Fundamental Problems and Solutions in Finance

This chapter explores the fundamental features of finance based on the right role of finance in social science as well as the right role of social science in our society, which is necessary for better understanding and solving financial problems. The main findings include, there are descriptive disciplines and decisional disciplines in social science, which is one of the most important differences between social science and natural science; finance belongs to the decisional discipline rather than descriptive discipline, which implies that finance should focuses on solving decisional problems rather than describing and explain phenomena; the basic method in finance is valuation, or quantitative trade off between return and risk; which is the main differences between finance and other quantitative disciplines as well as other decisional disciplines. Naturally, the insights revealed in this chapter are the ideological foundations to solve so many tough financial problems. In this sense, this chapter is on the top in importance in the whole book.

This chapter explores the valuation of bond, or specifically, the regular or common corporate bond. Asset valuation is the basic function of finance; regular corporate bond is the simplest asset. So regular bond valuation is often supposed to be a solved problem in finance. But this is not true. We discuss and find the benchmark for a right solution to this problem, that is, clean value should equal exactly to the bond face value when the frequency of interest payment is once a year and the coupon rate equals precisely to the discount rate. Apparently, no model in current mainstream finance can reach this level. We finally work out such a solution, i.e., the valuation models of bond in clean value and dirty value respectively factored in the frequency of interest payment and accrued interest.

This chapter explores the valuation of common stock or equity. For various reasons, common stock valuation is often supposed to be a solved problem in finance. In fact, there has been no qualified solution for stock valuation so far in mainstream finance. The multiple or ratio (P/E, P/B and P/S) method is not sound in theory; and the Gordon growth model is not feasible in practice! None of them can consider the growth of a stock properly. Deeper discussions reveal even more and bigger surprises, such as positive perpetual growth rate can never exist, DCF (discounting cash flow) method does not work for stock valuation, etc. Of course, a real solution to stock or equity valuation is worked out finally which is sound in theory and feasible in practice. This is a brand-new valuation method––valuation based on required payback period, which can overcome most defects of DCF method or the Gordon growth model, and can rescue or improve fundamentally the multiple or ratio method as well—by enhance both their theoretical soundness and practical valuation power with theoretical or bubble free ratio models.

This appendix explores a common saying that “practice has gone in front of theory”, and obtains some valuable insights. In history, practice might be ahead of theory for hundreds of years, such as the practice and theory of commercial banking. The practice of being ahead in several years is often concerned, but that of being ahead very long is often ignored. Based on reasonable division of labor, practice should be responsible for exploring new fields and providing problems to be studied for theory; theory should solve problems for practice and promote practical progress. Therefore, practice should be “ahead of theory”. Theory and practice should cooperate with each other to jointly promote the progress of human society. Based on these findings, further discussions reveal more insights, such as problem solving relies on theory rather than practice, because practice stresses more on timeliness rather than rightness. Other discussions, like how to make sure the usefulness of theories, how to evaluate theories, etc., also reveal relevant insights. The relationship between theory and practice is often puzzling. Sometimes people think that theory guides practice. Then, theory should precede practice. Sometimes people think that theory comes from practice. Then, practice should precede theory. In history, there are both cases where theory or practice is in front. It is necessary to discuss from the perspective of rational relations whether theory or practice should be in front.

This appendix makes some comparative explorations around social science, such as the similarities and differences between science and art, natural science and social science. The exploration focuses on the classification of social science. It turns out that social science is responsible to answer two kinds of questions: “what is it like” and “how should we do”. “it” here represents anything to be concerned, such as an industry, a company, a stock, a city, a group of people, etc. Disciplines that are responsible to answer the first kind of questions belongs to descriptive science, such as history, statistics, accounting, etc.; disciplines that are responsible to answer the second kind of questions belongs to decisional science, such as economics, finance, operation management, etc. The decisional science aims at providing guidance to the decision or behavior of organizations or people, which is a unique branch in social science. Relatively, natural science has only descriptive part, and cannot guide the action of various natural objects. This unique feature of social science is often neglected hence leads to a series of biases and errors in the research method and evaluation standard, etc., as well as the stagnation of some disciplines, such as finance, etc.

