The agency problem, investment decision, and optimal financial structure

Abstract

This article constructs a real options model in which a firm has a privileged right to exercise an irreversible investment project with a stochastic payoff. Supposing that the investment costs are fully sunk, a firm that exercises the investment option after debt is in place will then choose a better state to exercise this option as it issues more bonds. This debt-overhang phenomenon, however, benefits the firm since waiting is itself valuable. Accordingly, the firm will both exercise the investment option later and issue more bonds as compared with a firm that issues bonds upon exercising the investment option.

Keywords:

• bankruptcy
• financial structure
• irreversible investment
• limited liability

Acknowledgements

The authors would like to thank Professor Chris J. Adcock (the editor) and an anonymous referee for their helpful comments. The financial support under grant NSC-89-2416-H-002-068 from the National Science Council, Executive Yuan, R.O.C., is gratefully acknowledged.

Notes

Our definition regarding the first- and second-best firms differs from that of Leland (1998). Leland defines the first-best firm as the one that simultaneously determines its risk strategy and its debt structure to maximize total firm value, and the second-best firm as the one that chooses its risk strategy after debt is in place. Accordingly, Leland investigates how the agency cost associated with the asset substitution problem (Jensen and Meckling, 1976) affects a firm's optimal financial structure.

See the paper by Jou (2001b) that constructs a two-period model to reinvestigate Myers’ two conjectures in a framework where capital is not readily reversible and is more expensive to acquire later.

Capital investment may be irreversible because of asset specificity, the ‘lemons’ problem, or governmental interventions (Dixit and Pindyck, 1994).

Following Leland (1994) and Mauer and Ott (2000), one can easily admit finite average debt maturity by assuming that debt has not a stated maturity but is continuously retired at par at a constant rate.

Black and Cox (1976), Leland (1994) and Merton (1974) all assume that this value follows a geometric Brownian motion, while Mello and Parsons (1992) assume that this value follows a geometric Brownian motion plus the option value associated with liquidation possibilities. Mauer and Ott (2000) encompass these assumptions by assuming that this value is a non-negative function of the output price. Our assumption regarding this value is more simplified than that of those articles mentioned above.

Leahy (1993) demonstrates that without debt financing, the investment decision of a monopolized firm mimics that of a competitive firm in industry equilibrium. However, Leahy's conclusion cannot be generalized to the case where a firm is able to issue bonds, as Fries et al.(1997) demonstrate.

We thus preclude the ‘moth-balling’ of productive activities such as those considered by Brennan and Schwartz (1984) and Mello and Parsons (1992).

As pointed out by Fries et al.(1997), this happens if outside equity is available in any quantity. In this case, leverage will be set to maximize the ex ante value of the firm. If equityholders are cash constrained, then the firm may be forced to choose a debt level that is unable to maximize the ex ante value of the firm.

These authors also note that the first-best bankruptcy policy would lead to a violation of equityholder limited liability, i.e. equity value would be negative at a firm-value-maximizing bankruptcy trigger.

Condition (18″) follows because the critical level of the after-tax price that triggers investment,

, is higher than the flow-equivalent after-tax costs of investment,

.

This is the second-order condition for

to be an interior solution. We will assume it holds in what follows.

The negative sign of Δ˙₁₁ follows because the critical level of the after-tax price that triggers investment;

, is higher than the flow-equivalent after-tax costs of investment,

.

For

to be an interior solution, it is required that

. We will assume this condition holds in what follows.

The tax rate τ is chosen to reflect that personal tax advantages to equity returns will lower the tax advantage of debt below the corporate rate of 35 % (Leland, 1998).

A higher σ leads to a higher value of β₂. Accordingly, the term

in (13′) becomes higher. Therefore, the marginal tax shield benefit will be reduced, while the marginal bankruptcy cost may become higher, lower, or remain unchanged. The loss of the former, however, more than offsets the possible reduction in the latter. The firm's debt capacity will thus be lower.

This is because based on (13′), when P _{* f} becomes lower, the marginal tax shield benefit of debt financing becomes higher, while the marginal bankruptcy cost of debt financing becomes lower.

This is because when P _{* f} becomes lower, the firm's option value to later invest will then be raised by less than the net value from investing immediately, i.e. the value of

as defined earlier, will be lower.

This result is in line with the standard result in the real options literature that ignores debt financing (see, for example, Dixit, 1989; 1991).