Nietzsche scholar Brian Leiter has a rather strong opinion about this:
This typically idiotic remark in a recent NY Times book review caught my attention:
“Rand’s inclusion of businessmen in the ranks of the Übermenschen helps to explain her appeal to free-marketeers — including Alan Greenspan — but it is not convincing. At bottom, her individualism owed much more to Nietzsche than to Adam Smith (though Rand, typically, denied any influence, saying only that Nietzsche “beat me to all my ideas”). But “Thus Spoke Zarathustra” never sold a quarter of a million copies a year.”
Rand’s “individualism”–if that is what one wants to call her juvenile fantasies about her industrialist heroes–owes as little to Nietzsche as to Smith. Nietzsche loathed capitalism and capitalists (and the cultural and aesthetic vulgarity he saw as their legacy) and also despised what he called “the selfishness of the sick” (Thus Spoke Zarathustra) and the “self-interested cattle and mob” (Will to Power). What he admired was “severe self-love,” the kind “most profoundly necessary for growth” (Ecce Homo). “Virtue, art, music, dance, reason, spirituality”–all the things “for whose sake it is worthwhile to live on earth” (Beyond Good and Evil)–all demand such severe self-love, and for this reason, and this reason only, Nietzsche wanted to disabuse those capable of such excellences of their false consciousness about the morality of altruism. He certainly did not think everyone ought to be selfish, or that the pursuit of material goods had any value, or that indulgence of selfish desires was a virtue. What he did think is what is almost certainly true: namely, that if someone like Beethoven had taken Christian morality seriously, and lived a Christian life, he would not have accomplished what the actual Beethoven did (one need only read the famous Maynard Solomon biography to see that Beethoven was no moral saint). The “John Galts” of the world are just a more prosperous example of the “self-interested cattle and mob” Nietzsche always derided.