CFRI 3,4. Zhengwei Wang PBC School of Finance, Tsinghua University, Beijing, China and SEBA, Beijing Normal University, Beijing, China

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1 The current issue and full text archive of this journal is available at CFRI 3,4 322 constraints and cororate caital structure: a model Wuxiang Zhu School of Economics and Management, Tsinghua University, Beijing, China, and Zhengwei Wang PBC School of Finance, Tsinghua University, Beijing, China and SEBA, Beijing Normal University, Beijing, China Abstract Purose The suly-side effect brought about by the imerfection of the caital market has increasingly been concerned. The urose of this aer is to study how will the uncertainty of equity financing brought about by the equity financing regulations in emerging caital market affect comany s caital structure decisions. Design/methodology/aroach This aer establishes a theoretical model and tries to introduce equity financing uncertainty into the comany s caital structure decision-making. The aer uses mathematical derivation method to get some basic conclusions. Next, in order to characterize the quantitative imact of secific factor on caital structure, numerical solution methods are used. Findings The model shows that firm s value would decrease with the uncertainty of equity financing, because of the relationshi between firm s future cash and their financing olicies. The numerical solution of the model suggests that the uncertainty of equity financing is one of the imortant factors affecting the choice of otimal caital structure, the greater the uncertainty is, the lower otimal caital structure is. Originality/value The research of this aer has certain academic value for further understanding of the issues. Keywords Caital structure, Cororate financing, reference, uncertainty Paer tye Research aer China Finance Review International Vol. 3 No. 4, q Emerald Grou Publishing Limited DOI /CFRI Introduction The modern cororate financing theory originated from the achievement of Modigliani and Miller (1958). Under their strict assumtions, MM reached the conclusion that cororate caital structure was unrelated to cororate value by exloiting the thought of no-arbitrage. Scholars of cororate finance thereafter continuously loosened the assumed reconditions of MM theorem, exlored the realistic influencing factors of cororate financing and caital structure and ut forward several theoretical hyotheses and a lot of emirical results. However, if we divide the variation of comany s caital structure into three levels, namely between-industry variation, within-industry variation and within-firm variation, no matter from which level it is judged, current emirical model has an extremely limited ability to interret caital structure (Graham and Leary, 2011). The authors areciate the generous financial suort from the National Science Foundation of China for Projects No

2 Barclay and Smith (1999) had ointed out that the imortant thing in the studies of caital structure was to develo more realistic hyotheses, work out more owerful emirical tests and find imortant factors that could drive cororate financing decision-making and caital structure. Titman (2002) reviews the assumtions of MM theory and classifies MM assumtions into two tyes: (1) assumtions of exogenous cash flow, embracing assumtions of tax, bankrutcy cost, information comleteness and comlete contract; and (2) assumtions of market erfection. constraints 323 Titman oints out that the revious theoretical and emirical studies on cororate financing and caital structure mainly focused on loosening the assumtions of cash flow exogenesis in MM hyotheses and ignored the assumtions of market erfection. But in reality, financial market is imerfect and has various frictions or constraints. This leads to the estrangement between academic circles and ractitioners in the cognition of financing decision-making and caital structure. The former sends lenty of energy on cash flow assumtions, whereas the latter ays more attention to the imerfection of market. For this reason, Titman aeals to the studies on cororate financing and caital structure for more focus on the imerfection of caital market and calls this imerfection brought about by the features of caital suliers the suly-side effect. With resect to the future direction of studies on caital structure, Graham and Leary (2011) oints out again that the attention aid to the suly-side effect is too little and aeals for enhancement in this regard in future studies. The first theoretical hyothesis focusing on the suly-side effect was market timing hyothesis. In the wake of the asset ricing field s doubt about the efficiency market hyothesis, researchers started to ay attention to the imact of inefficient market on cororate investment/financing decision-making and caital structure. Stein (1996) studies the investment/financing behaviors of comany in the case of inefficient market and rational enterrise managers. His model indicates that in an inefficient market, the manager of the comany can exloit the inefficiency of market to reasonably arrange financing to obtain benefit. Baker and Wurgler (2002) formally ut forward the market timing hyothesis for the first time: along with the rice changes in stock market, there is the best financing timing or financing oortunity window for the comany, and most comanies should make additional issuance in the overall rise stage of stock market or the eriod when their own stock rice is rising high. The market timing hyothesis of enterrise financing is emirically suorted in the Western caital market. In recent years, some domestic studies have also focused on the effect of market timing factor on enterrise s financing behavior and caital structure and find that market timing does lay a significant role in equity financing of comany (Liu et al., 2005, 2006; Liu and Li, 2005; Wang et al., 2005). Since the market timing is one kind of manifestation of the suly-side effect of stock market, the debt market also shows the suly-side effect. Murfin (2012) oints out that banks write tighter contracts than their eers after suffering ayment defaults to their own loan ortfolios, even when defaulting borrowers are in different industries and geograhic regions from the current borrower, it will also be imlicated by such a suly-side effect; borrowers who are most deendent on the relationshi asect of the bank market are also most rone to receive stricter contracts from affected lenders.

