There is a good case for Yahoo to buy Tumblr. But there's a better case for it not to.

By John Saroff, contributor

FORTUNE -- It looks like Yahoo has offered to buy Tumblr for the sticker-shock price of $1.1 billion.

Maybe we shouldn't be surprised, since just a few days ago Yahoo CFO Ken Goldman spoke about the need for the company (YHOO) to be "cool" again. But Yahoo shareholders invest for returns, not for cool. Yahoo employees have a big chunk of their net worth tied to their stock. It may be sexy for Yahoo to buy Tumblr, but will it have a positive return?

I believe the answer is no.

To be sure, the power of math and corporate finance can build a good investment case for Yahoo/Tumblr.  Yahoo is a $28 billion media business with cash to spend and a substantial focus on display advertising.  Tumblr represents a ton of page views ripe for display monetization. It's a bulk play -- Tumblr adds mass.

According to Quantcast, Tumblr gets about 60 billion U.S. page views per year. If we assume no growth and no international, those pageviews will spin off $108 million per year if a net $1.79 RPM (revenue per thousand pageviews) is achieved. There are data points that can make that $1.79 hurdle rate much lower and strongly favor the acquisition:

• Ad networks can fill display units at $1.79 and there are some hilarious, useful and beautiful tumblrs for which direct sold brand advertisers will pay 10x the remnant rate.
• International doubles Tumblr's size. The international page views reduce the RPM hurdle rate to $0.89.
• The WACC of 9.8% feels high. If we instead use the risk-free rate of 4.5%, then the U.S.-only RPM hurdle rate drops to $0.81, the international-included RPM hurdle rate drops to $0.41.
• Yahoo COO Henrique de Castro is a smart and experienced display advertising executive who knows how to turn pages into dollars. (disclaimer: I worked in HDC's org at Google for many years and although he draws media attention for his unintentional comedy and pay package - his skills as an executive are undeniable and underestimated.)
• Tumblr is likely to keep growing. It is the blogging platform of choice for the immediate future and the more monetizable pages its bloggers create, the lower the RPM hurdle rate.

You can use the math to get the hurdle rate low enough to make the acquisition seem like a no-brainer, but I believe that there are many strategic challenges unique to Tumblr that make this acquisition a risky one.  If I were Yahoo, I would not buy Tumblr for $1.1 billion. 

Here are five big reasons why:

1. Tumblr CEO David Karp is correct in his resistance to the use of traditional display on Tumblr. Karp will have a new boss on Tuesday morning, but it appears as though he will remain in charge at Tumblr.  As the product visionary behind Tumblr, Karp has been very public about his resistance to display ads on the platform. I agree with him. One of the reasons that I love Tumblr both as a blogger and a reader is about how it feels. I can post a lobster roll, my godson and wistful thoughts on my career and they all "work" on my tumblr. Traditional display disrupts that aesthetic. Tumblr isn't built for display and I'm not sure if the product can be changed to accommodate display and still maintain its Tumblr-ness.

2. If traditional display is not used on Tumblr, then new forms of native advertising have to grow at incredibly rapid rates. That's hard.  Karp sees Tumblr as having great potential for new forms of advertising such as Tumblr sponsorship programs like Tumblr Radar and Tumblr Spotlight.  These "native" advertising formats are beautiful and fit with Tumblr, but it is unclear how much demand is out there for them. Selling these kinds of units earned Tumblr $13 million of revenue last year.  Generating $108 million peryear of net revenue with special native advertising units (both existing and to be developed) is a different and more difficult challenge than just making Tumblr a shelfspace for display.

3. *Tumblr doesn't own many of its page views, the bloggers do. Tumblr is a blogging platform/content management system first, and a destination site second. For Yahoo to place ads on tumblr.com is easy, for it to place them on johnsaroff.com is hard. To facilitate advertising on johnsaroff.com Yahoo will need to get my permission, put an ad unit on my page, cut me in on a rev share and then convince an advertiser that johnsaroff.com is worth something. It's a challenge similar to what YouTube has done with user-uploaded videos over the past several years to great effect. But, it requires product vision, engineering talent, business development work and account management skills that took Google (GOOG) and YouTube years to grow with many fits and starts. These skills may not be in either the Yahoo or Tumblr organizations right now and will likely take time to develop.

4. Many tumblrs are unhospitable to advertising.  I'll leave it to Sam Biddle over at Valleywag to explain why.

5. It is unclear if Tumblr has a sustainable competitive advantage. Channeling the lessons of my strategic management of media professor Bruce Greenwald and his books on competition and media, none of this makes sense if Tumblr doesn't have a sustainable competitive advantage and barriers for new entrants to enter its market. Just because Tumblr is wonderful and the preeminent blogging platform today doesn't mean it will be tomorrow. Over the course of the last ten years Blogger and WordPress have held the position that Tumblr holds now. I believe that the space in which Tumblr operates has very low barriers to entry, making Tumblr very susceptible to new entrants. This makes the growth rate very hard to predict with any degree of certainty.

This is a tough call. Assuming the deal goes through, only the future will show whether the rationale and the projections that back it up are vision, delusion or hallucination. Like most things, the math behind the rationale and the projections will probably end up somewhere in the middle.

To me, the strategic concerns overwhelm the math.  Team Yahoo can make this acquisition easily, but it makes the next one harder  from a cash, investor and culture perspective.

Instead of Tumblr, I propose that Yahoo focus its cash not on bulk of pageviews, but on acquisitions and R&D that erect barriers to entry (Buffett's famous moat) around its already robust display business. Those likely take the form of deep investments in the product and engineering corps and strategic acquisitions of adtech businesses. Those maneuvers will be less sexy, but they have the potential to reinvigorate Yahoo for the next twenty years. It is hard to see how, with all of the strategic risks inherent in the deal, acquiring Tumblr builds the moat for Yahoo that I believe it needs.

John Saroff (@saroff_nyc) is a media and tech executive based in New York City, and is a former head of strategic partnerships for Google's TV ads business.