Choosing between Projects with the Profitability Index Suppose the following two independent investment opportunities are available to Greenplain Ltd$.$ The appropriate discount rate is $10$ per cent.

Year Project Alpha $()$ Project Beta $()$

$05002,000$

$1300300$

$27001,800$

$36001,700$

a$)$ Compute the profitability index for each of the two projects.

b$)$ Which project$($s$)$ should Greenplain accept based on the profitability index rule?