Lease Extension Formula Part 1

einsteen sheep and formula

I’ll return later to the valuation caper. First I will work through an example of the formula using the case of ELMBIRCH PROPERTIES PLC [2017] UKUT 0314 (LC), as this was decided by the UT on 27 July 2017, well after the Mundy case.

The appeal involved two extension premiums. I will use just one, the calculation for 51 Humphrey Middlemore Drive, leaving you free to practice on the other. The Upper Tribunal’s maths are found on pages 20 and 21 of their decision.

The maths

A spreadsheet is indispensable. I recommend LibreOffice Calc as it is free and open source software. Using a spreadsheet allows use of built-in functions. We will need the Present value function a lot:-

Present Value function (PV)

PV(Rate,NPER,PMT,FV,Type)*-1

Rate = interest rate per period

NumPeriods = total number of periods (payment period).

Payment = constant payment made each period.

FV (optional) = future value remaining after the final instalment has been made.

Type = optional and not needed here

Note: The interest rate needs to match the periods, e.g. a monthly rate would need monthly periods, e.g.

5% pa for 5 yrs = 5%/12 = Rate: 0.004167, NumPeriods: 5 * 12 = 60

However, whereas relying on built-in functions is easier, knowing the raw maths is more useful when having to problem solve:-

PV formula

 

A = Present Value

P = Constant payment

i = interest rate per period

n = Number of periods

Road testing the PV function versus the formula:

Q: Solve the Present Value of an investment where a 33 year annuity pays £90 yearly. If interestis guaranteed at 5.5%, how much is the annuity worth at today’s value?

P = £90 (=Payment)    I = 5.5%(=Rate)     n = 33 years (=Numperiods)

PV = PV(Rate,NPER,PMT)*-1

PV = PV(0.055,33,90)*-1

PV = £1356.76

versus

A = (90/0.055)*(1-(1+0.055)^-33)

A = £1356.76

More raw formulas to know when reading UT cases:

Years Purchase(YP) =PV(rate,numperiod,1)*-1

e.g. =PV(0.055,0.62,1)*-1 = 0.5936

or in raw maths:

Years Purchase(YP) =(1/rate)*(1-(1+rate)^-numperiods)

e.g. =(1/0.055)*(1-(1+0.055)^-0.62) = 0.5936

(The YP step is used in tribunal calculations but is not needed in a spreadsheet).

Next we need to know how to calculate a present value on a future ground rent, i.e. allowing for the deferment.

Deferment = (1+rate)^-ndef

ndef = cumulative years this ground rent increment was deferred while all previous increments were in force. We use the deferment formula with the PV function:-

PV= PV(0.055,33,90)/(1+0.055)^1*-1

In this case £90 @ 5.5% was deferred for 1 year (i.e. the £90 increment starts in 1 year).

Armed with some useful maths we can now dive into the fun of a lease extension premium calculation. The variables have been pre-defined where applicable, such as:-

  • ground rent yield

  • discount rate for the reversion interest

  • “No Act” discount

  • freehold differential

  • market value of the lease with and without the proposed extension

  • schedule 10 rights discount

(I will return to all of these later).

Now we can follow a real Upper Tribunal case…

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