Sometimes Mr. Market gets confused and prices companies at a premium or discount to their true value. While big companies such as Apple (NASDAQ:AAPL) and Verizon (NYSE:VZ) historically trade at a discount to the overall market, they're currently trading at an even deeper discount than usual.

Verizon's share price has mostly stood still while the market continued to rally over the past year. Apple, meanwhile, is trading around the same P/E ratio as it did at the beginning of last year, while the S&P 500 is trading 21% higher on a P/E basis. Let's look at the numbers and see why both these tech titans are trading at massive discounts.

Wall Street street sign

Wall Street might be missing something on these two. Image source: Getty Images.

Verizon's 15-year low

Verizon's P/E ratio for the trailing 12 months is a mere 15.5. On a forward basis, it's just 12.9. That compares with the S&P 500's trailing P/E of 26.9. Verizon is trading at just 0.58 times the P/E ratio of the broader index. The last time it was even below 0.65 was in 2002, when the telecom industry tanked, according to analyst Craig Moffett of MoffettNathanson.

Historically, Verizon trades for just an 11% discount. The 42% discount it's trading at today represents a massive buying opportunity for long-term value investors -- not to mention that Verizon is also trading at a lower forward P/E compared with AT&T (NYSE:T), which trades for 14.3 times analysts' 2017 EPS estimates.

At the same time, it's worth looking at why Mr. Market is placing such a hefty discount on the wireless carrier.

First and foremost, the competition in the wireless industry is increasingly fierce. Pressure from T-Mobile (NASDAQ:TMUS) has finally gotten to Verizon, putting pressure on its pricing. Verizon recently introduced an unlimited-data plan in an effort to compete with the value offered by T-Mobile's plans. AT&T also bowed to the pressure, opening its unlimited-data plan to all customers and dropping the price.

Verizon's Unlimited logo

Image source: Verizon.

However, the strength of Verizon's wireless network and its position on the leading edge of 5G network development give it a significant competitive advantage over the long term. Additionally, its massive retail customer base -- the largest in the U.S. wireless industry -- will continue to throw off cash for its investments in its wireless network and digital advertising and video. That should allow the stock to rise back up toward its usual valuation levels over time.

In the meantime, investors can get a juicy 4.6% dividend for their patience.

Apple's recent run may be just the start

Shares of Apple have been on a tear over the last nine months, increasing 46%. That significantly outpaces the 14% increase the S&P 500 saw in the same period. But Apple was trading for a 35% discount on a P/E basis in 2015 and a 26% discount in 2016.

The largest company in the market typically trades for a discount to the S&P 500, but not nearly as deep as Apple's. Over the past 10 years, the average discount for the largest company by market cap was 16% to the S&P 500's P/E, according to BMO Capital's Tim Long. Apple shares traded near that level in 2012, 2013, and 2014, but the market hasn't caught up with the explosion in earnings from the release of the iPhone 6 at the end of 2014.

Today, Apple trades around a 25% discount to the S&P 500, below that 16% baseline. While the market is down on Apple's slow iPhone sales growth, there are a few reasons to believe Apple's earnings will continue to expand.

iPhone 7-Plus

The iPhone 7 Plus. Image source: Apple

First of all, the company continues to execute on its massive capital returns program. Share buybacks will force earnings per share to increase at a faster rate than net income.

Second, Apple's services business continues to grow at a strong pace. Services revenue is higher margin than Apple's core revenue. As such, it has an outsize impact on Apple's profit growth.

Investors looking for value have two great options with Verizon and Apple. While the latter is trading at an all-time high, it still has room to run. Meanwhile, Verizon is trading at historic lows while maintaining strong competitive advantages, indicating it should outpace the market from here. 

This article represents the opinion of the writer, who may disagree with the “official” recommendation position of a Motley Fool premium advisory service. We’re motley! Questioning an investing thesis -- even one of our own -- helps us all think critically about investing and make decisions that help us become smarter, happier, and richer.