convertible bonds

Suppose a company simultaneously issues $50 million of convertible bonds with a coupon rate of 9 percent and $50 million of pure bonds with a coupon rate of 12 percent. Both bonds have the same maturity. Does the fact that the convertible issue has the lower coupon rate su,,,:est that it is less risky than the pure bond? Would you regard the cost of capital as being lower on the convertible than on the pure bond? Explain. (Hint: Although it might appear at first glance that the convertible's cost of capital is lower, this is not necessarily the case because the interest rate on the convertible understates its cost. Think about this.)