The UK stock market has an abundance of quality high-yield dividend shares. In fact, when I’m scouting about in a bid to boost my passive income, I often find it difficult to choose.

Right now though, I think this FTSE 100 share stands out above the crowd.

A sin stock

I’m referring to British American Tobacco (LSE: BATS). The company owns cigarette brands Lucky Strike and Pall Mall, as well as smokeless brands like Vuse (vaping), Velo (nicotine pouches), and Glo (heated tobacco).

The stock is up 16.6% year to date but basically flat over five years.

Now, I get that tobacco companies aren’t for everyone, mainly because they sell harmful and addictive products. As Mark Twain famously said: “Giving up smoking is the easiest thing in the world. I know because I’ve done it thousands of times.”

In the past, recession-resistant earnings from cigarettes was a key attraction for investors. Today though, many feel uneasy about investing in so-called sin stocks (tobacco, alcohol, gambling, etc). Some also won’t invest in oil or miners, while ‘Big Pharma’ and monopolistic ‘Big Tech’ sometimes get a bad rep too.

Taken to the extreme, there’d hardly be anything left to invest in!

Bargain-basement valuation

Anyway, I digress. Overall cigarette sales have been falling in the West and vaping is facing increasing regulatory scrutiny. Both are risks to British American Tobacco’s earnings.

Yet the firm remains super profitable and sports a massive 8.8% forecast dividend yield. The payout isn’t guaranteed, of course, and normally I’d be suspicious of such a high yield.

But over the next five years, the company expects to generate around £40bn of free cash flow before dividends. And right now, the stock’s price-to-free-cash-flow ratio is around 7. That’s incredibly cheap!

£1,000 a year

As I write, one share is 2,677p (or £26.77). With a yield of 8.8%, that means I’d need 421 shares to generate £1,000 a year in passive income. That would cost me a little over £11,270.

But what if I couldn’t afford that? Well, I could use a pound-cost-averaging strategy where I build out my holding over time.

For example, buying 18 shares a month would cost me around £482 (as things stand). And if I did this consistently every month for two years, I’d have 432 shares. They’d hopefully pay me £1,028 in dividends each year.

Of course, the share price will fluctuate over this period and the firm might raise or cut the dividend next year. Also, I’d want to build a well-diversified portfolio to avoid putting all my eggs in one basket.

I want more

The company’s strong competitive position and cash flows make me optimistic that the dividend is sustainable for the foreseeable future.

Moreover, the tobacco giant owns around 25% of ITC, a fast-growing Indian conglomerate whose shares are up 100% in five years. This stake is worth some £15bn! Not a bad asset to have in your back pocket.

This is why British American Tobacco is in my high-yield income portfolio, and why I plan to buy more shares soon. Each time the stock pays me a dividend, I plan to reinvest and aim for higher future income.