# The effect of dividend on a firms capital costs

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As stated by Jensen (1873 - 1950), the policy of dividend will eventually influence the firm's capital cost, affecting the shareholders' wealth. Meanwhile, the dividends paid can be used to minimize the conflicts between managers and shareholders. In other words, the growth rate of the dividend plays an important role in determining the dividends payment to shareholders. Besides, the dividends affect the cost of capital as well. In fact, a common stock with a constant dividend acts almost the same like a preferred stock in a case where the payout of dividend remains unchanged.

In this case, to estimate the equity cost of capital, there are three main types of dividend model such as the zero-growth dividend model, the constant dividend growth model (CDGM) and the variable dividend growth model. Among these three models, the constant dividend growth model and the variable dividend growth model are used by most of the firms and organizations in estimating the future value of their stocks in the markets, according to John Campbell, Andrew Lo, and A. Craig MacKinley (1996).

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In this assignment, the model of constant dividend growth will be discussed further. It is a very vital topic as there are factors which will influence the output of calculation. Those factors are the input of data needed, the assumptions of the models and limitations practically. In fact, the growth rate has a direct-proportionate relationship with the investment return. Examples of cases will be shown and explained further in this assignment.

## 2.0 Background Studies

In this assignment, one of the models used to calculate and estimate cost of common stock capital which is the constant dividend growth model will be discussed.

## 2.1 Dividend Growth Model

Dividend Growth Model (AKA Stock Valuation Model) can be defined as a model that attends to the dividend as well as its growth related to contemporary discount. As what stated in the Farlex Financial Dictionary (2009), it says tat this model approves investors to check out the stock either is undervalued or overvalued. An undervalued stock is a stock whereby it is sold in a price lower than its real value whereas an overvalued stock is a stock whereby it is sold in a price higher than its real value. Thus, when dividend growth rate states that the stock is overvalued, investors will most probably to sell their stocks and prevent from buying any of the stock. On the other hand, if the stock is undervalued, investors will most likely to buy stocks and not sell any of their own stocks.

According to Jim Wang (2010), he stated that although there might be different kinds of risks in investments based on dividends due to its probability of experiencing changes, this model is still useful in estimating the cost of common stock capital. Besides, Ben McClure (2004) explained in his journal "Digging Into the Dividend Discount Model" that abundant of predictions about the respective company's payment of dividend, its growth trend and also future interest rates are needed while undergoing this model. There are 3 main models of dividend growth model, which are;

Zero-growth model

Assumption: all dividends incurred by stock will be the same

Constant-growth model

Assumption: dividends grow at a constant rate, no drastic changes

Variable-growth model (AKA two-stage growth model)

Assumption: dividends grow at 3 phase basically, which are a rapid initial phase, follow by a slower transition phase and end with a lower, sustainable rate over a long duration

## 2.2 Benefits and Side-Effect of Dividend Growth Model

There are some pros and cons of using the dividend growth model. In fact, the dividend growth model is understandable and user friendly. Yet, there are still some drawbacks for this model. First and foremost, this model can only be used by firms or organizations which are presently discharging dividends. Besides, it is not suitable for those firms or organizations whose dividends are not experiencing relevant constant-growth rate. Moreover, the model of dividend growth is strongly affected by the changes of estimated rate of growth whereby growth rate increases proportionally with the cost of capital. Last but not least, this model does not consider risk necessarily. These will definitely dangerous for the firms or organizations which applying this model.

## 3.0 Literature Review

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Among the 3 types of dividend growth model, the most regularly used model is the constant dividend growth model. According to Lee, Jeong (2002), under a 177 Fortune 1,000 companies survey conducted by Gitman and Mercurio (1982), it clearly portrays that most advanced and huge firms and organizations imply this model in estimating their cost of equity. Based on the journal of "Digging into the Dividend Discount Model" written by Ben McClure (2004), he states that constant dividend growth rate is also known as Gordon Model, which is named after its originator who is Myron Gordon (1960) on "Optimum Dividend Rate". Gordon had his further research which related to corporation investments, financing and valuation using mathematics and models, together with investment theory (1964).

## 3.1 Inputs and Assumptions Made While Practicing the Constant Dividend Growth Model (CDGM)

Berk, DeMarzo and Harford (2010) indicated that, in measuring and estimating cost of equity, the dominant subjects to be considered in the calculation are the present price of stock, expected dividend for the next year, and also future dividend growth rate. The formula will be as below:

Cost of Equity

## =

Dividend (one year)

## +

Dividend Growth Rate

Current Price

## =

Div1

## +

g

PE

Besides this, there are also a few important assumptions which are required to be made while applying this model. These include ensuring that estimation of dividend should be accurate, assuming that the rate of growth matches the market expectations, and the most important is assuming that the particular firm or organization's future growth of dividend be constant.

