以股東價值函數在公司定價理論的應用 - 政大學術集成

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(1)國立政治大學國際經營與貿易學系研究所碩士學位論文. 治政大以股東價值函數在公司定價理論的應用立 ‧ 國. 學. The Application of Shareholder Value Function in the Evaluation of Company. ‧. n. er. io. sit. y. Nat. al. Ch. engchi. i n U. v. 指導教授：胡聯國博士. 研究生：林盈妤撰. 中華民國一 O 四年七月.

(2) 謝辭. 在過去兩年來，我首先最要感謝我的指導教授－－胡聯國教授。老師不僅是課業的諄諄教誨，更常在課堂上和學生討論世界經濟的動向甚至是人生的哲理。無形之中，培養我許多正向和多元思考的能力。在論文的撰寫上面，老師更是傾注心力，總是在第一時間給予我指導和解惑。. 再者，我要感謝所有進德修業上的好朋友－－國貿所的同學。貿法組的同學. 政治大融的讀書會，幫助我複習許多艱澀的理論模型。財管組的幸芳、佳勳、振婷、莉立. 給予許多貿法觀念的釐清；行銷組的同學協助行銷報告；經濟組的同學開國際金. ‧ 國. 學. 婷、懿裴、宛頤更是我的好戰友，陪我度過組內的各種扎實的課程、論文撰寫的過程甚至是找尋人生第一個工作的迷茫期。這段旅程，因為有了你們這些可愛的. ‧. 夥伴們，我的腳步更加穩重，態度越臻成熟，更不畏未來進入職場後的種種挑戰。. sit. y. Nat. al. er. io. 最後我要感謝父母與家人，學弟妹們還有所有我愛的人。因為你們的支持和. v. n. 鼓勵，成就了我也成就了這篇論文。也感謝兩位口委，美麗的江怡蒨和吳菊華老. Ch. engchi. i n U. 師，你們的指教讓這篇論文更加完善與嚴謹。我希望將這篇論文獻給所有愛我與我愛的人，我想告訴你們，我未來也會秉持著認真的態度克服我往後的所有難關！.

(3) The Application of Shareholder Value Function in the Evaluation of Company. Ying-Yu Lin. 學. ‧ 國. 立. 政治大 Abstract. ‧. We consider a problem of finding the optimal solution for maximizing the value of a. y. Nat. io. sit. firm in a stochastic environment. In the paper, we apply a methodology that. n. al. er. determines a corporate value by using cash reserves as the main variables. We. i n U. v. examine the model by employing two empirical approaches to compare the corporate. Ch. engchi. value computed from the model to the market value. We find that there are slight differences between the stock value and shareholder value. Therefore, we may use the facts that we find to construct optimal trading strategies to exploit small price differences.. Key Words: cash reserves, value of firms, diffusion process. 1.

(4) Table of Contents. 1 Introduction ................................................................................................................. 1 2 Literature Review........................................................................................................ 3 3 the Model .................................................................................................................. 10 4 the Empirical Model ................................................................................................. 17 5 Conclusion ................................................................................................................ 42 Reference ..................................................................................................................... 43. 立. 政治大. ‧. ‧ 國. 學. n. er. io. sit. y. Nat. al. Ch. engchi. i n U. v.

(5) List of Tables Table I：the summary of the papers associated with diffusion models ........................ 8 Table II：the definition of the variables ...................................................................... 18 Table III：the definition of the parameters.................................................................. 19 Table IV：the comparison of Mc , Mq , and M ∗ ......................................................... 20 Table V：the comparison of V(Mc ) per share and share price on 2015/05/14 ......... 22 Table VI：the analysis of the trading strategy I (case A) ............................................ 25 Table VII：the results of the trading strategy I (case A) ........................................... 27. 政治大 Table IX：the transaction and the results of trading strategy II (case A) .................... 30 立. Table VIII：the analysis of the trading strategy II (case A) ........................................ 29. Table X：the comparison of V(ML ) per share and share price on 2015/05/14 ......... 34. ‧ 國. 學. Table XI：the analysis of the trading strategy I (case B) ............................................ 36. ‧. Table XII：the results of the trading strategy I (case B) ........................................... 38. sit. y. Nat. Table XIII：the analysis of trading strategy II (case B) .............................................. 39. io. n. al. er. Table XIV：the transaction and the results of trading strategy II (case B) ................. 40. Ch. engchi. i n U. v.

(6) List of Figures Figure I：the shareholder value function (without liquidation value) ........................ 23 Figure II：the shareholder value function (with liquidation value) ............................ 33. 立. 政治大. ‧. ‧ 國. 學. n. er. io. sit. y. Nat. al. Ch. engchi. i n U. v.

(7) 1 Introduction. A classical problem in corporate financing and corporate governance deals with the evaluation of a company. Historically, there are a least five types of approaches used by financial analysts and managers. The approaches include Bradford (1993) asset appraisal approach1, Miller and Modigliani (1961) cash discounted approach, Williams (1938) dividend discounted approach, the comparables approach, and Luehrman (1997) adjusted present value method.. 政治大 The methods mentioned at the first paragraph are simple and mostly based on 立. linear equations. Therefore, diffusion models studied on company valuation has. ‧ 國. 學. become more and more popular recently. The first literature to come up with the. ‧. concept, Jeanblanc and Shiryaev (1995) shows the shareholder value might be. sit. y. Nat. non-linear. Besides, shareholder value function method takes liquidity and risk. io. er. management into consideration. The outcome of the model may also give optimal financial policy to the firm on when to allocate the cash flows and distribute. n. al. dividends.. Ch. engchi. i n U. v. The objective of the paper is derive the shareholder value function for companies that can control their risk exposure through cash reserves but still face the possibility of bankruptcy. The dynamics of cash reserves Mt follow a Wiener process, and our goal is to maximize the dividends paid to the ruin date. In our model, we first solve the general case mentioned earlier and then reformulate the model proposed by Rochet and Villeneuve (2005) by introducing liquation value when the firm has no. 1. The approach is mostly used in accounting when accountants use the balance sheet to compute the company’s book value or liquidation value. 1.

(8) cash reserves left. Our concept is similar to Boguslavskaya (2003) but the derivation process is slightly different. In our case, the aim is to maximize expected total discounted dividends paid out to the ruin date with the discounted salvage value at the time of bankruptcy. With the proposed model, we conduct empirical models to test the model’s predictions for data gathered from Taiwanese electronic listed companies. Limitations of space and time prevent us from covering all empirical results collected from all electronic listed company in this paper. The object of the study only focuses on companies that manufacture other electronic parts and components.. 政治大 The purpose of our empirical models is not only to test predictive power of 立. models but hope to give the investors a different prospective on stock market when. ‧ 國. 學. they make their investment decision. In section 4, we will provide trading strategies. ‧. based on our findings for two different investors－institutional investors and general. y. sit. io. er. prices.. Nat. investors, to see if the shareholder value function help for determining the real stock. al. n. v i n The paper is organized asCfollows. Literature review h e n g c h i U is presented in section 2.. The methodology of the model derived by Jeanblanc and Shiryaev (1995) is presented in section 3. In section 4, we introduce the liquidation value in the model and use the properties we find in section 3 to construct the empirical model, and use the data collected from TEJ to prove the rationality of the method for 34 electronic listed. companies. The conclusion in section 5 is concerned with suggesting extensions for the study.. 2.

(9) 2 Literature Review. Dated back to fifty years ago when Miller and Modigliani (1961) first brought out the idea of the value of a firm is determined by the present value of the net cash inflows to shareholders over an infinite horizon. Under their perfect and complete markets assumptions, they showed that the value of a firm is determined by. ∞. V(0) = ∑. 政治大. t=0. 立. 1 [R(t) − O(t)] (1 + r)t. where V(0) represents the shareholder value, R(t) is the cash inflows during time t. ‧ 國. 學. , and O(t) is the cash outflows during time t. r denotes the discount rate and the. ‧. required rate of return as well.. sit. y. Nat. io. er. Besides cash discount models, the technique of discounting future dividends to date, best known as dividend discount model－see Williams (1938), Gordon (1962). al. n. v i n C hto evaluate a firm’s are widely used when it comes value. The cash inflows to engchi U. owners of common stocks come in two types, one is the dividends received during the holding period and the other is the expected price when selling the stock. The equation is given by:. V(0) =. D1 + V(1) 1+r. where V(0) is the shareholder value per share at time 0, V(1) is the expected value per share at the end of time 1, D1 is the expected dividends paid per share during 3.

(10) time 1, and r denotes the discount rate. Since V(1) can be also computed by discounting the future expected dividends D2 plus capital gains V(2), the equation can be rewrote as the present value of dividends through infinity:. ∞. V(0) = ∑ t=0. Dt (1 + r)t. For some emerging industries, the lead companies may gain a good profit. 政治大 competitors enter the industries, the profits earned by the lead companies would 立 during the initial stage of the company establishment. However, after more and more. smooth year by year. In that case, the pricing of the firm is given by:. ‧ 國. D0 (1 + g1 )(1 + g 2 )(1 + g 3 ) … (1 + g t ) DT (1 + g) 1 + × (1 + r)t r−g (1 + r)t. ‧. io. sit. y. Nat. where g t denotes the dividend growth rate at time t.. n. al. Ch. engchi. er. V(0) = ∑ t=0. 學. T. i n U. v. First introduced by Stewart Myers, Luehrman (1997) proposed adjusted present value model, publicly known as APV, which extended the cash discounted models by taking tax shield2 into consideration. In his model, cash flows contain two parts: 1. The net present value of cash flows from operating, such as revenues and operating costs, which are discounted by the return on assets or return on equity if unlevered. 2. The net present value of cash flows from financing, such as issue costs, which are. 2. Interest from leverage can be seen as financing benefits since it is deductible when computing the company tax. 4.

