5. Tax Shield, Bankruptcy Cost and Optimal Capital Structure

You can also choose an optimal equity size or ratio by trading-off the potential benefits and costs related to the equity financing. This is equivalent to the consideration from the debt side which is the academic convention.

We reveal in Chap.​ 4 (4.1 Alternatives to determine a discount rate) that the discount rate is different from the cost of capital (including the weighted average cost of capital, WACC), because the capital cost is the result of financing (decision), and may have nothing to do with the asset risk. The discount rate is the investors’ benchmark to value an asset (such as a project or firm etc.), and has much to do with the asset risk. However, financial scholars are used to refer to the discount rate as capital cost (including the WACC and the equity cost) in the discussion of capital structure since Modigliani and Miller. We continue to use such an appellation in this chapter to avoid unnecessary chaos or difficulties for readers. Nevertheless, readers should aware that the WACC and the equity cost in this chapter is the appropriate WACC and the appropriate equity cost, which incorporate the relevant risk and can be used as the discount rate to derive the value of the firm and its equity respectively. In other words, the cost of capital in this chapter is exactly the fair cost of capital or discount rate rather than the actual cost of capital.

There are some relevant prevailing terminologies, such as debt overhang (Myers 1977), asset substitution (Jensen and Meckling 1976), and asset fire-sales (Shleifer and Vishny 1992), etc.

Basically, financial distress cost is only a new name of indirect bankruptcy cost.

This may be close to the prevailing concept of distress cost, which may includes also agency cost, etc., but I will not distinguish those costs in detail, and just regard them as all aroused from the debt financing.

Some scholars study the capital structure decision with possible bankruptcy before the debt maturity, such as Ju et al. [13]. For the general validity and decisional efficiency of the solution, I will focus on the most simple and common situation, where the bankruptcy can only occur at the debt maturity.

Note that the risk free rate is positively related with the interest rate of the debt.

See also Graya et al. [14].

Most researches on capital structure choose 20 % as the typical volatility; but some choose a value close to 40 %, such as Ju et al. [13], etc. Here I just choose a value somewhere in between.

These relationships will be more easily to be understood when they related to the payoff or intrinsic value and time value of the relevant put option.

Such as Ross et al. [17], Brealey and Myers [18].

Growth rate is determined by the rate of return of the firm’s investment and its dividend policy. Given the dividend policy, the growth rate is positively related to the rate of return.

Such as Servaes and Tufano [19].

See among others, Bradley et al. [24], Graham and Harvey [22].

See among others, Mackie-Mason and Jeffrey (1990), Fama and French (2002).