Telstra (ASX:TLS) and 2 other dividend shares with yields over 6% today

Telstra Corporation Ltd (ASX: TLS) is one of the 3 ASX dividend shares offering fully franked yields of 6% or greater today. Too good to miss?

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Finding ASX dividend shares with dividend yields over 6% today is still a hard task. With interest rates at near-zero levels, the market has rushed into dividend shares offering large, inflation-beating yields. After all, there are not too many other investments you can find out right now that offer such a return on your capital.

So here are 3 such ASX dividend shares, all of which are offering a fully franked yield of 6% or greater today

A man happily kisses a $50 note scrunched up in his hands representing the best ASX dividend stocks in Australia today

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3 ASX dividend shares offering yields of 6% or more today

Telstra Corporation Ltd (ASX: TLS)

Telstra is the first dividend share that has a large dividend yield on offer today. The Telstra share price has actually had a top month or two, rising close to 14% since early March. Investors seem to be loving the idea of splitting up the telco a plan Telstra announced in March. This share price rise has reduced Telstra's trailing dividend yield somewhat, but even so, it still offers a relatively large yield compared with other S&P/ASX 200 Index (ASX: XJO) shares. This ASX telco has paid out 16 cents per share in dividends every year for a few years now. On current pricing, that would give us a yield of 4.6% today, or 6.57% grossed-up with Telstra's full franking.

Australia and New Zealand Banking GrpLtd (ASX: ANZ)

Investors finally got some clarity on ANZ's dividend this week after more than a year of payout uncertainty thanks to the coronavirus pandemic. Shareholders might have been relieved by the bank's 45% increase in profits to $2.94 billion that it reported. But I'm sure more attention was on the new ANZ dividend. And it didn't disappoint. ANZ told the markets that it would be paying a 70 cent per share interim dividend in July, up from the 25 cents per share payout shareholders got in September last year. I'm going to cheat a little with this one. That dividend, if annualised, would give ANZ shares a forward dividend yield of 5.04%, or 7.2% grossed-up with full franking. Just on the bank's trailing dividend yield, ANZ is offering a grossed-up yield of 5.4%.

AGL Energy Limited (ASX: AGL)

The AGL share price has been a very sad story over the past few years. The energy giant is now at a share price not seen for almost two decades. Concerns over a volatile electricity market, the future of coal and ageing infrastructure assets have all contributed to this brutal sell-off of AGL. But falling share prices has boosted the dividend yield one can expect from AGL today. On current pricing, AGL shares offer a trailing dividend yield of 9.26%. Now the company could well cut this dividend in the future if its cash position continues to deteriorate. But management has committed to paying out essentially all of AGL's earnings as dividends over the next couple of years. So it seems as though investors will continue to see hefty dividends going forward.

Motley Fool contributor Sebastian Bowen owns shares of Telstra Limited. The Motley Fool Australia owns shares of and has recommended Telstra Limited. The Motley Fool has a disclosure policy. This article contains general investment advice only (under AFSL 400691). Authorised by Bruce Jackson.

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