After being down by almost 11% at one stage in 2016, the shares of Telstra Corporation Ltd (ASX: TLS) have staged a comeback and have recently broken into positive territory for the year.

The question now is whether the shares can continue climbing higher. Well, I believe that Telstra has a lot going for it that could well take the share price beyond the $6 mark once again. In fact, if things go better than expected it could well make a new 52-week high.

Because interest rates in Australia are expected to head even lower, I believe Telstra is an appealing investment due to being one the most generous dividend payers on the S&P/ASX 200 (Index: ^AXJO) (ASX: XJO). At the current price the shares are expected to pay an estimated fully franked 5.5% dividend in FY 2016. This is well ahead of the market average dividend of 4.3%.

With the Australian market reasonably saturated, Telstra is looking to Asia for growth. It has aspirations of being the carrier-of-choice for businesses in the Asia Pacific region through its combination of subsea routes and overland fibre.

One of Telstra’s key projects in this area will be the rollout of a fibre optic backhaul link running overland in Taiwan and providing redundancy for traffic between Japan, US, Hong Kong and Singapore.

Researchers from the Bank of America Merrill Lynch believe Telstra’s offshore businesses will account for $2.2 billion of revenue by 2019. I believe there is an incredible amount of growth in the region and Telstra is positioning itself well to capture it.

Back on home soil and its focus on expanding its presence in the healthcare sector could be another source of growth. It is building out capabilities for providing solutions in numerous areas including primary, aged and residential care, hospitals, radiology, pharmacy, and health analytics.

I believe things have been looking very promising for this side of the business. Telstra recently secured an estimated $180 million three-year contract from the government to manage a new national cancer screening register from next year. I wouldn’t be surprised to see more announcements like this in the coming months.

Finally, its core business still looks very robust despite competitive threats posed by the likes of TPG Telecom Ltd (ASX: TPM) and Optus. It even managed to grow its mobile subscribers despite all its dropouts earlier this year. As of March 31, Telstra had grown its mobile market share to 41.1% from 39.7% a year earlier.

All in all, I believe Telstra is a great investment today. As well as paying a great dividend, I expect it will continue to steadily grow its earnings and provide share price gains for investors for a number of years to come.

Telstra is undoubtedly a great dividend share, but it's not the only one out there. If you're already invested in Telstra and are on the lookout for even more income then don't miss out on this fantastic dividend share. I believe that it will provide both a market-beating fully franked dividend and potentially strong share price gains in the months ahead.

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Motley Fool contributor James Mickleboro has no position in any stocks mentioned. The Motley Fool Australia has no position in any of the stocks mentioned. We Fools may not all hold the same opinions, but we all believe that considering a diverse range of insights makes us better investors. The Motley Fool has a disclosure policy. This article contains general investment advice only (under AFSL 400691). Authorised by Bruce Jackson.