I've been led to believe that it's much easier to get money (assistantships and fellowships) as a PhD student than as a master's student, and so it's cheaper to go straight to a PhD program if you know you want to get a PhD. This is supposing that you spend the same amount of time in grad school with both routes. Is this correct? And are there other significant factors in determining whether or not it's cheaper to go straight to a PhD program?

I've been led to believe that it's much easier to get money (assistantships and fellowships) as a PhD student than as a master's student, and so it's cheaper to go straight to a PhD program if you know you want to get a PhD. This is supposing that you spend the same amount of time in grad school with both routes. Is this correct? And are there other significant factors in determining whether or not it's cheaper to go straight to a PhD program?

Edit: I'm hoping to study computer science, if that's relevant. If I do a master's, it'll be in the US, but I'm not sure if I'd want to do a PhD in the US or in France. You can just assume the US for this question.