SC:impact on VS impact

[WWWL471]

One study found that although government policy and the industrial sector in which a company operates can influence its productivity and financial strength, management decisions have at least as great an impact on a company’s performance.

A.management decisions have at least as great an impact
B.decisions by management have a great impact
C.manager decisions impact greatly
D.decisions by a company’s management impact greatly
E.what a company’s management decides has a greater impact

The explanation of C said that Finally, decisions do not "impact on" performance; they impact performance. But I do not understand, please explain. Thank you.

[Sage Pearce-Higgins]

This is an example of an idiom: a combination of words in English. It's part of SC that you just need to learn - there's no logic here, just experience of formal written English. However, there might be some controversy in this case, as "impact on" seems to be a valid, if less used, idiom: https://en.oxforddictionaries.com/definition/impact