In the literature review, that is, the previous chapter, studies on the two valuation models were scrutinised. In this chapter, the valuation models namely Dividend Discount Model (DDM) and the Price Earnings Ratio model (PER) will be presented. The methodology that will be used in the study will be systematically presented from the derivation of the models to the calculation of each variable that will be used. These models aim to compute the intrinsic values of the companies that are listed on the 'Banks & Insurance' sector of the Stock Exchange of Mauritius (SEM) namely:
Companies
Mauritius Commercial Bank
MCB
Mauritian Eagle
MEI
Mauritius Leasing
MLC
Mauritius Union
MUA
State Bank of Mauritius
SBM
Swan Insurance
SWAN
Table 1: Banks & Insurance (SEM)
As mentioned earlier, the main aim of this study is to compute the intrinsic values of the six companies listed above. Thereafter, these intrinsic values will be compared to the respective quoted market prices of the six companies of the Banks & Insurance sector of the SEM. Theoretically, if the computed intrinsic values are greater than the quoted market prices, this will imply that the share value is underpriced. Otherwise, if the quoted market prices are greater than the computed intrinsic values, thus implying that the share value of the companies is overpriced. In the end this analysis will help to ascertain whether shares are being correctly valued or not. Furthermore, this information will prove to be useful for the stakeholders of the company as it may predict market prices and even determine whether market prices give a fair view of the companies' performance. Existing and even potential shareholders will want to know whether they are buying or selling the shares at the right price. This analysis may prove to be useful to the companies in their strategic planning and decision making.
Dividend Discount Model
Constant Growth Dividend Discount Model
The dividend discount model (DDM) is used for determining the value of a common stock with a constant growth rate for the dividends. In other words, dividend payments are expected to grow at a constant rate forever. We can express all the future dividends in terms of the upcoming dividend (D0) as follow:
Thus the following equations will be obtained.
The advantage of doing so is that the formula for the common stock's intrinsic value can be simplified as follows:
The DDM represented by the formula above (i.e. constant growth rate) is known as the constant growth DDM or the Gordon growth model.
Estimation of the Annual Dividend Growth rate (g)
There are a few things that must be taken into consideration before using the constant growth DDM to estimate the value of a common stock. The model is only suitable for stocks that have a growth rate that is lower than the required return. In order to estimate the growth rate in dividend the historical dividends will be used. Using the point-to-point estimation method, which is based on the first and last dividend of the growth period, the growth rate of the dividend during that period will be estimated as follows:
Actual Dividends paid by MCB
Year
2005
2006
2007
2008
2009
2010
DPS (Rs)
1.9
2.12
2.9
4.55
5.25
5.25
Source: MCB Annual Reports
Actual Dividends paid by MEI
Year
2005
2006
2007
2008
2009
2010
DPS(Rs)
4.75
4.75
0.75
1.83
1.83
1
Source: MEI Annual Reports
Actual Dividends paid by MLC
Year
2005
2006
2007
2008
2009
2010
DPS(Rs)
0.01
0.01
0.02
0.04
0.03
0.03
Source: MLC Annual Reports
Actual Dividends paid by MUA
Year
2005
2006
2007
2008
2009
2010
DPS(Rs)
0.84
3.4
3.5
3.9
9.4
4.4
Source: MUA Annual Reports
Actual Dividends paid by SBM
Year
2005
2006
2007
2008
2009
2010
DPS (Rs)
1.3
2
2.1
2.55
2.75
2.75
Source: SBM Annual Reports
Actual Dividends paid by SWAN
Year
2005
2006
2007
2008
2009
2010
DPS(Rs)
5
5
5.5
6
7
7.7
Source: SWAN Annual Reports
Computation of the Cost of Equity (K)
In order to estimate the cost of equity (K) the Capital Asset Pricing Model (CAPM) will be used where
K = Rf + Bi (Rm + Rf )
Where K is the expected cost of equity
Rf is the risk free rate of return
Rm is return on equity on the market
Bi is the company's systematic risk.
Calculation of the risk free rate of return (Rf)
The weighted average Treasury Bill rate for the Government of Mauritius with maturity of 364 days is being used as a proxy for the risk free rate (Rf). This risk free rate will be estimated by taking the average of all the weighted Treasury Bill rates from 2005 to 2010.
Weighted average Treasury Bill rate (364 days)
Year
2005
2006
2007
2008
2009
2010
Weighted average Treasury Bill rate
6.23
7.46
11.63
9.25
7.61
4.63
Source: Bank of Mauritius Annual Reports
Where x is the sum of all the weighted average Treasury Bill rate
n is the number of years from 2005 to 2010.
Calculation of the return obtained on equity on the stock market (Rm)
For the calculation of the return on the market the Stock Exchange of Mauritius Total Return Index (SEMTRI) will be used. The principal objective of the SEMTRI is to provide investors an important tool to measure the performance of the local market. The SEMTRI provides an indication for capital gain/loss and gross dividends on the SEM. Using the SEMTRI Rm can be calculated as follows:
Where SEMTRI DEC 2010 is the closing month end figure for SEMTRI at December 2010
SEMTRI DEC 2005 is the closing month end figure for SEMTRI at December 2005
n is the number of years from 2005 to 2010.
