What they did in the past is not relevant. In theory, the price of a company is the present value of their total future profits.
(... snip ...)
Even if you assume they will make $1 billion profit every year, that's a lot of years to add up to $32 billion value.
This is how you would value a small to mid-size company, or one in a niche market. This definitely isn't how big high tech companies are valued these days.
The value of a company is simply how much any other company is willing to spend on it. And this depends on a number of factors, including how competitive said market is (which implies: how many other companies would be interested in buying), the company's reputation (thus, yes, past and history definitely matter, they have a direct influence on the customer base), and how much value the company directly or indirectly brings to the overall economy. If a company makes $1 billion of revenue a year, but generates "only" $2 billion of revenue for all other companies using their products, it's definitely not the same as if it generates $100 billion of indirect revenue a year.
Again $32 billion may look like a lot, but think of it this way: try and estimate how much revenue all products in the world embedding ARM-based devices generate. This is mind-boggingly high. Now think of the situation if ARM cores suddenly became unavailable. Is there *currently* a viable alternative that would replace them altogether without any negative impact? There isn't. That is what will ultimately define the value. IMHO.
Now whether the acquisition is itself a viable financial operation at this price, this is another question. It's a complex one too: of course, just breaking it even will take a very long time. But OTOH, not buying (and letting a competitor buy) could have a negative impact on market share on a much shorter term... Oh, and also, not that I'm very fond of the situation, but a significant part of all this acquisition money, in such contexts, is kind of "virtual" anyway (well, at least until the company goes bankrupt...)