Shifting Sands Transport Company has been preparing quotations for transporting oil and gas employees to bases offshore. The Companys cost of capital is $6\%.$ A new contract is coming up for negotiation. This five$-$year deal would necessitate buying a ship for $60$ million. Annual fixed operating costs would be $600,000.$ The variable cost per passenger would be $60.$ At the end of the five$-$year contract the resale value of the ship will be $40$ million. $$ An alternative option is to buy a helicopter for $10$ million. This would take on average $9$ people at a time and the average operating costs would be $6,000$ per trip. Maintenance costs are expected to be $200,000$ in the first year and rise by $200,000$ each year up to $1$ million in year $5.$ At the end of five years the resale value of the helicopter is expected to be $3$ million. $$ The income from the contract for either option is a fixed $10$ million each year for the five$-$year period. The expected annual demand for transporting employees offshore and back again over the next five years is forecast as follows: $$ Passenger numbers Year $16,300$ Year $29,000$ Year $310,800$ Year $412,600$ Year $58,100$Required: $($a$)$ Present a table showing the cash flows for each option. $(10$ marks$)($b$)$ Using the cash flows from part $($a$)$: $($i$)$ Calculate the Net Present Value $($NPV$)$ of the net cash flows of both options. $(6$ marks$)($ii$)$ Calculate the Internal Rate of Return $($IRR$)$ of both options to one decimal place.$($iii$)$ Calculate the Payback Period of both options to two decimal places. $(4$ marks$)($iv$)$ Calculate the Profitability Index $($PI$)$ of both options to two decimal places.WhereProfitability Index $=$ PV of cash flows $/$ Initial Investment $(4$ marks$)($c$)$ Using the results from $($a$)$ and $($b$)$ above, explain which option the Company should take bearing in mind any other factors that should be considered before the final decision is taken.