With FTSE 100 shares alone paying out well over £1bn per week on average in dividends, the blue-chip index can make a great hunting ground for passive income streams.

For example, one company paying out huge sums in dividends each year is Lucky Strike owner British American Tobacco (LSE: BATS).

Now, I know tobacco stocks are not for everyone: some investors object on ethical grounds. But for those who do not, I think this is a share that merits consideration.

Long-term dividend growth

The share pays dividends quarterly. The current quarterly dividend is 61.3p per share, making for an annual total of around £2.45.

So, if someone bought 1,000 shares in British American Tobacco today – at a cost of around £45,680 — they ought to earn roughly £2,450 per year in dividends. That is a yield of 5.3%.

In fact, they could potentially do even better in future. British American Tobacco is one of a small number of FTSE 100 shares to have grown its dividend per share annually for decades.

It aims to keep doing so. Cigarette sales are highly cash generative, underpinning the payout.

No guarantees when it comes to dividends

But like any company, the dividend at British American cannot be guaranteed to last.

Management has a strong incentive to deliver on its aspirations, as passive income is a key plank of the company’s investment case.

But with cigarette use in decline, there is a risk that the dividend could become unsustainable even at its current level, let alone a higher one. UK rival Imperial Brands cut its dividend sharply in 2020.

A shifting landscape

This week, British American affirmed its performance guidance for its current financial year, excluding the impact of currency fluctuations. Those expectations include revenue growth.

I see that as positive for the investment case. It builds on 2.1% revenue growth last year (again, excluding exchange rate movements; taking them into account, revenues fell 1%).

But what I found more alarming this month was the news that the company’s cigarette sales volumes last year fell 8%. That is no small decline.

Strong pricing power

How did British American manage to grow revenue despite its biggest product category recording a steep fall in sales?

Thanks to the nature of nicotine and its premium brand portfolio, British American has strong pricing power. It can raise selling prices to help mitigate the impact of falling volumes.

That can only go so far, of course. But for now it is helping to blunt the commercial impact of falling cigarette sales volumes.

Also, British American has been growing its non-cigarette business in recent years.

There could be ongoing potential here

Declining cigarette sales are a real risk for the company nonetheless.

But so far, it is taking them in its stride and it may continue to do so.

Cigarette sales peaked in many markets decades ago, but British American has kept growing its dividend per share like clockwork each year.

From a passive income perspective, I see it as a share for investors to consider.