This chapter introduces the concept of option, the principle and method for option valuation or option pricing. Generally, discounting and option pricing are the two complementary rather than competing valuation tools. Discounting is suitable to value future cash flows which are volatile but certain in existence; while option pricing is suitable to value future cash flows which are contingent and uncertain in existence. Further, option as a financial instrument can divided risk from return or isolate risk absolutely. This implies that option pricing is the most powerful tool to consider or evaluate risk. In 1997, the Nobel Prize in economics was awarded to the contributors in option pricing achievements, Scholes and Merton, and affirmed the huge application potential of option pricing. Unfortunately, financial research has not fully tapped this potential after that, which is part of the reason for many fundamental and related financial problems remained unsolved so far. Of course, this chapter introduces the option pricing theory and method, especially the Black–Scholes model, classifies real options in investment, financing and operation, and further reclassifies the valuation methods. All those pave the way for the subsequent chapters to apply the option pricing method to solve the relevant financial problems.

This chapter explores the theory and method for determining discount rate. As well known in finance, discount rate can be estimated by a variety of methods, and the problem seems solved. Unfortunately, this is not the case. Discussions reveal that the only qualified structure for estimating discount rate is “risk free rate + risk premium”. Based on this standard, only the Sharpe CAPM is possible to be right. It turns out that Sharpe CAPM accounts for only systematic risk rather than total risk in determination of the “risk premium”. This cannot be right because the nonsystematic risk cannot be diversified out completely and prudence is the rule of thumb in decision making. To find the solution, we generalize the problem as how to account for total risk in decision making, and further transfer to quantification of the certainty equivalent, and further to the risk equivalent, and finally, we derive the discount rate model or the new CAPM incorporating in total risk, thus solve the problem, the determination of discount rate, or asset pricing. In addition, a windfall is the solution of modelling certainty equivalent and certainty equivalent coefficient.

This chapter explores the discount rate estimation for debt capital, or debt pricing. Similar to previous chapter, the standard of the solution is a discount rate model structured as “risk free rate + (debt) risk premium”. This is even more tough. A major obstacle is the quantification of bankruptcy cost which has been a tough problem unsolved after decades intensive research. So we model the bankruptcy cost first, and then find the solution to the debt risk premium and then the discount rate for debt capital. Our debt pricing model derived from the bankruptcy cost model coincides exactly with the debt pricing model derived by Robert C. Merton in 1974 via another reasoning path. The two debt pricing models hence can confirm each other and both are undoubtedly correct. However, the model has been idle over decades because it is deemed as serious defected. It turns out finally the deemed serious defects are nothing but the advantages of the model; in addition, the model can help to solve all three problems in bank loan decision. We further discuss some specific application issues for pricing a specific loan. The debt pricing model is further confirmed to be sound in theory and flexible in practice.

This chapter tries to solve the discount rate for equity, or equity pricing. Based on the models derived in Chapters “Certainty Equivalent, Risk Premium and Asset Pricing” and “Debt/​Loan Risk, Bankruptcy Cost and Debt/​Loan Pricing”, it is relatively easy to solve the problem. In the process, we find another easier way to work out the discount rate model for total capital, which can confirm each other with the reasoning in Chapter “Certainty Equivalent, Risk Premium and Asset Pricing”. Finally, a unified solution to capital asset pricing is built up, that is, a discount rate model series for debt, equity and total capital—all three models have unified structure (risk free rate + risk premium), based on the same risk measurement (company volatility) as well as unified concept and logic. Literally, our solution to discount rate or asset pricing is the fundamental solution. Based on such a solution, most issues concerning discount rate can be solved or answered. As examples, we further solve some related problems, such as the comprehensive application of ZZ growth model and ZZ CAPM, the relationships among the three discount rates, the long run tendency of the discount rates. The tendency of the discount rates has been hotly debated but can be solved soundly with our discount rate models.

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.

