Question on convertible debt's impact on WACC

The question is: When you are calculating WACC, let's say that the company has convertible debt. Do you count this as debt when calculating Levered Beta for the company?

Answer: If the convertible debt is in-the-money then you do not count it as debt but instead assume that it contributes to dilution, so the company's Equity Value is higher. If it's out-of-money then you count it as debt and use the interest rate on the convertible for Cost of Debt.

My thought: I think the question is actually asking if the convertible debt should be considered as debt or equity in WACC. I think when the convertible debt is in-the-money, we should count it as equity. But I am not sure the impact on Cost of Equity. I think the answer only mentions that equity value will be higher because there are more shares. What's the impact on Cost of Equity when the convertible debt is in-the-money?

Thanks!