(11) discounted by cost of debt financing during the period.. The central principle of APV method is value addtivity, which enables financial specialists to value each project individually or split a project into several parts, and add the value together. One of the major flaws in adjusted present value model is that it ignores the bankruptcy cost since the discount rate will increase when a firm operates by taking on debts. That is to say, the present value of cash flows from operating if unlevered will be less.. 政治大 However; in reality, the expected cash inflows are too hard to estimate. That’s 立. why most investors, debt-holders, financial managers and analysts use the method of. ‧ 國. 學. valuation by comparables. The fundamental rule of the approach involves comparing. ‧. a firm to its key rivals or the peer group. The definition of the peer group is that the. sit. y. Nat. firms may operate in the similar bases, such as similar industry, business model,. io. er. company size, and capital structure. The most common performance metrics and valuation multiples experts use are as follow: price to earnings (P/E), price to book. al. n. v i n C h and price to sales (P/B), price to free cash flow (P/FCF) ratio (P/Sales). By multiply engchi U the ratio with the denominator, we can compare the value to the market value to see if the stock is undervalued or overvalued.. Nowadays, Diffusion models for firms that can control their liquidity via their dividend payments and cash reserves have attracted much attention in the recent studies. Jeanblanc and Shiryaev (1995) consider a diffusion model:. dXt = μdt + σdWt − dZt 5.

(12) where X = (Xt )t≥0 represents the cash capital of the firm, and W = (Wt )t≥0 is a Brownian motion. Define Z = (Zt )t≥0 as a non-negative and non-decreasing process, which stands for a series of dividend payments. The purpose of their paper is to solve the general solutions for the dividend process under three different conditions.. In Radner and Shepp (1996), the firm may go bankrupt at time t, at which the cash reserves reach zero, and their ambition is to maximize its profits by discounting all the expected dividends distributed during the life of the firm. In this model, the. 政治大 The pairs of the drift term and the diffusion term are chosen by the manager from a 立. cash reverses are also driven by Brownian motion with drift and diffusion parameter.. finite business plan set. They found the optimal management would depend on the. ‧ 國. 學. current cash reserves, Xt . Whenever the cash reserves hit the threshold, a, the excess. ‧. are paid out as dividends. In the third part of the paper, they proposed a more general. sit. y. Nat. formulation, discounting the salvage value of the firm’s assets at the time of. io. n. al. er. bankruptcy, c(c＞0). (c can also be denoted as the constant salary paid to the managers through the life of the firm, c＜0.). Ch. engchi. i n U. v. Asmussen and Taksar (1997) considered the problem with two situations: one with a restricted dividend rate, and the other with unrestricted rate. The control variable, a(t) in their model, is t-adapted, which means the firm can only make decision based on the information available at time t. They found the same result as the papers mentioned above: when the dividend rate is between [0, a0 ] for some a0 ＜∞, firms should hold back earnings when the cash reserves are below the critical value, m, and pays a0 when the cash reserves is above m. The second case is that when there is no restriction on the dividend rate, the firm should pay out all the 6.

(13) exceeds when the cash reserves are above m while not doing when the reserves are below m.. Sethi and Taksar (2002) studies a model for firms that can control their risk management by paying dividends and external financing (issuing new equity). Their formulation is aim to maximize the amount of the expected discounted dividends paid minus the expected discounted cost of issuing new equity. They further assume that there is no transaction cost in external equity in the paper.. 政治大 In the recent literature, Rochet and Villeneuve (2005) proposed the same 立. controlled diffusion process model as before, assuming the firm is banned to issue. ‧ 國. 學. more securities and equity and will go bankrupt once the value of cash reverses falls. ‧. to a certain value. However, they extended some limitations, which included setting. sit. y. Nat. up the remuneration rate (the risk-free rate) of cash reserves and debts. Moreover,. io. er. they introduce flexibility of investment. Flexibility of investment refers to no frictions in the investment technology, which means we can easily adjust the proportion. al. n. v i n invested in risky assets without C any costs. They had aU h e n g c h i similar but yet slightly different. result, that is, dividends are paid out only when the value of the firm’s assets is above a certain threshold. However, due to the flexibility of investment, it turns out that there exists an intermediate region where the firm can optimally invest all of the money in the risky assets without keeping any cash reserves.. Løkka and Zervos (2005) follows the same model built by Sethi and Taksar (2002), is concerned with formulation of three control process. The first one is mentioned and solved in previous literature, which is under the assumption of no issue of new equity. The second one examines the optimal strategy in the presence of 7.

(14) proportional issuance of equity costs. The last one aims at the same objective as the second one, but is no longer subject to the constraints of the reserves and the issuance of new equity. It is somewhat paradoxical since in reality there are always regulatory requirements for firms to meet so as not to be liquidated. Table I summarizes the papers associated with diffusion models.. Table I the summary of the papers associated with diffusion models Paper. Model. Jeanblanc and. dX t = μdt + σdWt. Shiryaev (1995). −dZt. ‧ 國. −dZt. term are chosen by the manager from a finite business plan set.. y. sit. er. dr(t) = (μ − a(t))dt Consider the case one with restricted. io. + σ dw(t). al. n. Taksar (1997). The pairs of the drift term and the diffusion. Nat. Asmussen and. dX t = μt dt + σt dWt. ‧. Shepp (1996). 立. 治 the general solutions for the dividend 政 Solve process. 大學. Radner and. Highlights. dividend rate, and the other with. v i n Ch rate. U i e n gunrestricted h c. Sethi and Taksar. dXt = r(X(t))dt. Allow external financing (issuing new. (2002). +σ(X(t))dw(t). equity).. +cdE(t) − dD(t) Rochet and. dX t = It {μdt + σdWt }. 1.Set up the remuneration rate (the risk-free. Villeneuve(2005) +r(Xt − It )dt − dZt. rate) of cash reserves and debts 2. The firm can easily adjust the proportion invested in risky assets without any costs.. 8.

(15) Løkka and Zervos (2005). dX t = μdt + σdWt. No the constraints on the reserves and the. −dLt + dGt , X0 = x. issuance of new equity. Similarity: 1. The firm will go bankrupt once the value of cash reserves falls to a certain value. 2. The optimal management would depend on the current cash reserves.. 立. 政治大. ‧. ‧ 國. 學. n. er. io. sit. y. Nat. al. Ch. engchi. 9. i n U. v.

(16) 3 the Model. We propose the same model as Rochet and Villeneuve (2005). Consider a firm characterized by the following balance sheet. Productive assets(A) Cash reserves(M).  1.. Debt(D) Equity(E). 政治大 Productive assets (A), which are fixed with no re-investments nor depreciation, 立 In our model, the assets have two parts:. generate the stream of cash inflows R (net revenues).. ‧ 國. 學. 2. Cash reserves (M), liquid assets which can be increased from retained earnings as. ‧. well as interest produced by cash reserves. The remuneration rate is r0 .. sit. y. Nat.  The debt (D), D is also fixed, and the firm has to pays a constant interest d per unit. al. v i n C hvalue of the firm. U Equity (E) represents the book We assume that the firm cannot engchi n. . io. down.. er. of time. Under the stationary condition, whenever M hits zero, the firm is shut. issue more equity to ask for external funds.. Let R t denote the net earnings through time t, which can be either positive or negative. R t follows a diffusion equation associated with Brownian motion with expected earnings μ and the volatility σ, which is given by. dR t ＝μdt + σdWt , 0 ≤ t ≤ T. (1). where the bankruptcy time T is defined as the first date which Mt ≤ M0 , M0 is the 10.

(17) maximum amount of overdraft limit given by the banks－that is when Mt falls below M0 , the firm becomes bankrupt. At date T, shareholder may lose all its investment. The productive assets are sold to help repay the debt holders and joint creditors. The remains of the total worth of a firm’s assets L are known as the liquidation value.. Based on the assumptions above and we denote the dividends paid out during time t as θt ≥ 0. And dZt ≥ 0 represents the cumulative amount of dividends paid. 政治大 nonnegative, and non-decreasing. That is, we don’t allow dividend recapitalization. 立. out up to time t. The major requirement on the control process dZt is that it is. Because the additional debt burdens caused by recap may increase the odds of. ‧ 國. 學. financial distress.. ‧. dMt = dZt = 0, t≥ T. er. io. sit. y. Nat. (2). Therefore the dynamics of cash reserves Mt according to the model:. n. al. Ch. engchi. i n U. v. dMt = (μ − d + r0 Mt )dt + σdWt − dZt , 0 ≤ t ≤ T. (3). Then we define Vt as the shareholder value function at each date t, which is equal to the expected present value of total discounted dividends up to the bankruptcy date T:. T. Vt = E [∫ e−r(s−t) dZs ] t. 11. (4).

