Exercise about Monopoly price charging
I do not understand your attempt very well. 

Assuming that the monopolist cannot directly price discriminate (i.e. charge different prices to old and new consumers in the same period), then in the second period it is optimal to offer a price of 50 and sell to everyone, regardless of whether the old guy bought or not. 

Knowing this, the old guy would buy in the first period iff the price gives him a total surplus of 50 (which he can get by waiting). Hence, the initial price should be 150.

If, on the other hand, the old guy has a value of only 20, then in the second period the monopoly price would still be 50. Hence, the old guy has no surplus from waiting and the monopolist should charge 40 to him in the first period.