Please show step by step solution and where each calculation comes from.

$($a$)$What is the main purpose of the refundable dividend tax rules in the Income Tax Act?

b$)$ Why is income allocated to permament establishments in the Income Tax Act $?$

c$)$ Why does Part IV tax exist in the Income Tax Act $?$

d$)$Why do rules exist on taxable capital limits for CCPC$$s in the Income Tax Act?

e$)$Hackers Inc. is a non$-$associated CCPC that had $ $4,200,000$ of SR&ED expenditures in $2021$ and has no taxable income in the current or prior three years. Calculate how much of a cash refund Hackers Inc. can expect when filing its $2021$ corporate income tax return $?$