(18) Since the shareholder value function Vt is a function of Mt , we may rewrite Vt :. Vt = f(Mt ). (5). The stochastic differential equation of Vt is given by:. 1 dVt = f ′ (Mt )dMt + f ′′ (Mt )σ2 (Mt )dt 2. (6). 政治大. Using the equation (3), we then take expectation on both sides and put forward dt,. 立. (7). ‧. ‧ 國. 學. 1 E[dVt ] = [f ′ (Mt )(μ − d + r0 Mt ) + f ′′ (Mt )σ2 (Mt )] dt 2. where E[dMt ] = (μ − d + r0 Mt ). We now assume Vt denote the expected. y. Nat. sit. discounted value of cash stream θ(Ms )ds from date t to date T. Moreover, we take the. n. al. er. io. conditional expectation of Vt with respect to Mt , which means the expected. i n U. v. discounted value is obtained under the value of variable Mt ,. Ch. engchi. T. Vt ≡ f(Mt ) ≡ E [∫ e−r(s−t) θ(Ms )ds|Mt ]. (8). t. where r denote the appropriate discount rate.. Next we add a definite integral of the cash stream from time t to time 0 and compute the present value of Vt ,. 12.

(19) t. T. ∫e. −rs. θ(Ms )ds + e. 0. −rt. Vt = E [∫ e−rs θ(Ms )ds|Mt ]. (9). 0. e−rt Vt is the present value of Vt when time is continuous, i.e. when compounding takes place continuously. The right hand of the equation equals the conditional expectation of the present value of all future cash stream from 0 to T with respect to Mt . Using the law of iterated expectations3, we can show the equation has a constant result.. 立. t. 政治大 T. constant ≡ E [∫ e−rs θ(Ms )ds + e−rt Vt ] ≡ E [∫ e−rs θ(Ms )ds] 0. ‧ 國. 學. 0. (10). ‧. We then differentiate the equation with respect to the variable t:. (11). er. io. al. v i 1 n ] =h[f ′ (Mt )(μ − d + rU E[dVtC Mt ) + 2 f ′′ (Mt )σ2 (Mt )] dt 0 engchi. n Using the fact that. sit. y. Nat. e−rt θ(Mt )dt − re−rt Vt dt + e−rt E[dVt ] = 0. and. divide equation (11) by e−rt , we can show. 1 θ(Mt )dt − rVt dt + [f ′ (Mt )(μ − d + r0 Mt ) + f ′′ (Mt )σ2 (Mt )] dt = 0 2. (12). To solve the equation for all Mt , we divide the equation by dt and add up rVt dt on both sides,. 3. The basic statement of the law of iterated expectations is as follows:. E(Y) = E(E(Y|X )). 13.

(20) 1 rVt = f′ (Mt )(μ − d + r0 Mt ) + f′′ (Mt )σ2 (Mt ) + θ(Mt ) 2. (13). Substitute Vt for f(Mt ), we can see that for all M,. 1 r f(M) = f′ (M)(μ − d + r0 Mt ) + f′′ (M)σ2 (M) + θ(M) 2. (14). Recall our assumptions made before, since we fix all the size of the productive. 政治大. assets and debts, and put restrictions on issuing new equity, which means the firm. 立. manager can only control the amount of cash retained or dividends paid-out. The. ‧ 國. 學. optimal choice is to retain earnings when M ≤ M ∗ , and to pay out the excess cash when M ≥ M ∗ . So the shareholder value function satisfies the homogeneous. ‧. second-order differential (Ito differential), which is given by. n. Ch. engchi. M0 ≤ Mt ≤ M ∗. er. io. al. 1 2 ′′ σ Vt (Mt ), 2. sit. y. Nat V(Mt ) = (μ − d + r0 M) Vt′ (Mt ) +. i n U. v. (15)4. For simplicity, we assume r0 = M0 = 0, finding that the solutions to equation (15) has the form Me δM . Define α and β being the roots of the quadratic equation:. 1 (μ − d)δ + σ2 δ2 − r = 0 2. (16). Let α be the positive solution and β be the negative solution,. 4. For M0 ≤ Mt ≤ M ∗ , we will not distribute any dividends and thus we have θ(M) = 0. 14.

(21) −(μ − d) + √(μ − d)2 + 2rσ2 α= σ2. (17). −(μ − d) − √(μ − d)2 + 2rσ2 β= σ2. (18). Then we use the two elementary solutions to set:. V(M) = ω1 e αM + ω2 e βM. (19). 政治大. To solve ω1 and ω2 , the shareholder value function satisfies two boundary. 立. 學. 1. V (0) =0. ‧ 國. conditions: (20). When cash reserves falls to zero, the firm is ruin. For M=0, we will have (19). n. al. (22). sit. er. io 2. V ′ (M ∗ ) = 1. (21). y. ‧. Nat. V(0) = ω1 + ω2 = 0. Ch. engchi. i n U. v. When M reaches the target threshold M ∗ , the firm will start to distribute all the excess money and thus the marginal value of cash is 1. For M=M ∗ , (19) will hold as. ∗. ∗. V ′ (M ∗ ) = ω1 αe αM + ω2 βe βM = 1. (23). Based on (11) and (13), we may solve. ω1 =. ∗ αe αM. 1 ∗ − βe βM 15. (24).

(22) ω2 =. −1 ∗ − βe βM. ∗ αe αM. (25). Using the results of (24) and (25), we obtain (19) as. e βM − e αM V(M) = βM∗ ∗ βe − αe αM. (26). To maximize the shareholder function provided by (26), we must minimize its denominator, which indicates:. 立. 政治大 ∗. ∗. βe βM − αe αM = 0. (27). ‧ 國. 學 ∗. ∗. By solving the first order condition of equation (27), i.e. β2 e βM − α2 e αM = 0,. ‧. the optimal cash reserves is given by:. n. Ch. engchi. 16. (28). er. io. al. 1 β2 log 2 β−α α. sit. y. Nat M∗ =. i n U. v.

(23) 4 the Empirical Model. Taiwan is an export-oriented economy, indicating that foreign trade has been the engine of Taiwan's rapid growth for the past four decades. Among all, the electronics sector is Taiwan's most central industrial export sector, accounting for sixty percent of the gross export value. There are 383 electronic listed companies in Taiwan. Electronic listed companies are divided into 8 categories, which include semi-conductors manufacturing, computers and peripheral equipment manufacturing, industry, electronic parts and components 政治大 manufacturing, electronic channel industry, information industry, and other electronic 立 optoelectronic,. communication. components manufacturing.. 學. ‧ 國. parts and components manufacturing. The object of study is other electronic parts and. ‧. y. Nat. This section implements the shareholder value methodology with a set of. er. io. sit. parameter values obtained from 34 Taiwan electronic listed companies5. The data on the parameters used in the empirical model are compiled from Taiwan Economic. al. n. v i n C hcollect quarterly finance Journal (TEJ). For each firm we reports data for thirteen engchi U. years, from 2002Q2 to 2014Q4. From the original sample of 34 firms, 5 firms (ELASER6, PT TECH7, CyberPower8, BHI (BizLink)9, VOLTRONIC10) are short of 40 quarterly finance reports because data are not sufficient in TEJ.. In reality, the monthly interest payment d may change due to the change of loan 5. There are originally 35 firms in our category but since the data of KYET is not enough to be convincing we then reject the data 6 39 pieces of data 7 36 pieces of data 8 33 pieces of data 9 24 pieces of data 10 15 pieces of data 17.

(24) amount, interest rate, and accrual rate. Since it’s hard to estimate the parameter of the constant interest payment d in (16), we will use net income plus depreciation to denote the variable μ − d. Table I and II states for the definition of these variables.. Table II：the definition of the variables Parameters R. Statistics Net income plus depreciation. Net income is the remains after subtracting all the costs, including. 政治大 depreciation back to denote the net cash inflows. 立. depreciation, interest, and taxes from a firm’s revenues. We add. Expected earnings(expected net income plus depreciation). ‧ 國. 學. μ−d. The variance of the net income plus depreciation. R. The risk free rate=1.36％(APR).. ‧. σ2. sit. y. Nat. Since Taiwan bonds are lack of liquidity, we use the 1-year Interest. io. al. n. rate.. er. Rate on Deposits of Five Leading Banks11 to represent the risk free. Ch. engchi. i n U. v. We then run 34 pieces of the series of net income plus depreciation raw data to estimate the main descriptive statistics, including the mean (expected earnings μ) and the volatility σ. Putting μ, σ2 , and r, into the equations in our empirical model, we can compute the optimal cash reserves. Table II lists the parameters and corresponding definitions we use in our model. The results of optimal cash holdings are shown at Table III.. 11. Interest rate on Deposits of five leading banks is the weighted average interest rate on time savings deposits of the following five leading banks: Bank of Taiwan, Taiwan Cooperative Bank, First Commercial Bank, Hua Nan Commercial Bank and Chang Hwa Commercial Bank. 18.

