Texas Instruments Inc reported better-than-expected fourth-quarter chip sales as customers in a broad array of industries replenished depleted inventories.

TI shares rose more than 3.4 percent in late trade on Monday after the maker of chips for a broad array of manufacturers in everything from consumer electronics to industrial equipment said

it saw a December demand improvement that continued in January.

After shaving back their stocks of chips since around mid-year, TI's clients began speeding up orders last month because demand from the consumers and businesses that buy their products was not as light as they had feared.

We think our customers have reached a point where their (inventory) numbers were extremely lean, Chief Financial Officer Kevin March told Reuters.

TI said it would hire new workers in some factories this quarter to cope with increasing demand. But it also plans to close older factories -- one in Texas and another in Japan -- in the next 18 months to cut costs.

TI's outlook for the current quarter was not very strong due to a drop off in sales in a wireless business it is shuttering. But analysts were still encouraged by the fourth quarter.

Everybody feared we'd end the holiday season with abysmal sales. The reality is that end-demand is better than TI customers had originally feared, said Williams Financial analyst Cody Acree. We're not calling for great growth but we're not heading into the abyss.

Before TI issued results, upbeat forecasts by smaller rivals Linear Technology and Xilinx last week had already made investors optimistic that a drawdown of chip inventories in the broader market may be ending.

Much of the chip industry has been in a funk since mid-2011, when manufacturers began to cut orders of new product and use up existing inventories due to jitters about a gloomy economy.

Also on Monday, European chipmaker STMicroelectronics suggested that customers had resumed buying chips after depleting their stocks.

REVENUE BEATS ESTIMATES

TI reported a fourth-quarter profit of $298 million, or 25 cents per share, compared with $942 million, or 78 cents per share, in the year-ago quarter.

Revenue fell to $3.42 billion from $3.53 billion, but above Wall Street's expectations of $3.25 billion, according to Thomson Reuters I/B/E/S.

TI had warned December 8 that chip demand was weak, forecasting quarterly earnings per share in a range of 21 to 25 cents on revenue of $3.19 billion to $3.33 billion.

But March said that orders started to improve right away after the December warning.

TI's forecast for first-quarter revenue in a range of $3.02 billion to $3.28 billion was much weaker than Wall Street expectations for $3.47 billion, according to Thomson Reuters I/B/E/S.

March blamed TI's weak revenue guidance for the current quarter primarily on a decline in its baseband chip segment, which it plans to shutter by the end of this year.

Revenue from the baseband business, whose main customer is Nokia , will fall to about $75 million this quarter from $279 million in the fourth quarter, March said.

Excluding the decline in baseband revenue, he said TI's first-quarter revenue would have fallen 2 percent from the fourth quarter, compared with the more typical sequential decline of 4 percent.

The Dallas-based chip maker also said it would incur charges of about $215 million from the closure of a factory in Hiji, Japan, and another in Houston, Texas, in the next 18 months.

It already shouldered just over half the cost of the closures in the fourth quarter and expected the rest to hit in the next several quarters.

But once the closures are complete, TI said they would cut annual costs by about $100 million.

TI shares were up more than 3.4 percent at $34.34 in after-hours trading on Monday, compared with their Nasdaq closing price of $33.19.

(Additional reporting by Noel Randewich in San Francisco, Editing by Steve Orlofsky, Matthew Lewis, Bernard Orr and Lisa Shumaker)

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