Yahoo! (NASDAQ: YHOO) stock keeps hitting new 52-week highs, so you may want to pick up a few shares. But you're scared.

While you may think the stock trades cheaply at a P/E of 7.5, there's good reason to believe that Yahoo! stock is expensive. When analyzing the company's business, critics contend that Yahoo!'s all-star CEO, recent string of acquisitions, and its foreign investments conceal a weak domestic business ill-suited for today's world.

But that's not the whole picture. Technology has changed, and Yahoo! has shown it has changed as well.

Looking at its business in a positive light, Yahoo! stock may, in fact, be a good buy today.

Is Yahoo! stock cheap?
Yahoo! stock reports a low P/E of 7.5, yet it may be higher.

Don't forget, Yahoo! owns a 35% stake in Yahoo! Japan and still owns a 20% stake in Alibaba, China's largest e-commerce company. Given that Yahoo! Japan trades for about $28 billion and Alibaba may soon IPO for $63 billion to $120 billion, Yahoo!'s financials may be hiding something .

Luckily, Fool contributor Alex Planes has done the math. Factoring in Yahoo! Japan and Alibaba's stake, he estimates that Yahoo! trades for a P/E between 8 and 14.

While 14 is still almost twice as much as Yahoo!'s reported P/E, the range is still relatively inexpensive. For comparison, remember that the S&P 500's traditional averages a P/E of 15.

You could argue that Yahoo! is expensive at a forward P/E of 16.8, but, for practicality's sake, let's not.

While you want to buy Yahoo! stock at its cheapest price, "it's far better to buy a good business at a fair price" -- per Charlie Munger. Whether the P/E is 14, 15 or 16, Yahoo! stock seems to trade at a fair price. So with that, let's take a look at Yahoo's business.

Does Yahoo! lack a "core strategy"?
Fool Travis Hoium thinks Yahoo! can't figure out what it's identity is. Unsure if it wants to be a search engine, a leader in display ads, or an Internet portal, he says:

Yahoo! has become an amalgamation of websites that don't seem to have any cohesion. As a finance person, I use Yahoo! Finance every day, but the site doesn't look anything like the main page, Flickr, shopping, or any of the company's other sites. Being a finance user simply doesn't draw me into the Yahoo! platform.

That's understandable. In the past, Yahoo! has done a terrible job of integrating its product together into a consistent feel. However, there are signs that this is changing.

Over the past year, Yahoo! redesigned key products. In December, it released a new interface for Mail. In the past two months, Yahoo! changed its front-page newsfeed and gave Flickr a facelift. While Yahoo! Finance still looks the same, you can bet that it'll have a new look soon.

Why?

Because Yahoo! has Marissa Mayer -- a product-focused CEO. Listed as one of Time Magazine's Most Influential People for 2013, Mayer -- according to Google Chairman Eric Schmidt -- touched the design of "virtually all of [Google's] major products and services."

Still, critics say she's in over her head. They say she is focused on outside, not organic, growth.

Will Yahoo!'s acquisitions pay off?
Yes, Yahoo! has made a staggering 11 acquisitions this year. While no one likes a company throwing around a bunch of money, it seems that these acquisitions were necessary to some extent. Whether because of talent or intellectual property, Yahoo! bought the start-ups in order to build up its mobile presence fast. Though only time will tell if these were smart decisions, I think that, given the war for talent in Silicon Valley, this was a smart move.

Perhaps the biggest acquisition-related criticism Mayer has received regards the $1.1 billion Tumblr deal. Apparently, Tumblr is a "loss-making" company that may simply be the latest "Flavor of the Month." If not done right, the deal could be a telltale sign that Yahoo! will become like Zynga. After buying OMGPOP, the creator of Draw Something, for $180 millionZynga wrote off up to $95 million last October and is completely shutting the studio down to save another $80 million. If Zynga can't turn a profit soon -- it's delivered negative profits for the past two quarters -- then Zynga stock will continue to see another precipitous fall. Yahoo! watchers should take note: Tumblr could be the beginning of the end.  

But that's not likely. I think Tumblr has long-term value. 

As the 18th most visited website in the U.S. according to Alexa.com, Tumblr got to where it is thanks to its fanatically focused founder David Karp. In a recent Charlie Rose interview, you can see that David Karp is not the serial entrepreneur type -- creating companies to sell them off for huge profits. Spurning the need to raise money and instead focusing on developing the product, he's fanatically focused founder who's overseen Tumblr's skyrocketing growth.

In this sense, the deal seems more like Facebook (META -11.86%) acquiring Instagram or Amazon.com (AMZN -2.44%) acquiring Zappos for about $1 billion each. In both cases, Instagram founder Kevin Systrom and Zappos CEO Tony Hsieh maintained independent control of their companies. While it's uncertain whether Instagram or Zappos have paid off, two things are for sure: Instagram usage keeps growing, while Facebook usage slows. And Zappos is still the Internet's largest online shoe store.

I don't doubt that Tumblr will maintain its place as the "best place to blog online."

Should you buy Yahoo!?
It depends. I think Mayer's Yahoo! is doing a great job at unifying and streamlining its products. While Yahoo! isn't moving as fast as you may like, the company has made acquisitions to bolster its mobile experience.

That said, the biggest question is whether Tumblr can actually drive value for Yahoo! shareholders. I think it will, but, if you're still weary, find solace in the fact that the stock is trading at a fairly cheap P/E. Perhaps you should buy a few shares today, just to keep Yahoo! on your radar.