Woolworths Limited (ASX: WOW) and Telstra Corporation Ltd (ASX: TLS) shares offer big dividend yields, but is that enough to make you purchase shares today?

Telstra Corporation

Until recently, Telstra’s share price moved lower month after month as investors swallowed lacklustre profit growth and mulled its long-term outlook. The simple facts are that Telstra is a $70 billion behemoth operating in many mature medium-sized markets. Further, it’s given up the right to own its once lucrative copper cable system to the NBN Co (for a hefty price, mind you), so its dominance in fixed services like broadband is now getting tested. Also, mobile market competition could be set to heat up and the pay-tv market is changing quickly.

All-in-all, investors want Telstra shares because it is a dominant company in some lucrative industries. But with competition mounting, Telstra is now being forced to invest its money in other parts of the world where its track record is yet to be proven.

Woolworths

Woolies is still Australia’s leading supermarket operator, but, to a greater extent than Telstra, its dominance is being challenged. Not only is Aldi, Coles and Costco disrupting the grocery channel, Woolworths’ Big W business is under threat and undergoing a comprehensive review.

Following the divestment of the Home Improvement business, which includes Masters and Home Timber and Hardware, investors may begin wondering where Woolworths’ long-term growth can come from. I know I am.

However, a leaner business may also be what Woolworths needs, especially under its new management team.

Buy, Hold or Sell?

At today’s prices, both Woolworths and Telstra shares appear around fair value. Reuters has analyst consensus as a ‘Hold’ for both companies’ shares. Personally, I’d buy Telstra before Woolworths — but only if it were cheaper — because the road back for Woolworths may take some time. Remembering that patience won’t lose you money might be some sage advice after all.

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Motley Fool Contributor Owen Raszkiewicz does not have a financial interest in any company mentioned. Owen welcomes -- and encourages -- your feedback on Google+, LinkedIn or you can follow him on Twitter @ASXinvest.

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.