Before we present the numerical results, a discussion of the managers’ incentives is in order. In our model, the managers have incentives to overinvest in the growth option because of two reasons: first, theirfixed payments increase when the firm exercises the growth option, and second, theirfixed payments are more secure after the exercise of the growth option due to a reduction in default probability. Without the ownership in the firm’s equity, the managers have incentives to exercise the option immediately and to switch to the low-risk level as soon as possible to reduce the probability of losing theirfixed payments. In this situation, the managers’ interests are completely aligned with those of the debtholders.
The managerial equity ownership in thefirm’s equity plays two important roles. First, it reduces the managerial incentives to overinvest because overinvestment destroys the equity value, and by extension, their own compensation. Second, the equity ownership gives the managers incentives to take on high risk because the value of the equity that they own increases withfirm risk. As the level of ownership increases, the managers’ interests become more aligned with those of the equityholders.
When the ownership is determined optimally ex ante, it can significantly reduce the agency costs, but it may not completely resolve the conflict of interest of the managers; it may still has to trade off the marginal costs of increasing and reducing risk.
We now turn to the numerical results under the managerial compensation maximization scenario. For the base case, we assume that the managers’ fixed paymentsαare 0.10but increase by η = 25 percent when the growth option is exercised. We first discuss the case in which thefirm hasflexibility to manage risk and then discuss the case in which thefirm commits to maintaining risk at the lowest level at all times.
6.1
The Firm with Risk Flexibility
Panel A of Table 2 shows that, before the option is exercised, the firm defaults when the asset value falls below VB0= 29.1, which is the level at which the wealth constraints bind.
The managers use the low-risk strategy when the asset value is lower thanVS0= 72.9and switch to the high-risk strategy when the value is higher. Observe that VS0 is slightly lower than that in thefirst-best case, implying thatfirm risk is higher. As a result, the optimal leverage is slightly lower at34.8percent, and the yield spread is slightly higher at69.2basis points.
When the asset value reachesVG= 264.9, the managers exercise the growth option. Notice thatVG is lower than that in thefirst-best case, indicating that the managers overinvest in the growth option. After the exercise, the managers switch to the low risk level immediately, which is indicated by VS1=∞, and thefirm goes into default when the asset value falls toVB1= 19.4.Before and after the exercise, the wealth constraints bind, soVB0andVB1are proportional to the debt level, which is slightly lower than that in the
first-best case due to lower leverage. The option value, the tax benefits, the expected bankruptcy costs,
and the totalfirm value are18.5,7.9,1.3, and125.1, respectively.
Although the choice variables chosen by the managers still differ from those in thefirst-best scenario, the differences are relatively small, so the agency costs are low at0.1percent. The optimalβ, which gives the managers the incentives to implement the aforementioned policies, is7percent.
6.2
The Firm with No Risk Flexibility
In Panel B of Table 2, we report the results when thefirm has noflexibility to manage risk and is committed to the low-risk strategy at all times. The default level before the exercise of the growth option VB0 =
37.4, which is the level at which the wealth constraints bind, and the option exercise level VG is 264.9. After the option is exercised, thefirm defaults atVB1 = 24.9. This is an endogenous default level that is chosen by the managers, which is higher than the level at which the wealth constraints bind. The option value, the tax benefits, the expected bankruptcy costs, and the totalfirm value are14.9, 10.2, 1.7, and
123.4,respectively.
Not surprisingly, the total firm value is lower than that in the preceding case. However, the optimal β increases significantly to16.5percent. Recall that the optimalβ in Panel A must simultaneously solve the managers’ overinvestment problem and reduce their tendency to take too little risk. The level of β that completely eliminates the overinvestment problem will make the managers take on too much risk, so the optimal β cannot be that high. But in the case in which the managers do not have riskflexibility, the optimalβbecomes larger to completely eliminate the managers’ incentives to overinvest. One would expect that in this case the firm’s investment policy should coincide with that in the first-best case. However, observe that VG in this case is lower than that in thefirst-best case, indicating that the overinvestment problem still exists. To understand this, recall that the higher β is, the more the managers behave like the equityholders, and the higher is the endogenous default level. If the managers were to implement the first-best option exercise policy, β must be higher than 16.5percent, which would increase VB0 and
decrease the total firm value. This example shows that, even when thefirm does not manage risk, the optimalβ may still need tofind a balance between the investment and default policies.
The result that thefirm with noflexibility to manage risk may have higher managerial equity ownership is consistent with empiricalfindings by Tufano (1996) and Schrand and Unal (1998); these authors report that hedging increases with the level of managerial ownership in the firm. Smith and Stulz (1985) and Stulz (1996) explain this relation by arguing that if the managers have large concentrated equity ownership, the volatility of their compensation tends to be highly correlated with the volatility of the firm. If the managers are risk averse, they will reduce the volatility of their compensation by engaging in hedging activities. The explanation of our model differs from that of Smith and Stulz (1985) in that the ownership is not given exogenously but is determined endogenously to motivate the managers to implement the best possible risk management and investment strategies.