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Stock Assessment Using a Dividend Discount Model with Growth Rate Following a Time Series Pattern

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Stock Assessment Using a Dividend Discount Model with Growth Rate Following a Time Series Pattern Proceedings of the International Conference on Industrial Engineering and Operations Management Pilsen, Czech Republic, July 23-26, 2019 Stock Assessment Using a Dividend Discount Model with Growth Rate Following a Time Series Pattern Sukono, Dwi Susanti, Isah Aisah, Agus Supriatna Department of Mathematics, Faculty of Mathematics and Natural Sciences, UniversitasPadjadjaran, Indonesia [email protected],[email protected],[email protected], [email protected], Jumadil Saputra School of Social and Economics Development, Universiti Malaysia Terengganu, Malaysia e-mail: [email protected]; [email protected] Abdul Talib Bon Department of Production and Operations, University Tun Hussein Onn Malaysia, Malaysia [email protected] Abstract Determination of the theoretical price of a stock using a dividend discount model is done by setting various levels of dividend growth. The problem is what if dividend growth is assumed to follow a time series. In this paper it aims to discuss stock valuation using a fluctuating dividend discount model along with the time series. It is assumed that the expected dividend fluctuate with time series model. To estimate the magnitude the expected dividend was performed using a Autoregressive Integrated Moving Average (ARIMA) model. As for determining the theoretical price of the stock is done by using the dividend discount models, which include some level of growth. Based on the dividend discount model of stock prices in the period to n +1 shows the current value of all dividend payments over a period of 2( n +1through infinite time). Keywords: Dividend, ARIMA model, dividend discount models, the growth rate of dividends. 1. Introduction One form of investment that is often chosen by investors to invest is stocks. In order for the investment decision to generate returns as expected, investors need to make a prior assessment of the shares they will choose (Adebiyi, Adewumi& Ayo, 2014; Charumathi&Suraj, 2014). This stock valuation is important to produce information on intrinsic value, and then it will be compared with the stock market price to determine the buy or sell position of a company's stock. The discount dividend model is one of the useful tools for determining the intrinsic price of shares.The assessment of the intrinsic price of shares is carried out by establishing various assumptions about the level of dividend growth (Olweny, 2011). The usual assumptions used are starting dividends without growth, dividends with constant growth, dividends with multiple growth rates, dividends with two levels of growth, and dividends with three growth rates (Gray & Hull, 2013). The problem is what if it is assumed that the dividend growth rate follows the time series model. With regard to price valuation, Gottwald (2010) measures stock price volatility using a dividend discount model. Olweny (2011) evaluates the reliability of the dividend discount model in the valuation of capital market share prices in Nairobi. Gray & Hall (2013) estimated the cost of equity using a discounted dividend model. Both Gottwald and Olweny and Gray & Hall, determine the returns required by using the Capital Asset Pricing Model © IEOM Society International 1574 Proceedings of the International Conference on Industrial Engineering and Operations Management Pilsen, Czech Republic, July 23-26, 2019 (CAPM) regression.Furthermore, related to the time series model, Adebiyi, et al. (2014) predict stock prices using the autoregressive integrated moving average (ARIMA) model. Whereas, Mondal, et al. (2014) conducted a study of the effectiveness of time series models (ARIMA) in forecasting stock prices. The results of the study show that the ARIMA model is effective enough to predict the price of shares being analyzed. Therefore, the authors suspect that the rate of dividend growth can also be predicted using the time series model (ARIMA). Based on the description above, in this paper a stock valuation analysis is carried out using a fluctuating dividend discount model along with changes in time, using the ARIMA model approach. The aim is to get an alternative method of valuing stock prices using a more suitable dividend discount. As a numerical illustration, in this paper analyzed a stock traded on the capital market in Indonesia. 2. Research Method The discussion in this section is explained about the dividend discount model which includes: zero growth, constant growth, not constant growth, and growth following a time series, and determining the required rate of return. 