(25) Table III：the definition of the parameters Parameter Mc. Definition The amount of cash and cash equivalents reported on the balance sheet.(in thousands). Mq. The sum of the amount of cash and cash equivalents, short-term investment, accounts receivables, and other receivables. 12 (in thousands). M∗. The optimal cash reserves (in thousands). 政治大 Table III summarizes the results of the cash and cash equivalents held in firms 立. ‧ 國. 學. and the optimal cash reserves computed by the shareholder value function. The Mc to M ∗ ratio are rounded off to the third decimal place. We use the Mc to M ∗ ratio to see. ‧. if the firm is in good liquidity management condition. Based on our theory, over two. sit. y. Nat. third of the companies hold back the cash more than the optimal reserves they actually. io. al. er. need. In the contrast, twelve companies’ Mc to M ∗ ratios are below one, meaning that they should keep more money in reserves for precautionary reasons, especially. n. v i n C himplies that the firm HUXEN and Kinpo. This may also e n g c h i U won’t pay dividends until the cash reserves cumulated to a certain level. In all, it’s safe to drop the conclusion that. some of the firms keep too much cash, which indicates the excess money should pay out as dividends, buyback stocks from their shareholders or invest in other projects that have NPV> 0. The reason why we list the amount of Mq is because Mq contains lots of quick assets, which can also be seen as cash equivalents sometimes.. 12. Those assets altogether are known as quick assets, which are easy to be sold and turned into money. 19.

(26) Table IV：the comparison of Mc , Mq , and M ∗ # stock symbol. Company. Mc. Mq. M∗. Mc /M ∗. 1,486,366. 21,775,920. 9,369,273.08. 0.159. 2312. Kinpo. 2. 2317. HON HAI. 3. 2354. FTC. 35,253,120. 72,948,621. 15,149,332.38 2.327. 4. 2359. Solomon. 1,655,218. 3,325,971. 3,457,312.68. 0.479. 5. 2360. Chroma. 1,847,648. 7,324,285. 1,754,978.96. 1.053. 6. 2373. AURORA. 1,041,662. 3,278,470. 1,415,545.78. 0.736. 7. 2390. Everspring. 346,262. 505,468. 571,292.81. 0.606. 8. 2404. UIS. 6,607,792. 8,117,062. 1,041,235.98. 6.346. 9. 2423. GW. 249,704. 948,722. 0.967. 10. 2433. HUXEN. 1,584,517. 0.0631. 11. 2461. K LASER. 138,994.50. 7.959. 12. 2464. 立 Mirle. 99,951 治 2,413,111 政大 1,106,260 3,106,130. 258,218.40. 1,006,789. 1,796,968. 625,932.20. 1.608. 13. 2474. CATCHER. 46,310,267. 69,705,485. 23,332,017. 1.985. 14. 2477. MEILOON. 965,106. 1,821,996. 2,685,288.27. 0.359. 15. 2482. UIC. 233,274. 412,438. 206,529.10. 1.129. 16. 2488. HANPIN. 1,045,776. 1,625,473. 379,198.70. 2.758. 17. 2495. Infortrend. 835,484. 2,702,425. 1,899,058. 0.440. 18. 2497. E-LEAD. 428,673. 643,555. 994,278.40. 0.431. 19. 3018. TUNG KAI. 342,876. 682,054. 49,709.78. 6.898. 20. 3030. 1,668,301. 1.635. 21. 3043. -756,629. -0.183. 22. 3305. v i n PCM 498,320 C 138,190 h i U e h n SHENMAO 1,888,071g c3,824,900. 551,302. 3.425. 23. 3450. ELASER. 1,180,601. 2,276,542. 1,571,737. 0.751. 24. 3518. PT TECH.. 1,107,389. 2,416,218. 1,264,176. 0.876. 25. 3617. CyberPower. 1,831,298. 3,005,292. 555,805. 3.295. 26. 3665. BHI (BizLink) 1,200,453. 3,173,311. 730,277.70. 1.644. 27. 6139. L&K. 3,334,175. 7,998,720. 987,956.90. 3.375. 28. 6192. LUMAX. 1,461,862. 3,575,906. 648,162.30. 2.255. 29. 6196. MIC. 1,358,155. 4,167,141. 723,666.50. 1.877. 30. 6201. YAHORNG. 1,366,290. 1,995,954. 449,629.40. 3.039. 31. 6215. Aurotek. 228,200. 799,221. 163,355.90. 1.397. 32. 6409. 4,416,643. 1,039,771. 2.992. 33. 8021. Topoint. 1,505,062. 2,756,604. 830,494.40. 1.812. 34. 8201. BESTA. 292,402. 425,119. 1,439,127. 0.203. n. 2,727,326. VOLTRONIC 3,111,228. 20. 4,044,279. y. sit er. io. al. ‧. Nat. TRI. 679,037,301 1,501,815,861 184,358,850.90 3.683. 學. ‧ 國. 1.

(27) In our empirical model, we show two cases of shareholder value, one with liquidation value and the other without. We then provide trading strategies based on our statistics to see if the shareholder value function help for determining the real value of the market’s true worth.. Case A: Shareholder value was computed by Mc .. 立. 治政 e −e 大(29) βMc. V(M) =. αMc. ∗. ∗. βe βM − αe αM. ‧ 國. 學. For comparison, we divide shareholder value by the number of shares. ‧. outstanding, that is V(Mc ) per share is equal to V(Mc ) divided by numbers of. sit. y. Nat. shares outstanding. Table IV summarizes the comparison of estimates to actual share. n. al. er. io. price on 2015/05/14. Previous results have shown that most of the firms hold excess. v. cash. Since the shareholder value is a function of cash reserves, we expect the V(Mc ). Ch. engchi. per share is greater than the share price.. 21. i n U.

(28) Table V：the comparison of V(Mc ) per share and share price on 2015/05/14 stock symbol. Company. V(Mc ) per share. Share price13 on 2015/05/14. 1. 2312. Kinpo. 21.662. 12.3. 2. 2317. HON HAI. 366.476. 93.7. 3. 2354. FTC. 309.426. 93.9. 4. 2359. Solomon. 67.183. 17.9. 5. 2360. Chroma. 172.349. 75. 6. 2373. AURORA. 165.627. 53.8. 7. 2390. Everspring. 1.842. 27.6. 8. 2404. UIS. 175.898. 35.1. 9. 2423. GW. 84.241. 10. 2433. 11. 2461. 12. 2464. 治政 158.748 K LASER 43.748 大立Mirle 121.073. 19.85. 13. 2474. CATCHER. 638.853. 14. 2477. MEILOON. 74.824. 15. 2482. UIC. 43.627. 16. 2488. HANPIN. 126.161. 17. 2495. Infortrend. 111.342. 18. 2497. E-LEAD. 51.605. 19. 3018. TUNG KAI. 6.776. 20. 3030. 21. 3043. 22. 3305. 23. 3450. ELASER. 359.856. 139. 24. 3518. PT TECH.. 222.276. 45.5. 25. 3617. CyberPower. 234.54. 61.4. 26. 3665. BHI. 263.181. 133. 27. 6139. L&K. 166.505. 22.45. 28. 6192. LUMAX. 208.29. 58. 29. 6196. MIC. 118.245. 26.9. 30. 6201. YAHORNG. 196.435. 26.35. 31. 6215. Aurotek. 59.143. 20.2. 32. 6409. VOLTRONIC. 440.485. 378.5. 46.6 14.9 29. 學 sit. y. 21.8. er. io. n. 22. 13.25 17.55. 164.926 a l TRI v i PCM 0.754 n Ch e n g162.797 chi U SHENMAO. The closing price on 2015/05/14. 347. ‧. ‧ 國. HUXEN. Nat. 13. #. 16.75 67.7 20 61.7 3.51 29.85.

(29) 33. 8021. Topoint. 175.524. 27. 34. 8201. BESTA. 12.344. 11.9. Using the data collected from stock AURORA, we draw mathematical graphs as shown in Figure I. It shows that shareholder value is an increasing function of cash reserves. Case A is under the assumption that when cash flows fall to zero, the firm is liquidated. Therefore, when M0 ≤ 0, the marginal value of cash is zero. Though the shareholders lose all their investment, they are protected from liability for the acts of the firm.. 立. ‧. ‧ 國. 學. Shareholder value. 政治大. n. er. io. sit. y. Nat. al. M0. Ch. engchi. i n U. v. M (cash reserves). Figure I：the shareholder value function (without liquidation value). Trading Strategy I. By comparing the differences between the V(Mc ) per share and the share price on 2015/5/14, we can construct an arbitrage based on our findings. Assume there is no. 23.

(30) transaction cost14 and taxation in the stock markets and it is possible to buy and sell any amount, even fractional15, of the stock16. Furthermore, we make the assumption that no interest is charged on margin accounts, so keeping a short sale open for a long time will cost no more.. Trading strategy I is suitable for institutional investors since the portfolio contains both long and short position in numerous securities. Second, the V(Mc ) per share to the share price varies everyday, which suggests the stocks and the weightings. 政治大 periodically to reflect changes in the index. This spending of strategy I can be too 立 of the allocations would change frequently. Adjustments would have to be made. costly to bear, since it requires an investor to create a large portfolio and make. ‧ 國. 學. hundreds of transactions a year. That’s why it’s for institutional investors.. ‧. sit. y. Nat. The strategy is long equities that are expected to increase in value (the V(Mc ). io. er. per share is higher than the share price) and short equities that are expected to decrease in value (the V(Mc ) per share is lower than the share price). The numbers of. al. n. v i n shares we buy were computed C by the V(Mc ) per share h e n g c h i U divide by the share price on 2015/05/14. The purpose of the previous step is to purchase more on the stocks that. are believed to be seriously undervalued in our model. According to Table V, we have long position in 30 companies, which indicates that 30 companies’ value are undervalued based on the model, and the estimated total spending is NT$5,465.785.. To determine the numbers of short sale shares, we first use the share price on 2015/05/14 divide by V(Mc ) per share to calculate the short sale ratio for stock 2390, 14 15 16. This assumption implies frictionless market. In reality, trading commissions for odd lots are much more expensive than round odds. One of the assumptions used in B-S-M model. 24.

