"At $500 billion, Apple is worth more than Poland" - so shouted the headlines last week. Can the technology giant really be worth more than this entire country? No, and here's why.

CNN started this news line , which was picked up by media organisations around the world.

It seems like an amazing fact - that Apple's stock market value, or market cap, of $506bn (£323bn) makes it worth more than Poland, whose Gross Domestic Product is about $470bn (£300bn).

This would make Apple around the 20th biggest economy in the world.

But it is not true. It makes no sense to compare the two like this. You might as well compare… apples and pears.

This is because the market value of a company is linked to the expected value of all future profits. GDP, on the other hand, is a measure of the value of goods and services a country has produced in a single year.

It is possible to compare the size of a company and a country, but it has to be done properly, says Prof Paul De Grauwe, of the London School of Economics.

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"We would have to make a forecast of future growth of GDP in Poland, and then you would take the present value and use an interest rate," he says.

"My guess is that it would multiply the Polish number by a factor of at least five."

This would give Poland a comparative value of almost $2.5 trillion (£1.6tn), putting it well ahead of Apple.

There is another respectable way to compare the two. For this, calculate Apple's "added value" and compare that to Poland's GDP. (The Financial Times' business glossary defines added value as "an increase in the value of something that has been worked on, so that it can be sold in a new form".)

This makes sense because GDP is essentially a measure of a country's added value - it is the value of all the goods and services there, minus anything that has been imported.

"We would take the sales of Apple and subtract everything that is in the iPhone, but that Apple has not produced itself," De Grauwe says.

"For example, some chips, or the screen, which has been produced in China somewhere. And the difference then is what you could call the value added by Apple. And that we compare with GDP which is the value added in Poland."

Just looking at the size doesn't tell us much about relative power of the company v the country Paul De Grauwe

Apple's relative value would shrink four or five-fold if you did the comparison this way, De Grauwe estimates. This would make it the 56th largest economy in the world, not the 20th. It would be 36 places behind Poland, just ahead of Bangladesh and just behind Vietnam.

Even with these corrections, it is true that Apple is a big company.

But if a company is bigger than a country, does that mean it is more powerful?

Not necessarily, says De Grauwe.

"Just looking at the size doesn't tell us much about relative power of the company v the country. Countries are still sovereign in the sense they can set the rules of the game. They can tax companies, and they do."

And he points out that companies tend to have much more dramatic ups and downs in their fortunes than countries. The market cap - properly called "market capitalisation" - of a company is calculated by multiplying the current value of a single one of its shares by the number of shares in existence.

"When you take the market cap of a company like Apple this can change very quickly," says De Grauwe. "It is quite possible that in five years the market cap of Apple could have dropped to $100bn or $200bn.

"Look what happened to Microsoft. Not so long ago Microsoft was the biggest company in the world. Now it has weighed down. The price of a company's shares can move up a lot, but can [also] crash."