the spreadsheet PV function is simpler. I guess tribunals prefer to be more obscure and work in the old fashioned way? I won’t repeat the UT method for the next ground rent.
(c) Reversion to future ground rent £180
Counting from the date of valuation, £180 is payable for 35 years, deferred 33.62 years. This is how it is recorded in the UT calculation:
=PV(0.055,35,180)/(1+0.055)^33.62*1 = £457.91
Total reversion of ground rent:
=£27 + £1,312 + £458 = £1,797
(d) Reversion to freehold vacant possession
This is recorded in the UT calculation as:
For now all that matters is that the UT decided on £118,200 by valuing the proposed lease at £117,000 and topping this by 1% for the ‘freehold differential’. In fact the result was only £118,170 but was rounded up by £30. The extra £30 assists the freeholder.
In other cases there may be a claimed discount/allowance for Schedule 10 rights. Any discount off the proposed freehold vacant possession helps the leaseholder. None is applied here. The UT observed:
“23. ...(it was not suggested in these cases that the tenant would take advantage of rights under Schedule 10 to the Local Government and Housing Act 1989).”
Whereas, in Contactreal Limited and Ms Hannah M Smith [2017] UKUT 0178 (LC) the leaseholder achieved 2.5% allowance off to counter the 1% freehold differential.
Enough of this diversion and back to the maths…
=PV(0.055,68.62,,118200)*1 = £2,999.40
Again, notice the £118,200 is the future value. The PMT variable is empty.
To complete this first stage we add the total GR present value to the reversion to the future freehold interest:
= £1,797 + £2,999 = £4,796
As recorded by the UT: