Long-term Rolls-Royce (LSE: RR) shareholders have already had a great run of it. Over the past five years, Rolls-Royce shares have moved up by 851%.

Over the past couple of months though, the share price has fallen by a couple of pounds to its current level (as I write 13 October) of around £13.71.

Could this potentially be a buying opportunity for me to add the share to my portfolio? Might it again go higher from here?

There could be more business growth to come

That fall back in the share price is no surprise in some ways. After all, Rolls-Royce shares still sell for 47 times earnings. For many investors – myself included – that does not look cheap.

But while the share valuation may have been looking stretched, the business itself has continued to do very well.

First half revenues were up by a fifth. Rolls has a brimming order book and customer demand remains robust. In civil aviation, defence and power systems, the engineer is benefitting from a structural uplift in demand that looks set to last.

Growing profits as well as revenues

Translating higher sales into higher earnings is not always easy. But on that 21% profit uplift in the first half, Rolls managed a 17% increase in statutory operating profit and 41% growth in underlying basic earnings per share.

That contrasts sharply with statutory basic earnings per share, which fell 63% year-on-year for the period.

But Rolls’ complex business with its long-term projects has often thrown up sharp contrasts between statutory and underlying numbers so in this case that does not concern me too much.

The broad story is one of strong growth, aided by a strong market and Rolls’ own business improvements in recent years.

Looking ahead, Rolls expects to deliver a thumping £4.7bn-£4.9bn in underlying operating profit and £3.8bn-£4bn of free cash flow for the full year.

What about the share price?

Could that help propel Rolls-Royce shares higher? Take £18 as an example. That would be around 14% above Rolls’ all-time high share price achieved this year. And it would be around 31% above the current share price.

Growth of over 30% is ambitious, especially when the valuation already looks punchy. However, I do think it is possible, if two conditions are met: Rolls grows profitability solidly, and it does not disappoint investors even once in delivering against its stated targets. In recent years it has done both of those things.

Given its cost discipline and strong customer demand environment, I think that could continue. I would therefore not be surprised if Rolls hits £18 over the next several years.

I’m looking for the next big growth story…

That will require a lot to go right though – and some things are outside the firm’s control. Civil aviation is prone to occasional demand slumps for reasons such as high oil prices pushing up ticket costs, geopolitical risks and terrorist risks. We have seen all of those already this year.

Indeed, US giant Delta — having ordered 62 engines from Rolls this year — recently warned on its own profits.

I do not think the current trading environment’s risks are properly priced into Rolls-Royce shares right now. So although I believe they could potentially move higher, I will not be investing and instead looking for more attractively priced growth opportunities elsewhere in the market.

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Christopher Ruane does not hold any positions in the companies mentioned.