Vodafone has said it needs to reduce the book value of its German acquisition to take account of a sharp drop in telecom share prices since the deal was completed.

The company has argued that offsetting the sum written down against tax is in line with German law, and is common practice in the telecoms industry.

Vodafone's proposal is currently being weighed up by the tax authorities in the state of North Rhine-Westphalia, where the firm has its German base.

A final decision may not be reached for up to three years.

But there has been speculation that the authorities in North Rhine-Westphalia may come under political pressure to reject the proposal, which comes as the Social Democrats are struggling to hold onto power in the state.

At the same time, North Rhine-Westphalia's finances are overstretched because of weaker-than-expected tax revenues.

I don't understand hyphens in the last sentence. Why on earth you should write 'weaker-than-expected' ? It is perfectly fine to write 'weaker than expected'.
In British English, the words "weaker than expected" must be hyphated if, as in this sentence, they are used as an adjective.

In American English this rule also exists, but is treated as flexible.

Most Americans would agree that two-word adjectives such as "worst-case scenario" or "senior-level employee" deserve hyphenation. But when it comes to adjectives upwards of two words, Americans are inclined to abandon the rule as though it didn't exist.
~waves hello~

"At the same time, North Rhine-Westphalia's finances are overstretched because of weaker-than-expected tax revenues."

Andrei, you say that "weaker than expected" is fine. And it is, but not when you want to use the whole phrase as the premodifier of a noun.

You wouldn't need the hyphens if the sentence were:
""At the same time, North Rhine-Westphalia's finances are overstretched because tax revenues have been weaker than expected."
'weaker than expected' is used differently in this last sentence.

The problem comes when you wish to use several words, or a phrase, to premodify a noun. In certain cases, it will be very difficult to see/understand the sentence unless hyphens are used.

"My niece is four years old."
"I have a four-year-old niece."
and even
"Four-year-olds are difficult kids to deal with."

In the last sentence, the adjective has been 'nominalised' (= it has nominal force and can replace the actual noun kids or children so the noun is not required. We say the adjective has been nominalised because it is now inflected for the plural -the final 's'-.

So it all depends on where in the sentence you wish to place a certain phrase/group of words.

I hope I haven't obscured Dave's explanation with mine!

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I appreciate taiwandave and miriam's exlanations to my question. I would say the replies are brilliantly concoted. You are all very clever.

By the way, I hope my apostrophe in the first sentence is fine. I wrote only '' miriam's '' .
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Here's another example of a multi-word adjective:

"I can't stand that person's holier-than-thou attitude," she said.