Equity Risk Premium Question

Hello,

Regarding the equity risk premium (and additionally cost of equity) how do we know when to use the LT Government Yield or the ST Governement yield? I’ve seen a couple of practice problems in both Kapland the CFA practice questions where they are (seemingly) using the LT or ST yield interchangably. Does anyone know how to differentiate?

Additionally, could anyone confirm whether private or public companies require a higher rate of return on equity? Not sure if private or public companies should have a higher required rate.

Thanks!

Always use the Long Term Government Bond Yield except for Fama and Pastor.