## 3.2 Major Usage of Constant Dividend Growth Model (CDGM)

The Constant Dividend Growth model is found useful in determining the firms or organizations' stock value, especially for those companies who have stable and steady development with constant dividend growth rate for each and every year. Normally, excellent companies has constant dividend growth rate whereby their current stock value can be examined within a short duration, together with this model. In addition, also notes that this model can be used effectively in calculating growth of retirement funds and income to be withdrawn each period

## 3.3 Effective Use of Constant Dividend Growth Model (CDGM)

Basically, the constant dividend growth model (CDGM) is applied when estimating the cost of equity of the common stock for the respective firm or organization. In a more high-standard level, this model can actually be used in analyzing security or cases related with security issuance, mergers and acquisitions of firms and organizations, and also problems involving valuation of stocks. Referring to Payne and Finch (1999), almost all sources mention that it is normally being assumed that the rate of return on equity cost of capital (rE) must be larger than estimated growth rate in earnings and dividends (g) so that this model can be realized. Nevertheless, there will still be stock valuation error found when implying this model.

## Valuation error

From the studies, valuation error normally is caused by different forms of dividend model being implemented. First of all, it is stated by Jacobs and Levy (1988) that the expected return of the model is usually unpredictable and will correlated with the actual ones negatively. Furthermore, errors approximately 88% of the actual price as well as errors percentage of price-earnings methods of about 4.21 times, will be resulted by the dividend approaches. Moreover, in Gehr's opinion (1992), required return and error in predicting growth errors will cause biases in price estimation in the model itself. Hence, he proposes a probability weighted range of parameters estimate application. Lastly, due to the dividend for the next period is mostly a known quantity, Good (1989) explains that the model's reliability is basically depends on the required return estimation and growth rates.

## Applying the Constant Dividend Model (CDGM) Effectively

As usual, the formula of Constant Dividend Growth Model (CDGM) is as shown below;

Constant Growth, P0

## =

Div

## +

Div (1+g)

## +

Div (1+g)2

## + â€¦â€¦.

1+rE

(1+rE)2

(1+rE)3

## =

Div

rE-g

Whereby

Div = estimated dividend for the next period

rE = rate of return on equity cost of capital

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Examples of our workg = estimated growth rate in earnings and dividends

## Relationship between the Changed Effect of A (rE-g) and estimation of stock value (P0)

Here's an example of figures which illustrates in a clearer manner on the relationship between the changes effect of A (rE-g) on estimation of stock value (P0), which is in table form.

## A (rE-g)

## Estimated Value (P0)

35%

$ 8.57

30%

$ 10.00

25%

$ 12.00

20%

$ 15.00

15%

$ 20.00

10%

$ 30.00

5%

$ 60.00

Valuation Estimation

From the graph shown above, it clearly portrays that when A decreases, the estimated value of P0 will rise. In another words, A is directly proportional to the estimated value, P0. A slight change of A will cause the estimated value to change as well. Therefore, this is a vital factor which should be alert in this model.

## Example of Effective Application of Constant Dividend Growth Model (CDGM) Case

Here's a scenario. In 2006, the company's earning per share (EPS) ratio was $3.00 and it increased to $3.40 in the year of 2009. The company was able to stabilize its ratio of dividend payout at 50% and its return on equity (ROE) was 12% in 2009. It is forecasted that the growth of earnings of company's stock will rise from 8% to 10% in the following years. It is given that the risk-free return rate in the market is about 8%, the company's beta is 2.10 and market expected return is 15%. The management of the company predicted that there will be a premium of 9% for stocks over bonds and the yield to maturity for those long-term bonds is 9.75%.

With these given information, the estimated value of stock (P0) is estimated. Steps are shown as follow;

Step 1: Calculating for the Expected Return of Security E[Ri]

There are 2 ways of calculating E[Ri];

Using the Capital Asset Pricing Model (CAPM)

E[Ri] = rf + Î²i (E[RMkt] - rf)

= 8% + 2.1 (15% - 8%)

= 0.227

= 22.7%

Using the Addition of Bond Yield and Risk Premium Approach

E[Ri] = Yield to Maturity + Risk Premium for Systematic Risk

= 9.75% + 9%

= 18.75%

Therefore, the average expected return E[Ri] will be;

E[Ri] = (22.7% + 18.75%)/2 = 20.725% = 20.73%

Step 2: Calculating estimated Growth Rate, g

Unlike to Step 1, there are 3 ways of calculation;

Using Retention Growth Model

g = Retention Rate x Return on New Investment

= 0.50 (12%)

= 6.0%

Using Estimation of Point to Point

FV = PV (1 + g) n

$3.40 = $3.00 (1 + g) 3

â†’ g = 4.26%

Using Forecast by the Company Itself

1st Growth Estimation, g1 = 8%

2nd Growth Estimation, g2 = 10%

â†’ Average Growth Estimation, g = (8% + 10%)/2 = 9%

Therefore, the average estimated growth will be;

g = (6.0% + 4.26% + 9%)/3

= 6.42%

Using the Constant Dividend Growth Model (CDGM), we know that dividend of previous year was $3.40 (0.50) = $1.70, thus the estimates value of stock under this CDGM model will be;

P0

## =

$1.70 (1 +0.0642)

0.2073 - 0.0642

## =

$1.70 (1.0642)

0.2073 - 0.0642

## =

$1.80914

0.1431

## =

## $12.64

## 3.4 Limitations Using Constant Dividend Growth Model (CDGM)

As a matter of fact, the constant dividend growth model (CDGM) is a user-friendly and understandable method which is widely used by firms and organizations. Nevertheless, there are yet some shortcomings for this model that should be taken notice before implementing this model. According to Richard Constand (1999-2001), he mentioned that the limitations for this model include the possibility whereby the estimated dividend may alter from time to time and the growth rate assumption may be false or inaccurate. Besides, he added that there are some firms or organizations which do not pay dividends.

