First of all, the notice is legally optional, and so a notice not conforming to any standard does no harm. But if one wishes to conform, under US law,17 USC 401 (b) provides that:
(b) Form of Notice.—If a notice appears on the copies, it shall consist of the following three elements:
(b) (1) the symbol © (the letter C in a circle), or the word “Copyright”, or the abbreviation “Copr.”; and
(b) (2) the year of first publication of the work; in the case of compilations or derivative works incorporating previously published material, the year date of first publication of the compilation or derivative work is sufficient. ...; and
(b) (3) the name of the owner of copyright in the work, or an abbreviation by which the name can be recognized, or a generally known alternative designation of the owner.
Note that it is the name of the owner of the work, not of the author or first owner. It is the year of first publication, not the yer the owner acquired the copyright.
So in your example the technically proper notice would be:
Copyright 2015 New Company Ltd.
I believe this would suffice as a proper notice in any country that complies with the Berne Copyright Convention or the TRIPS agreement (which is the vast majority of all countries in the would). The symbol © can be substituted for the word "copyright" and might be more comfortable internationally.
The phrase "All Rights Reserved" was never required under US law, but was once standard, because it was required for full protection under the Buenos Aires Convention. As the Wikipedia article says of this statement:
As the Buenos Aires Convention was not modified, the presence of a simple copyright notice was sufficient to ensure mutual recognition of copyright between countries which became parties to the UCC (which only Honduras never did). As of 23 August 2000, all parties to the Buenos Aires Convention are also parties to the Berne Convention for the Protection of Literary and Artistic Works, which provides for mutual recognition of copyright without any formalities (Art. 5.2 Berne)
So "All Rights Reserved" is even less required than the optional copyright notice, although it does serve to remind people that a work is not under an open-source or permissive license. And of course it does no legal harm. But it can safely be omitted, its retention is essentially a matter of habit and tradition, its legal value ceased in 1952 when the UCC effectively superseded the Buenos Aires Convention.
The same notice would be suitable for a notice displayed when the program runs, and indeed for any copyright notice on any kind of work (although in some cases the year can be omitted).
Effect of Notice in US
17 USC 401 (d) provides that:
(d) Evidentiary Weight of Notice.—If a notice of copyright in the form and position specified by this section appears on the published copy or copies to which a defendant in a copyright infringement suit had access, then no weight shall be given to such a defendant’s interposition of a defense based on innocent infringement in mitigation of actual or statutory damages, except as provided in the last sentence of section 504(c)(2).
The cited sentence of 504(c)(2) deals with an employee or agent of a nonprofit educational institution, library, archive, or public broadcasting entity who reasonably believes that copying fell under fair use.