CRS Plc$,$ a UK$-$based clothes manufacturer, is considering adding a new line of clothing to its current production line. The success of the new line depends on general market conditions. CRS$$s current share price is $50.$

If the conditions are good, the revenues from the project are estimated to be $16$ million a year for $7$ years, starting a year from now, and the share price will be $70$ in year $1.$ On the other hand, if the conditions are bad, the revenues are expected to be $4$ million a year for the first $5$ years, and $2$ million for the remaining $2$ years of the project, and the share price will be $33$ in year $1.$ The initial cost of the project is $50$ million. The risk$-$free rate is $10\%.$

Required:

a$)$ Calculate the Net Present Value $($NPV$)$ of the project.

b$)$ CRS$$s CEO thinks that the project is too risky and wants to wait for a year and only invest in the project if the conditions are good. Assume that, if the decision is delayed, the project$$s cash flows and its time duration will not change but the positive cash flows will start in $2$ years$$ time.

Calculate

i$.$ the NPV of the project if the CEO$$s proposal is accepted

and

ii$.$ the value of the option to delay the project.

c$)$ Calculate the price of a call option on CRS$$s stock that expires in one year$$s time, with an exercise price of $55,$ and show all your workings, using the tracking portfolio $($no arbitrage$)$ approach.

d$)$ CRS$$s CEO is considering decreasing the firm$$s dividend from $0\mathrm{.}5$ per share to $0\mathrm{.}3$ per share. Briefly discuss how the market is expected to react to this decision, and why.