(31) 2497, 3018, and 3043. Second, add the short sale ratio together, divided by the estimated total spending of NT$5,465.785, and we get the proportion of proceeds from each short sale. At last, we divide the proceeds from each selling of a stock by its stock price. Table V summarizes the results of the transaction we made on 2015/5/14.. Table VI：the analysis of the trading strategy I (case A) #. stock. Company. 治政 12.3 Long 大1.761138211. Position on 2015/05/14. 2312. Kinpo. 2. 2317. HON HAI. 93.7. Long. 3.911163287. -366.476. 3. 2354. FTC. 93.9. Long. 3.295271565. -309.426. 4. 2359. Solomon. 17.9. Long. 3.753240223. -67.183. 5. 2360. Chroma. 75. Long. 2.297986667. -172.349. 6. 2373. AURORA. 53.8. Long. 3.078568773. -165.627. 7. 2390. Everspring. 27.6. Short. 124.1429. 3426.345. 8. 2404. UIS. 35.1. Long. 5.011339031. -175.898. 9. 2423. GW. 19.85. Long. 4.243879093. -84.241. 10. 2433. HUXEN. 46.6. Long. 3.406609442. -158.748. 11. 2461. a K LASERl. 12. 2464. Mirle. 13. 2474. CATCHER. 347. Long. 1.841074928. -638.853. 14. 2477. MEILOON. 13.25. Long. 5.64709434. -74.824. 15. 2482. UIC. 17.55. Long. 2.485868946. -43.627. 16. 2488. HANPIN. 21.8. Long. 5.787201835. -126.161. 17. 2495. Infortrend. 16.75. Long. 6.647283582. -111.342. 18. 2497. E-LEAD. 67.7. Short. 4.431185. 299.991. 19. 3018. TUNG KAI. 20. Short. 33.74724. 674.945. 20. 3030. TRI. 61.7. Long. 2.673030794. -164.926. 21. 3043. PCM. 3.51. Short. 303.2776. 1064.504. 22. 3305. SHENMAO. 29.85. Long. 5.453835846. -162.797. 23. 3450. ELASER. 139. Long. 2.588892086. -359.856. 24. 3518. PT TECH.. 45.5. Long. 4.885186813. -222.276. io. sit. Nat. y. ‧. ‧ 國. 立. 學. 1. er. symbol. Share price Long/Short V(Mc ) / share on price 2015/05/14. n. v i 14.9 Long 2.936107383 n Ch 29 e n g cLong h i U 4.174931034. 25. -21.662. -43.748 -121.073.

(32) 25. 3617. CyberPower. 61.4. Long. 3.819869707. -234.54. 26. 3665. BHI. 133. Long. 1.978804511. -263.181. 27. 6139. L&K. 22.45. Long. 7.416703786. -166.505. 28. 6192. LUMAX. 58. Long. 3.591206897. -208.29. 29. 6196. MIC. 26.9. Long. 4.395724907. -118.245. 30. 6201. YAHORNG. 26.35. Long. 7.45483871. -196.435. 31. 6215. Aurotek. 20.2. Long. 2.927871287. -59.143. 32. 6409. VOLTRONIC. 378.5. Long. 1.163764861. -440.485. 33. 8021. Topoint. 27. Long. 6.500888889. -175.524. 34. 8201. BESTA. 11.9. Long. 1.037310924. -12.344. Our strategy is not to speculate with day trading, nor to seek long-term. 治政 investment, and that’s why our stock holding time lasts大 for two weeks. On 2015/5/29, 立 we close the short position by buying back the securities while selling the same ‧ 國. 學. numbers of shares we purchased on 2015/05/14. By calculating the profit or loss from. ‧. each offsetting position, we eventually make a profit of NT$652.050. The results see Table VI. We can discover that we make money from all short position, but some of. y. Nat. io. sit. our long portfolio holdings had declined, which erode our total returns. The star. n. al. er. symbol denotes the stock which is losing value during the holding period.. Ch. engchi. 26. i n U. v.

(33) Table VII：the results of the trading strategy I (case A) #. stock symbol. Company. share price Long/Short share price on on Holding shares 2015/05/1 2015/05/2 4 9. 1. 2312. Kinpo. 12.3. Long. 13. 2. 2317. HON HAI. 93.7. Long. 99.1. 3.911163287 387.5963. 3. 2354. FTC. 93.9. Long. 108. 3.295271565 355.8893. 4. 2359. Solomon. 17.9. Long. 18. 3.753240223 67.55832. 5. 2360. Chroma*. 75. Long. 69.1. 2.297986667 158.7909. 6. 2373. AURORA*. 53.8. Long. 53.6. 3.078568773 165.0113. 7. 2390. Everspring. 27.6. Short. 26.62. 124.1429296. 8. 2404. UIS*. 9. 2423. GW. 10. 1.761138211. 22.8948. -3304.68. 4.243879093 85.30197. 2433. 立 46.6 HUXEN*. Long. 46.2. 3.406609442 157.3854. 11. 2461. K LASER. 14.9. Long. 15.6. 2.936107383 45.80328. 12. 2464. Mirle*. 29. Long. 28.6. 4.174931034. 119.403. 13. 2474. CATCHER. 347. Long. 360. 1.841074928. 662.787. 14. 2477. MEILOON*. 13.25. Long. 13.1. 5.64709434. 73.97694. 15. 2482. UIC. 17.55. Long. 17.65. 16. 2488. HANPIN. 21.8. Long. 22.4. 17. 2495. Infortrend*. 16.75. Long. 15.9. 6.647283582 105.6918. 18. 2497. E-LEAD. 67.7. Short. 62.3. 4.431184503. -276.063. 19. 3018. TUNG KAI. Short. -533.206. 3030. TRI. 61.7 e n gLong c h i U 67.6. 33.74723676. 20. C20h. iv n15.8. 21. 3043. PCM. 3.51. Short. 3.28. 303.2775548. 22. 3305. SHENMAO*. 29.85. Long. 29.5. 5.453835846 160.8882. 23. 3450. ELASER. 139. Long. 186.5. 2.588892086 482.8284. 24. 3518. PT TECH.. 45.5. Long. 55. 4.885186813 268.6853. 25. 3617. CyberPower. 61.4. Long. 63.4. 3.819869707 242.1797. 26. 3665. BHI. 133. Long. 146.5. 1.978804511 289.8949. 27. 6139. L & K*. 22.45. Long. 21.45. 7.416703786 159.0883. 28. 6192. LUMAX. 58. Long. 58. 29. 6196. MIC*. 26.9. Long. 26.4. 4.395724907 116.0471. 30. 6201. YAHORNG*. 26.35. Long. 26.25. 7.45483871. 31. 6215. Aurotek*. 20.2. Long. 19.9. 2.927871287 58.26464. 32. 6409. VOLTRONIC. 378.5. Long. 398. 1.163764861 463.1784. y. 2.485868946 43.87559 5.787201835 129.6333. sit. er. n. 27. ‧. io. al. 學. 5.011339031 174.3946. Nat. 35.1. ‧ 國. 治 34.8 政 Long 大20.1 19.85 Long. Position on 2015/5/2 9. 2.673030794 180.6969. 3.591206897. -994.75. 208.29 195.6895.

(34) 33. 8021. Topoint*. 27. Long. 25.8. 6.500888889 167.7229. 34. 8201. BESTA*. 11.9. Long. 10.9. 1.037310924 11.30669 652.0504. Trading Strategy II. To avoid selection bias, we singled out the stock whose V(Mc ) to share price ratio lies between one and three. This is because there is little chance a stock price will rise or drop 300 percentages in only two weeks. The second reason is because the. 政治大 hand, it may expose that the firm is in the inappropriate liquidation management 立. higher V(Mc ) to share price ratio indicates the higher shareholder value. On the other. ‧ 國. 學. condition.. ‧. For trading strategy II, we do not leverage by establishing both long and short. sit. y. Nat. position simultaneously since short positions are generally initiated by more. io. er. adventurous and advanced investors. Trading strategy II is a relatively passive investment strategy suitable for conservative investors. It doesn’t need to create a. al. n. v i n large portfolio nor obey margin C requirement. the only thing the investors have U h e n g Instead, i h c to do is to select the stocks which fall within the interval. Here, we simply long the. stock whose V(Mc ) to share price ratio falls between one and three. After selecting the stocks, we buy ten lots of stocks for each on 2015/05/14. Table VII summaries the data collected for the trading.. 28.

