Convertibles

If their is a high conversion premium, because investors think the shares will have a high value on the conversion date, then the debt can be issued at a high price. If the debt is issued at a high price then they need to issue less debt to raise the amount needed. If they issue less debt, then they will need to issue fewer shares on conversion. With regard to the last stamens, yes - if the market value falls to the minimum it means that the investors are expecting to prefer taking cash to shares and therefore attach no value to the conversion rights.