Buy-to-let investors need to do their sums

I'm not going to complain about the Budget. It wasn't imaginative, interesting or particularly funny, and we won't be able to look back on it in a decade as representing any kind of turning point in the miserable state of the UK's public finances.

But the chancellor did do something if which I approve. There will be, said Philip Hammond, "more maths for everyone".

His £177m plan to encourage schools to work harder on numeracy includes some extra funding to push Singapore-style maths teaching into primary schools; a bung of £600 for schools for every additional pupil nudged into taking A-levels in maths, further maths or core maths; and a call for more applications for new specialist maths schools in England.

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This is all excellent news. For years now, various groups in the UK have been lobbying heavily for cash for personal-finance education in schools, on the basis that if kids understand how mortgages, savings accounts, credit card bills and basic investment products work, they are more likely to be savers and less likely to be ripped off by the UK's particularly rapacious financial industry.

I've never been mad for the idea. There's plenty of research to show that if people don't need this kind of information immediately, it goes in one ear and straight out the other. No waiting around. So teaching schoolchildren about mortgages is a waste of everyone's time particularly when they will be 50 before they can afford one.

It is better to produce "just in time" personal-finance education as required (this is what the government's Pension Wise service is supposed to do for the over-50s, for example) and to teach children maths really, really well. This will give them the tools to help themselves financially as and when they need to, and to interpret the financial events happening around them.

Given the gloomy economic backdrop, it's also worth noting that a good understanding of maths is helpful in another way it can alert us to the bits of the Budget that pretend to be about real numbers, but are nothing of the sort.

With this in mind, if the Office for Budget Responsibility (OBR) forecasts that UK GDP will grow at a rate of 1.3% in 2020, what rate will GDP actually be growing at in 2020? The answer is maybe a lot more than 1.3%, or maybe rather less. But almost certainly not 1.3%.

Like all forecasters, the OBR has an almost unblemished history of wrongness. There is no mathematical formula that can take into account what will happen to inflation, oil prices, immigration, productivity, technology and that most fickle of all things, human behaviour, over a six-month period, let alone a three-year one.

Better to ignore these numbers and focus on the ones you know will affect you, and you know you can calculate correctly after your Singapore-style maths class, at least.

With this in mind, let's do a few quick sums on the Budget both to see how we might be affected immediately and to get a sense of the signals that Hammond is sending us about the future. As you will see, a bit of maths can often tell us who the government regards as a plus or a minus.

First, if a house is listed for sale at £300,000, how much more will it cost a buy-to-let investor to get their hands on the keys than it costs a first-time buyer?

The answer is simple. The first-time buyer pays £300,000 (their stamp duty has just been abolished). The buy-to-let investor pays £314,000 (theirs hasn't been abolished, and they have to pay the additional 3% second-home surcharge on top). This gives you a sense of who the chancellor approves of and who he does not (or who he wants to approve of him, perhaps). But the next two sums well and truly make this point.

If a buy-to-let investor bought a house for £200,000 in 2007 through a company structure (something lots of landlords are doing now to avoid the slashing of tax relief on mortgage interest) and sells it this year for £300,000, how much tax on the capital gain will he pay?

The answer is not straightforward. Until now, assets bought inside a company have been eligible for indexation (your gains are adjusted for inflation) based on figures provided by HM Revenue & Customs. You take the number given by them that works for your timeframe 0.313 in this case, according to tables on the HMRC website and multiply it by the price you paid.

Then take that sum (£62,600) away from your profit to get your taxable amount (£34,000). Finally, multiply that by 19% (the corporation tax rate). The answer is £7,106.

Hold that thought while you calculate the following. If a landlord bought a buy-to-let property now for the same £200,000 price and also sold it in a decade for £300,000 how much tax on the capital gain would they be likely to pay?

The answer to this is easier. The gain multiplied by the tax rate which is set to fall to 17%. So £17,000, which is nearly £10,000 more than they would have paid on a similar investment gain a decade earlier. There you have it. A few sums that tell you the current government thinks buy-to-let isn't all that.

If you were thinking of becoming a landlord, maybe don't. If you are already, maybe read the runes the way Hammond wants you to and sell your rental property to your tenant (you'll get good price all the money they were saving for stamp duty can now be offered to you instead).

There's a useful sum available as a hint for those with houses that are "substantially unfurnished" and unused as well. You own a six-bedroom holiday home by the sea in Padstow that you are too busy to visit or furnish, what with the demands your international speaking schedule puts on you. How much has Hammond probably just added to your cost of ownership?

The answer to this is £3,371.02, the level of Band H council tax in Padstow which can now be doubled for empty homes. It couldn't be much clearer could it? In Hammond's world, houses are for owners to live in full time and that's that. Something to bear in mind if you are still convinced that you can't go wrong with property.

There are many more fun numbers to play around with in the Budget. No doubt FT columnist-turned maths teacher Lucy Kellaway is already planning her next lesson around them.

Given the gloomy economic backdrop, it's also worth noting that a good understanding of maths is helpful in another way it can alert us to the bits of the Budget that pretend to be about real numbers, but are nothing of the sort.

With this in mind, if the Office for Budget Responsibility (OBR) forecasts that UK GDP will grow at a rate of 1.3% in 2020, what rate will GDP actually be growing at in 2020? The answer is maybe a lot more than 1.3%, or maybe rather less. But almost certainly not 1.3%.

Like all forecasters, the OBR has an almost unblemished history of wrongness. There is no mathematical formula that can take into account what will happen to inflation, oil prices, immigration, productivity, technology and that most fickle of all things, human behaviour, over a six-month period, let alone a three-year one.

Better to ignore these numbers and focus on the ones you know will affect you, and you know you can calculate correctly after your Singapore-style maths class, at least.