Testing serial communication programming
In order for your customer to use your .net application you have to:

Make sure the correct version of the .net framework is installed.

For this, you might want to ship your application by an installer like InstallShields.
That installer will check all the dependancies that your application has and will prompt the user for installing the missing ones.

Make sure the PC has an available serial port.

It may sound silly but sometimes the end-user doesn't even know what a comm port is.
On some PC's, for some reasons, comm port 1 is mapped onto comm port 2. Maybe because they installed a third party hardware PCI card that let the user remap comm port names.
You might want to modify your code in order to let the user chose the comm port he wants.
Once you set the baud rate (example: BAUDRATE = 9600) the CPU speeds is nothing you should concern about: the OS will take care of anything to make your comm port run at 9600 baud per second.