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2023 | OriginalPaper | Chapter

Tax Shield, Bankruptcy Cost and Optimal Capital Structure

Author : Zhiqiang Zhang

Published in: Fundamental Problems and Solutions in Finance

Publisher: Springer Nature Singapore

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Abstract

This chapter solves the problem of optimal capital structure. It reconfirms the reasonable way to solve the problem of optimal capital structure is to trade-off between the tax shield and bankruptcy cost resulted from debt financing. Based on the new derived models for valuing tax shield and bankruptcy cost, the theoretical solution to the optimal capital structure is finally derived. The solution to optimal capital structure reveals that there is indeed an optimal debt ratio for every company, but the trade off value or the benefit from the optimal use of debt capital is very small and the loss resulted from overuse of debt capital (over leverage) is relatively larger. It is not worth to adjust the capital structure so long as a company is not over levered; and the best way to adjust capital structure for a company is taking advantage of next financing. Based on the solution, various capital structure puzzles can be easily and soundly explained, like why firms incline to conservatism or perhaps no leverage target, etc.

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Footnotes
1
Most of the problems discussed in this book are on the top in importance in finance; however, most of the solutions in this book are not old enough to be accepted as the mainstream of financial theory.
 
2
Modigliani and Miller (1958). Modigliani and Miller (1963).
 
3
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.
 
4
We reveal in Chapter “Certainty Equivalent, Risk Premium and Asset Pricing” 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 a 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 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 understanding. Nevertheless, readers should aware that the WACC as well as the equity and debt cost in this chapter are the appropriate or fair ones, which incorporate the relevant total risk and can be used as the discount rate to derive the value of the firm and its equity, etc.
 
5
The same as Fig. 1 in Chapter “Capital Asset Pricing:​ An Easy and Unified Solution”.
 
6
This may be close to the prevailing concept of distress cost, which may include also agency cost, etc., but I will not distinguish those costs in detail, and just regard them as all aroused from the debt financing.
 
7
Some scholars study the capital structure decision with possible bankruptcy before the debt maturity, such as Ju et al. (2005). 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.
 
8
Note that the risk free rate is positively related with the interest rate of the debt.
 
9
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.
 
10
Such as Stephen A. Ross, Randolph W. Westerfield, Jeffrey Jaffe, Corporate Finance (Chap. 16), The McGraw Hill Companies, Inc., 2005; Richard A. Brealey, Stewart C. Myers, Principles of Corporate Finance (Chap. 18), The McGraw Hill Companies, Inc., 2003.
 
11
See among others, Bradley et al. (1984), Graham and Harvey (2001).
 
12
See among others, Lemmon et al. (2008).
 
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Metadata
Title
Tax Shield, Bankruptcy Cost and Optimal Capital Structure
Author
Zhiqiang Zhang
Copyright Year
2023
Publisher
Springer Nature Singapore
DOI
https://doi.org/10.1007/978-981-19-8269-9_10

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