Asset beta or Equity beta in calculating Ke in CAPM?

The cost of equity is always - without exception - determined by the equity beta. In order to find the equity beta, we usually have to determine the asset beta by looking at similar companies, and then find the equity beta using the asset beta formula on the formula sheet. The equity beta will only ever equal to asset beta if there is no gearing. Trosoft specifically asks for an APV approach, and Intergrand effectively asks for it (because it says to discount at the all equity rate). With APV we always calculate the base case NPV as though it is all equity funded, in which case (as I have written above) the equity beta will be equal to the asset beta). It would seem that you have not watched my free lectures on APV (and CAPM) and I do suggest that you do.

What if the company is ungeared? Asset beta=equity beta. Can this beta then be used in CAPM?

OK think I got it. Only Equity Beta in CAPM. This could however equate to the asset beta if no debt so in essence you are plugging in the asset beta into CAPM-although it is the equity beta

Yes - what you have written is correct :-)