(35) Table VIII：the analysis of the trading strategy II (case A) V(Mc ) share price share price V(Mc )/ share per share on on price 2015/05/1 2015/05/2 4 9. #. stock symbol. Company. 1. 2312. Kinpo. 21.662. 12.3. 13. 1.761138211. 2. 2360. Chroma. 172.349. 75. 69.1. 2.297986667. 3. 2461. K LASER. 43.748. 14.9. 15.6. 2.936107383. 4. 2482. UIC. 43.627. 17.55. 17.65. 2.485868946. 5. 3030. TRI. 164.926. 61.7. 67.6. 2.673030794. 6. 3450. ELASER. 359.856. 139. 186.5. 2.588892086. 7. 3665. BHI. 263.181. 133. 146.5. 1.978804511. 8. 6215. Aurotek. 19.9. 2.927871287. 9. 6409. VOLTRONIC 440.485. 378.5. 398. 1.163764861. 10. 8201. 12.344. 11.9. 10.9. 1.037310924. 立 BESTA. 政59.143治 20.2大. ‧ 國. 學. On 2015/05/29, we offload all the stock holdings and cash out to see the. ‧. holding returns for the period. Table VIII shows the results of our transaction. We use. Nat. sit. y. simple return17 to calculate the return on the investment. As we can see at Table VIII,. n. al. er. io. only three out of ten stocks decreased in value, which are Chroma, Aurotek, and. i n U. v. BESTA. Overall, trading strategy II has a gross profit of NT$80,700 and the rate of. Ch. engchi. return is nearly 10 percent. Individually, stock 3450 yields the biggest payoffs, rising 34 percent to NT$186.5 while BESTA drop 8.4 percent to NT$10.9. Using weighted average formula, we find out that, among all the stocks ELASER performed the best, accounting for 5.5 percent of the total return. VOLTRONIC ranked the second-best performing stock with 10 percent rising in stock price and 2.2 percent increase for the total return.. 17. simple return(ROI)=net proceeds/total cost=(Earnings-initial investment)/ initial investment 29.

(36) Table IX：the transaction and the results of trading strategy II of case A #. stock symbol. Company. 1. 2312. 2. Proportion Weighted of average of investment return. value of position on 2015/05/14. Shares. value of position on 2015/5/29. Kinpo. 12300. 1000. 13000. 0.056911 0.014235. 2360. Chroma. 75000. 1000. 69100. -0.07867 0.086801 -0.00683. 3. 2461. K LASER. 14900. 1000. 15600. 0.04698. 4. 2482. UIC. 17550. 1000. 17650. 0.005698 0.020311 0.000116. 5. 3030. TRI. 61700. 1000. 67600. 0.095624 0.071408 0.006828. 6. 3450. ELASER. 139000. 1000. 186500. 0.341727. 7. 3665. BHI. 133000. 1000. 146500. 0.101504 0.153926 0.015624. 8. 6215. Aurotek. -0.01485 0.023378 -0.00035. 9. 6409. VOLTRONIC. 0.051519 0.438053 0.022568. 10. 8201. BESTA. 1000 19900 治政 378500 1000 398000 大 11900 1000 10900 立 864050. 0.093397. 0.017244. 0.16087. 944750. 1. y. Nat. Shareholder value is also computed by Mc , but it contains liquation value.. er. io. sit. We make an alteration on the model, assuming there exists a liquation value, that is when M = 0, the firm is in financial distress. If the firm is liquidated at the. n. al. Ch. i n U. v. time when M = 0, it will have salvage value LT . Hence the shareholder value. engchi. function Vt is equal to the expected present value of total discounted dividends up to the bankruptcy date T plus the liquation value. Thus we rewrite (10):. T. Vt ≡ f(Mt ) ≡ E [∫ e−r(s−t) θ(Ms )ds|Mt ] + e−r(T−t) LT. (30). t. where r denote the appropriate discount rate and T as the time when M = 0. Other notations for the variables are the same as the ones mentioned in section 3. We reset (11): 30. 0.00081 0.00081. 0.054974. -0.08403 0.013772 -0.00116. ‧. ‧ 國. 20200. 學. Case B:. ROI. 0.093397.

(37) t. T. ∫ e−rs θ(Ms )ds + e−rt Vt = E [∫ e−rs θ(Ms )ds|Mt ] + e−rt LT 0. (31). 0. Following the previous proving process, equation (10) will become. T. t. constant ≡ E [∫ e−rs θ(Ms )ds + e−rt Vt ] ≡ E [∫ e−rs θ(Ms )ds] + e−rt LT 0. (32). 0. Since e−rt LT. 政治大 is a constant, we differentiate the equation (31) with respect to t 立. will get the same result as that equality holds in (11). We later follow the derivation. ‧ 國. 學. process of the formulas demonstrated in Section 3, the equation (19) satisfies two. sit. y. Nat. When cash reserves falls to zero, the firm is on the verge of bankruptcy and it. io. er. 1.. ‧. boundary conditions:. don’t have extra money to finance its business. Although the firm can survive via. al. n. v i n negotiating a line of creditC with the bank, it isUstill on the line. The value the hengchi 18. firm left when the cash reserves falls to zero is its liquidation value. L0 is the liquidation value at time t.. V(0) = ω1 + ω2 = L0. 2.. (33). When M reaches the target threshold M ∗ , the firm will start to distribute all the excess money and thus the marginal value of cash is 1.. 18. An arrangement between financial institution and a customer that establishes a maximum loan balance that the bank will permit the borrower to maintain. 31.

(38) ∗. ∗. V ′ (M ∗ ) = ω1 αe αM + ω2 βe βM = 1. (34). Based on (33) and (34), we may solve. ∗. 1 − L0 βe βM ω1 = ∗ ∗ αe αM − βe βM. (35). ∗. −1 + L0 αe αM ω2 = ∗ ∗ αe αM − βe βM. (36). 政治大. Using the results of (35) and (36), we obtain the shareholder value as. 立. ∗. ∗. (37). ‧. ‧ 國. 學. e βM − e αM − L0 αe αM e βM + L0 βe βM e αM V(M) = ∗ ∗ βe βM − αe αM. y. sit. io. er. liquation value19. Nat. Using accounts on the balance sheet, we define the liquation value as:. = short − term investment + accounts receivables. al. n. v i n C h+ prepaid expense + other receivables + other current assets engchi U. + other assets + inventory ∗ 0.8 + long − term investment ∗ 0.7 + fixed assets ∗ 0.5 − all debts20.. Using the data collected from stock AURORA, we draw mathematical graphs as shown in Figure II. The shareholder value on the date when M reaches zero is labeled as liquidation value. We can observe from Figure II, when m falls between 19. Asset liquidity is the degree to which assets can be sold. The easier the assets can be turned into cash, the more liquid the assets are. Therefore, we multiply each asset by one or a constant below one to represent the ease of liquidity. For example, fixed assets like plants and equipment are less liquid, so the weight assigned to the asset price is less as well. 20 All debts=current liabilities + long-term liabilities + other liabilities 32.

(39) M0 and zero, indicating that the firm experience financial distress. The marginal value of cash for shareholder in this regime is especially high.. Shareholder value. 立. 政治大. ‧ 國. 學. M0. M (cash reserves). ‧. Figure II：the shareholder value function (with liquidation value). sit. y. Nat. io. er. For simplicity, we assume V(ML ) per share is equal to V(ML ) divided by numbers of shares outstanding. Table VIIII summarizes the comparison of the. al. n. v i n estimates to actual share priceC on 2015/05/14. Compare h e n g c h i U the same company profile. listed on Table IV and Table VIIII, we may find out that adding liquidation value mostly increase the shareholder value. For example, Everspring’s V(ML ) per share is. three times larger than its V(Mc ) per share, while the ratios of V(ML ) per share to V(Mc ) per share of other companies are close to one.. 33.

(40) Table X：the comparison of V(ML ) per share and share price on 2015/05/14 V(ML ) per share Share price on 2015/05/14. #. stock symbol. Company. 1. 2312. Kinpo. 36.9153. 12.3. 2. 2317. HON HAI. 366.4799. 93.7. 3. 2354. FTC. 4. 2359. 5. 309.5220. 93.9. Solomon. 68.4718. 17.9. 2360. Chroma. 172.3821. 75. 6. 2373. AURORA. 166.7770. 53.8. 7. 2390. Everspring. 6.2378. 27.6. 8. 2404. UIS. 175.8707. 35.1. 9. 2423. GW. 84.2565. 10. 2433. 11. 2461. 12. 2464. 166.0609 治政 K LASER 86.9150 大立 Mirle 121.0879. 19.85. 13. 2474. CATCHER. 639.0335. 14. 2477. MEILOON. 75.3357. 15. 2482. UIC. 43.6870. 16. 2488. HANPIN. 126.1929. 17. 2495. Infortrend. 111.4988. 18. 2497. E-LEAD. 52.1568. 19. 3018. TUNG KAI. 9.92356. 20. 3030. 164.9619. 21. 3043. al. PCM. 22. 3305. SHENMAO. 23. 3450. ELASER. 359.9297. 139. 24. 3518. PT TECH.. 222.4196. 45.5. 25. 3617. CyberPower. 234.584. 61.4. 26. 3665. BHI. 263.247. 133. 27. 6139. L&K. 166.5801. 22.45. 28. 6192. LUMAX. 208.3244. 58. 29. 6196. MIC. 118.2743. 26.9. 30. 6201. YAHORNG. 196.4522. 26.35. 31. 6215. Aurotek. 59.1635. 20.2. 32. 6409. VOLTRONIC. 440.4886. 378.5. 33. 8021. Topoint. 175.5492. 27. 34. 8201. BESTA. 20.2497. 11.9. n. -1.06336. e n g162.8317 chi U. 34. 29 347 13.25 17.55. y. sit er. io. Ch. 14.9. ‧. Nat. TRI. 46.6. 學. ‧ 國. HUXEN. v ni. 21.8 16.75 67.7 20 61.7 3.51 29.85.

