By Cara Lombardo

Dell Technologies Inc. is examining options including a spinoff for its roughly $50 billion stake in VMware Inc. as the PC maker seeks to boost the value of its shares.

Dell recently kicked off a process to explore the possibility of unloading the stake or taking other steps that could include buying the rest of the cloud-software giant, according to people familiar with the matter. The companies are working with outside advisers, these people said.

The review is at an early stage and no decision is imminent and it is possible Dell will choose to do nothing.

The goal of the review is to address a gap between Dell's market value -- roughly $36 billion as of Tuesday afternoon -- and the value of its 81% stake in VMware, a differential that suggests the market is assigning little or no worth to Dell's core personal-computer and data-storage business. Separating the companies could help highlight the value of one or both businesses.

A transaction involving VMware, a major player in the fast-growing market for cloud software, could also be designed to help reduce Dell's $48 billion debt load.

To the frustration of Dell investors, the company's stock has barely budged since returning to the public markets in 2018. That is despite a more-than-50% rise in the same period for the tech-heavy Nasdaq Composite Index, which set a record high Tuesday as investors pile into stocks of companies that are thriving amid the coronavirus lockdowns.

In a sign of investor enthusiasm for a transaction that would unlock value, shares of both companies jumped in after-hours trading when The Wall Street Journal reported on the review. Dell shares rose 18% to $57.80 after rising 1.5% in regular trading. VMware shares, which were little changed during the day's session, rose 8% to $161.50.

Dell has recently organized working groups to explore various possibilities for the VMware stake. The primary option is a spinoff to Dell shareholders of the stake, some of the people said. Dell is assessing various implications of such a move, from corporate governance to capital structure and how the companies would work together following a separation, these people said.

Any deal is unlikely before next year. Dell can't spin off its VMware stake tax-free until September 2021, or roughly five years after the PC maker combined with EMC Corp., because of a rule requiring both companies involved in a spinoff to have operated continuously for five years to qualify for such tax treatment.

Dell, founded by Michael Dell in 1984, has become known for its complicated financial engineering over the years. It went private in a 2013 leveraged buyout by Mr. Dell and private-equity firm Silver Lake that was one of the largest on record. After buying EMC, they undertook a complex financial move that returned Dell to the public markets using the shares of a publicly listed vehicle that tracked Dell's stake in VMware. They were ultimately forced to sweeten the deal to fend off resistance from shareholders including activist Carl Icahn.

Dell shares closed at $49.01 Tuesday, which compares with $45.43 on their first day of trading in late 2018. Dell finance chief Tom Sweet said in a June 15 blog post that the company's priorities include optimizing its capital structure by managing cash flow, paying down debt and making the right investments.

VMware has a strong position in the market for "hybrid" cloud, where large companies mix public cloud services like those of Amazon.com Inc. and Microsoft Corp. with their own private networks. It has a market value of around $62 billion.

The demand for cloud computing, which enables customers to rent computing horsepower rather than invest in their own, has exploded in recent years. Startups and other businesses that couldn't support in-house IT departments were among the earliest cloud adopters, but now companies across most every industry rely on cloud services, making them a priority for many technology giants.

The personal-computer sector, on the other hand, no longer enjoys the heady growth it once did after the market condensed into a few key players and consumers turned their attention to smartphones and tablets. That is partly what led Dell to push further into data storage with its purchase of EMC, which at the time was the largest technology merger in history.

Included in that purchase were several other businesses such as cybersecurity firm RSA Security LLC, software-development company Pivotal Software Inc. and VMware, which has since bought Pivotal. Dell sold RSA to a private-equity firm

Write to Cara Lombardo at cara.lombardo@wsj.com