If the convertible bonds are in-the-money, meaning that the stock price is higher than the conversion price, then the bonds will convert into equity. This means more shares will be created, which will dilute the share price since the same enterprise value has to be spread over a larger share count.
If the convertible bonds are out-of-the-money, meaning that the stock price is lower than the conversion price, then the bonds will stay as bonds.
However, in a DCF, we value the company using unlevered free cash flows (UFCF), which is the free cash flows without the effects of debt, so we don’t care about this interest expense. In a DCF, we assume a target capital structure for the entire projection period, which is reflected in the WACC, so any temporary changes in debt won’t matter since the cost of debt is already reflected in the discount rate. Therefore, nothing will happen to the DCF implied value of the stock if the convertible debt is not in-the-money.