Could these be 3 of the ASX's most undervalued shares right now?

TPG Telecom Ltd (ASX:TPM) is one of three shares that is offering a compelling value proposition right now.

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Finding 'bargain' shares on the ASX is a pretty challenging task at the moment as many of the best quality shares have enjoyed a nice rally following strong earnings results.

For example, the CSL Limited (ASX: CSL) share price has jumped more than 25% over the past three months after the biotech company surprised the market with an impressive profit upgrade.

Despite this, I still believe there are some attractive investment opportunities available to investors right now, including:

TPG Telecom Ltd (ASX: TPM)

The TPG share price has been one of the worst performers over the past six months, but I think the market will slowly become more comfortable with the telco's outlook following this week's profit result. Pleasingly, the company expanded its operating margins over the first-half and appears to be on-track to easily meet its full-year guidance. The shares trade on an undemanding price-to-earnings (P/E) ratio of around 15 and offer a growing dividend that is currently yielding around 2.5%.

Healthscope Ltd (ASX: HSO)

The Healthscope share price has also taken a beating over the past six months after the private hospital operator warned that it was experiencing weaker-than-expected patient admissions. Unfortunately, the company has noted that these conditions are likely to persist in the short term and this means investors are unlikely to see the shares rebound quickly from here. Despite this, I think patient investors could do quite well at current prices considering the longer-term outlook for the sector remains compelling and the shares now trade on a P/E ratio of less than 20.

Amaysim Australia Ltd (ASX: AYS)

Amaysim is a niche player in the telco sector and is well placed to continue to chip-away at the market share of some of the bigger players in the sector. Importantly, the company's growing subscriber base will provide it with a big opportunity to leverage its new broadband service which is expected to be launched over the next few weeks. Amaysim expects to pay dividends worth 10 cents per share for the full-year, which means the shares currently offer an attractive dividend yield of 5.6%.

Motley Fool contributor Christopher Georges owns shares of Amaysim Australia Ltd and TPG Telecom Limited. 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.

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