|Actually Vishal, the MAC address of your interface not only can, but in many many instances does have everything to do with your external IP address.|
I don't know about where you live, but here in North America, the majority of ISP's have their DHCP setup to continue leasing the same IP to the same customer based on MAC address. If your MAC doesn't change, you keep getting the same IP. They do this because it's the easiest setup for them to configure and maintain.
In those cases, changing your IP is as simple as spoofing your MAC. If you were to check, you'd find most, if not all, SOHO Router's have a setting that allows you to change (spoof) your MAC.
Some ISP's take it one step further and have customer connections restricted to two (or sometimes more) MAC addresses. If you change hardware a third time, your new one won't get TCP/IP settings because it's MAC is not registered with the ISP. The customer then has to contact their ISP and have them delete the existing MAC mappings for their connection. Most of these types of providers actually have a place for customers to change their MAC mapping on the ISP's website. Which is to say, delete the MAC of a device that's no longer connecting so you can then add the MAC of the new device.
I recently replaced the combo modem/router/access point my provider initially gave me when I signed on with them 5+ years ago. Instead of a combo unit, I asked for a modem only and got it. I then bought a SOHO Router and spoofed the MAC of my old combo unit on the replacement router so I'd get the same IP.
It matters not how straight the gate,
How charged with punishments the scroll,
I am the master of my fate;
I am the captain of my soul.