There has been a paper published in "Photosynthesis Research Magazine" which is a peer reviewed journal in which a spinoff from Harvard, Joule Research, outlines its process.
The claims are nothing short of extraordinary.
Allegedly, Joule has bio-engineered an organism which is capable of continuously excreting what amounts to bio-diesel without the need for energetically expensive pre-processing of biomass.
The result is allegedly 10X greater than predicted yields from algae or 50X greater than the best biomass crops of today.
If we assume an extremely skeptical eye (i.e. not believing in magic) and imagine that the process works but it's not 50X but more like 2X or even 1X then we could still conceivably have a lower cost process depending on the cost of the industrial plant required.
I suspect we would be looking at some kind of bioreactor so the costs could be anywhere from "more expensive" to "significant" and thus the at-the-pump cost would of course depend on yield.
Let's wait and see on this one.