Bulk Updating .NET Framework Versions In Legacy Projects With Powershell

For one of our customers, I recently had to change the target .NET Framework version from 4.5.1 to 4.6.1 because a new version of some important Nuget package requires .NET 4.6.1. Changing the framework version in newer SDK-based projects is not a problem but the old csproj files, the big ones with the packages.config file, need some special treatment.