Owners of Wesfarmers Ltd (ASX: WES) shares have received a pleasing level of dividend payouts over the years. After all, passive income from an ASX blue-chip share can be precisely the steady income-generating strategy that people are looking for.

Wesfarmers owns a variety of leading Australian retailers, including Bunnings, Kmart, Officeworks and Priceline.

Bunnings and Kmart Group (which includes Target) make enormous profits each year for the ASX retail conglomerate. In the FY24 first-half result, Bunnings made $1.28 billion of earnings before tax (EBT), while Kmart Group earned $601 million in EBT.

Profit is very important because that's what funds dividend payments. So, how much passive income would $10,000 in Wesfarmers shares generate?

Wesfarmers has a stated goal of increasing its dividend over time "commensurate with performance in earnings and cash flow".

The company has highlighted that Bunnings and Kmart can provide customers with what they need during this high cost-of-living environment – good products at good prices.

Its ongoing profit growth could help push the annual dividend payment up slightly higher to $1.95 per share in FY24, according to Commsec. That would be a grossed-up dividend yield of 4.1% in the current financial year.

If an investor had $10,000 in Wesfarmers shares today, the 4.1% grossed-up dividend yield would translate to around $410 in dollar terms, including the franking credits. The upfront cash part of the dividend would be almost $290.

But, the dividend isn't expected to stay below $2 per share for long.

The estimates on Commsec suggest the payout could rise to $2.13 per share in FY25 and $2.35 per share in FY26.

In FY25, the company's grossed-up dividend yield could be 4.5%, which would mean $450 of grossed-up income with a $10,000 investment in Wesfarmers shares.

It could then have a grossed-up passive dividend income yield of around 5% in FY26 — that would mean $500 of grossed-up income with a $10,000 investment today.

The retailer has proven its ability to deliver a slight profit rise even when some households are struggling in this economic environment.

Perhaps unsurprisingly, the Commsec forecast suggests EPS could rise to $2.23 in FY24, $2.43 in FY25 and $2.70 in FY26. If it does manage to reach that projected profit for FY26, it would mean the Wesfarmers share price is valued at 25x FY26's estimated earnings.

The company is investing in areas like healthcare and lithium mining to grow and diversify its earnings, which may help the Wesfarmers share price in future years.

Past performance is not a guarantee of future performance, but Wesfarmers has a long-term track record of paying pleasing passive income and delivering capital growth as it expands its core businesses.