As all the world knows, Yahoo is paying $1.1 billion to acquire social media platform Tumblr. That’s a very nice exit for investors who sunk in about $125 million, according to Business Insider. But was it a fair price for Yahoo?

A number of people besides Marissa Mayer seem to think so. Matt Mullenweg, founder of Automattic and founding coder of Wordpress thinks the company could be worth 10 times what Yahoo paid. Paul Buchheit, a Valley entrepreneur (FriendFeed) told the New York Times, “If a company has a 1% chance of becoming a $100 billion company, then it’s worth about $1 billion.”

Let’s run the numbers.

Finance 101 says the value of a company lies in the annual cash flow it generates, to be profitably reinvested in the company or returned to shareholders via dividends. To turn cash flow into valuation, analysts divide the annual cash flow by the company’s cost of capital. (Think of cost of capital as a measure of a company’s riskiness; the higher the risk, the higher the cost of capital.) A company with a stable $10 million cash flow and a 10% cost of capital would thus be worth an estimated $100 million.

What doesn't get you to $1 billion

In 2012, Tumblr generated $13 million in revenue and $25 million in expenses. Losing $12 million a year obviously doesn’t earn you a $1 billion valuation. But Business insider says Tumblr’s goal for 2013 is to generate $100 million in revenues with $40 million in expenses. Since Tumblr is a risky investment, you might assume its cost of capital is 20% annually. Then the $60 million cash flow divided by 20% gives you a $300 million valuation. That’s still only about 25% of what Yahoo paid.

But what if the company can eventually generate $1 billion revenue and have the same 34.4% cash margin that Facebook now enjoys? (Just for perspective: to hit the billion mark in five years would take a 140% compound annual growth rate in revenue; to do it in 10 would take 54% a year growth.) With a successful revenue model, Tumblr’s cost of capital could decline to, say, about 10% annually. Thus, the $344 million cash flow would yield a valuation of about $3.44 billion, or more than three times this week’s price for Tumblr.

It's all in the expectations

Moreover, investors would presumably not expect that Tumblr’s cash flow would stop growing at $344 million. They’d expect it to keep going, which means they’d put an even higher value on each dollar of current cash flow. If investors rated growth prospects for this future Tumblr as optimistically as they do the outlook for Facebook (whose stock trades at 33 times operating cash flow), then Tumblr would be worth $11.4 billion.

Now let’s look at the Buchheit methodology: What would it take for Tumblr to be worth $100 billion? Well, based on Facebook’s market valuation, Tumblr would have to have to generate $8.8 billion in revenue, $3.03 billion in annual operating cash flow, and have the same growth prospects currently in Facebook’s $62.4 billion valuation.

The winner's curse

Assumptions are everything in valuing any early stage company. I would say the probability that Tumblr would have been the next $100 billion market cap company are significantly lower than 1%. My hunch is that management would not have sold themselves to Yahoo for $1.1 billion if they were on target to generate $60 million operating cash flow this year. It's what economist Richard Thaler calls the winner's curse: All you know for sure after an acquisition is that you paid more than other potential buyers thought the company was worth.

The prove the wisdom of this purchase, the managements of Tumblr and Yahoo will have to turn 18 billion monthly page views into revenue with a very healthy cash flow margin and a white hot growth rate. Yahoo CEO, Marissa Mayer, posted on her Tumblr blog, “we promise not to screw it up.” That’s an excellent mission statement if ever I heard one.