Telstra Group Ltd (ASX: TLS) shares are appealing for a few different reasons, and I'm considering whether this is the right time to invest in the ASX telco share.

Despite Telstra making more underlying profit than it did two years ago, the Telstra share price is down around 10% from May 2023. Interestingly, the company is forecast to make more profit in this financial year and the coming financial years.

In my eyes, Telstra can certainly be counted as one of the ASX's blue chips – it is the biggest telecommunications business in Australia, with a leading market position and the largest mobile network coverage.

When I'm searching for large businesses, there are normally a few key things I'm looking for: a strong brand, dividend growth, and profit growth.

Telstra certainly does have a leading brand – it attracted over 560,000 more mobile subscribers in FY24. This is a key driver for profit growth, which looks promising for the coming years.

Profit growth

User growth in FY24 helped Telstra achieve a 5% growth in mobile income to $10.7 billion and a 9% increase in mobile operating profit to $5 billion. The company's overall net profit for shareholders rose 5.8% following a 1% growth in total income. Profit growth is a key driver of the Telstra share price.

Telstra is an exciting business to me because of its defensive existing earnings and the likelihood of growing profit. Given how integral an internet connection is, I believe many subscribers would choose to pay their Telstra bill over many other expenses before losing it.

Not only could Telstra continue growing its mobile subscriber numbers, but I'm very optimistic about how its broadband business could become more profitable in the future. Most of Telstra's margin is being handed over to the NBN, but with 5G-powered wireless broadband, it could capture a lot of that margin back.

The company is working on reducing its costs, which also helps improve profitability across the business.

UBS projects Telstra's net profit could reach $2.15 billion in FY25 and grow to $2.47 billion in FY26, $2.74 billion in FY27, $2.95 billion in FY28, and $3.24 billion in FY29.

While predictions aren't guarantees of future success, it shows how the business is expected to grow its net profit by 50% between FY25 and FY29. That's a pleasing level of profit growth I'd like to see from a solid ASX blue-chip share.

If profit grows by close to 10% per year, it could deliver share price growth of a similar level if the price-earnings (P/E) ratio didn't change. It's currently valued at 14x FY29's estimated earnings.

The rising profit could also unlock stronger dividends for owners of Telstra shares.  

Dividend payments

Telstra has had a reputation as an ASX dividend share for some time, and I think the rest of the 2020s will cement its place as one of the best passive income blue-chips on the ASX.

It's predicted to pay a dividend per share of 19 cents in FY25, which translates into a grossed-up dividend yield of 6.9%, including franking credits.

UBS predicts the Telstra dividend could rise each year until it reaches an annual payment of 24 cents per share in FY29. This translates into a projected dividend yield of 8.7%, including franking credits. That's an attractive level of return, in my eyes, and it would help reward long-term shareholders.