Utility-based Pricing Of The Contingent Convertible Bonds And Corporate Capital Structure

This paper considers the design and pricing of a contingent convertible bond(CCB) and the optimal capital structure with a CCB. We assume the cash flow evolvesaccording to an arithmetic Brownian motion. The investor has access to one risk-freeasset or the market portfolio to smooth his consumption. The cash flow isnon-tradable and the equity takes on the high idiosyncratic risk. Therefore, we derivethe implied values of equity by a consumption utility indifference pricing approachand derive the consumption utility indifference prices or equilibrium prices ofCCB/straight bond. We provide numerical sensitivity analysis for the value of aCCB and the optimal capital structure of a firm by numerical method. We also analysethe impact of investor protection on the value of CCB and discuss the deferred andtake-it-or-leave-it investment problems that involve CCB financing.First, in order to illustrate the behavior about the consumption utilityindifference price of CCB and the capital structure in the incomplete market, weignore the tax and bankruptcy cost. And the investor only has access to one risk-freeasset to smooth his consumption. We derive the implied values of equity, CCB andstraight bond by a consumption utility indifference pricing approach under anexogenous bankruptcy triggering level, an exogenously specified conversion rule.Numerical calculations show that the value of a firm is determined by how it isfinanced which is different from Modigliani-Miller theory. The CCB can not onlydirectly decrease the coupon of straight bond and the bankrupt risk, but also cansignificantly increase the total firm value. The higher the business risk or the morerisk-averse the agent is, the more (less) the CCB (straight bond) should be issued. Ourmodel explicitly finds that a straight bond will decrease the implied value of theequity by strengthening precautionary savings motive of the equity holder, but on thecontrary, a CCB will increase the implied value by weakening the savings motive.This is a hidden merit of a CCB, which is overlooked in a risk-neutral world.Second, we consider the tax and bankruptcy cost. The investor has access to onerisk-free asset and the market portfolio to smooth his consumption. For the firm thatlack of liquidity or high stock concentration, considering the mixed characteristic ofCCB, it can induce the transfer of control rights. And the equity after conversion maytake on non-diversifiable idiosyncratic risk just as the original equity. So, We derive the implied values of equity and CCB by a consumption utility indifference pricingapproach under an endogenous bankruptcy triggering level, an exogenously specifiedconversion ratio. Because of the higher liquidity of straight bond, the straight bondholder is fully diversified. We provide the equilibrium price of straight bond. Theresults show that the CCB not only decreases bankruptcy risk but also considerablyincreases the total firm value without tax. The total firm value is a convex function ofconversion ratio and there is a unique global maximum point. The optimal conversionratio increases with the risk aversion index. If investors are risk-averse enough, asidiosyncratic risk rises, the firm should sell less CCB and equity but more straightbond. However, if the investors are risk-neutral, the opposite holds true. If the cashflow is sufficiently negatively correlated with the market portfolio return, the equityholder might have risk-taking incentives. In general, there are risk taking incentivesfor a risk-neutral investor but there are not if the investor is a little more risk-averse.The higher the conversion ratio or the larger the risk aversion index, the weaker arethe incentives.The risk premium for the CCB is determined not only by systematicrisk but also by idiosyncratic risk.Third, under the poor investor protection, we assume the firm with CCBfinancing chooses the endogenous conversion trigger and the converson ratio thatkeeping control right. The CCB holder is a large-scale investment company. There aredifferent types of investment. So, the CCB holder is fully diversified. And the straightbond holder is also fully diversified. So, we provide implied values of equity by aconsumption utility indifference pricing approach and the equilibrium prices of CCB,straight bond. After that we discuss the take-it-or-leave-it investment problem. Theresults show that under the poor investor protection and for a higher coupon ofstraight bond, the higher the risk aversion, the bigger the optimal conversion ratio.But it presents the opposite result for a lower coupon of straight bond. Comparingwith the external equity financing, it presents the weaker dilution effect toentrepreneur’s equity. Even under the highly poor investor protection, a CCB stillcan improve the total firm value.In the last, we discuss the deferred investment problem that involves CCBfinancing. The numerical results show that the higher the risk aversion, the lower arethe implied value (the consumption utility indifference price) of real option and theinvestment trigger level. The higher the idiosyncratic risk, the lower the implied valueof real option but the higher the investment trigger level. In general, the implied valueof real option will increase with the conversion ratio. A CCB financing can improve the implied value of real option, and decrease the investment trigger level. Under thefinancing constraint, the entrepreneur might have higher risk-taking incentives.However, under the optimal financing condition only with CCB financing, theentrepreneur might have lower risk-taking incentives. If the firm only has CCBfinancing, the enterprise will obtain less amount of the financing comparing with thesame condition of other bonds.