# How to Calculate the Diminution in Value of the Freeholder’s Interest

### Tuesday, 15th February 2011 | by: Peter Barry

In my last post we said that we would start to look at how ‘The diminution in value of the freeholder’s interest in the subject property’ is calculated.

Generally there will be two elements to take into account. This will be the loss of the income from the ground rent and the loss of the potential reversion at the end of the original lease term.

As you will recall from our earlier posts, when a new lease is granted under the Leasehold Reform Act it is at a ‘peppercorn rent’, which means effectively no rent is payable. Most original leases will have provision for ground rent to be paid by the lessee to the freeholder on an annual basis. The rent is usually quite low and is often in the region of £50 to £100 per annum.

The freeholder has to be compensated for the loss of the ground rent and it is probably easiest to illustrate this by using some examples. Let’s assume that we have a flat with an unexpired lease of 70 years and that the ground rent is £100 a year. For the purposes of this illustration we will also assume that the flat would be worth £200,000 on the open market.

If the lease were to run to the end of its term the freeholder would expect to receive £100 a year for the next 70 years. In calculating the freeholder’s financial loss we have to work out what the present value of the right to receive £100 a year for the next 70 years is. To put it another way, how big a lump sum would you have to invest today to give you an income of £100 a year for the next 70 years.

To make this calculation we have to assume that our lump sum investment would attract interest. We have to decide on a percentage return and the courts have generally accepted that this kind of investment would provide a return of about 8%. Unfortunately, we now have to use some equations.

The equation to calculate the present value of the right to receive £1 per annum would be as follows:-

1/r-1/[r(1+r)^t ]

In the above equation r is the annual interest rate and t is the length of time in years. In our case the interest rate (r) is 8% and the time in years (t) is 70. Using these figures, the equation gives us a result of 12.4428.

The ground rent in our case is £100 a year and we have to multiply 12.4428 by £100. This gives a figure of £1,244.28. We would have to invest £1,244.88 today to produce an income of £100 a year for the next 70 years.

To compensate the freeholder for the loss of income from the ground rent we would, therefore, have to pay £1,244.28.

The next thing to consider is the freeholder’s loss of the reversion at the end of the existing lease. If the lease were allowed to run its course the freeholder would potentially have a flat that would be worth £200,000 in 70 years time.  We have to carry out a similar calculation to work out the present value of the right to receive £200,000 in 70 years time. Again we need to assume a rate of interest. In the case of the reversion the courts have accepted that a reasonable rate of return is 5%.

We then need to produce an equation that will tell us what the present value of £1 is where r is the annual interest rate and t is the length of time in years. The equation is as follows:-

1/(1+r)^t

In our case the interest rate (r) is 5% and the time in years (t) is 70. Using these figures, the equation gives us a result of 0.0328662. The market value of the flat in our case is £200,000, so we have to multiply £200,000 by 0.0328662 which gives us a figure of £6,573.24.

This means that we would have to invest £6,573.24 today to amount to £200,000 in 70 years time. It follows then that this is the amount that the lessee would have to pay to the freeholder in compensation for the loss of reversion.

You will probably have noted that the calculation does not take any account of the possibility of the value of the flat increasing over the next 70 years. This isn’t an oversight; the legislation does not allow for potential property inflation in the calculation.

We have now considered in principle the various ways in which the freeholder has to be compensated for the grant of new lease under the Leasehold Reform Act. In the next few posts we will show some worked examples, which will, hopefully, make things a bit clearer.