I know that this is a very simple question, but i want to make sure to grasp the concept of ex dividend and value of portfolio.
Suppose that we have a two period binomial tree of a stock with initial value of $S_0= 100$ and $u=1.2$ and $d=1/u$. The stock pays fixed discrete dividends: $d_1=10$ in the first period and $d_2= 5$ in the next period.
What is the Value of this portfolio at times $1$ and $2$?
$1)$ If the stock goes up then: $V_1= 100*(1.2)-10=110$
if the stock goes down then $V_1=100*(1/1.2)-10=73.33$
$2)$ if the stock goes up up then: $V_2= 110*(1.2)-5=115$
if the stock goes up and down then $V_2= 110(1/1.2)-5=86.66$
if the stock goes down and up then $V_2= 73.33(1.2)-5= 83$
if the stock goes down and down then $V_2= 73.33(1/1.2)-5= 56.11$
I would really appreciate if you can tell me if this is the correct value of the portfolio, or if I´m doing something wrong.