Why is a sodium chloride molecule stable?
What you have calculated is the energy required to make two separated ions out of two separated $\ce{Na}$ ad $\ce{Cl}$ atoms. When they are separated, these ions do not make a molecule or a crystal of salt. Separated ions attract one another and are able to release a huge amount of Coulomb energy when approaching each other.
Anyhow your calculation should still take into account the fact that chlorine atoms do not actually exist. They must be produced by breaking a $\ce{Cl2}$ molecule. And this requires some energy. You may also introduce the sublimation energy of sodium atoms