## 4.0 Supporting Theories

## 4.1 Theories in relation to the variable dividend growth model

As stated by Berk, DeMarzo and Harford (2010), it is not necessary that the model of Constant Dividend Growth can be implemented in every situation. This model cannot be used when;

There are no dividends paid for the firm when it is just built up.

The firm's growth of dividends is changing unsteadily from time to time until they are well-established.

Thus, the non-constant dividend growth model will be used if the situation as above happens. As stated in Background Studies, variable dividend growth model is a model whereby the growth rate of the firm's dividend experiences a non-steady phase.

## 4.2 Comparison between Constant Dividend Growth Model (CDGM) and Variable Dividend Growth Model

As compared to the constant dividend growth model (CDGM), the variable dividend growth model is a much more difficult to be calculated. Yet, it is a more advanced model than constant dividend growth model. Since the variable dividend growth model approves two different growth rates, it is more sensible as compared than the constant dividend growth model. Furthermore, it will be alright when the discount rate is happened to be lower than the first-phase of rate of growth.

## 4.3 Major Usage of Variable Dividend Growth Model

In fact, not all companies may successfully maintain their growth rates in stock market. This model allocates adjustments to predict their present values. This can be done by taking in the aspect of time assumption as well as the present growth magnitudes of those respective companies. In other words, the variable dividend growth model includes diversified rate of growth which are applied into the valuation of shares analysis.

## 4.4 Application of Variable Dividend Growth Model

In accordance with what stated by Payne and Finch (1999), the variable dividend growth model comprises three main steps, which are;

Determine the high growth period(s) dividend separately

Determine the final growth stage price of share through the constant dividend growth model (CDGM)

Ensure that the future cash flow is discounted back to current required return rate and the total

## Example of Case Application of Variable Dividend Growth Model

Applying the same example case used in the constant dividend growth model (p.6) but with minor changes, given that the company is estimated to have 18% of dividend and earnings annual growth rate, together with consequent growth to the past predicted annually average rate that is 6.42%. The dividends of the following 3 years are analyzed to be as calculated below;

Div1 = $1.70 (1 + 0.18) = $2.01

Div2 = $2.01 (1 + 0.18) = $2.37

Div3 = $2.37 (1 + 0.18) = $2.79

Hence, the estimated value of stock will be;

P0

## =

$2.01

## +

$2.37

## +

$2.79

## +

$2.79 (1.0642) / (0.2073 - 0.0642)

1.2073

(1.2073)2

(1.2073)3

(1.2703)3

## =

$1.66

## +

$1.63

## +

$1.59

## +

$11.79

## =

## $16.67

## 4.5 Limitations Using Variable Dividend Growth Model

Similar to constant dividend growth model, the variable dividend growth model uses forecasted future value. As reported by Dardan, Busch, and Sward (2006), the usage of this estimated future values has unintentionally brought risks to the firms or organizations who apply the model itself. They added that it is assumed that future benefits are predicted to be the similar as the actual one. The possibility of this to occur is 100%. However, it is difficult to achieve this 100% for each and every firms and organizations as it is sensitively affected by the factors of technology, management as well as human capital. These 3 factors will never be perfect as the economy alters every year.

## 5.0 Conclusion

The constant dividend growth model is a very effective and understandable method in calculating the equity cost of capital. Due to this reason, this model should be applied properly to the particular situation so as to achieve a higher-accuracy estimated future value of stocks. For instance, when implementing the constant dividend growth model, the dividend growth rate should be assumed to be at a constant pace of growth and the growth rate should be relevant to the market growth rate.

In addition, this model can not only be used in estimating cost of capital, but also in calculating the retirement funds. In advance, constant dividend growth model can also be applied in scenarios related to investments of the corporations, financing-related cases and valuation using mathematical models. Valuation error must be centered so as to maximize the accuracy of future value of capital stocks. Yet, not every company can apply this model in calculating their future stock values.

In the condition whereby the dividends grow in a non-steady rate, the variable dividend growth rate should be implemented. This model might be more complicated than constant dividend growth model, but it is more sensible than constant growth dividend model. As for both constant dividend growth model and variable dividend growth model, both are facing the similar limitation that is both require estimation of future dividend growth rate. This condition has eventually increases the risk for the company on its capital cost.