The investment policy and the pricing of equity in a levered firm: a re-examination of the 'contingent claims' valuation approach

Abstract

In this study we re-examine the pricing of equity and the risk incentives of shareholders in levered firms. We derive a down-and-out call equity valuation model which rests on the assumption that shareholders choose the optimal investment and asset returns' volatility as a function of current leverage. Contrarily to the Black and Scholes framework where, irrespective of the firm's leverage, they would always select infinite volatility projects, here the more deep out-of-the-money the shareholders' claim, the greater their incentives to select riskier investment projects. The model is thus consistent with and quantifies the asset substitution problem previously acknowledged by the agency literature.Agency Problems, Asset Substitution, Contingent Claim, Down-and-out Call Option, Capital Structure, Leverage, Risk Incentives,

A market-based framework for bankruptcy prediction

“…sell) an underlying asset at a prespecified date (maturity date) for a prespecified price (strike), provided the underlying asset has not crossed a prespecified bound between the time the option was written and the maturity date. 3 Following Black and Cox (1976), Leland and Toft (1996), Chesney and Gibson-Asner (1999) and Brockman and Turtle (2003), we see shareholders as having in effect sold the firm to their creditors; however, shareholders hold the option to reacquire the firm if they repay the debt, provided the assets of the firm have not sunk in the meantime below a critical level. If the assets of the firm do reach this lower bound at any time between the date at which the option is written (money is borrowed) and the maturity date of the option (debt's repayment due date), bankruptcy is triggered, followed by the firm's takeover by bondholders and the shareholders' loss of any claim they had on the firm's cash flows (early bankruptcy).…”

A Compound Option Model to Value Moral Hazard

“…First of all, we can express the market value of firm capital as the premium of a barrier option, particularly a down-and-out call written on the firm assets with strike equal to the face value of the firm debt (see Chesney and Gibson [1994b] and Chesney and Gibson-Asner in this issue). This fact transforms the economic value of the incentive fee into the premium of a compound option (i.e., an option written on another option).…”

“…Chesney and Gibson [1994a] show that under some standard assumptions such a value can be expressed as the premium of a downand-out call option written on the firm assets with a strike equal to the face value of the firm debt. The down-andout call is a standard European call vanishing as soon as the value of the underlying hits a prespecified floor, set in this case equal to Ĥ , so that the condition C i (t ) = H is met, where H is the threshold value of the parameter of absolute performance used to define the incentive fee in Equation (1)…”

Reducing Asset Substitution with Warrant and Convertible Debt Issue

“…The down-and-out call equity valuation model was developed originally by Chesney and Gibson [1999] to examine the optimal volatility choice of shareholders in ordinary debt-levered firms. We show how the model can be used in the presence of reputation constraints to analyze the risk incentives of shareholders in all-equity financed firms.…”

“…We extend the Chesney and Gibson [1999] down-andout call option model of equity valuation to show that it is possible to recast the asset substitution problem in a contingent claims valuation framework. We thus show that equity in a reputation-constrained firm that has issued convertible debt or debt with attached warrants can be valued as a portfolio consisting of two down-and-out call options with different exercise prices held in long and short positions.…”