Looking for some deals in the stock market? If you've got $5,000 that you are looking to invest in some established growth stocks, there are some bargains worth considering. Three cheap stocks backed by promising businesses that would make for solid long-term investments right now are Alibaba Group (BABA 0.59%), United Parcel Service (UPS 0.14%), and AstraZeneca (AZN 0.19%).

1. Alibaba Group

Chinese stocks have been undervalued for several years due in part to ongoing tensions between China and the U.S. But China is an attractive market to invest in. In the last quarter of 2023, the Chinese economy grew at a rate of 5.2%, compared with 3.3% for the U.S.

Growth in both economies could slow down this year, but the difference is that while many U.S. growth stocks are overpriced due to better-than-expected economic growth, Alibaba remains discounted. Investors can get the e-commerce giant for an incredibly cheap valuation of less than 8 times its expected future profits. By comparison, the S&P 500 averages a forward price-to-earnings multiple of 22.

Alibaba has a broad business that includes online shopping platforms Taobao and Tmall, along with digital media and a growing cloud infrastructure business that 80% of China's technology companies rely on. Alibaba also makes for an underrated AI stock, as it has been working on its own chatbot, Tongyi Qianwen.

Although its growth rate has been modest in recent periods, often below 10%, Alibaba's potential remains promising in the long run. Buying the stock now, while it trades near its 52-week low of $66.63, could be an excellent move for long-term investors.

2. United Parcel Service

United Parcel Service, also known as UPS, is also trading at a modest multiple -- less than 17 times its future expected profits, UPS is also around $10 away from its 52-week low of $133.68.

The company is coming off a tough quarter. Its Q4 revenue was $24.9 billion -- down from $27 billion in the prior-year period. But geopolitical issues and challenging economic conditions have weighed on demand for its services.

Management is forecasting a minor improvement this year, projecting 2024 revenue of between $92 billion and $94.5 billion, up from the $91 billion it reported in 2023. But in the longer run, as geopolitical conditions improve and e-commerce picks up, demand should be even stronger.

As a leader in the logistics industry, UPS plays a key role in the U.S. economy's growth, which is why it's a good stock to hold in your portfolio for the long haul. Investors would be well-advised to follow Warren Buffett's wisdom of betting on America. While UPS' business is facing challenges right now, these aren't problems that should hold the company down.

3. AstraZeneca

AstraZeneca is a top healthcare company, but it's not trading like one. Investors can buy its stock for less than 16 times its estimated future profits, and just a few dollars above its 52-week low of $61.73.

What's promising about the business is that it is broad and contains many different growth opportunities. The company's business encompasses products in multiple therapeutic areas, including oncology; cardiovascular, renal, and metabolism; rare diseases; respiratory and immunology; and vaccines and immune therapies.

The company has many blockbuster drugs in its catalog: Through just the first nine months of 2023, Tagrisso, Imfinzi, Lynparza, Calquence, Farxiga, Symbicort, Fasenra, Soliris, and Ultomiris, had all already breached the $1 billion mark in annual sales. And with 167 projects in its research and development pipeline, expect the company to add to that tally in the future. Over the last four reported quarters, the company has generated nearly $45 billion in revenue, with net income totaling just under $5.9 billion.

With an extensive pipeline and a modest valuation, AstraZeneca appears to be an overlooked stock that could make for a great option for long-term investors.