The AP Stylebook recommends abbreviating the words "Company" in addition to "Corporation" as Co. as well as Corp., respectively, when they show up at the end of a proper content label, but not if the phrase occurs elsewhere inside name.
Examples:
Ford Motor Corp.. . . . . . . . . Light weight aluminum Company regarding America
Gulf Fat Corp.. . . . . . . . . . . Corporation for Public Broadcasting
Subsequent references for you to "the company" or even "the corporation" should be spelled out and not capitalized.
Examples:
Quirky Car Company. brought out a new model, the particular Zoomer. The company believes the following progressive "green" car will make fuel obsolete.
The Perfidius Corp. has been indicted with regard to offering bribes to help unusual countries to routine for fat. Tag heuer is also being sued by means of stockholders for deception.
For plurals, Corp. becomes Cos., as in U . s . Broadcasting Cos.
For possessives, strangely within the Co. gets the Co.'s, and the factor on the Corp. becomes the particular Corp..
For plural possessives, the thing with the companies becomes the actual Cos.'