please answer and show full work please

2. Space X, is looking into the development of a new rocket engine with varying initial investments captured in year zero for each project. Using specified discount rates and the future cash flows of each project, which rocket engine project should they accept using profitability index? Cash Flows Project U Project V Project W Project X Year zero -$2,000,000 -$2,500,000 -$2,400,000 -$1,750,000 Year one $500,000 $600,000 $1,000,000 $300,000 Year two $500,000 $600,000 $800,000 $500,000 Year three $500,000 $600,000 $600,000 $700,000 Year four $500,000 $600,000 $400,000 $900,000 Year five $500,000 $600,000 $200,000 $1,100,000 Discount Rate 6% 9% 15% 22%