After I cut down my frangipani tree, new leaves have grown on the old stumps. However, the plant has stopped producing flowers altogether. Before it was cut down, it was flowering non-stop.
The same thing is happening to the other stump which I had planted in a pot. As you can see here, flower buds are already showing at the tips of the bare branches.
In case you're wondering, these branches are really short, less than a foot high.
Therefore, if you should ever cut down your frangipani plant, don't throw away the branches. Just poke them into a pot of soil and you'll be rewarded with pretty blooms in no time.