3 CFRI 3,4 324 The study on the suly-side effect is in the stage of reliminary develoment, and a uniform framework has yet to form. Besides, these exansions are based on the situation of develoed caital market. Myers (2003) had ointed out that a majority of caital structure theories were constructed based on the US listed comanies, but due to different conditions of caital market, all theories had their own alicable assumtions, so established theories and interretations did not necessarily aly to emerging caital market, for which, as a matter of fact, the condition of caital suly lags far behind that of the Western mature caital market on various asects, such as the variety of financing instruments, government regulation environment, etc. The suly-side effect is more rominent in the emerging caital market. In the develoment rocess of China s stock market over the ast more than 20 years, strict regulations on initial ublic offering and refinancing are still followed today, giving rise to the relatively high uncertainty of cororate equity financing. Equity financing regulation is reflected in two asects. First, stock issuance regulation: under the standard of high unity of develoment, normalization and market bearing caacity in the stock market of China, the government imlements comaratively rigorous regulation on securities issuance: a comany needs to satisfy financial thresholds (net return on equity, cash dividend distribution, etc.) first of all for the urose of issuing securities; next, a listed comany comlying with issuance access conditions is also subject to administrative regulations on issuance ricing, issuance timing, issuance temo, issuance scale, and so on. For examle, the regulatory authority will susend stock issuance in the eriod of stock market downturn or due to a secial need and loosen the regulation on issuance temo when the stock market goes u. Second, the government, based on the needs for macro-control, industrial develoment and stock market stability, limits and even susends normal suly of financial roducts. Even though an enterrise meets the conditions for stock issuance, it is not for sure that it can obtain equity caital when needing equity financing. For instance, the China Securities Regulatory Commission (CSRC) will limit the listing and refinancing of real estate enterrises to coincide with the national regulatory olicies of real estate. During full-circulation share reform, the CSRC had once shut the door to stock issuance. Since November 2012, IPO had been discontinued again. From a macroscoic view, the regulation and limitation on stock issuance are helful for facilitating the sustainable steady develoment of emerging securities market (Zhu and Cheng, 2005) and imroving the effectiveness of macroeconomic regulation and control. But for enterrises, under the situation of increasingly fierce roduct market cometition, regulation and limitation bring about great uncertainty for cororate equity financing, and it is difficult for a comany to determine whether it can smoothly raise caital through stock market in the future. This uncertainty of future equity financing is obviously an imortant content of the suly-side effect. (There is generally no such an effect in the develoed caital market. For examle, there is raid refinancing system in many develoed caital markets.) How will the uncertainty brought about by the regulation and limitation on financing in stock market affect the equity financing behavior and caital structure of comany? Wang et al. (2011) find from the study with the data of China s listed comanies that the changes of refinancing regulatory olicies for listed comanies significantly affect the otimal caital structure of listed comanies, but on account of the difficulty of variables design, their study does not oint out the secific directions

4 of the affect of refinancing regulation on caital structure. For instance, by loosening or tightening the refinancing olicy, will the otimal caital structure of comany become higher or lower? Furthermore, what is the influence mechanism behind it? Studies on this asect have yet to be seen so far[1]. The innovation of the aer is that by establishing a mathematical model, it deicts the suly-side effect of equity financing (reflected as the robability of equity financing in the future) on comany brought about by equity financing regulation and its affect on caital structure decision-making in the oerating rocess of comany. It is found through the model that the uncertainty of external equity financing of comany will result in value loss of comany s shareholders, which increases along with the magnification of uncertainty; additionally, the uncertainty of financing in stock market will also affect the choice of otimal caital structure of comany, and the greater the uncertainty is, the lower otimal caital structure is. The model of the aer is helful for understanding the influence of external equity financing environment on comany s caital structure. The structure of the aer is arranged as follows: in Section 2, we establish a mathematical model of financing regulation in stock market and cororate otimal investment/financing decision-making; in Section 3, the influence of several main variables of the model on the choice of otimal caital structure of comany is deicted with the method of numerical analysis; Section 4 is the conclusion of the aer. constraints Model 2.1 Basic assumtions We assume the oeration objective of comany is the value maximization of all shareholders, and the cash flow of comany is related to investment. Most models studying caital structure assume the future cash flow of comany is exogenous and unrelated to financing decision-making (Modigliani and Miller, 1958; Hackbarth et al., 2006; Strebulaev, 2007), imlicitly assume the comany can raise funds in caital market for investment oortunity with NPV. 0 at any time with no friction. However, in fact, when caital market is imerfect and there are constraints on cororate financing, the available funds of comany will inevitably affect the investment ability of comany and thereby the cash flow of comany. Make the investment of comany in stage ti t ; this investment roduces rofits in stage t þ 1; suose the ayoff on investment is a tþ 1 f(i t ), among which f is increasing function and satisfies the rincile of diminishing marginal returns. That is to say, f(0) ¼ 0, f 0. 0, and f 00, 0; a tþ 1 is a random variable, which means the uncertainty factor affecting the return on investment at the level of macro-economy or comany. In stage t, a t is given information. Suose the liabilities of comany in stage t are D t, and the interest rate of liabilities is r D ; t reresents the tax rate of comany; then the ayoff on equity investment of comany in stage t þ 1 redicted in stage t, tþ 1, can be shown as: tþ1 ¼ða tþ1 f ði t Þ 2 I t 2 D t r D Þð1 2 tþ ð1þ Define d t ¼ 2e t ; d t refers to the dividend given by the comany to shareholders in stage t (when d t, 0, it means that the comany has made external equity financing, which can be understood as negative dividend). According to the dividend discount model, the objective of comany at resent moment (t ¼ 1) can be shown as:

