Corrigan Limited, an experienced park operator, is considering a proposal by Newtown Limited to enter into a $50/50$ joint venture project $($the $$JV$).$ The JV is to acquire a $15-$year franchise to run a large theme park. The JV is expected to generate the following cash flows, which will be received at the end of each year:

From Year $1$ to Year $5$: $$60$ million per year. From Year $6$ to Year $15$: $$80$ million per year.

The discount rate for the JV is $12\%.$ Corrigan has a WACC of $8\%,$ and Newtown has a WACC of $10\%.$

The up$-$front investment cost of the JV is $$400$ million, or $$200$ million for each partner. Newtown also gives Corrigan an option to sell its $50\%$ share of the JV to Newtown within the first $3$ years at a price of $$170$ million.

$($i$)$ Is this a call or a put option? $(1$ point$)$

$($ii$)$ Complete the inputs $($S$,$ K$,$ t$,$ and y$)$ below for using the Black Scholes model

to calculate the option price:

Value of the Underlying Assets $($S$)=?(1$ point$)$ Strike Price $($K$)=?(0\mathrm{.}5$ point$)$

Time to Expiration $($t$)=?(0\mathrm{.}5$ point$)$

Dividend Yield $($y$)=?(0\mathrm{.}5$ point$)$

Risk free rate is $2\mathrm{.}5\%,$ and the standard deviation of the value of the underlying assets is $30\%.$

$($iii$)$ Assuming that the option value is $$21$ million, what is the net present value of the project to Corrigan? $(1$ point$)$