(41) Trading Strategy I. Following the same instruction and assumption in case A, we first compare the differences between the V(ML ) per share and the share price on 2015/5/14, and then construct an arbitrage-based trading strategy designed to exploit small differences.. We long if the V(ML ) per share is higher than the share price, while short equities that the V(ML ) per share is lower than the share price. The numbers of. 政治大 The analysis is shown at Table V. It shows that we have long position in 立. shares we buy were determined by the V(ML ) per share divide by the share price on 2015/05/14.. greater than the amount of money spent in case A.. 學. ‧ 國. 30 companies, and the estimated total long position cost NT$ 5,556.92, which is. ‧. sit. y. Nat. The determination of the number of short sale shares is also same as case A. Table. io. er. X summarizes the results of the transaction we made on 2015/5/14 based on the V(ML ) model. Judging by Table X, we hold short position in stock 2390, 2497, and. al. n. v i n C h noteworthy that 3018. From Table X, it is particularly V(M ) per share of PCM is engchi U L. negative, which suggests it may go bankrupt based on our model and cannot be traded. in open market, we therefore do not hold or borrow any of its stocks. The star symbol appeared at Table XI denotes the stock which is losing value during the holding period.. 35.

(42) Table XI：the analysis of the trading strategy I (case B) #. stock symbol. Company. V(ML ). V(ML ) / share price. Share Long/S price on hort 2015/05/1 4. Position on 2015/05/14. 1. 2312. Kinpo. 36.9153. 12.3. Long. 3.001243902. -36.9153. 2. 2317. HON HAI. 366.4799. 93.7. Long. 3.911204909. -366.4799. 3. 2354. FTC. 309.522. 93.9. Long. 3.29629393. -309.522. 4. 2359. Solomon. 68.4718. 17.9. Long. 3.825240223. -68.4718. 5. 2360. Chroma. 172.3821. 75. Long. 2.298428. -172.3821. 6. 2373. AURORA. 180.159. 53.8. Long. 3.348680297. -180.159. 7. 2390. Everspring. 6.2378. 27.6. Short. 0.226007246 3177.463772. 8. 2404. UIS. 9. 2423. GW. 10. 2433. 11. 2461. 12. 2464. 13. 2474. 14. 2477. 15. 2482. 16. 2488. 17. 35.1 Long 政治 84.2565 19.85 大 Long. 175.8707. -175.8707. 4.24465995. -84.2565. Long. 3.563538627. -166.0609. K LASER. 86.915. 14.9. Long. 5.833221477. -86.915. Mirle. 121.0879. 29. Long. 4.175444828. -121.0879. CATCHER. 639.0335. 347. Long. 1.841595101. -639.0335. MEILOON. 75.3357. 13.25. Long. 5.685713208. -75.3357. UIC. 43.687. 17.55. Long. 2.489287749. -43.687. HANPIN. 126.1929. 21.8. Long. 5.788665138. -126.1929. 2495. Infortrend. 111.4988. 16.75. Long. 6.656644776. -111.4988. 18. 2497. E-LEAD. 19. 3018. TUNG KAI. 20. 3030. TRI. 21. 3043. PCM. -1.06336. 3.51. Short -0.302951567. 22. 3305. SHENMAO. 162.8317. 29.85. Long. 5.454998325. -162.8317. 23. 3450. ELASER. 359.9297. 139. Long. 2.589422302. -359.9297. 24. 3518. PT TECH.. 222.4196. 45.5. Long. 4.888342857. -222.4196. 25. 3617. CyberPower. 234.584. 61.4. Long. 3.820586319. -234.584. 26. 3665. BHI. 263.247. 133. Long. 1.979300752. -263.247. 27. 6139. L&K. 166.5801. 22.45. Long. 7.420048998. -166.5801. 28. 6192. LUMAX. 208.3244. 58. Long. 3.5918. -208.3244. 29. 6196. MIC. 118.2743. 26.9. Long. 4.396814126. -118.2743. 30. 6201. YAHORNG 196.4522. 26.35. Long. 7.455491461. -196.4522. 31. 6215. 59.1635. 20.2. Long. 2.928886139. -59.1635. 32. 6409. VOLTRONIC 440.4886. 378.5. Long. 1.163774373. -440.4886. io. n. Aurotek. v i 9.9236 20 Short n Ch e n g c61.7 h i ULong 164.9619 52.1568. 67.7. 36. y. sit. Nat. al. er. ‧ 國. 46.6. 學. 166.0609. ‧. 立 HUXEN. 5.010561254. Short. 0.770410635 932.1390499 0.49618. 1447.317178. 2.673612642 -164.9619 0.

(43) 33. 8021. Topoint. 175.5492. 27. Long. 6.501822222. -175.5492. 34. 8201. BESTA. 20.2497. 11.9. Long. 1.701655462. -20.2497. Table XI record the amount of money we earn or spend on every trading occurred on 2015/5/29. On the date, we sell the identical number of shares to neutralize the long position while purchasing back the stocks to offset the short position. By doing so, we incur capital gains of NT$788.2747. Observing the trading record from both case A and B, it’s easy to find out their portfolio are extremely similar. The major difference is that case B has relatively more long position besides. 政治大. stock 2404. However, case B does not own a short position in stock 3043. The. 立. differences of their profits attribute to stock 2390, 2497, 3018, and 3043. For risk. ‧ 國. 學. assessment, we don’t hedge in both cases, implying that we may suffer losses once the stock price of our long position goes down or the stock price of our short position. ‧. soars. Since the size of short position in case B is bigger, which suggests case B is. sit. y. Nat. more risky21. In short, case A and B prove the shareholder value is one of the reliable. n. al. er. io. methods on identifying a firm’s true value.. 21. Ch. engchi. i n U. v. Logically, there is no upper bound of capital losses in a short position because there is no maximum restriction on a stock’s price. 37.

(44) Table XII：the results of the trading strategy I (case B) #. stock symbol. Company. 1. 2312. Kinpo. 12.3. Long. 13. 3.001244 39.01617. 2. 2317. HON HAI. 93.7. Long. 99.1. 3.911205 387.6004. 3. 2354. FTC. 93.9. Long. 108. 3.296294 355.9997. 4. 2359. Solomon. 17.9. Long. 18. 3.82524. 5. 2360. Chroma*22. 75. Long. 69.1. 2.298428 158.8214. 6. 2373. AURORA*. 53.8. Long. 53.6. 3.34868. 179.4893. 7. 2390. Everspring. 27.6. Short. 26.62. 115.1255. -3064.64. 8. 2404. UIS*. 9. 2423. GW. 10. 2433. HUXEN*. 11. 2461. 12. 2464. 13. 2474. 14. 2477. 15. 2482. 16. 2488. 17. 2495. 18. 2497. E-LEAD. 19. 3018. TUNG KAI. 20. 3030. TRI. 21. 3043. PCM. 22. 3305. 23. 5.010561 174.3675 85.31766. 46.2. 3.563539 164.6355. K LASER. 14.9. Long. 15.6. 5.833221 90.99826. Mirle*. 29. Long. 28.6. 4.175445 119.4177. CATCHER. 347. Long. 360. 1.841595 662.9742. MEILOON*. 13.25. Long. 13.1. 5.685713 74.48284. UIC. 17.55. Long. 17.65. 2.489288 43.93593. HANPIN. 21.8. Long. 22.4. 5.788665 129.6661. Infortrend*. 16.75. Long. 15.9. 6.656645 105.8407. 67.7. Short. 62.3. 13.76867. -857.788. 20. Short. 72.36586. -1143.38. n. er. Nat. al. ‧. ‧ 國. Long. 學. 46.6. y. 4.24466. sit. 35.1 Long 34.8 治政 19.85 Long 大 20.1. 68.85432. io. 立. Share price Long/Short share price holding Position on on on 2015/05/14 2015/05/29 shares 2015/05/29. v 15.8 i n C h61.7 e n g cLong h i U 67.6. 2.673613 180.7362. 3.51. Short. 3.28. SHENMAO*. 29.85. Long. 29.5. 5.454998 160.9225. 3450. ELASER. 139. Long. 186.5. 2.589422 482.9273. 24. 3518. PT TECH.. 45.5. Long. 55. 4.888343 268.8589. 25. 3617. CyberPower. 61.4. Long. 63.4. 3.820586 242.2252. 26. 3665. BHI. 133. Long. 146.5. 1.979301 289.9676. 27. 6139. L & K*. 22.45. Long. 21.45. 7.420049 159.1601. 28. 6192. LUMAX. 58. Long. 58. 29. 6196. MIC*. 26.9. Long. 26.4. 22. 0. 3.5918. 0. 208.3244. 4.396814 116.0759. Same as before, the star symbol denotes the stock which is losing value during the holding period. 38.