5 CFRI 3,4 " X # T d t max V ¼ E 1 ð1 þ r E Þ t21 t¼1 ð2þ 326 E refers to the exectation oerator for dividend, r E reresents the cost of equity use of comany, and r E. r D. Here, we do not consider the effect of behaviors like management confidence on the financial issues of comany. 2.2 Financing constraints in financial market The constraint of bank loan on comany is considered in the first lace. The reayment of caital with interest of bank loan is a hard constraint on comany, but in the event of bankrutcy and liquidation, the comany only bears limited resonsibilities for the bank loan. Therefore, the bank always makes certain limitation on the debt ratio of comany. With reference to Baker et al. (2003), we assume the comany will face the limit of the highest debt ratio ð LÞ set by the bank while using bank loan, namely: D t D t þ E t # L ð3þ Next, the financing constraint in stock market confronting the comany is considered. This makes it uncertain for the comany to obtain equity financing in stage t. Let whether the comany can obtain equity financing hinge on an indeendent and identically distributed random state variable b t, which comlies with (0-1) distribution; the value of b t is 1 with a robability (indicating the comany can obtain equity financing in stock market) and 0 with robability 1 2 (indicating the comany cannot obtain equity financing in stock market, i.e. d t $ 0); then the constraint can be shown as: d t $ 0; if b t ¼ 0 ð4þ The financing constraint most immediately affects the comany s available caital and investment. In the model herein, the available caital of comany can be shown as E t þ D t. An intuitive constraint on investment is that the investment of comany in current eriod cannot exceed current available caital, namely: I t # E t þ D t ð5þ Formulas (3) through (5) are the financing constraints on comany during its normal oeration (i.e. in case of E t. 0). When the net assets of comany are negative (i.e. in case of E t # 0), the imact of financing constraints on comany will be greater. Under such a circumstance, the comany actually sinks into financial distress and is on the verge of bankrutcy. Thus, it is hard to raise caital and make investment, let alone dividend olicy. Under such a condition, the constraints on comany can be shown as: d t ¼ 0; D t ¼ 0; I t ¼ 0; if E t, 0 ð6þ Under the objective and the constraints mentioned above, we are unable to solve the model by directly using Lagrange multilier method, because due to the existence of random variables, all the variables may not be necessarily derivable everywhere. To solve the model, we need to analyze it on the basis of the distribution of a t.

6 2.3 A static model A static model is first considered: at the time when t ¼ 1, the comany makes an investment decision I 1 and financing decisions D 1 and E 1. At the time t ¼ 2, the comany is liquidated. The simle schematic diagram is shown in Figure 1. At the time t ¼ 2, if the net assets of comany is negative (i.e. a 2 f ði 1 Þ 2 I 1 2 D 1 r D þ E 1, 0), the shareholder ayoff will be 0 (the limited liability nature of comany limited by shares). Besides, if the rofit of comany is negative (i.e. a 2 f ði 1 Þ 2 I 1 2 D 1 r D, 0), the government cannot levy the tax. Then, the shareholder objective of comany can be shown as: constraints 327 Z a * 2 E 1 þ a 2 f ði 1 Þ 2 I 1 2 D 1 r D max V ¼ 2E 1 þ dgða 2 Þ a ** 1 þ r 2 E Z 1 E 1 þ½a 2 f ði 1 Þ 2 I 1 2 D 1 r D Šð1 2 tþ þ dgða 2 Þ 1 þ r E a * 2 ð7þ D 1 Subject to : I 1 # E 1 þ D 1 # L D 1 þ E 1 where G( ) reresents the distribution function: and: a * 2 ¼ I 1 þ D 1 r D f ði 1 Þ a ** 2 ¼ I 1 þ D 1 r D 2 E 1 : f ði 1 Þ By rearranging and solving the objective above, we can reach the conclusion that the otimal investment I 1 of comany satisfies: ð1 þ r E Þð1 2 LÞþ Lð1 þ r D Þ 1 2 G a ** f t ð1 þ Lr D Þ 1 2 G a * 2 ði 1 Þ¼ R 1 a ** a 2 dgða 2 Þ 2 t R 1 ð8þ a * a 2 dgða 2 Þ 2 2 And the following roosition can be obtained: Proosition 1. In a static model, due to the absence of the going-concern ressure of comany, the investment amount of comany satisfies formula (8); the financing amount of comany satisfies E 1 þ D 1 ¼ I 1, namely that the financing amount exactly satisfies its investment demand. Meanwhile, the debt ratio of comany will reach the uer limit L. t = 1 The comany makes investment decision I 1 and financing decisions D 1 and E 1 t = 2 Cororate liquidation Figure 1. Static model of comany s investment and financing decisions

