Shares of office-supply store Office Depot (NASDAQ:ODP) skyrocketed by 25% yesterday following the company's third-quarter earnings release. The stock ended the day at a multiyear high.

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Office Depot 5-Year Stock Chart, data by YCharts.

Office Depot's stock gain was well deserved. The retail chain delivered strong earnings growth in the quarter due to faster realization of synergies from its merger with former rival OfficeMax. Just as importantly, the company increased its projection for total cost savings and offered a stellar forecast for earnings growth in 2015.

Synergies flowing through
In the third quarter, Office Depot's adjusted operating income reached $126 million -- more than double the combined total of Office Depot and OfficeMax from the prior-year period. Earnings per share doubled to $0.10, beating the average analyst estimate by $0.01.

Office Depot is starting to see large synergy gains from the merger. The company captured $90 million of merger integration synergies last quarter, more than explaining the year-over-year increase in adjusted operating income.

Additionally, Office Depot raised its full-year adjusted operating income guidance for a third time. In February, Office Depot provided initial guidance for at least $140 million. It raised that guidance to $160 million in May and then to $200 million in August. Office Depot now expects adjusted operating income of $255 million-$265 million in 2014, nearly double the original guidance.

More savings ahead
Office Depot's profit will continue to rise rapidly as it captures more merger synergies. The company is consolidating its supply chain by closing overlapping distribution centers. The first distribution center closed last quarter, and a total of five will be shuttered by the end of first-quarter 2015.

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Office Depot is closing stores in markets where Office Depot and OfficeMax stores are competing with each other. Photo: The Motley Fool.

Office Depot is also rationing its store footprint by closing Office Depot and OfficeMax stores that are competing with each other. Over 100 stores will close in the next two months alone, followed by 135 more closings in 2015. This will cut costs, and Office Depot expects to recapture a solid chunk of those stores' sales in nearby locations and online.

These moves and other cost-reduction initiatives will lead to higher merger synergy savings for Office Depot in 2015. As a result, the company expects adjusted operating income to reach approximately $475 million, up about 80% from the projected 2014 figure.

Additional cost reductions should be implemented by 2016. For example, Office Depot last month announced a broad restructuring of its European business. By moving from a geographic structure to what it calls a "business-channel focus," Office Depot will cut annual costs in Europe by $90 million.

In total, annual merger synergies and restructuring savings are now expected to reach $840 million by the end of 2016. That compares to the $90 million realized in the last quarter (a $360 million annual rate). In other words, most of the merger upside is still on the way.

Room to run
Office Depot's market cap is about $3.4 billion following the stock's big gain on Tuesday. The company continues to suffer from secular declines in some key office supply categories, but its cost-cutting efforts can more than compensate for those headwinds.

As synergy savings rise from $260 million in 2014 to at least $840 million by 2017, Office Depot's net income and free cash flow will rise exponentially. Staples, which is 40% larger than Office Depot by sales volume, is valued at $8.4 billion -- about 2.5 times Office Depot's market cap.

As merger synergy and restructuring savings flow through in the next few years, Office Depot's margin structure should approach that of Staples. Even if Office Depot doesn't achieve quite as high a valuation as its rival, the shares could still rise another 50% in the next two years .

Adam Levine-Weinberg owns shares of Office Depot. The Motley Fool owns shares of Staples. Try any of our Foolish newsletter services free for 30 days. We Fools may not all hold the same opinions, but we all believe that considering a diverse range of insights makes us better investors. The Motley Fool has a disclosure policy.