This chapter conducts some extensive discussions based on the optimal capital structure model derived in previous chapter. The discussions mainly involve how to adjust the model to obtain the specific optimal leverage ratio of a company under a variety of circumstances. The specific circumstances considered include abnormal growth, bankruptcy expectancy, market value versus book value, guaranteed debt, transaction costs, personal income tax, inter-firm’s investments, etc. The relevant solutions are illustrated with a case study of Haier, a home appliance giant in China. This chapter also discusses an issue with top importance: what is the standard or hallmark of a problem is solved. This issue seems simple and clear but actually neither simple nor clear in finance. This issue belongs to the basic concept of finance and should have been discussed in Chapter “Finance and Its Fundamental Problems”. However, after all the discussions on various financial problems in previous chapters, here it is more convenient to illustrate the relevant opinions or ideas with examples.

This chapter explores two problems: bankruptcy probability and company life expectancy. Bankruptcy probability and bankruptcy cost are the major bankruptcy risk measurement and major concern of the relevant parties of a company. However, neither bankruptcy probability nor bankruptcy cost can be calculated in mainstream finance. This chapter solves this quantitative problem based on the bankruptcy cost model derived in Chapter “Debt/​Loan Risk, Bankruptcy Cost and Debt/​Loan Pricing”. In addition, the bankruptcy probability and cost can be calculated for potential current bankruptcy and overall bankruptcy respectively. Such new bankruptcy risk analyses are illustrated based on the case of the three home appliances giants in China. Further, the findings in the bankruptcy risks setup the theoretical foundation for us to further predict the company life expectancy. We then explore the estimation of company life expectancy. Based on the queueing theory, the estimation of company life expectancy depends on the long run applicable annual bankruptcy probability. Further discussion reveals the logic from cumulative bankruptcy probability to annual bankruptcy probability and further to the long run applicable annual bankruptcy probability. Hence the problem of company life expectancy estimation is ideally solved.

Human progress depends on scientific progress; Scientific progress depends on the contributions of scientists. Why do scientists make scientific discoveries? Seeing the fall of apples, different people may make different conclusions, and more people are blind or indifferent to the phenomenon, while Newton could discover the law of gravitation. Why? In fact, the important source of scientific discovery is scientific thinking, which Engels called theoretical thinking. The lack of scientific or theoretical thinking is one of the important reasons for the lack of progress of disciplines like finance. In the form of a novel, this Further Discussion reveals and emphasizes the importance of theoretical thinking, hoping to enlighten the financial science that is trapped in the mire.

It is difficult to see the theories or models set up after the 1980s in finance related textbooks, most or all important theories and models were established before 1980. For example, portfolio theory (1952), MM models (1958, 1963), capital asset pricing model (1964), and Black–Scholes model (1973). It turns out that the financial theory or models found in early years can really solve problems, while the theories created in recent decades, such as information asymmetry theory, behavioral finance theory, pecking order theory, etc., does not solve any problem. For example, “information asymmetry” is just a phenomenon or common sense; some theories set up in recent years is even at a level below common sense. Common sense is not a theory, do not mention the theories below the level of common sense. Theory should be higher than common sense in order to guide practice; otherwise, there is no significance for the scientific research. But why financial research in recent decades can only create theories or conclusions at or below common sense? This Further Discussion makes a deep discussion on it. After the World War II, with the recovery and development of the economies of main countries, the research of financial theory had also boomed over about 30 years and obtained a lot of theoretical discoveries. These theoretical discoveries not only solve relevant financial problems and promote the understanding of relevant issues, but also promote financial research from experience-based level to the height of science and theory, becoming milestones one after another in the development of financial theory. For various reasons, in recent decades since 1980s, the financial research and findings went back to experience-based or even common sense level, such as information asymmetry theory, behavioral finance theory, pecking order theory, etc. Perhaps most people have not realized that those new and popular “theories” are just well known common senses being renamed; and the new stylized financial research does not intend originally to solve decision problems in finance, but just to describe various and endless phenomena in finance and to make some explanations based on subjective guesses. Related to the common sense level in research, after decades of research in full swing, the remained financial problems have basically not been further solved, and there is even no progress in the relevant understanding. However, the problem is, why is financial research has been stayed at the common sense level or even lower than common sense level? The reasons behind this phenomenon deserve our deep thinking and reflection.