Every day, Wall Street analysts upgrade some stocks, downgrade others, and "initiate coverage" on a few more. But do these analysts even know what they're talking about? Today, we're taking one high-profile Wall Street pick and putting it under the microscope...

2017 is still young, but shares of Alcoa Corporation (NYSE:AA) are already up nearly 29% since the new year began. And here's the best news: Goldman Sachs thinks Alcoa stock has more room to run.

In a new upgrade just announced this morning, Goldman Sachs makes its case for why Alcoa stock is a buy. It's an argument that begins in China and stretches all the way to the bottom of Alcoa's cash flow statement. Here are three things you need to know about it.

Aluminum rolls.

Goldman Sachs sees profits for Alcoa's aluminum business. Image source: Getty Images.

1. China throttles back on aluminum...

Goldman lays out its buy thesis for Alcoa in three parts. The first part begins in China, where in a bid to cut wintertime pollution, the government has announced that it will reduce aluminum production by 30% in the winter of 2017 (when pollution is exacerbated by coal-burning for residential heating).

Goldman believes that this will result in 1 million fewer tons of aluminum being produced this year, and 2 million tons less produced in 2018. And with reduced supply, Goldman expects prices to rise to as much as $1,950 per ton for aluminum this year, $2,100 per ton in 2018, and $2,200 per ton in 2019. (If it's right about that, then price growth alone should allow for 6% annual growth in Alcoa earnings at stable production rates.)

2. ...while Alcoa amps up

But price inflation isn't the end of this story. Goldman believes Alcoa will also be expanding production. According to the analyst, Alcoa has plans to spend $370 million on expansion capex this year, increasing production and adding about $300 million in earnings before interest, taxes, depreciation, and amortization (EBITDA) to the company's annual income.

3. Aluminum math

What does this mean for Alcoa stock? Simply put: Massively bigger profits.

Goldman believes that the price hikes permitted by China's aluminum cutbacks, combined with greater output from Alcoa's foundries, will more than double Alcoa's profits going forward: From $1.45 per share previously estimated for 2017, the analyst now goes to $2.40. In 2018, estimates rise from $1.22 to $2.68 per share. And in 2019, Goldman sees Alcoa earning not $1.23 per share, but $2.89 -- a 135% bump in profit projections!

Goldman even goes so far as to predict that Alcoa -- often a burner of cash in the past -- will transform itself into a "cash machine" in the promised "supportive commodity environment." Over the next two years, Goldman believes we will see Alcoa stock produce free cash flow yields -- as high as 12%.

For those who've followed (and perhaps invested in) Alcoa stock in the past, that's a pretty astounding claim. On Alcoa's $6.7 billion market capitalization, a 12% "free cash flow yield" works out to a prediction that Alcoa will generate positive cash profits in excess of $800 million annually over the next couple of years. To put that in context, Alcoa generated less than $500 million free cash flow in 2015, less than $400 million in 2014 -- and burned cash 2013, and again in 2016.

Result: Over the past four years, Alcoa has averaged positive annual free cash flow of not $800 million, but only...$13 million.

Bonus thing: Do you believe it?

So I ask you, is this likely? I personally don't think so, and I'll tell you why.

First and foremost, go back to the beginning: China's promise to cut aluminum production by 30%. It's important to point out here (as my Foolish colleague Matt DiLallo did last week) that even if China sticks to its plans, a 30% reduction in aluminum production during three winter months of the year will result in only "about a 5% loss in China's annual aluminum production." I question whether such a reduction in production will suffice to produce the 100%-plus increases in Alcoa's per-share profits that Goldman Sachs is promising.

And again, this is if China's throttle-back sticks.

Why might it not? Well for one thing, as The Wall Street Journal points out today, Chinese Premier Li Keqiang just laid out a 6.5% GDP growth target for this year. Not only is that target weaker the 6.5%-to-7% range set for 2016, but the Journal notes, "Mr. Li made clear even one notch below 6.5% would be a disappointment." So what, I ask you, will happen to China's proposed aluminum production cutbacks if, toward the tail end of this year GDP growth looks likely to fall short of 6.5%? Will they forge ahead and cut production, or will they stomp on the gas and try to goose that number up above 6.5%?

I personally suspect the latter -- especially if Goldman Sachs' upgrade of Alcoa stock results in a self-fulfilling prediction, making aluminum even more valuable to produce. And this, dear Fools, is why I believe that any prediction of "12% free cash flow yields" at Alcoa is nothing but a pipe dream.

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.