Stocks climbed higher Tuesday as the first of two key U.S. inflation reports this week came in cooler-than-expected. The Dow Jones Industrial Average rose over 400 points, while the S&P 500 Index and Nasdaq Composite advanced about 1.7% and 2.4%, respectively.

Here's how the market settled on Tuesday:

S&P 500 Index (SPY  ): +1.68% or +90.04 points to 5,434.43

Dow Jones Industrial Average (DIA  ): +1.04% or +408.63 points to 39,765.64

Nasdaq Composite Index (QQQ  ): +2.43% or +407.00 points to 17,187.61

Moving Markets:

Wholesale Prices increased at a less-than-expected rate in July, boosting investor optimism towards a near-term interest rate cut from the Federal Reserve.

The producer price index (PPI) rose 0.1% on the month, the Bureau of Labor Statistics reported Tuesday; the index tracks the selling prices that producers pay for goods and services. On an annual basis, PPI rose by 2.2% in July, below June's increase of 2.7%.

On a core basis, which excludes volatile food, energy and trade prices, month-to-month PPI rose 0.3% and increased year-over-year 3.3% in July.

The PPI reading comes ahead of July's consumer price index (CPI) reading set to release on Wednesday, which measures the prices consumers pay for a series of goods and services. Economists expect both headline and core CPI to increase by 0.2% on the month.

In the News:

Starbucks (SBUX  ) announced Tuesday its replacing CEO Laxman Narasimhan with Chipotle (CMG  ) CEO Brian Niccol, rallying the coffee chain's shares higher to its best day since its initial public offering in 1992. Starbucks CFO Rachel Ruggeri will serve as interim CEO until Sept. 9, while Niccol will officially assume the role; Narasimhan's departure as CEO and board member is effective immediately.

Niccol has served as Chipotle's CEO since 2018, with its stock soaring about 775% during his tenure.

Separately, Elliott Investment Management released a statement on Tuesday revealing the activist investor's stake in the chain.

"Elliott has become one of the largest investors in Starbucks because of our confidence in the long-term value-creation opportunity we see at one of the world's most important brands. Elliott has been engaged with Starbucks' Board over the past two months regarding our perspectives on the Company's key issues, and we view today's announcement as a transformational step forward for the Company," managing partner Jesse Cohn and partner Marc Steinberg said in a joint statement. "We welcome the appointment of Brian Niccol, and we look forward to continuing our engagement with the Board as it works toward the realization of Starbucks' full potential."

On the Earnings Front:

Home Depot (HD  ) reported better-than-expected second-quarter earnings and sales on Tuesday, but issued cautious forward guidance as high interest rates and waning consumer demand is expected to impact sales growth in the second half of the year.

The home improvement retailer now expects full-year comparable sales to decline by 3% to 4% compared with the previous fiscal year, down from previous projections for comparable sales to fall about 1%.

"Pros tell us that, for the first time, their customers aren't just deferring because of higher financing costs," CEO Richard McPhail told CNBC in an interview on Tuesday. "They're deferring because of a sense of greater uncertainty in the economy."

For Wednesday:

Market participants will turn their attention towards July's CPI report due out Wednesday morning.