Elliott, the $65 billion hedge fund best known for its , has made a $2.5 billion investment in and is urging the company to improve its free cash flow by adopting a less rigid plan for capital expenditures.

In a 13-page letter viewed by CNBC, Elliott proposes that Texas Instruments introduce what it calls a "dynamic capacity-management strategy" that would allow the company to achieve free cash flow of as much as $9 a share by 2026, which is roughly 40% above current consensus of the analysts who follow the world's largest maker of analog semiconductors.

Shares of TI jumped about 3% on the news before paring back the gains in morning trading.

Elliott believes Texas Instrument's rigid adherence to a capital expenditure plan put in place in 2022 has eviscerated shareholder returns by greatly reducing a metric by which TI has always asked to be judged – free cash flow.

Citing the reduction of free cash flow from $6.40 a share in 2022 to an expected $1.83 a share this year, Elliott maintains that TI has alienated investors who might otherwise gravitate toward its dominant position in serving the automotive and industrial complexes with analog chips. Its stock price, Elliott insists, has suffered as a result, trailing its peer group by substantial margins over the last two, four, six and 10-year periods.

The focus of Elliott's letter is the 2022 capital expenditure plan, which called for TI to ramp its capex spending to a high of $5 billion a year from 2023-26, bringing that spending to as much as 23% of revenues from what had been capex spending of roughly 5% of revenues over the preceding decade.

That allocation of capital will result in the addition of capacity allowing for the company to almost double current annual revenues to $30 billion.

The problem, Elliott maintains, is that a reversal in the cycle of demand for TI's chips since the plan was put in place will result in capacity levels that are "50% above consensus revenue expectations in 2026 and 2030."

The letter's signatories are Jesse Cohn, who runs activism at Elliott and senior portfolio manager Jason Genrich, who has overseen activism efforts in , and , among others. The duo believes the key question for TI's management and board is " not whether TI has a thoughtful long-term strategy but rather: Is the fixed magnitude and pace of its capacity buildout appropriate given the expected level of excess capacity?"

Elliott suggests the company either communicate more forcefully why it believes such an increase in capacity is justified or move to a more dynamic approach to capex in which it builds new fabrication facilities but is more deliberate about equipping them, allowing for a more precise response to market demand.

The letter maintains a far less adversarial tone than is often the case for Elliott, making it seem unlikely that the firm will challenge management or the board more forcefully in the near term.

In fact, the only threatening passage comes on page 11 in which Elliott charges the board with failing to hold management accountable to one of the company's core values: prudent capital discipline. In that passage, Elliott urges it to recapture its oversight responsibility by instituting a more dynamic approach to capacity expansion.

A spokesperson for Elliott declined to comment on the letter. Representatives from TI could not be reached.