Very well possible that the Royal Family generates a lot more money than they cost. They have one of the best world wide networks, and can open many doors. Also, media and tourists are very fond of royalty
Yes this is a commonly used argument by monarchy enthousiasts, yet I have never seen any proof that supports this.
Reminds me of the "calculations" of the CPB: If we increase "tax x" with 15% we will have 326 millions more income annually, yet rebound effects and the underlying mechanisms are never taken into account.
It is possible to make any calculation look feasible to suit the policy makers agenda, you just have to use certain "data selecting strategies".