Royal Dutch Shell (LSE:RDSB) is a £75bn company listed on the FTSE 100. It explores for, produces and refines both oil and gas products and has a long and proud dividend history. In February 2016 it acquired gas firm BG, meaning it now produces more gas than oil. So far, so straightforward.

But it has been hit hard by falling commodity prices, as both the value of oil and gas have tumbled over the past year.

Shell was hugely profitable

Currently Shell pays out a 6.1% dividend yield. That’s a high income, and it gives the company strong appeal to dividend investors. The question is, how sustainable is that yield?

Well, let’s dig a little deeper. The reason Shell has such a high dividend is that it has been an immensely profitable company. In 2013 it made £10.6bn in net profit. And it pays out much of these earnings as dividends.

What’s more, because the share price has been falling, the level of the income payment relative to the share price has been amplified, meaning that the firm has one of the higher yields in the FTSE 100. But before you rush to buy into Royal Dutch Shell, let’s take a step back.

While the current dividend is dependent on past profits, future payments are dependent on how much money the company will make in years to come. And the game has been changed completely by the collapse in the oil price.

In 2013 turnover was an astonishing £289bn. In 2015 that had nearly halved to £172bn. And the impact on profitability is even more stark. 2013’s net profit of £10.6bn has turned to a profit of just £1.4bn in 2015.

Tumbling oil prices mean falling profits, and dividends

What really determines the share price is the earnings per share, and they’ve gone from 167p in 2013 to just 19p in 2015. So profitability has been sliding rapidly, and that’s why the share price has been trending downwards.

That in turn means the 6.1% yield is a red herring. It’s high at the moment, but isn’t at all sustainable, and it’s pretty much inevitable that it will be cut. That’s why we need to warn investors that a surprisingly high yield is often not a good thing.

Other instances of this happening include Aviva at the time of the Eurozone crisis, when profits turned to losses, and there was the appeal of a high income, but this was soon cut; and AstraZeneca at the time of a series of key patent expiries.

What’s more, I think the low oil price isn’t something temporary, but a long-term trend that could last over a decade. So I believe profitability will remain low and won’t rebound, the dividend is likely to be reduced, and then stay low.

That means I would advise readers not to buy into Shell as an income investment, despite the current yield. You’re likely to see not only the dividend fall, but also the share price.

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Prabhat Sakya has no position in any shares mentioned. The Motley Fool UK has recommended Royal Dutch Shell B. We Fools don't all hold the same opinions, but we all believe that considering a diverse range of insights makes us better investors.