2.1 Dividend Discount Model Dividend discount model to determine the estimated stock price by discounting all dividend flows that will be received in the future. Mathematically, the dividend discount model can be stated as follows: ~ D D D D∞ P = 1+ 2 + 3 +... + 0 ∞ (1+ k ) (1+ k )2 (1+ k )3 (1+ k ) ∞ ~ D P = t , (1) 0 ∑ t t=1 (1+ k ) ~ where P0 intrinsic value of shares with a discounted dividend model, Dt ( t =1,2,..., ∞ ) dividends that will be received in the future, and k the level of return required (Nag& Liu, 2004). 2.2 Zero Growth Dividend Discount Model In the dividend discount model with zero growth, it is assumed that the company divides dividends in the same amount over the life of the stock. Mathematically, a dividend discount model with zero growth can be expressed as: ~ D0 P0 = , (2) k ~ where P0 intrinsic value of shares with a discounted dividend model, D0 dividends that will be received in the future, and k level of return required (Gottwald, 2012; Mungikar & Muralidhar, 2014). 2.3 Discount Dividend Model with Constant Growth The dividend discount model with constant growth assumes that dividends grow constantly (fixed) throughout the life of the stock, where gt+1 = g t for all time t =1,2,..., ∞ . Mathematically, the dividend discount model with constant growth can be expressed as: ∞ ~ D(1+ g ) D(1+ g )2 D(1+ g )3 D(1+ g ) P = 0 + 0 + 0 +... + 0 , 0 ∞ (1+ k ) (1+ k )2 (1+ k )3 (1+ k ) ∞ ~ D(1+ g )t P = 0 . (3) 0 ∑ t t=1 (1+ k ) If k> g , then equation (3) can be simplified to be: ~ D1 P0 = , (4) k− g where g the rate of dividend growth, and k level of return required (Gottwald, 2012; Mungikar&Muralidhar, 2014). 2.4 Dividend Discount Model with Non-Constant Growth (Double) © IEOM Society International 1575 Proceedings of the International Conference on Industrial Engineering and Operations Management Pilsen, Czech Republic, July 23-26, 2019 The dividend discount model of growth is not constant (double), it is assumed that dividend payments increase with several growth rates. In particular, dividend growth is grouped in several time frames. Each time span has a certain growth rate, different from the growth rate in other time frames. In the last span of time, dividends have grown constantly. Another assumption, that dividend growth in the earlier period, is higher than the growth rate in the next time span (Norman et al., 2012). The process of valuing stock prices using a dividend discount model, not constant growth can be done with the equation: n t ~ D0(1+ g 1 ) Dn(1+ g c ) 1 P0 = + , (5) ∑ t k− g n t=1 (1+ k ) c (1+ k ) ~ where P0 intrinsic value of shares with growth is not constant, n number of years during the period of supernormal dividend payments (dividends above normal), D0 first year dividend (initial), g1 supernormal dividend growth, Dn dividends at the end of the year supernormal growth, gc constant dividend growth, and k the level of return required (Gottwald, 2012; Mungikar&Muralidhar, 2014). The weakness of the method of valuing stock prices using a dividend discount model of non-constant growth is that the division of time span depends on the subjectivity of the analyst. 2.5 Dividend Discount Model with Growth Following Time Series The estimated rate of dividend growth that follows the time series is done using the approach of the autoregressive moving average (ARMA) model. Suppose Dt is a dividend growth rate data that follows the time series pattern, the ARMA degree model p and q written as ARMA( p , q ), which generally has an equation (Mondal, Shit &Goswami, 2014): p q Dt =φ0 + ∑ φiD t− i+ a t − ∑θ j a t−1 , (6) i=1 j=1 Where{}at residual squence that are white noise, as well as p and q non-negative integer. As well φi ( i= 0,1,..., p ) autoregressive coefficient parameters, andθ j ( j= 1,..., q ) moving average coefficient parameter. The process of estimating the dividend growth rate that follows the time series is carried out with the following stages: (i) Stationary data return testing; (ii) Model identification; (iii) Estimated model parameters; (iv) Model diagnostic testing; and (v) Future l-period predictions (Tsay, 2005; Sukono et al., 2017; Sukono et al., 2016). So, based on equation (5) the estimator of the rate of dividend growth can be stated as: p q ˆ ˆ ˆ ˆ Dt =φ0 + ∑ φiD t− i− ∑θ ja t−1 . (7) i=1 j=1 Furthermore, using equation (7), the prediction of the rate of dividend growth in the future l-period the future is: p q ˆ ˆ ˆ ˆ DT+ l =φ0 + ∑ φiD T− i + l− ∑θ ja T− j + l . (8) i=1 j=1 where T the starting point of the prediction is done (Sukono et al., 2017; 2016). Referring to equation (1), the dividend discount model that follows the time series can be stated as follows: ~ Dˆ Dˆ Dˆ Dˆ P = TT+1+ + 2 + T +3 +... + ∞ 0 ∞ (1+ k ) (1+ k )2 (1+ k )3 (1+ k ) ∞ ~ D P = T +1 , (9) 0 ∑ l l =1(1+ k ) ~ ˆ where P0 intrinsic value of shares with a discounted dividend model, DT+ l ( l =1,2,..., ∞ ) dividends that will be received in the future, T starting point of predictions, and the level of return required.
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