Owning CSL Ltd (ASX: CSL) shares over the past decade has been very rewarding, with good dividend growth and enormous capital growth. As shown on the chart below, the CSL share price has soared more than 200% in the past decade.

In my view, CSL may be the most impressive business on the ASX, with a market capitalisation of $100 billion. Its growth and global success are commendable.

Long-term shareholders are receiving much bigger dividends and are predicted to see even larger payments.

Let's have a look at how the CSL dividend could grow between now and the 2029 financial year.

This year, FY25

We're already close to halfway through the CSL 2025 financial year, so it won't be long before shareholders learn the FY25 interim dividend payment with the half-year result, which is expected in February 2025.

As for the annual dividend per share, UBS is currently forecasting that the CSL dividend could jump by 12% to US$2.96 per share. At the current CSL share price, that would represent a dividend yield of close to 1.7%.

UBS also considers the "possibility of a less vaccine-friendly US administration", which could impact CSL's vaccine business.

Next year, FY26

In the 2026 financial year, UBS is expecting CSL's profit to rise by more than 10%, and this can help the company's dividend rise too.

UBS is projecting that the CSL dividend could jump by another 12% to US$3.31 per share. That would represent a dividend yield of close to 1.9%. Not huge, but it's growing at a good pace.

After that, FY27

The 2027 financial year could see the business continue to grow its profit and dividend at a pleasing double-digit speed.

UBS projects that owners of CSL shares could receive an annual dividend per share of US$3.71, an increase of 12%. At the current valuation, that would represent a dividend yield of 2.1%.

Then, FY28

As an ASX healthcare share, it's quite possible that the company could deliver consistent profit growth over this period of time.

According to UBS, in the 2028 financial year, CSL could deliver a dividend increase of close to 12%, taking the annual payment to US$4.15. At the current CSL share price, that would represent a dividend yield of 2.35%.

Finally, FY29

The 2029 financial year is projected to be the best year of all – it could see yet another double-digit increase in percentage terms of both profit and dividend.

UBS forecasts that CSL's dividend could increase by another 12% in FY29 to US$4.65. At the current valuation, this payout would mean a dividend yield of 2.6%.

A 2.6% dividend yield isn't huge, but it shows how the dividend could scale upwards. Rising profit could also be exactly what investors want to see with CSL shares.