$(5)$ A firm is considering an investment in a new machine with a price of $21\mathrm{.}5$ million to replace its existing machine. The current machine has a book value of $5$ million and a market value of $6\mathrm{.}5$ million. The new machine is expected to have a $5-$year life, and the old machine has five years left in which it can be used. If the firm replaces the old machine with the new machine, it expects to increase sales by $1\mathrm{.}5$ million and to save $5$ million in operating costs each year over the next five years.

Both machines will have no salvage value in five years. The required return on the investment is $12$ percent and the effective tax rate is $30$ percent. The company uses straight$-$line depreciation. What is the NPV of the decision to replace the old machine?

$19$:$50$