7 CFRI 3,4 328 In other words, because at the time t ¼ 2 the comany faces liquidation, it will avoid using equity as far as ossible and exloit liabilities to the uer limit to the greatest extent during financing at the time t ¼ 1 (this is consistent with the caital structure theory of MM (1963) when only tax is taken into consideration). Under such a condition, equity financing constraint does not work in the static model. 2.4 A three-stage dynamic model On the basis of the static model, we can consider a three-stage dynamic model to study how the comany comrehensively selects its otimal caital structure in combination with its current investment demand and future develoment in a dynamic rocess. The same with the two-stage static model, at the time when t ¼ 1, the comany makes an investment decision I 1 and financing decisions D 1 and E 1 ; at the time t ¼ 2, state variable a 2 of the return on investment is realized, and state variable b 2 of whether the comany can imlement external financing is also realized. On this ground, the comany needs to make investment decision I 2 and financing decisions D 2 and E 2 in stage 2; at the time t ¼ 3, the comany is liquidated. The simle schematic diagram is shown in Figure 2. To obtain the otimal investment and financing demands of comany at the time t ¼ 1, we can emloy the backward induction, that is, first determining the otimal investment and financing demands of comany at the time t ¼ 2, and then working out the otimal investment and financing demands at the time t ¼ 1. Use I * 2, D* 2 and E* 2 to, resectively, reresent the otimal investment and financing decisions of comany at the time t ¼ 2. It can be known through static analysis that when t ¼ 2, the investment and financing decisions of comany satisfy D * 2 þ E* 2 ¼ I* 2, and comany s caital structure will reach the uer limit L, i.e. D * 2 ¼ I* 2 L. Meanwhile, I * 2 is the function of random variable a 3 and satisfy: f 0 I * 2 ¼ where: and: ð1 þ r E Þð1 2 LÞþ Lð1 þ r D Þ 1 2 F a ** 3 2 t ð1 þ Lr D Þ 1 2 F a * 3 R 1 a ** a 3 dfða 3 Þ 2 t R 1 a * a 3 dfða 3 Þ 3 3 a ** a * 3 ¼ I 2 þ D 2 r D f ði 2 Þ 3 ¼ I 2 þ D 2 r D 2 E 2 : f ði 2 Þ t = 1 t = 2 t = 3 Figure 2. A dynamic model of comany s investment and financing decisions The comany makes investment decision I 1 and financing decisions D 1 and E 1 a 2 and b 2 are realized. The comany makes financing decisions D 2 and E 2 and investment decision I 2 Cororate liquidation

8 Based on the otimal investment and financing demands of comany at t ¼ 2, we can analyze the investment behavior and shareholder income of comany at this moment. Here, we need to discuss them under the following cases. Case 1. If E 1 þ½a 2 f ði 1 Þ 2 I 1 2 D 1 r D Šð1 2 tþ $ E * 2, it means the shareholder ayoff generated by the investment of comany in stage 1 can meet the otimal equity demand of comany at the time t ¼ 2. In such a case, whether equity financing can be realized in caital market has no affect on cororate investment. As a result, the funds of comany at the time t ¼ 2 can satisfy the otimal investment amount I * 2, so the investment amount of comany at t ¼ 2isI * 2, and the equity is E* 2. It can be known from the conclusion in Section 2.3 that because the comany is liquidated at the time t ¼ 3, the comany will reserve no more equity after its investment demand is satisfied; thus the dividend of comany at t ¼ 2isE 1 þ½a 2 f ði 1 Þ 2 I 1 2 D 1 r D Šð1 2 tþ 2 E * 2. At the same time, the resent value to t ¼ 2 of the equity ayoff at t ¼ 3isV 2 I * 2 ; E* 2 ; D* 2 þ E * 2,where function V 2 () reresents the value function of shareholder income generated by cororate investment, following the result of formula (8). Case 2. If E 1 þ½a 2 f ði 1 Þ 2 I 1 2 D 1 r D Šð1 2 tþ, 0, it means the comany suffers a serious loss and becomes insolvent at the time t ¼ 2. In such a case, no matter whether future investment can bring ositive net resent value, current negative net assets are a kind of burden. At the moment, the otimal decision of comany is bankrutcy and reorganization[2]. The incomes of shareholders brought by the comany when t ¼ 2 and t ¼ 3 are both zero. Case 3. If 0 # E 1 þ½a 2 f ði 1 Þ 2 I 1 2 D 1 r D Šð1 2 tþ, E * 2, it means although the comany is not insolvent at the time t ¼ 2, its equity cannot meet its otimal equity demand. In such a case, whether equity financing can be realized in market aears to be crucial. If b ¼ 1, namely that the comany can realize equity financing in caital market, meaning the comany does not have the roblem of insufficient equity financing, the available funds of comany can still satisfy the otimal investment amount I * 2 at the time t ¼ 2; therefore the investment amount of comany is I* 2, and the equity is E * 2 at t ¼ 2. It can also be known from the aforesaid conclusion that because the comany is liquidated at the time t ¼ 3, the comany will reserve no more equity after its investment demand is satisfied; thus the dividend of comany at t ¼ 2is E 1 þ½a 2 f ði 1 Þ 2 I 1 2 D 1 r D Šð1 2 tþ 2 E * 2, and at the same time, the resent value to t ¼ 2 of the equity ayoff at t ¼ 3isV 2 I * 2 ; E* 2 ; D* 2 þ E * 2. But if b ¼ 0, namely that the comany cannot realize equity financing in caital market, the comany will be confronted with the roblem of insufficient equity. It can be known from the otimality of I * 2, D* 2 and E* 2 that the equity investment of comany can only be in a subotimum state, reresented by suerscrit ** ; then, the equity investment amount of comany E ** 2 # E 1 þ½a 2 f ði 1 Þ 2 I 1 2 D 1 r D Šð1 2 tþ, the dividend of comany at t ¼ 2 is E 1 þ½a 2 f ði 1 Þ 2 I 1 2 D 1 r D Šð1 2 tþ 2 E ** 2, and meanwhile, the resent value to t ¼ 2 of the equity ayoff at t ¼ 3 is V 2 I ** 2 ; D** 2 ; E** 2 þ E ** 2, where I** 2 and D ** 2 reresent subotimum total investment level and debt level, resectively. By combining the three cases above and noticing the robability that the comany cannot raise money in caital market is 1-, we use V * 2 and V ** 2 to reresent constraints 329

