Two mutually exclusive projects $-$ Project Alpha $($A$)$ and Project Beta $($B$)-$ are being considered for investment.$$Project A has a greater internal rate of return than Project B$\text{'}$s$.$Project B has a greater net present value than Project A$.$Both Project's A and B$\text{'}$s internal rate of return exceeds the Company's cost of capital and both projects have positive net present values.$$Which project$($s$)$ should be chosen?

Project A

Both Projects A and B

Project B

Neither project