Biogen’s Alzheimer’s treatment has reached the market. And all of a sudden, a plodding value stock has a compelling growth story.

U.S. regulators gave the green light to the drug known as aducanumab, the first such approval of any drug that promises to slow the progression of the fatal disease. Millions of patients world-wide potentially stand to benefit.

Accordingly, Wall Street thinks Biogen has a blockbuster on its hands. While the company has said to expect a slow rollout at first, analysts estimate about $10 billion in annual sales later this decade at its peak. Biogen shares surged 38% on Monday, and a broad biotech index gained nearly 5% on the day.

For Biogen, that prospective growth is badly needed: The company expects to book roughly $10.6 billion in total revenue this year. Sales of its top-selling multiple sclerosis drug Tecfidera are falling as generic competition comes online in the U.S.

There are reasons to be skeptical that aducanumab can ever meet analysts’ lofty expectations. For starters, patients will require testing before receiving the drug that can result in hefty out-of-pocket costs for patients insured by Medicare.

It is possible that the controversy surrounding the drug’s approval will hinder sales. An outside panel of experts assembled by the U.S. Food and Drug Administration voted overwhelmingly not to support approval last year for lack of efficacy. Some prescribing physicians may agree.

And even if those concerns don’t end up limiting demand, Biogen might not enjoy market exclusivity for as long as Wall Street thinks. Rival drugmakers have mothballed similar treatments over the years and could now choose to revive them, given the FDA’s evident flexibility. And the drug’s list price of $56,000 a year is bound to raise eyebrows in Washington, D.C.

Those concerns won’t likely matter to Wall Street any time soon, however. Biogen was trading at less than 12 times last year’s earnings on Monday before the news broke.

Monday’s rally still leaves Biogen at 16 times earnings, according to generally accepted accounting principles. That hardly seems unreasonable. After all, the stock traded as high as 25 times earnings back in 2015, when aducanumab showed promising results in early trials.

Besides, in today’s frothy stock market, investors often find tales of a bright future far more appealing than real cash being generated in the present. Biogen now has a better story to tell.

Write to Charley Grant at charles.grant@wsj.com