On this tool the shank is morse taper but it does not cut a morse taper, details about the cut are below

This morse taper shank as it is will not fit most morse taper sleeves, the taper is the same, but This one has a Flat male drive lug system at the large end of the taper that measures 15/16" wide (seen in the 2nd photo) and if your drill press does not have the female drive slot for this to slide in to then it will not slide on to the taper far enough to wedge in place.  The easiest option would be to get a second sleeve, cut off about 1" of the large end of your morse taper adapter sleeve so this male drive lug does not hit the end of the taper, then slide that sleeve in to your drill press, or another option would be to chuck it up and grind down the 1.793" diameter section so that it would slide on further, or to just turn the morse taper shank down to straight shank.

Item ........................ Tapered Ream Cutting Reaming tool

Size ................. The angle of taper is Unknown But with this info you should be able to Calculate the angle, the taper drops about .553" in diameter over a distance of 4.556" of the Flute length. This is not the same as morse taper or Brown and Sharpe Taper. It might be a taper pin size?

Manufacturer ......... SDR

Type ......................... High speed steel M2 Finisher Spiral Flute

Shank ....................... Morse Taper #3

Flute Length ............ 4.556" of cut.  

Overall Length ........ 14"

Number of flutes ...... 6

Condition .................. Super sharp, still coated in plastic, I believe it is a Resharpened cutter.  As you can see in the one photo there is some chamfer on the leading edge of the Flutes like you see on most chucking reamers, I have a had a few of these and used the same photo for all of them.

Additional Info ....... Diameter at the small end of the taper measures approx. 1.539" and at the large end it is approx. 2.092" The 1" round shaft that extends out 5" past the Flutes can be cut off if it is in your way or you could use it as a shank to hold on to depending on your application. The one in the photo is still partially covered in a plastic protective coating which is why it looks the way it does. The overall Flute length is a little longer than the actual length of taper cut, at the 2.092" diameter the Flutes Continue on at the size for a short distance.