Sony signs hang from a store in Tokyo, Feb. 7, 2013. A U.S. hedge fund has proposed that Sony Corp. selling up to 20 percent of its entertainment business to use that money to strengthen its ailing electronics unit. (Junji Kurokawa/AP)

Sony has a $100 billion reason to consider Daniel Loeb’s breakup proposal.

Loeb, whose Third Point hedge fund has taken a $1.1 billion stake in Sony, is pushing the Tokyo-based company to sell as much as 20 percent of its entertainment business and focus on the “considerable and underappreciated value” of its electronics unit. After Loeb’s proposal sparked the biggest rally in Sony shares in more than four years, the $21 billion company still languishes at a cheaper valuation relative to profit than 90 percent of similar-sized consumer electronics makers.

Loeb is approaching Sony after shareholders lost more than $100 billion in market value since 2000. CLSA Asia-Pacific Markets said Sony would be worth 28 percent more in a separation. While estimates from Macquarie Group’s Damian Thong fall short of Loeb’s targeted 60 percent stock gain, the analyst said the activist’s claim that spinning off the entertainment unit and boosting its profitability may raise the company’s market value by about 30 percent “seems reasonable.”

“Sony is a chronic underperformer,” said Joshua Strauss, co-manager of the Appleseed Fund at Pekin Singer Strauss Asset Management, which oversees about $1 billion, including investments in Japan and Korea. “Should they spin off the entertainment division? Would it create shareholder value? Probably. When you do that sort of thing, the sum of the parts is greater than the whole.”

Loeb said in a May 14 letter to Sony chief executive Kazuo Hirai that the company should sell as much as 20 percent of Sony Entertainment in an initial public offering, giving current Sony shareholders priority in owning the shares and reducing leverage for the electronics business.

“As president and CEO Kazuo Hirai has said repeatedly, the entertainment businesses are important contributors to Sony’s growth and are not for sale,” Sony said.

Independently listed, the entertainment business — featuring artists including Bruce Springsteen and the top-grossing U.S. film studio — could improve its margins and boost earnings as much as 50 percent, wrote Loeb, whose firm owns about 64 million Sony shares. Loeb said that could add 625 billion yen ($6.1 billion) to Sony’s market value, or 540 yen per share — an amount that Thong said “seems reasonable.”

Sony shares, which rose Friday, gained another 0.5 percent to in Tokyo. The stock closed at 1,877 yen on May 14 before Loeb’s letter was disclosed.

In addition, Loeb said Sony should focus on streamlining its electronics offerings, as that unit is poised to return to profitability. Sony makes consumer electronics such as the PlayStation game console and Xperia smartphones.

“The value realization within the entertainment business was always secondary to the turnaround in the electronics business,” Thong said. “What this has done is shine a search beam right on a part of the business that should be valued more.”

Founded in 1946, Sony was emblematic of Japan’s post-World War II rise, inventing the Trinitron cathode-ray tube TV in the 1960s and the Walkman portable music player a decade later. Its market value, which topped $120 billion in 2000, has since plunged as consumers shifted to flat-panel TVs, smartphones and mobile devices made by South Korea’s Samsung and the United States’ Apple.

While a weaker yen, box-office successes such as “Skyfall” and the sale of its New York headquarters helped return Sony to its first profit in five years, the company’s valuation has lagged its historical highs and its peers.

The value of Sony’s entertainment division — which makes the “Spider-Man” movies through its Culver City, Calif.-based Sony Pictures and also represents music artists including Grammy winner Adele — isn’t being realized in the company’s current structure, said Michael Souers, an equity analyst at Standard & Poor’s.

“It’s totally being weighed down by the struggling consumer electronics unit and the fact that it’s had to subsidize that unit,” Souers said. A partial spinoff “would make sense for them. And from a managerial perspective, they could focus a little bit more on turning around the electronics business.”

Still, Loeb’s push faces hurdles in a culture that traditionally hasn’t been welcoming to overseas activist investors, Strauss said.

In the early 1990s, oilman T. Boone Pickens failed to win a board seat at auto parts dealer Koito Manufacturing. Last month, Seibu Holdings said it won’t offer any concessions to New York-based private-equity firm Cerberus Capital Management, the hotel and rail operator’s biggest investor, in its push for board seats and a bigger stake.

“The Japanese don’t care,” Strauss said. “They’re not beholden to shareholders in that country. Some guy in New York is not going to convince Japanese companies to change their way of doing things.”

Still, Nobuo Sayama, a partner at Tokyo-based private-equity firm Integral, said the return of activist investors to Japan is a positive development.

Loeb’s interest “is something Sony or Japan as a whole should welcome,” he said in a phone interview. “The industry should be grateful for such proposals from investors at home or abroad.”