9 CFRI 3,4 330 V 2 I * 2 ; E* 2 ; D* 2 and V 2 I ** 2 ; D** 2 ; E** 2, resectively; then, the shareholder objective function of comany at the time t ¼ 1 can be shown as: max V 1 ¼ E 1 2 ði 1 þ D 1 r D Þð1 2 tþ 1 2 G a * 2 1 þ r E Z 1 V * 2 þ þð1 2 tþa 2 f ði 1 Þ dgða 2 Þ 1 þ r E ð9þ a * 2 2 ð1 2 Þ Z a ** 2 a * 2 V * 2 2 V** 2 1 þ r E dgða 2 Þ 2 E 1 Subject to : I 1 # E 1 þ D 1 ; E ** D 1 D 1 þ E 1 # L; 2 # E 1 þ½a 2 f ði 1 Þ 2 I 1 2 D 1 r D Šð1 2 tþ a * 2 ¼ I 1 þ D 1 r D 2 E 1 =ð1 2 tþ ; f ði 1 Þ I 1 þ D 1 r D þ E * 2 ¼ 2 2 E 1 =ð1 2 tþ f ði 1 Þ a ** It is worth noting that under the constraint condition E ** 2 # E 1þ ½a 2 f ði 1 Þ 2 I 1 2 D 1 r D Šð1 2 tþ, any a 2 has a E ** 2 corresonding to it, so E ** 2 is the function of a 2.I 1, D 1 and E 1 that make the value of formula (9) maximum are the otimal investment and financing decisions at the time t ¼ 1. In formula (9), V ** 2 shows the shareholder value of comany is in the subotimum state, whereas V * 2 shows this value is in the otimal state. It can be known from the analysis of case 3 that V ** 2, V* 2 ; in addition, because a* 2, a** 2 : Z a ** 2 a * 2 V * 2 2 V** 2 1 þ r E dgða 2 Þ $ 0: Thus, we obtain the following roosition: Proosition 2. In the dynamic model, the uncertainty of external equity financing in the next stage will bring about value loss of shareholders. The lower the robability that the comany can obtain external equity financing, the larger the value loss of shareholders is brought about by financing uncertainty. To work out the otimal I 1, D 1 and E 1 in formula (9), we can write the Lagrangian equation of formula (9) and constraint condition and solve the first-order otimal condition. Since it is difficult to work out the analytical solution of formula (9), we will resort to the method of numerical solution in the next section. 3. Numerical analysis In the dynamic model, although we give the determining equation of otimal investment and financing decisions, as well as the solving method, it is very hard to obtain the

10 exlicit solution of model in view of its comlexity. In order to observe the result of model in a more intuitive way, we can give the secific function form of f(i) and the secific distribution form of a, and then the otimal L and I 1 with the method of numerical solution. We might make f ðiþ ¼20 ffiffi I ; then f(i) satisfies assumtions f(0) ¼ 0, f 0. 0, and f 00, 0[3]. The oorest condition of cororate investment is af(i) ¼ 0, so we might assume that the random distribution a of the return on investment in the future is geometrical normal distribution. In addition, because a 1 is a known variable at the time when t ¼ 1, for simlicity, we might suose a 1 ¼ 1. a tþ1 ¼ a t* ~h tþ1, where ln ~h tþ1 comlies with the normal distribution of N m tþ1 ; s 2 tþ1, in which mtþ 1 reresents the exected growth rate of the return on investment from stage t to stage t þ 1 and s 2 tþ1 measures the risk in future economy. constraints robability and comany s caital structure We first of all ay attention to the effect of robability that the comany can obtain external equity financing at the time when t ¼ 2 on the otimal caital structure. Make arameters L ¼ 80%, t ¼ 25%, re ¼ 10%, r D ¼ 5%, m 2 ¼ m 3 ¼ 1, and s 2 ¼ s 3 ¼ 0.3[4], substitute them into the original equation, and solve the equation; then we obtain the changes of otimal caital structure along with, shown as in Figure 3. In the left subgrah of Figure 3, we can find that with the given arameters, when aroaches to zero, the otimal caital structure of comany is also zero, and as increases, the numerical value of otimal caital structure increases accordingly. When ¼ 1, the otimal caital structure of comany is at the oint L ¼ 80%. L-best maxv 3,990 3,985 3,980 3,975 3,970 3,965 3,960 3,955 3,950 3, Notes: Parameters: f(i) = 20 I, r E = 10%, r D = 5%, L = 80%, t = 25%, m 2 = m 3 = 1, s 2 = s 3 = 0.3 Figure 3. robability vs otimal caital structure and shareholder value

11 CFRI 3,4 332 The result of this numerical solution indicates that the larger the financing constraint in stock market (in the model, reflected by the smaller robability that the comany can obtain external equity financing at t ¼ 2) is, the lower the otimal caital structure based on enterrise value maximization is. The right subgrah of Figure 3 intuitively shows us the effect of robability that the comany can obtain external equity financing at t ¼ 2 on the current shareholder value of comany. It can be observed from the subgrah that along with the increase of, shareholder value increases as well. To be more intuitive, the smaller the uncertainty of cororate financing in stock market in the next stage is, the larger the shareholder value is. This result is consistent with the conclusion of Proosition Debt ratio limit, equity financing robability and otimal caital structure Based on the results above, we can also investigate the imact of bank s limit to the highest debt ratio of comany on the otimal caital structure of comany and then the effect of the combined change of highest debt ratio limit and on cororate caital structure, which hels us know the marginal effect of on caital structure in different cases. To make it comarable with the results of Figure 3, we still set arameters as follows: t ¼ 25%, r E ¼ 10%, r D ¼ 5%, m 2 ¼ m 3 ¼ 1 and s 2 ¼ s 3 ¼ 0.3. Table I and Figure 4 give the otimal debt ratios of comany in case of different values of in the range of L from 65 ercent to 90 ercent. In Table I, with other arameters given, we rovide the otimal shareholder values of comany corresonding to assigned and L. It can be seen in the table that the shareholder value of comany tends to rise in the direction of south-east. That is to say, the shareholder value of comany rises gradually with the increase of. On the other side, along with the increase of L, the shareholder value of comany also rises, indicating that L is also one of the factors influencing the shareholder value of comany. The results in Table I are shown in Figure 4 in a more comrehensive and intuitive manner. It can be observed from the figure that as L decreases (namely that the bank L-bar P 65 (%) 70 (%) 75 (%) 80 (%) 85 (%) 90 (%) Table I. Imact of debt ratio limit and equity financing robability on otimal caital structure Notes: Parameters are set as follows: f ðiþ ¼20 ffiffi I, re ¼ 10%, r D ¼ 5%, t ¼ 25%, m 2 ¼ m 3 ¼ 1 and s 2 ¼ s 3 ¼ 0.3; L-bar reresents the limit of highest debt ratio, and reresents the robability of equity financing in market in the next stage; results in the table are the otimal debt ratios corresonding to L-bar and

