Actually, Rand's ethics seem to be derived in a manner that roughly parallels the derivation of Descartes famous statement (See post 255). And the following are my words, not hers.
Rand's ethics seems to be premised on the common sense involved in saying -- I exist, my continued existence is good, and my ethics is concerned with the continuance of good existence.
Well, OK, continued existence is one (the only?) of her moral axioms. The statement "the continuance of good existence" implies that there is some other moral axiom at work as well, which quantifies or qualifies the state of existence. What would that be? - In any case, you are getting to the heart of her (arbitrary) morality.