How do corporations make their capital budgeting decisions to ensure optimal allocation of resources $($capital$)?$

How can risk be incorporated into the capital budgeting process, and how does it impact decision$-$making?

How is each of the four capital budgeting methods, i$.$e$.,$ Payback Period, NPV$,$ Profitability Index and IRR, being used in real world for making capital

budgeting decisions?