12 L-best L-bar = 0.9 L-bar = 0.85 L-bar = 0.8 L-bar = 0.75 L-bar = 0.7 L-bar = 0.65 constraints Figure 4. Effect of debt ratio limit and equity financing robability on otimal caital structure of comany tightens the limit to the debt ratio of comany), the line reresenting the otimal shareholder value of comany gradually declines, showing the financing friction brought about by debt ratio limit from the bank will also reduce the shareholder value of comany. Besides, with every given L, along with the increase of, the shareholder value of comany gradually rises, which is coincident again with the conclusion of Proosition 2. Additionally, through observing the shaes of all curves, we can find that when L is relatively high, the curve is relatively gentle, whereas when L is lower, the curve is steeer. This result indicates that along with the increase of L, the sensitivity of the otimal shareholder value of comany to decreases; similarly, along with the increase of, the sensitivity of the otimal shareholder value of comany to L also decreases. 3.3 Growth oortunity, equity financing robability and otimal caital structure In the model herein, random variable ~a 2 is an imortant variable. Its characteristics may be an imortant factor influencing the otimal caital structure. In our assumtion about ~a, m tþ 1, as an imortant characteristic variable of ~a, reresents the exected growth rate of the return on investment from stage t to stage t þ 1, so it is necessary to investigate the combined change of m tþ 1 and (reresenting future growth) on the otimal decision-making of comany. Similarly, to make it comarable with the results above, we still set arameters as follows: t ¼ 25%, r E ¼ 10%, r D ¼ 5%, L ¼ 80% and s2 ¼ s 3 ¼ 0.3. Table II gives the otimal caital structures of comany in case of different values of in the range of m gradually increasing from 0.5 to 1.2. It can be seen in Table II that in each column, as increases, the otimal caital structure rises, which coincides with the conclusion of Section 3.1 again; in each row, as m increases, the otimal caital structure shows a trend of decline this result is consistent with the theoretical study of Myers (1977). According to Myers, when the future growth oortunity is higher, the comany has more real otions; if the comany adots debt financing in such case, it means that the comany may give u these otions, because such investment transfers wealth from shareholders to the creditor.

13 CFRI 3,4 334 Table II. Effect of growth oortunity and equity financing robability on otimal caital structure m 0.5 (%) 0.6 (%) 0.7 (%) 0.8 (%) 0.9 (%) 1.0 (%) 1.1 (%) 1.2 (%) Notes: Parameters are set as follows: f ðiþ ¼20 ffiffi I, re ¼ 10%, r D ¼ 5%, t ¼ 25%, L ¼ 80% and s 2 ¼ s 3 ¼ 0.3; m reresents the growth of future cororate income, and reresents the robability of equity financing in market in the next stage; results in the table are the otimal debt ratios corresonding to m and The results in Table II are shown in Figure 5 in a more detailed and intuitive way. The grahical results clearly show us that consistent with the result above, the financing friction in stock market is still an imortant factor influencing the otimal caital structure of comany: with other arameters given, the larger the financing friction in stock market is (reflected by smaller ), the lower the otimal caital structure of comany is. Meanwhile, it can be seen from the ositions of all curves that the future cororate growth also significantly influences the otimal caital structure of comany along with m increases, the curve of otimal caital structure declines gradually. This result reliminarily demonstrates that in our three-stage dynamic model, when the comany makes a decision on current otimal caital structure, the future cororate growth is one of the imortant factors that should be considered; secifically, the higher the future cororate growth is, the lower the current otimal caital structure of comany is. It is esecially worth noting that 0.8 L-best µ2 = µ3 = 0.5 µ2 = µ3 = 0.6 µ2 = µ3 = 0.7 µ2 = µ3 = µ2 = µ3 = 0.9 Figure 5. µ2 = µ3 = 1.0 Effect of growth 0.1 oortunity and equity µ2 = µ3 = 1.1 µ2 = µ3 = 1.2 financing robability on 0 otimal caital structure

