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Jay Yao | Wednesday, 16th December, 2020 | More on: RR I would like to receive emails from you about product information and offers from The Fool and its business partners. Each of these emails will provide a link to unsubscribe from future emails. More information about how The Fool collects, stores, and handles personal data is available in its Privacy Statement. Rolls-Royce shares: Here’s what I think is next for the dividend As a result of the pandemic, Rolls-Royce (LSE: RR) management suspended the dividend for the first time since 1987, and the company’s stock fell substantially in the earlier part of the year. With the recent stock rally driven by vaccine optimism, however, Rolls-Royce shares have rebounded strongly from its year’s lows. 5G is here – and shares of this ‘sleeping giant’ could be a great way for you to potentially profit!According to one leading industry firm, the 5G boom could create a global industry worth US$12.3 TRILLION out of thin air…And if you click here we’ll show you something that could be key to unlocking 5G’s full potential…Given the optimism in Rolls-Royce shares, here’s what I think management might do with the company’s dividend in the coming years. It’s going to get betterRolls-Royce’s dividend depends on how well the company does fundamentally. Fortunately, I think there will be better times ahead for the company financially speaking. Thanks to the pharmaceutical industry developing a vaccine for Covid-19 in record time, there’s hope for Rolls-Royce’s financials to bounce back. In December, both the US and the UK approved coronavirus vaccines developed by Pfizer and BioNtech. Other vaccine candidates for Covid-19 could be approved next. As a result of the vaccines, there is hope that things could return closer to normal in many parts of the developed world by the end of next year or 2022. Ryanair CEO Michael O’Leary elaborated on that hope in November, “I’ve heard a lot of rubbish coming from legacy airlines that it’ll be 2035 till the volumes come back. Rubbish. Volumes will go back in 2021 or 2022 pretty quickly – they will go back because Ryanair will discount prices, hotels will discount.”Rolls-Royce shares: Trading updateIn December, RR management also elaborated on their expectations for the coming years via a trading update. Management disclosed that their restructuring plan to deliver a targeted £1.3bn of cost savings by 2022 is on track. Management also expects RR to turn cash flow positive at some point in the latter half of 2021. They are targeting at least £750m in free cash flow (FCF) excluding disposals as early as 2022 as well.What I think management might do with the dividendIf things turn the way management expects in terms of free cash flow, I imagine Rolls-Royce shares will pay a dividend for the 2022 year. Although there is a chance that RR pays a dividend for the latter half of 2021, I don’t believe it’s very high given that management will probably err on the side of caution. In terms of the potential total annual dividend for 2022, I reckon it could be less than 2.28p per share or less. I think this because RR reported free cash flow of 45.9p per share and paid an annual dividend of 11.7p for 2019. That gives RR a dividend to FCF ratio of 25.5% for 2019.Assuming that RR achieves £750m in free cash flow in 2022 and management pays the same dividend to free cash flow ratio, RR would pay around £191m in dividends for that year. Given the 8.37bn shares outstanding, according to Bloomberg, RR would pay around 2.28p per share for 2022. Given that there’s still a lot of uncertainty left and management might decide to use free cash flow to pay down debt, I reckon there’s a pretty high chance that the initial annual dividend per share for 2022 will probably be less than that. On the other hand, if management very well executes and free cash flow comes in higher than £750m, the annual dividend could be higher for 2022.Given the RR’s prospects, I’d hold on to Rolls-Royce shares because I’m long-term bullish on air travel.