(45) 30. 6201. YAHORNG*. 26.35. Long. 26.25. 7.455491 195.7067. 31. 6215. Aurotek*. 20.2. Long. 19.9. 2.928886 58.28483. 32. 6409. VOLTRONIC. 378.5. Long. 398. 1.163774 463.1822. 33. 8021. Topoint*. 27. Long. 25.8. 6.501822. 34. 8201. BESTA*. 11.9. Long. 10.9. 1.701655 18.54804. 167.747 788.2747. Trading Strategy II. Following the same steps described in case A, the stock selection is to long. 政治大 real stock market condition in Taiwan, the trading volume for each stock is ten lots. 立 stocks whose V(Mc ) to share price ratio lies between one and three. Regard to the. ‧ 國. 學. Table XII summaries the information of trading strategy II. Compared to case A, case B portfolio includes 9 different stocks instead of 10. Moreover, by selecting stocks. ‧. from the criteria we use in both cases, we get similar result patterns－that is, to invest. sit. y. Nat. in stocks 2360, 2482, 3030, 3450, 3665, 6215,6409, and 8201. Namely, the difference. io. V(ML ) share price share price V(ML )/ share per share on on price 2015/05/14 2015/05/29. n. al. er. of their performance only depends on the stock 2312, 2461, 2474.. i n C Table XIII：the analysis of tradinghstrategy II (case B)U engchi. v. #. stock symbol. Company. 1. 2360. Chroma. 186.869. 75. 69.1. 2.491586667. 2. 2474. CATCHER. 674.57. 347. 360. 1.944005764. 3. 2482. UIC. 50.615. 17.55. 17.65. 2.884045584. 4. 3030. TRI. 173.437. 61.7. 67.6. 2.810972447. 5. 3450. ELASER. 372.193. 139. 186.5. 2.677647482. 6. 3665. BHI. 285.924. 133. 146.5. 2.149804511. 7. 6215. Aurotek. 59.1635. 20.2. 19.9. 2.928886139. 8. 6409. VOLTRONIC 441.41. 378.5. 398. 1.166208719. 9. 8201. 11.9. 10.9. 2.392773109. BESTA. 28.474 39.

(46) We close our long position to eliminate the initial exposure on 2015/05/29. Table XIII shows the results of our transaction, including the analysis of the return on investment. The transaction of case B has an approximately gross profit of NT$92,300 and its return on investment is about 8 percent. The top three percentage gainers among these nine stocks are ELASER, BHI, and TRI, which rose 34 percent to NT$186.5, 10 percent to NT$146.5, 9.6 percent to NT$67.6, respectively. As for the stock performance in the investment, ELASER, VOLTRONIC, and BHI are the top. 政治大 lower return on investment yet generates more profits than case A is due to the initial 立. three, accounting for 4 percent, 1.6 percent, 1.1 percent each. The fact that case B has. investment.. ‧ 國. 學. Company. Shares. io. 1. 2360. Chroma. 2. 2474. CATCHER. 3. 2482. UIC. a75000 l C 347000 h. 4. 3030. TRI. 61700. 1000. 5. 3450. ELASER. 139000. 6. 3665. BHI. 7. 6215. 8 9. value of position on 2015/5/29. y. value of position on 2015/05/14. sit. Nat. stock symbol. er. #. ‧. Table XIV：the transaction and the results of trading strategy II (case B). iv 1000 360000 n e n1000 g c h i U17650. 0.037464. 0.293111 0.010981. 0.005698. 0.014825 8.45E-05. 67600. 0.095624. 0.052118 0.004984. 1000. 186500. 0.341727. 0.117414 0.040123. 133000. 1000. 146500. 0.101504. 0.112345 0.011403. Aurotek. 20200. 1000. 19900. -0.01485. 0.017063 -0.00025. 6409. VOLTRONIC. 378500. 1000. 398000. 0.051519. 0.31972 0.016472. 8201. BESTA. 11900. 1000. 10900. -0.08403. 0.010052 -0.00084. 1276150. 0.077966. 1 0.077966. n. 0.063353 -0.00498. 1183850. 69100. investment return -0.07867. 17550. 1000. ROI. Proportion Weighted of average of. Though we get mixed results from trading strategy I and II in both cases, it roughly shows that the shareholder value criterion is efficient in determining and 40.

(47) forecasting the stock price. We can use the variable of cash reserves and its historical data like the mean and the volatility of its earnings to project its genuine value. Nevertheless, the mean and the volatility of its earnings may be influenced by the size23, business cycle, loss from lawsuits, innovative technical breakthroughs, and even employee productivity24 . For example, a company that get through radical changes by losing a lawsuit whose earnings volatility may vary extremely and thus the shareholder value computed from it would be abnormal and with no credibility. That’s why in trading strategy II, we only select stocks whose V(ML ) to share price ratio or. 政治大. V(MC ) to share price ratio intermediate between one and three; in other words, to detect outliers.. 立. ‧ 國. 學. In conclusion, there are no significant differences between adapting the method. ‧. mentioned in case A or case B. Furthermore, there is no assurance that V(ML ) and. sit. y. Nat. V(MC ), which is more accurate in deciding a firm’s value. Of course, case B seems to. io. er. gain more money in two strategies, but it also bear more risks as well. In practical, case B would be a more appropriate method. Since when a firm is terminated, there. al. n. v i n are liquid and fixed assets leftC to be sold before dissolution. In that case, the firm hengchi U value is not exactly zero when cash reserves decline to zero. The intractable thing lies in the evaluation of liquidation value because there is no precise formula to assess them. The liquidity of assets may vary from one industry to another.. 23. Hall, M and Weiss, L. (1967) [11] Kruse, D.L. (1992) [12] considers employee bonus will motivate employees, enhance their productivity and thus increase the company profits. 41 24.

(48) 5 Conclusion. In our paper, we have studied the method of shareholder value methodology, which is previously used to solve the problem of finding the optimal dividend-payout strategy for insurance company. Our main contribution is not to formulate and solve the problem within the mathematically more advanced framework of diffusion models. Instead, we focus on the implement of the model. We employ two types of empirical models to evaluate a firm.. 政治大 In general, there is inconsistency exists between the stock value and shareholder 立. value. The empirical results indicate that most of the electronic listed companies keep. ‧ 國. 學. too much cash reserves which may be the key reason to the overestimation of their. ‧. stock prices. Additionally, the fluctuating incomes may cause the same problem as. sit. y. Nat. mentioned. This leads us to the following question: What can we apply the. io. er. methodologies to selecting stocks, with the aim of achieving a rate of return that beat the market？In section 4, we show two short term trading strategies both work for. al. n. v i n making money. That is, we canC distinguish the difference h e n g c h i U between a stock price and a stock's fair market value.. However, many factors affect a company's state of operation that it is nearly impossible to create a formula that will predict success at all times. In our simple model, we view cash reserves as the crucial variable, focusing on the impact of liquidation management. In fact, many other variables are needed to be taken into consideration, such as the financing and investing decisions. The further extension should allow companies to control their cash reverses through issuing new equity, capital reduction or even stock repurchase. 42.

(49) Reference:. 1. Asmussen, S., Taksar, M. (1997) : Controlled diffusion models for optimal dividend pay–out. Insurance: Math Econ 20, 1–15 2. Boguslavskaya, E. (2003) : On Optimization of dividend flow for a company in a presence of liquidation value, Working paper. 3. Cornell, B. (1993) Corporate Valuation: Tools for Effective Appraisal and Decision Making Homewood, IL: Business One Irwin.. 政治大 Economics and Statistics, 49 (3), 319 – 331 立. 4. Hall. M & Weiss, L. (1967), “Firm Size and Profitability”, The Review of. 5. Jeanblanc–Pique, M., Shiryaev, A. (1995): Optimization of the flow of dividends.. ‧ 國. 學. Russian Math. Surveys 50, 257–277. ‧. 6. Kruse, D.L. (1992), Profit Sharing and Productivity: Microeconometric Evidence. sit. y. Nat. from the United States, The Economic Journal 102 (410), 24-36.. io. Harvard Business Review, pp. 132-142.. n. al. Ch. 8. Løkka, A.and Zervos, M. (2005): “Optimal. engchi. er. 7. Luehrman, T. A. (1997): What's it worth? A general manager's guide to valuation.. v i n dividend U and. issuance of equity. policies in the presence of proportional costs,” Insurance: Mathematics & Economics, vol. 42, no. 3, pp. 954–961, 2008. 9. Miller, M.H. and Modigliani, F. (1961). “Dividend Policy, Growth and the Valuation of Shares.” J. Business, 34(34): 411-433 10. Myron J. G. (1962): The Investment, Financing, and Valuation of the Corporation , Homewood, IL: R.D. Irwin) 11. Radner, R., Shepp, L. (1996) : Risk vs. profit potential: A model for corporate strategy. J. Econ. Dynam. Control 20, 1373–1383 12. Sethi, S. P. and Taksar, M. (2002): Optimal financing of a corporation subject to 43.

(50) random returns. Math. Finance 12, no. 2, 155-172. 13. Williams, J. B. (1938) “The Theory of Investment Value.” Harvard University Press, Cambridge.. 立. 政治大. ‧. ‧ 國. 學. n. er. io. sit. y. Nat. al. Ch. engchi. 44. i n U. v.

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