A franchise restaurant chain is considering a new store in an unserved part of town. Its finance group estimates an NPV of $$10$ million if population growth is $10\%(40\%$ probability$),$ an NPV of $$4$ million if the population neither grows nor shrinks $(30\%$ probability$),$ and an NPV of $-$$$4$ million if the population shrinks $5\%(30\%$ probability$).$ What is the expected NPV of opening up the restaurant in this unserved part of town?

$E[NPV]=$$