When acquiring a property entailing a new lease, the issue of Net Present Value (NPV) for Stamp Duty Land Tax purposes immediately becomes apparent.
(Net Present Value for Scottish lease transactions is calculated using the formula shown on the documentation on Land and Buildings Transaction Tax (Scotland) Act 2013).

Net Present Value in this instance is a statistical method that should be familiar to accountants for projecting a present-day estimate of the future value of a lease.

Put another way, if we know how much is being paid in accumulated rent over a period of x years into the future, NPV is the government's chosen method to estimate what that would be worth in “today's money”.

Why is that important? Because the government wishes to levy SDLT on that accumulated rent in the here and now. I can imagine your shock.

## The Mystery That Is Net Present Value

It is abundantly clear, however, that few lay people know how the government mandates that NPV be calculated.

The government's own tax guidance is frustratingly vague when referencing NPV; their wording loosely defines it as

"the total rent over the life the lease"

(Cited from: GOV.UK's online overview of Stamp Duty Land Tax)

At first glance, then, it would appear that NPV is merely the sum of all the annual rent figures throughout the duration of the lease.

However, dig into the government's awkard-to-use online calculators and you will see why that assumption would be very much amiss (as anyone trained in statistical mathematics will already know). A quick experiment with sample figures will reveal that NPV is something other than all the rents added together.

But why the obfuscation? Why does the government's tax guidance only proffer its own calculators as the means to determine NPV in any given instance, rather than providing a detailed methodology?

The answer almost certainly lies in one or more issues with the method the government's calculators - and, by inference, this website's calculators too - use in working out NPV.

Stated more explicitly, things get slightly complicated once a lease duration exceeds five years. Essentially, there is a subtle change in how NPV is calculated once the five year mark is passed.

## Leases Lasting 5 Or Less Years

Up to the five year demarcation line, everything is relatively simple, as shown in **Figure 1** below.

The NPV element for any given year (years 1 to 5) is derived from that year's rent divided by a special, but simply arrived at, denominator consisting of 1 plus a “discount” of 3.5% raised to the power of that year's number (i.e. 1 for year 1, 2 for year 2, 3 for year 3, etc.)

The NPV elements for each year (again, this only applies for years 1 to 5), are then added together to provide the overall NPV for the purposes of SDLT on new leases.

So, for example, the NPV for 3 years would consist of the first three NPV elements added together. Likewise, the NPV for 4 years would consist of the first 4 NPV elements added together.

Note that if the new lease lasts for, say, 3 years and 1 day, it is treated as being a 4 year lease. In other words, the years are rounded up to the next full year.

Also note how the Taxman defines a year in this case. A lease lasting from 1st July 2017 to the 1st July 2018 will be treated as 1 year and 1 day, not simply 1 year. For the example to be classed as a 1 year lease, it would have to end on the 30th June 2018.

**FIGURE 1:** Net Present Value formulae for SDLT on new leases lasting 5 or less years

## Leases Lasting More Than 5 Years

Once the lease duration exceeds the 5 year mark, things become a little more complex.

Whereas previously a lease lasting, say, 4 years and 2 days would be treated for NPV purposes as a 5 year lease, ultra precision is now applied. That is, a lease duration of, for example, 6 years and 47 days will be taken as exactly 6 years and 47 days, not rounded up to 7 years.

What actually happens in this example is that the 47 days are divided by the number of days in the final lease year to create a fraction that will be used in calculating that year's NPV element. I, quite arbitrarily and for no particularly compelling reason, have assigned this fraction the name of “gap factor” - see **Figure 2** below.

An added complication is where leases traverse leap years, or to be more accurate, where the final year of the lease overlaps all of, or any part after the 28th of February on, a leap year. In such instances, the gap factor's own little formula has to be adjusted accordingly.

The other important point about leases lasting longer than 5 years is that the maximum annual rent in the first 5 years is used as the basis for calculating the NPV element for every year after year 5.

**FIGURE 2:** Net Present Value formulae for SDLT on new leases lasting more than 5 years

## The Need For A Specialist Calculator Reiterated

By now you will hopefully appreciate why the government has been so unforthcoming with specifics about how it calculates NPV; they seem to think it's too complicated for most people.

Personally, trying to do this by hand for anything more than a few years past the 5 year threshold would appear an exercise in extreme care and patience, particularly where the lease ends with a fraction of a full year.

Accordingly, I too recommend that you use a bespoke application to work it out. And naturally, I recommend my own stamp calculator in preference to the government version, given that mine has been designed to provide a smoother user experience than theirs, and mine also allows you to generate a presentation standard downloadable, printable report of your calculations with one click (or tap).