A borrower got a mortgage loan $5$ years ago for $$410,000$ at $6\%$ interest for $30$ years with no prepayment penalties or closing costs. The borrower just got a call from her friendly mortgage broker suggesting she refinance into an $7/1$ ARM $($indexed to one$-$year Treasury yields with an $8\%$ margin$).$ The $7/1$ ARM has a $30-$year amortization. The $7/1$ ARM has teaser rate of $5\%,$ a fully adjusted rate of $9\%,$ and closing costs of $$10,000.$

The borrower plans to move to San Antonio, TX when she retires in $6$ years. When she moves she must payoff all outstanding mortgages. Should she do the refinance $--$ use the IRR & NPV $($assume the discount rate or opportunity cost of capital of $5\%)$ criteria to make the decision?