Visual Studio 2015: An equivalent project is already present in the project collection

Simply "Clean Solution" worked for me.

This happened to me after messing around with my project files with an external editor. I was able to solve the problem by exiting from VS and also killing, VsHub.exe.

It seems that VsHub.exe caches some portion of the project and becomes confused or out-of-sync with VS.

This link provided me with a simple prophylactic, one much less drastic than running {VSpath}\devenv.exe /resetuserdata

I found that by adding a Filter to the project (even though I didn't particularly need one) I could force VS2015 to create a .vcxproj.filters file. Once in place, I stopped seeing the problem.

BTW, in my case the problem was triggered by unloading the project, making tricky changes in the .vcxproj file (stuff involving [MSBuild] arithmetic on property values), then trying to reload the project, and having that fail due to syntax errors. Fixing the errors, removing/re-adding the project, etc. did not work. The 'already present' bug persisted.