The stock market had another solid day on Thursday, sending the Nasdaq Composite (^IXIC 0.32%) up by half a percent. Market participants continued to cite hope for economic support from the federal government as a key reason for their optimism about stocks.

In addition, Wall Street analysts were generally upbeat on Thursday. In particular, favorable comments about Tesla (TSLA -2.32%) and Paychex (PAYX -1.68%) reflected the positive tone that the investment community has had about stocks recently.

Another push of the gas pedal for Tesla

Tesla shares didn't react all that much to the latest news on its stock. The electric vehicle pioneer saw its share price inch ahead by less than 1%.

Blue Tesla vehicle on a road with sun behind, on a road next to a picturesque landscape.

Image source: Tesla.

Analysts at New Street were the latest to weigh in on Tesla's prospects. The analyst company upgraded Tesla from neutral to buy, and set a price target of $578 per share on the stock.

In New Street's view, Tesla has already achieved an extremely important milestone. It wasn't that long ago that many questioned whether the automaker would ever be able to turn a profit producing its own vehicles. Now, that no longer seems to be up for debate, as the company has been consistently profitable in recent quarters.

The only thing limiting Tesla right now as New Street sees it is its currently constrained production capacity. As the automaker works to solve that problem with new production facilities and by obtaining the raw materials it needs, the always-controversial Tesla should be able to reach its full potential while also growing into adjacent businesses as well.

Paychex pays off

Elsewhere, Paychex saw its shares respond more positively to the favorable comments it earned from analysts Thursday. The stock closed higher by nearly 2%.

Paychex got an upgrade from analysts at Citi, who weighed in on the payroll services specialist after it reported its fiscal first-quarter financial results earlier this week. Citi boosted its rating from neutral to buy, and moved its price target on the stock higher by $18 to $93 per share.

Citi believes that Paychex should be able to handle current industry trends well. In particular, more businesses are shifting toward automating their payroll and human capital management resources, using digital platforms that improve productivity and make it easier for people across organizations to access and share information.

Some might think those trends would be a potential challenge to Paychex, however. The longtime payroll specialist faces competition from upstarts that started out with digital platforms. It'll be up to Paychex to make sure it can hang on to as many of its clients as it can, even as cloud-based companies in payroll offer some interesting advantages to woo customers away.

In addition, economic concerns could slow down Paychex's future growth in the near term. Typically, Paychex feels the impact when businesses have to let their workers go. With COVID-19 pandemic-related pressures still rattling the economy, investors in Paychex need to be prepared to wait for optimal growth.

Even so, Paychex's fiscal first-quarter results included limited revenue decreases of 6% and earnings that fared better than most had expected. If the payroll specialist can keep up that strong performance even under tough conditions, it bodes well for Paychex's long-term success.