-- U.S. stock futures were largely muted on Tuesday after hopes for Federal Reserve interest rate cuts later this year spurred on a jump in equities in the prior session. Richmond Fed President Thomas Barkin says that borrowing costs are currently "restrictive" enough to corral elevated inflation. Walt (NYSE:) gears up to unveil its first quarterly results since it won a fierce proxy battle with activist investors.

1. Futures muted

U.S. stock futures were mixed on Tuesday, as investors poured through fresh inflation commentary from Federal Reserve policymakers and looked ahead to a new batch of quarterly earnings.

By 03:32 ET (07:32 GMT), the contract had gained 46 points or 0.1%, were mostly unchanged, and had edged down by 10 points or 0.1%.

The main indices on Wall Street rose in the prior session, buoyed by hopes that softer-than-anticipated monthly U.S. labor market report may persuade the Fed to slash interest rates down from more than two-decade highs as soon as September. Prior to the data, markets were expected the central bank to roll out a cut in November.

Chipmakers were among the best performing stocks on Monday, with Holdings (NASDAQ:) in particular rising 5.2% ahead of its fiscal fourth-quarter results after the closing bell on May 8. Paramount Global shares also advanced following the expiration of exclusive negotiations with Skydance Media over a potential deal, which will give the entertainment giant the opportunity to explore competing bids.

Shares in (NYSE:), meanwhile, slumped following a weak current-quarter revenue outlook from the low-price carrier.

2. Interest rates "restrictive" enough to cool inflation - Fed's Barkin

Interest rates in the U.S. currently stand at such "restrictive" heights that they can help tamp down demand and cool sticky inflationary pressures, according to Richmond Fed President Thomas Barkin.

Speaking in South Carolina, Barkin said he is "optimistic" that the current level rates -- a range of 5.25% to 5.50% -- should be enough to bring the pace of price growth back down to the Fed's target.

Barkin also said he does not believe the economy is on track to overheat, a concern that has factored into the central bank's decision not to ratchet down rates earlier this year as initially expected. Should the economy slow significantly, he added, the Fed has the "firepower" at its disposal to supply the necessary support.

But Barkin noted that inflation, the central focus of a steep recent tightening cycle by the Fed, is proving difficult to ease.

"It's a stubborn road back," Barkin said. "It doesn't mean you won't get it back. It just means it takes a while."

3. Disney earnings ahead

Walt Disney is due to report its second-quarter results prior to the opening bell on Tuesday, weeks after the entertainment giant emerged victorious in a proxy battle with activist investors.

In April, shareholders largely backed Chief Executive Bob Iger and his plan to turnaround performance at the company, marking a defeat to a challenge from a cadre of large investors led by Trian Partners boss Nelson Peltz. Shares in Disney have now gained more than 28% in 2024, but remain far below highs touched three years ago.

Stakeholders will now be looking for Iger to provide further details on his future strategy for the company, including a goal of making its all-important streaming business profitable by the end of the year.

Analysts expect the streaming service, which has been attempting to entice customers by bundling together offerings like Disney+, Hulu, and ESPN+, to post subscriber growth. Operating losses at Disney's direct-to-consumer unit are also seen narrowing.

Group-wide, adjusted earnings per share and revenue are projected to climb to $1.10 and $22.1 billion, respectively.

4. Apple developing AI chip for data centers - WSJ

Apple Inc (NASDAQ:) is developing an in-house chip intended to run artificial intelligence programs in data centers, the Wall Street Journal reported on Monday, as the tech giant seeks to gain an edge in the fast-growing industry.

The project is internally code-named ACDC -- Apple Chips in Data Centers, the WSJ report said.

Apple began designing its own chips for its flagship iPhones and other devices over the past decade, as it sought to cull its reliance on other chip developers such as Intel (NASDAQ:).

The WSJ report comes amid growing speculation over just how Apple plans to incorporate AI into its product line-up, given that it has somewhat lagged its U.S. tech peers in rolling out AI products.

5. Crude hovers around flatline

Crude prices hugged the flatline on Tuesday after Israeli strikes on the city of Rafah in southern Gaza raised doubts about a potential ceasefire in the region.

By 07:32 ET, the futures and the contract were mostly unchanged at $78.47 a barrel and $83.35 per barrel, respectively.

Palestinian militant group Hamas on Monday agreed to a Gaza ceasefire proposal from mediators, but Israel said the terms did not meet its demands while planning to continue negotiations on a deal.

A lack of settlement between the parties in the now seven-month long conflict has supported oil prices, as investors worry regional escalation of the war will disrupt Middle Eastern crude supplies.

That said, the benchmarks posted the steepest weekly losses in three months last week as traders fretted about the prospect of higher-for-longer interest rates curbing growth in the U.S., the top global oil consumer.