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# Free Example of Earnings Statistics Essay

The connection between dividend policy and stock price volatility has been investigated by the application of multiple least square regressions. The regression approach used provides with a connection involving price volatility and the main measures of dividend policy. These are a dividend payout ratio as well as the dividend yields (Walter, 1963). A number of control variables have been included to account for particular factors that have a direct effect on dividend and stock price volatility- in terms of earnings volatility, firm size, and asset growth.

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The model was evaluated on an annual basis over a period of 10 years in order to determine the periodic consequences of dividend policy on stock price volatility. Multiple regression analysis has been used to describe the relationship, and a correlation analysis was done to analyze the variables. Initially, the regression analysis involved price volatility as the dependent variable in relation to other payout ratio and the dividend yield, which represent the independent variables (Ross, Westerfeld & Jaffe 1996). This enabled obtaining of a crude test for the relationship involving dividend policy and share price volatility with the equation:

The analysis has shown that there exists a negative relationship between the dividend yield and dividend payout and share price volatility. A positive relationship has been reported between share price volatility and dividend payout (Petit 1972). The close proportionality between dividend payout ratios is considered to be less problematic, since there are numerous factors that affect both dividend policy as well as price volatility. In order to minimize these difficulties, a number of control variables were incorporated in the process of analysis. The regression of the dependent variable was done compared to the two independent variables and the control variables in the regression equation:

(Modigilani 1982).

### 2. FTSE Guide to UK Calculations

This part of the paper describes the methods of index calculation, which enable users to replicate the indices in order to assist them in their trading purposes. It is also useful in helping users get an understanding of the component factors that affect the performance of indices.

#### 2.1. Statement of Principles

There are certain principles, which are useful in the calculation of the indices.

One of the principles is that the indices are calculated for use in the calculating investment approaches as an evaluation of portfolio performance for prospective investors in various fields such as insurance companies and investors in the institutions (Miller & Modigliani 1961). The other principle is that the calculations are based on declared dividends. Furthermore, the indices should be replicated by users. The method of calculation should not be complicated, and the data used should not be easily available (Lintner 1956). In addition, it recommends the use of mainly historic data in index calculation.

The user also requires that the data used in the indices should be from an authoritative source (Lintner 1962). The data can be obtained from the published materials such as audited accounts and public institutions that are used with minimal corrections.

#### 2.2. UK Index Calculation Methods

The FTSE Actuaries Share Values for the UK are the arithmetic values, where the exact values represent the market value of each company (Kinder 2002). The price index represents the sum of market values of the index. The value for each company is weighted based on its market values, where shares-in-issue are multiplied by the price of each share and investability rate that is fundamentally 1.00 (Guo 2002). Therefore, the index will be affected by the price movement of a large company compared to a smaller company.

The formula for the index calculation is elaborate. On the contrary, there are a lot of complexities in calculating the capitalization of each company’s component and determination of capitalization adjustments in the index (Gordon & Shapiro 1956). The index value is a numerical value that represents the overall market value of corporation in the index during a particular period of time in comparison with similar estimation at a starting point (Fama & French 2001). In order to calculate the daily index value, the total market value of all companies is divided into a number called the divisor. The divisor is usually an arbitrary number selected at the point of the index in order to find the staring values for the index such as 100.00. An adjustment of the divisor is made, when amendments of capitalization are made to the components of the index enabling the value of the index to be comparable with time (Easterbrook 1984).

The formula for the index value calculation is shown:

The following point is the example of a calculation method. These calculations have been used as the examples, and rounding of numbers has been done for the purpose of simplicity. The actual calculation of indices is done with the most accurate significant figures (Drury 2008).

 Company Share Price (p) Shares-in-Issue (m) Free Float Factor Market Value (£m) A corporation 270.0 61443 1.00 165,896.10 B corporation 605.0 22579 1.00 136602.95 C corporation 698.0 9229 1.00 89336.72 Total  Market Value 391835.77

The starting value of the index is set at, say, 100.0

The procedure for calculation of the index divisor is the following:

Using the data above, we calculate the index divisor as following: 391835.77/100

= 3918.36

The next step involves calculation of the constituent companies’ capitalization on the end date. The data below provides the samples for calculation (Black 1976).