Calculation of the company's systematic risk (Bi)
The betas of the companies will be calculated by taking the daily returns in the market quoted share prices and using the daily returns from the SEMDEX as the benchmark. The betas will be calculated using EXCEL (Please refer to Appendix ..). Hereunder is a table showing the betas of the respective companies.
BETA
R2
MCB
0.9805
0.8904
MUA
0.5731
0.2558
SBM
1.2447
0.8900
SWAN
0.5847
0.4043
Two-Stage Dividend Discount Model
The constant dividend growth model is only suitable for determining the value of stocks of an established company. The model will only work when:
(1) the growth rate is constant and
(2) the growth rate is less than the required return.
The previous model i.e. the constant growth model can be modified and changed into a two-stage model. The first stage is considered the abnormal growth stage, where the company is experiencing a rapid growth . The second stage is where the company matures and its growth rate has slowed. It is assumed that the company will sustain that lower growth rate indefinitely.
Abnormal growth stage
If the company goes through the abnormal growth stage for T periods. The present value of all the dividend payments in the abnormal growth stage can be calculated as follows:
Thus, if, the dividend payments are approximated based on the estimated abnormal growth rate (ga) the above formula will be as follows:
Constant (or normal) growth stage
In the normal growth stage, the dividends are assumed to grow at a constant rate (gn) indefinitely. Therefore, we can use the constant growth dividend discount model to estimate the value (PVn) of the stock in time T.
Once again, it often time necessary to estimate the DT+1 based on the prior dividend (DT). But here the dividend will now be growing at the normal rate as this is the normal growth stage. The formula for the value of the stock in the constant growth stage (in time T) is as follows:
Now, to determine the present value of the stock at time 0 (i.e. the current period):
Total value of a two-stage growth stock
The value of a two-stage growth stock is simply the sum of its present value in the abnormal growth stage and the present value in the normal growth stage:
In the above model, it has been assumed that the required return for the stock is the same for both the abnormal and constant growth stages. However, investors are very likely to have different returns for the two stages. Since company generally faces more risks during its abnormal growth stage, investors will require a higher return during this stage. On the other hand, the company is maturing during the normal growth stage and thus faces less risk. As a result, investors are also demanding a lower return during this stage.
Estimation of the growth rates for the two different periods.
The growth rate for the two different periods will be calculated in the same manner as it was calculated previously for the Constant Growth Dividend Discount Model. However, the time period which was previously 10 years for the Constant Growth Dividend Discount Model, will now be divided into two. The first 5 years will be the abnormal growth stage and subsequently the remaining 5 years will the normal growth stage. Hereunder a table indicating the growth rates for the respective companies and periods is presented.
2000-2004 (ga)
2005-2009 (gn)
MCB
6%
10%
MUA
10%
9%
SBM
13%
12%
SWAN
8%
9%
Calculation of the cost of equity (k) for Two Stage Dividend Discount Model
The same cost of equity that was used for the Constant Growth Dividend Discount Model will be used for the Two Stage Dividend Discount Model. In the current model the cost of equity is assumed to be the same for the two different periods.
Price to Earnings Ratio
Another approach to identifying desirable stocks is the use of the P/E ratios (or price-earnings multiples), which is very common among many investors.
Unlike the dividend discount model, there is really no clear-cut answer on what the size of a P/E ratio should be in order for a company to be considered as a good investment. It depends on the investor's investment philosophy. Regardless of your investment philosophy, it is important for you to understand how the P/E ratio of a company is determined and what are some of the factors that influence it.
Deriving the P/E Ratio
This is quite simple as the P/E ratio is obtained by dividing the price per share by earnings per share. However, in order to know what influences the P/E ratio, the constant growth dividend discount model will be used. The formula for the original model is as follows:
The future dividend, D1 = (1-b)E1, where b is the retention rate and E1 is the earnings per share in time 1, when integrated into the above model will be as follows:
By manipulating the formula and the following results will be obtained:
If there is no retained earnings (i.e. b = 0), therefore, the company is not investing in any new projects and will not be growing (i.e. g = 0). Consequently, the P/E ratio of a no growth company is simply:
Referring to the previous model, the following term of a company's P/E ratio represents its growth potential:
Growth potential
For a mature company to grow, it has to have a positive growth potential. Therefore, the following conditions must hold:
First the required return must be greater than the growth rate. (k > g)
And secondly, in order for a company to have a positive growth potential, the company will have to invest in projects that generate returns (ROE) that is greater than the investors' required return. If ROE is less than k this implies that the return from the new projects is less than the investors' required rate of return. In such a situation, it is better for the company to simply distribute all the earnings as dividend payments rather than retaining all or part of it for new projects. (g - kb > 0  b(ROE)- kb > 0  ROE > k)
Data sources and sampling
