The convertibility feature can reduce the need for some bond covenants and thus give the firm more flexibility in case a great project were to appear suddenly. Bondholders would be happy because they would benefit, too. (Of course, bondholders get more if the firm does well, and shareholders get a lower interest rate, but this is just state reallocation. The important aspect here is that the net effect of the alignment of interests would be a reduction in the firm’s overall cost of capital.)