My answer is limited to US university, since you have not mentioned specific country in mind.
Most PhD programs in US university provides stipend, along with tuition waiver for the first year. In my knowledge on the field of Economics, you have to 'work' for the university as a RA or TA for the subsequent years of PhD as an exchange for tuition waiver, all the while receiving stipends. I am aware that it is field-dependent, so it may be different in your field.
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
In general, this is indeed true. PhD students are more likely to be under assistantships and fellowships, though some excellent Master's student may compete with PhD students. However, if you are referring to opportunity cost, the answer becomes more of personal preference than an absolute answer. If you know that you ultimately want to do PhD, it is better financially to go straight into PhD without having to pay for your tuition for Masters. However, going through masters may provide a better chance for your admission acceptance. You will also be more sure about your research interest; jumping into PhD is a huge investment, so it's wise to explore before committing.
And are there other significant factors in determining whether or not it's cheaper to go straight to a PhD program?
I think ultimately you have to check with the graduate programs about their funding. Many departments differ in their funding policies for Masters, and I do know many programs that offers at least partial tuition waiver for Masters program.
If finance is one of your concern, the advice that I've heard is to work after undergraduate in research institutions. In that way, you can earn some money for yourself, while boosting your resume and giving time for yourself to discover if you like the research topic you were initially interested in. After such experience, you can go directly into PhD without considering Master, since Master's degree is sometimes considered as terminal degree (again, this is hugely field-dependent).