$2.(15$ pts$)$ An initial investment of $$75$ million $($in time $0)$ is expected to generate the following cash flows over a three$-$year project life as follows:

Year Cash Flow Probability of Occurrence

$1$ $ $30$ million $40\%$

$+$ $ $20$ million $60\%$

$2$ $ $45$ million $55\%$

$+$ $ $25$ million $45\%$

$3$ $ $45$ million $70\%$

$+$ $ $20$ million $30\%$

What is the risk adjusted NPV of the investment for a minimum rate of return $=12\%?$