With Rolls-Royce Holdings (LSE:RR.) announcing its ninth earnings upgrade in just over two years, it’s no surprise its share price continues to rise.

But there’s another stock – Space Exploration Technologies (NASDAQ:SPCX), or SpaceX as it’s best known – that also continues to grab the headlines.

So which of these two’s likely to double its share price first? I have my own view. But for a bit of fun, I’ve also consulted ChatGPT. This is what it told me…

Sitting on the fence

The software’s initial response was to hedge its bets. It said: “My pick… is Rolls-Royce — but SpaceX could get there faster if sentiment turns strongly bullish”.

For Rolls-Royce to reach the milestone, ChatGPT said it “would require several more years of substantial earnings and cash flow growth rather than simply another rerating”. As for SpaceX, it reckoned it “would imply an extraordinarily large company valuation”.

When pushed, it chose Rolls-Royce, specifying a timeframe of three-to-five years. Over two years, it said SpaceX was the more likely winner.

Of course, it’s important not to base investment decisions on the advice of a piece of software. There’s no substitute for human-led research. With this in mind, what do I think?

My view

A big issue is that SpaceX is loss-making, so this makes earnings-based measures irrelevant.

However, Elon Musk appears to have the Midas touch when it comes to stock market valuations. His other high-profile business, Tesla, has an eye-watering price-to-earnings ratio of 188. Apply this to Rolls-Royce and it would have a share price of £67.74, over four times higher than today’s (10 August).

Personally, I rate Starlink, SpaceX’s satellite-based internet service. I think it could grow exponentially. And successfully commercialising Starship, the world’s largest rocket, could be a game-changer.

I also like Rolls-Royce’s diversified business model. All three of its divisions — civil aerospace, defence, and power systems – are performing strongly and, in my opinion, are likely to benefit from increased air travel, continuing geopolitical uncertainty, and further AI data centre growth respectively.

Of course, neither of their market-caps might double. SpaceX is a highly speculative venture with only Starlink being profitable. It also has huge capital expenditure requirements, having spent $18.4bn during the second quarter. At this rate, the $85.7bn raised from its IPO won’t last long.

As for Rolls-Royce, it remains heavily dependent on its aircraft engines business which, as the pandemic reminded us, makes it vulnerable to a period of extended travel disruption. It’s also unclear how much of its small modular reactor programme has already been priced in to its share price. As with any new technology, there’s no guarantee of success.

Final thoughts

In some respects, it doesn’t matter whether the two stocks double or not although, over the long term, I would be surprised if they didn’t. However, I’m not going to stick my neck out and give a timescale.

Personally, I think SpaceX is more likely to get there first although it’s a much riskier investment. There’s so much hype surrounding the stock that it could achieve this feat even if its financial performance doesn’t justify such a high valuation. But that doesn’t mean I don’t rate Rolls-Royce, which recently announced another earnings upgrade.

In fact, I own both these stocks. Others could consider them too.

Should you invest £5,000 in Rolls-Royce Plc right now?

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James Beard owns shares in Rolls-Royce Holdings plc and Space Exploration Technologies.