Which one of the following statements is correct concerning capital budgeting?

a$.$ The positive return on stock investment implies positive NPV$.$

b$.$ For mutually exclusive projects, both PI and IRR lead to the same conclusion.

c$.$ When analyzing several projects with different period, we have to estimateNPV over the greatest common divisor of all projects' periods

d$.$ If all machines function the same, we can use the NP method to select the best machine even if we have only the cash outflows.

e$.$ We have to use the same discount rate for the projects we analyze.

Please explain why each option is true$/$false$.$