Sir what does one mean when its said debt beta is zero? Does that mean there is no gearing in the company and hence we will only use the asset beta to calculate cost of equity?
If there were no gearing then there would be no debt and no debt beta!!!!
Beta is a measure of risk. If the debt beta is zero then it means it has zero risk.
In the formulae we assume debt is risk free and therefore the debt beta is zero. In practice debt does have a bit of risk and so does have a beta bigger than zero, but you would expect it to be small.
If there is no gearing then the equity beta will be equal to the asset beta, but this has nothing to do with the debt beta being zero.
This is all explained in detail in my free lectures.