 Company Share Price (p) Shares-in-Issue (m) Free Float Factor Market Value (£m) A corporation 283.0 61443 1.00 173,883.10 B corporation 588.0 22579 1.00 132764.52 C corporation 945.0 9229 1.00 87214.72 Total  Market Value 393862.26

The Index value at the end date is calculated as following:

Index Value =

= 100.5

Value of Index at:

• Start Date = 100.0
• End Date = 100.5

### 2.3. Dividends and Earnings Statistics

A variety of statistics on the subject of earnings and dividends on FTSE Actuaries UK Share Values is publicized by the Financial Times on a daily basis.

##### 2.3.1. Dividend Yield

They are mainly used to measure income return on a stock. Data is obtained from the company announcements service of the London Stock Exchange as well as other public company information. A free float adjustment is applied to the dividend yields. The dividend yield of each company is used to produce ‘actual yield’ (Battacharya 1979).

Dividends published before 16.30 hours are included in the dividend yield of a particular day (Baskin 1989). Additional announcements after this time are transferred to the following day with corrections made for the current dividends. If the announcement of dividends is in the other currency than sterling, the 16.30 hour WM Reuter’s closing rate on the day of dividend declaration is applied to convert the dividend into sterling.

##### 2.3.2. Earnings Calculation

Earnings are considered to be the important elements in valuation of the companies. The use of earnings in estimation of statistics on FTSE Actuaries is based on published data from the company. Initially, there were small adjustments to such data (Al-Najjar & Hussainey 2009). On the other hand, the accounting procedures have become complex and based on objects in the past years.

The tax adjustment for a number of earnings is obtained from the company’s most recent assessed report and accounts with all tax liabilities required to be paid as well as tax credits expected to be fully received for the present year taking into consideration determination of corporate profit for that particular year (Al- Malkiwi 2007).

The earnings data for FSTSE Actuaries UK Share Indices are determined on the basis of ‘as reported’. That is to say, they indicate the reports from last year’s earnings. This is different from the most of calculations by brokers that are calculated on the basis of ‘as earned’ grounded on the most current forecast earnings (Allen&Rachim 1996). This results into a range of time differences between the two values, particularly at the times of economic conditions, where there are considerable upward or downward movements in earnings. Furthermore, losses are included in the calculations of the FTSE Actuaries UK Share Indices.

##### 2.3.3. Tax Adjustments to Earnings Arising from IIMR Guidelines

When a company publishes the tax results of each item in the report and accounts, they will form the foundations for any tax adjustments to be made (Walter 1963). In the case, when a company does not make any particular disclosure, but there is a need to make adjustments, the guiding principle will be to implement the average rate of tax on FRS3 gains to any achieved corrections  (Ross, Westerfeld & Jaffe 1996).

The dividend cover represents the ability of a company to meet the payments based on its present earnings. The traditional method for the calculation of dividend earning is the following:

Price-earnings ratio (P/E ratio) is the illustration of the price investors, who are able to pay in relation to the company’s earnings (Ross, Westerfield & Jaffe 2008). The calculation of the ratio is based on net earnings, which are founded on calculations of using formula known as IIMR Headline Earnings and represents the entire market value of all company components divided by the net earning summation sof the constituent indices. Script issues in every respect to cash dividends are regarded as the bonus issues and are not totaled in the dividend yield estimations (Petit 1972). The addition of shares to the index takes place on the ex-date.

Cash dividends with particular alternatives are considered to be completely taken as cash and, consequently, the XD corrections adopted for the overall amount are implemented. Any share matters are included to the index, when they are listed based on the 1% rule.

If the company pays a special dividend, the market capitalization of that company is corrected by the amount of dividends, and the sum of market capitalization will be reduced proportionally (Parkinson 1980). Adjustment is done on the index divisor in order to ensure that the constant index vale is maintained.

