In light of what you mention, perhaps I should rethink what I've said. Sohphisticated tech is one way to make the thing seem what we, right now, would call "affordable". Several other things might, and any of them might apply to another species on another planet.
1)Economy - what counts as "affordable" depends on how much wealth you have. If, for example, you have a species that doesn't need sleep, so for similar populations they can produce much more wealth than we can, the thing might seem affordable. Or, maybe the advent of fusion power lends enough oomph to the economy to make this project reasonable.
2)Danger - even if you can colonize other worlds in your solar system, doesn't mean those colonies are necessarily ultimately independent from their home biosphere. If that home has been endangered (by pollution, by natural disaster, by war, etc), perhaps the idea of flinging yourself to the stars makes sense.
3)Psychology - really, they do think in alien ways, so that they have higher priority for such a project than we can imagine for ourselves now.
I note you disallow this last, and then turn around and say that "it doesn't make sense". "Sense" is subjective. Of course,if you assume they are working with your personal sensibilities, it won't make sense. But how likely is that? How many ways could they differ from your sensibilities?