Per the "Model A Restoration Guidelines & Judging Standards" page 17-2:
"The screw driver had a wood handle with an unfinished or black enamel, steel blade shaft passing entirely through it. The handle was finished with a dull black wood preservative. The ferrule was plain steel or nickel plated. The rivet was installed perpendicular to the blade and was approximately 3/8" from the large end of the ferrule. The overall length was 8-9/16". There were no markings on the blade and no knurl on the ferrule."
The screw driver in your photo has a "B" stamped on the blade, knurling on the ferrule and no rivet through the ferrule. It is not correct for judging. I am not 100% certain, but I think your screw driver is for a later model Ford, after the Model A. I have attached a photo of a Model A screw driver below.