14 when m is relatively large and relatively low, the otimal caital structure of comany is in the state of zero caital structure; on the contrary, when m is relatively small and relatively high, the otimal caital structure of comany is at the highest limit osition (in this result, zero caital structure is helful for interreting the financial conservative behavior while the highest caital structure for financial radical behavior). 3.4 Income volatility, equity financing robability and otimal caital structure of It is observed that in our assumtion about ~a, s 2 tþ1 reresents the fluctuation degree of the return on investment from stage t to stage t þ 1, therefore it is another imortant characteristic variable of ~a. As a result, it is necessary to investigate the combined change of s tþ 1 and (reresenting future income volatility) on the otimal decision-making of comany. Similarly, to make it comarable with the results above, we still set arameters as follows: t ¼ 25%, r E ¼ 10%, r D ¼ 5%, L ¼ 80% and m 2 ¼ m 3 ¼ 1. Table III describes the otimal caital structures of comany in case of different values of in the range of s increasing from 0.1 to 0.5. It can be seen from Table III that the otimal caital structure tends to rise along the direction of left bottom. To be secific, in every column, as increases, the otimal caital structure gradually rises, which coincides with the aforesaid conclusion again; in every row, as s increases, the otimal caital structure shows a trend of decline. The results in Table III are shown in Figure 6 in a more detailed and intuitive way. The grahical results clearly show that consistent with the result above, the financing friction in stock market is still an imortant factor influencing the otimal caital structure of comany: with other arameters given, the larger the financing friction in stock market is (reflected by smaller ), the lower the otimal caital structure of comany is. Meanwhile, it can be seen from the ositions of all curves that the future income volatility of comany also significantly influences the otimal caital structure of comany along with s increases, the curve of otimal caital structure declines gradually. This result reliminarily demonstrates that in our three-stage dynamic constraints 335 s 0.1 (%) 0.2 (%) 0.3 (%) 0.4 (%) 0.5 (%) Notes: Parameters are set as follows: f ðiþ ¼20 ffiffi I, re ¼ 10%, r D ¼ 5%, t ¼ 25%, L ¼ 80% and m 2 ¼ m 3 ¼ 1; s reresents the future income volatility of comany, and reresents the robability of equity financing in market in the next stage; results in the table are the otimal debt ratios corresonding to s and Table III. Effect of income volatility and equity financing robability on otimal caital structure

15 CFRI 3,4 336 L-best s = 0.1 s = 0.2 s = 0.3 s = 0.4 s = 0.5 Figure 6. Effect of income volatility and equity financing robability on otimal caital structure model, when the comany makes a decision on current otimal caital structure, aart from several imortant factors mentioned above, the future income volatility is one of the imortant factors that should be considered; secifically, the higher the future income volatility is, the lower the current otimal caital structure of comany is. It is worth articularly noting that when s is relatively high and relatively low, the otimal caital structure of comany is in the state of zero caital structure. 4. Conclusion Through a model and numerical analysis, the aer discusses the effect of the equity financing robability on the otimal caital structure of comany. The study conclusion demonstrates:. In the static model, due to the absence of the going-concern ressure of comany, the otimal financing always uses liabilities as far as ossible to maintain the otimal caital structure at the uer limit. This is consistent with the conclusion of MM (1963) when only tax is taken into consideration.. In the dynamic model, the comany needs to consider the oeration in the next stage. Since the future cash flow of comany is related to its current investment and financing activities, the uncertainty of comany s external equity financing will imact the shareholder value. Secifically, the smaller the robability that the comany can realize external equity financing in the next stage, the greater the loss of shareholder value will be caused.. The numerical solution of dynamic model shows that with model arameters set, the robability of financing in stock market has a significant effect on the otimal caital structure of comany: the smaller the robability that the comany can realize financing in stock market, the lower its otimal caital structure is; next, the loan amount limit of comany from the bank is another factor influencing the otimal caital structure. The stricter the bank limit of loan amount is, the lower the current otimal caital structure of comany is.

16 The study conclusion of this aer can add a new factor for the interretation of equity financing reference of A-share listed comanies. Such comanies mostly belong to cometitive industries in the stage of raid growth and exansion and need to make continual investment on the remise of steady finance. However, stock issuance regulation increases the uncertainty of cororate financing in stock market. Therefore, as to entity comanies, the oortunity of equity financing is very recious: by seizing this oortunity, the comany is able to reserve equity funds to coe with the ossible equity uncertainty in future, strengthen the ability to comete and the flexibility to gras develoment oortunities, including investment in necessary rojects or merger and acquisition, and maintain a high credit rating; esecially under the circumstances of uncertain business environment, fierce cometition and strict financing conditions in stock market, the comany can gradually reduce financial leverage and caital cost and increase shareholder value by means of subsequent debt financing. For these reasons, listed comanies refer to equity financing and strive to meet the access conditions of stock issuance and obtain the qualification of stock issuance even through earnings management. Such a behavior cannot be totally attributed to low financing cost, cororate governance, insider control and other cororate factors, but also involves the factor of rational reaction to the equity financing uncertainty brought about by stock market conditions and financing regulations. The study in this aer also has some enlightenment significance for regulatory authorities. One of the aims of regulatory authorities of caital market by taking strict regulatory measures for equity refinancing of listed comanies is to allocate limited caital to better investment rojects by means of government intervention, thereby imroving the allocation efficiency of caital. But seen from actual oeration, such a regulatory mode is liable to make comany intentionally hoard equity caital and thereby reduce the utilization efficiency of equity caital. As a result, regulatory authorities need to further think about how to imel listed comanies to imrove the use efficiency of equity caital with more effective measures. constraints 337 Notes 1. In the academic circle of cororate finance, there are many studies focusing on the effect of financing constraints on caital budget, dividend olicy, cash reserve and risk management. For examle, it is shown by the result of the general model established by Almeida et al. (2011) that the greater the future financing constraints are, the more the comany currently tends to invest rojects with shorter ayback eriod and lower risk, as well as assets with good investment liquidity and high mortgage value. But the financing constraints mentioned by these studies are generally defined as the condition that current cash flow cannot meet current investment demand, but still imlicitly assume the comany is able to acquire financing from external market, desite the high financing cost. 2. The insolvency of comany here means the net assets are negative in a urely theoretical sense, that is, all equities of comany (including intangible assets, human caital, etc.) are exhausted. In reality, insolvency of comany does not necessarily lead to bankrutcy, because the comany still has the value of existence, i.e. having net assets, for examle, the assessed value of intangible assets of comany, and so on. 3. Note: Coefficient 20 in f ðiþ ¼20 ffiffi I has no essential meaning, and the urose of using 20 is merely for the convenience of unitization making the value of f(i) 2 I maximum when I ¼ 100.

