By Deborah Mary Sophia

(Reuters) -Macy's Inc on Tuesday decided against a push by an activist investor to spin off its online business and forecast better-than-expected annual sales after a bumper holiday quarter that was driven by strong demand for apparel and jewelry.

Shares rose as much as 10% after the department store chain announced a $2 billion share buyback plan and raised its quarterly dividend by 5%.

Its e-commerce business grew 12% in the holiday quarter and is expected to account for 37% of overall sales in 2022, with modernization efforts resulting in an 81% surge in app downloads compared to the prior quarter.

Still Macy's does not want to spin off the unit even though it was pushed to review the business following a demand from activist investor Jana Partners in October last year.

Jana had argued the online business could be worth a multiple of Macy's market capitalization, which is now nearly $8 billion.

"In every scenario we considered, we found the combination of our profitable digital platform with our national footprint will deliver greater value to shareholders than a separation ... ," Chief Executive Jeff Gennette said.

Jefferies analysts said the decision was not a "big surprise" as the push for a split had eased as the risk ratio was high. Jana earlier this month said it cut its holdings by 84% in the last months of 2021, before which it held a 1.5% stake in Macy's.

In the holiday quarter, Macy's also benefited from its plan to hold ample stock of key categories such as jewelry, apparel, fragrances and toys amid supply chain constraints.

Quarterly sales rose to a better-than-expected $8.67 billion and Macy's earned $2.45 per share, beating analysts' estimates.

It expects annual sales between $24.46 billion and $24.70 billion, above analysts expectations, betting on sustained demand as wages rise and social events become more frequent.

Executives, however, warned that record levels of inflation could offset some of the gains.

(Reporting by Deborah Sophia in Bengaluru; Editing by Arun Koyyur)