Analyzing Callable and Convertible Bonds when the Modigliani-Miller Assumptions are Violated

Abstract

We analyze callable, convertible, and callable-convertible bonds in a dynamic model with restructuring, taxation, and transaction/bankruptcy costs. In this setting, calling when conversion value equals call price is not generally optimal. Late (early) calls are optimal when the conversion ratio is high (low) and the debt coupon is low (high). If volatility is fixed, pure callable bonds with a substantial call premium maximize firm value, committing equity to second-best restructuring policies. Convertibles are dominated in this context, since the backdoor equity component of the bond is tax-inefficient. The model is extended to allow for instantaneous risk shifting. Call provisions shorten effective maturity, but are not sufficient to induce hedging. Convertible bonds induce hedging, and the optimal conversion ratio trades off incentive provision against tax costs. Convertibles dominate pure callable bonds only when costs of risk shifting are sufficiently high. Although they mitigate risk shifting incentives, no convertible bond can induce global hedging, since equity is infinitely risk loving near default. In addition, convertible bonds exacerbate underinvestment incentives, since conversion privileges reduce marginal q.