##### 2.3.4. Total Returns

The introduction of total returns took place in 1993. By the use of price and total price indices, investors are able to get the right approach towards the capital performance and reinvested income returns (Modigilani 1982).

This is the value of dividends declared by the component organizations on the XD date and expressed in the index points. These adjustments are done for FTSE Actuaries UK Share Indices and published on a daily basis in the FT regularly for each financial year. XD corrections are calculated on the basis of declared dividends. The following formula is used to calculate the XD adjustments:

The companies, which declare dividends in different currencies from the Sterling, use the equivalent published Sterling if it is available. If there is unavailability of Sterling equivalent, there will be the conversion of dividend into Sterling by the use of WM/Reuters 4PM rate prior to the conversion of stock into XD (Miller& Modigliani 1961).

Based on the previous case, if A PLC and B PLC have declared dividend payments from today as the XD date, the calculation will be as it is shown in the table below.

 Company Dividends (p) Shares (m) Market Value (£m) Free-Float Factor Xd adjustment (points) A PLC 12.56 62445 7804.8 1.00 1.96 B PLC 14.01 22567 3061.0 1.00 0.82 Total XD adjustments                                                                                                2.78 Index divisor = 10865.8

The technique for the calculation of XD adjustments is based on the use of the divisor at the end of the financial year on the preceding day following implementation of any capitalization changes. In the case, when the organization has more than a single line of shares incorporated into its indices, the separate calculation of XD is done on each line (Lintner 1956). On the other hand, if an eligible secondary line is much insignificant to be included in the indices, the calculation of XD adjustments is based on dividends issued on the main line and the overall share weighting.

##### b. Calculation of Total Returns Indices (TRIs)

Total Returns Indices determine the overall return of the main indices, combining both capital outcome and ploughed back income (Lintner 1962). The TRIs are determined using the declared dividends. Despite the existence of delay time between the XD date and the reception of dividends, it is preferable to assume all revenues spent on the XD date in the place of complications in view of a time lag prior to reinvestment of the declared dividends.

The calculation of TRI takes place in real time on a daily basis. This calculation varies based on whether dividends are declared on a particular day (Guo 2002). The following table and procedure represents the method for the calculation of TRI.

Calculation of TRI

 Capital Index (CI) Xd Adjusts (xd) TRI Day 1 3190 - 1000.00* Day 2 3200 - 1003.14 Day 3 3220 5 1010.97

In the case, where there is no occurrence of XD values:

Where there is occurrence of XD adjustments:

In testing the relationship between dividend policy and share price, the study was conducted in two perspectives: the management and shareholders. The reason is that management needs the retention of profit in order to ensure satisfaction of the long-term company needs such as investment and liquidity requirements (Grinblatt, Masulis & Titman 1984). This puts emphasis on the retention of dividends configuration instead of dividends only. This configuration varies across companies on the basis of circumstances surrounded the activities of such a company.

On the contrary, the shareholder’s priorities are dependent on their income level, which was contributed by many factors such as tax effect. The results into the tendency of shareholders to invest in the firms, whose dividend policies match their preferences (Fama & French 2001).

This is accompanied by the hypothesis that dividend policy affects share prices of the firm. The utility function represents a function, which optimizes the market value of the firm (Easterbrook 1984). The market value of the firm is represented in such a way:

In keeping with the initial research, the following control factors were used during the study:

• Size: There exists a link between size of the market and market value. It was based on the fact that small companies do not apply extensive diversification in their operations and are not thoroughly scrutinized by the investors. Information regarding the stocks of smaller companies can be less updated and illiquid in nature. Since the small companies are the subject of bigger changes in prices due to the above conditions, it was necessary to include a size control variable.
• Liquidity: There is a connection between liquidity of dividend policy and market value (Easterbrook 1984). The companies that have low liquidity are expected to be less able to increase operations in new investments and are not able to increase their dividends, resulting into less scrutiny of the investors in the company. Such companies are the subject of bigger changes in prices as a result of the above contributed factors. Hence, it is necessary to introduce a liquidity control variable.

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