Suppose I am not paying any dividend then why is there a cost for cost of equity that is my cost of equity should be zero?

The answer is, if you are not paying any dividend then there is opportunity cost for my investor and that opportunity cost is reflected in CAPM, so even if dividend is not being paid there is always a cost. It is measured using CAPM model which does not depend on whether the company is paying dividend or not and it depends on the risk involved
In the company as measured by market risk premium and data and the formula for the same is as follows:
ERi​=Rf​+βi​(ERm​−Rf​)
where:
ERi​=expected return of investment
Rf​=risk-free rate
βi​=beta of the investment
(ERm​−Rf​)=market risk premium​

Study Smart: The Ultimate Exam Guide by Yugantar Gupta
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