17 CFRI 3, Parameters are selected based on the following: it can be found from the data on the interest-bearing debt/total caital inut of listed comanies in 2012, excet financial comanies and comanies titled with ST, the ratio of about 95 ercent s comanies is lower than 90 ercent, and that of 80 ercent s comanies is lower than 80 ercent; therefore the aer selects 80 ercent as the highest debt ratio limit of comany, but this arameter will be adjusted and comared in the analysis below; considering that the income tax rate of comany in force in China is 25 ercent, t ¼ 25%; since 2009, the interest rate of short-term bank loans in China fluctuates between 4.86 ercent and 6.10 ercent, so r D ¼ 5% in the aer (besides, the interest rate of cororate bonds is maintained at about 5 ercent in recent years); since 2009, the average annual rate of return in Shanghai Comosite Index of China is aroximately 10 ercent, so r E ¼ 10%; because the aer adots a three-stage model, it is not easy for arameter a to find a corresonding arameter in the real economy; therefore m 2 ¼ m 3 ¼ 1 and s 2 ¼ s 3 ¼ 0.3 for the time being here, and secial arameter changes are conducted for these two variables below. References Almeida, H., Camello, M. and Weisbach, M. (2011), Cororate financial and investment olicies when future financing is not frictionless, Journal of Cororate Finance, Vol. 17 No. 3, Baker, M. and Wurgler, J. (2002), Market timing and caital structure, Journal of Finance, Vol. 57 No. 1, Baker, M., Stein, J. and Wurgler, J. (2003), When does the market matter? Stock rices and the investment of equity deendent firms, Quarterly Journal of Economics, Vol. 118 No. 3, Barclay, M.J. and Smith, C.W. (1999), The caital structure uzzle, another look at the evidence, Journal of Alied Cororate Finance, Vol. 12 No. 1, Graham, J.R. and Leary, M.T. (2011), A review of emirical caital structure research and directions for the future, Annual Review of Financial Economics, Vol. 3, Hackbarth, D., Miao, J. and Morellec, E. (2006), Caital structure, credit risk, and macroeconomic conditions, Journal of Financial Economics, Vol. 82 No. 3, Liu, D., Chen, J. and Chen, S. (2005), Effect of market timing on financing imlement selection, Systems Engineering, No. 8, Liu, D., Chen, S. and Chen, J. (2006), Study on the sustained effects of market timing on caital structure, Chinese Journal of Management, No. 1, Liu, L.B. and Li, G.M. (2005), A test of the market timing theory in China, The Study of Finance and Economics, No. 11, Modigliani, F. and Miller, M. (1958), The cost of caital, cororation finance, and the theory of investment, American Economic Review, Vol. 48 No. 3, Modigliani, F. and Miller, M. (1963), Cororate income taxes and the cost of caital, a correction, American Economic Review, Vol. 53 No. 3, Murfin, J. (2012), The suly-side determinants of loan contract strictness, Journal of Finance, Vol. 67 No. 5, Myers, S.C. (1977), The determinants of cororate borrowing, Journal of Financial Economics, Vol. 5 No. 2, Myers, S.C. (2003), Financing of cororations, in Constantinides, G., Harris, M. and Stulz, R. (Eds), Handbook of the Economics of Finance: Cororate Finance, North-Holland, New York, NY.

18 Stein, J. (1996), Rational caital budgeting in an irrational world, The Journal of Business, Vol. 69 No. 4, Strebulaev, I.A. (2007), Do tests of caital structure theory mean what they say, Journal of Finance, Vol. 62 No. 4, Titman, S. (2002), The Modigliani and Miller theory and market efficiency, Financial Management, Vol. 31 No. 1, Wang, Z.W., Wang, S.M. and Zhu, W.X. (2011), The regulation of the financing of stock markets, and the otimal caital structure of comanies, Management World, No. 2, Wang, Z.W., Zhu, W.X. and Zhao, D.Q. (2005), Market timing in seasoned equity offerings with security issue regulation and its imact on caital structure, Nankai Business Review, No. 6, Zhu, W.X. and Cheng, J.Y. (2005), Securities issuance regulation and securities market sustainable develoment, China Journal of Economics, Vol. 1 No. 1, constraints 339 Further reading Brau, J.C. and Fawcett, S.E. (2006), Initial ublic offerings: an analysis of theory and ractice, Journal of Finance, Vol. 61 No. 1, Graham, J.R. and Harvey, C.R. (2001), The theory and ractice of cororate finance, evidence from the field, Journal of Financial Economics, Vol. 60 No. 2, Corresonding author Zhengwei Wang can be contacted at: wangzhw@sem.tsinghua.edu.cn To urchase rerints of this article lease rerints@emeraldinsight.com Or visit our web site for further details: