Re-installing MacOS should be a piece of cake. Just go into recovery mode by pressing Command+R during boot and start recovering. It should be…
But that is only true for the common case. If you perform the internet recovery and you are using a brand new Apple ID, then you are screwed. In that case you will see a message like this:
This Apple ID has not purchased Lion. You must sign in with an Apple ID that was used to purchase OS X Mavericks.
This happened to me, when I purchased a Mac online with a new Apple ID and tried to activate it. Well, it simply doesn’t work out of the box.
But fear not, there is quite simple fix, although it requires an activated Mac.
On that activated Mac log into the Mac App Store with your fresh Apple ID. Then find the MacOS version that you want to install, in this case Mavericks. Click download and it will give you some hard time, because it is already installed. But simply ignore that. Click continue to download the installer. You will see the download process in purchase area. You can go there and pause the download, because you don’t really want to install it. Now you should log out of the Mac App Store, if this is not your machine. And now, as a last step restart the Mac. Of course the one that you want to re-install. You can now use your fresh Apple ID that just “bought” MacOS.