If you're good with a bobcat. You can't get dirt from yard? Might be better off paying someone with a blade and a bucket.  

Yea, what are you bobcat skills like? My parents had their backyard regraded and that bobcat driver was superb. He even dug a 20'x24' patio excavation to a depth of 12" nearly perfectly and didn't disturb any of the base soil. Bobcat driving is a skill, and leveling/grading isn't just hopping in and driving.

I'd at least inquire with a landscape company about grading it. You might be surprised if all it involves is a couple hours with a bobcat. They may charge less than you think once you factor in what you'd pay to rent one and the extra time you'd take to learn it and do it.

In before the Oh god my yard looks like a WWI battlefield thread.     just kidding, but for real  if you dont know what your doing you can mess a yard up.

 
It's not easy at all. Honestly farm out sod/lawn work. It's not worth your time and sore back.


 

For someone with the skills and equipment it's a weekend job if they take their time.

That seems really high.
How many cubic yards of dirt would you need?

In my area fill sand is $8/cubic yard, topsoil is about $25 per yard.
Someone with a tractor and a front end loader or a heavy box blade can do some spreading and leveling if you can have the fill dumped.

I just did this yesterday by hand and a dump cart on the back of my Bolens

I did not want a bobcat driving over my septic and skidding around creating MORE work by fixing ruts from tires and shit. I moved 6 yards of topsoil around my house. Started with one end and worked my way around. Shoveled the dirt to the foundation and spread out with a rake and used my eye and a 4' level (wish I had an eight) to check pitch away from house.  Added window wells for my basement windows   And when I was done, it all pitches away from my house and continues from the high spots out to my lawn (8' from foundation) I payed $20 for topsoil per yard. And spent 100 or so on grass seed and window wells.  
If you cannot run a bobcat good, you WILL create more work for yourself by having to go back to fix the damage caused by the bobcat.  Have a buddy run it or do it by hand.

They do have small skid loader equipment that you walk behind or ride on standing up.   They are easy to learn how to use and can move a lot of material .  They are also cheaper to rent.

It almost seems like you might be better off hitting it with a rock rake attachment on the front of the bobcat and then switching over to a bucket and backblading with the bobcat.  

been a while since I have been in one but it really isn't that hard after a couple days....about the time you would finally be getting done I suspect.  The tire rut damage can be minimized by minimizing skidding.

Se he wants to put an average of 1.6" of dirt across your entire 150' x 40' front yard? That seems like a lot of dirt, but if you truly need that much, that's over $1,000, maybe even $1,500, of dirt if you want nice dirt for a lawn and not just fill.

A friend of mine just put an ad on Craigslist explaining exactly what excavating he wanted done and he got many good offers.
You might find someone who is finishing up a job in the morning and needs to fill an afternoon.