**Abstract:**

We consider the problem of computing the lower hedging
price of American options of the call and put type
written on a non-dividend paying stock in a non-recombinant tree model with multiple exercise
rights. We prove using a simple argument that an optimal exercise policy for an option with $h$ exercise rights is to delay
exercise until the last $h$ periods. The result
implies that the mixed-integer programming model
for computing the lower hedging price and the optimal exercise and hedging
policy has a linear programming relaxation that is exact, i.e.,
the relaxation admits an optimal
solution where all variables required to be integral have integer values.