$($a$)$ Define the term $$profitability index$$ and briefly explain how it may be used when a company faces a problem of capital rationing in any single accounting period, and state any three $(3)$ weaknesses of its usage. $(6$ Marks$)$

$($b$)$ The Telescope Company is considering five projects:

Project Initial outlay NPV of project

A K$6,000$ K$1,200$

B K$4,000$ K$200$

C K$10,000$ K$6,000$

D K$8,000$ K$3,200$

E K$7,000$ K$2,100$

Projects C and D are mutually exclusive and the firm has K$20,000$ available for investment. All projects can only be undertaken once and are divisible.

$($i$)$ Which project$($s$)$ should be undertaken $($if any$)?(10$ Marks$)$

$($ii$)$ What is the maximum possible NPV from the undertaken project$($s$)$ in $($i$)$ above?