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Gordon Growth Model for Equity Valuation

Assumptions in the model:

1. The firms dividends will grow abruptly in the first five years then at a constant rate thereafter.2. The firms capital structure is known and constant.


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The Model:

The Gordon Growth Equity Valuation Model

Company Name HERI de ELIJAH Sdn. Bhd. (Name)

First Period Dividend (D0) $ 1.50 (In currency)

Growth rate for the first 5 years (g1-5) 20% (In percentage)

Growth rate after 5 years (gp) 5% (In percentage)

Required Rate of return (Ks) 25% (In percentage)

Time 0 1 2 3 4 5 (Years)

Dividend $ 1.80 $ 2.16 $ 2.59 $ 3.11 $ 3.73 (In currency)

Terminal Value $ 19.60 (In currency)

Total Cash Flow $ 1.80 $ 2.16 $ 2.59 $ 3.11 $ 23.33 (In currency)

Present Value $ 1.44 $ 1.38 $ 1.33 $ 1.27 $ 7.64 (In currency)

Equity value $ 13.07 (In currency)

Estimated Share Price $ 19.60


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Outputs of the model:

Estimated dividend in Year 6 $ 3.92

Estimated Share Price (P) $ 19.60

Market valuation model using free cash flows of the firm for equity valuation

Assumptions in the model:

1. The firms free cash flow would form a level of perpetuity beginning in year 5 (2015).2. The firms capital structure is known and constant.3. The industrys cost of capital is constant at 12%.4. The chargeable tax rate is 35%


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The model:

FREE CASH FLOW CORPORATE VALUATION MODEL

Company Name: Heri de Elijah Sdn. Bhd.

Inputs:

Sales for 2010 (Year 0 sales) $ 300,000.00

Sales growth rate from year 1 - 4 10%

Operating profit margin ratio 20%

Net working capital to sales ratio 12%

Fixed assets to sales ratio 19%

Tax rate 35%

Cost of capital 12%

Number of outstanding shares 20,000

Current liabilities $ 4,000.00

Market Value for Preference shares (Par value $ 1) $ 9,900.00

Years 2010 2011 2012 2013 2014 2015

Time 0 1 2 3 4 5

Sales $ 300,000.00 $ 330,000.00 $ 363,000.00 $ 399,300.00 $ 439,230.00 $ 439,230.00

Operating Income (EBIT) $ 66,000.00 $ 72,600.00 $ 79,860.00 $ 87,846.00 $ 87,846.00

LESS: Tax $ (23,100.00) $ (25,410.00) $ (27,951.00) $ (30,746.10) $ (30,746.10)

Net operating profits after tax (NOPAT) $ 42,900.00 $ 47,190.00 $ 51,909.00 $ 57,099.90 $ 57,099.90


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Less Investments:

Investment in Net Working Capital $ (3,600.00) $ (3,960.00) $ (4,356.00) $ (4,791.60)

Capital Expenditures $ (5,700.00) $ (6,270.00) $ (6,897.00) $ (7,586.70)

Free Cash Flow (FCFs) $ 33,600.00 $ 36,960.00 $ 40,656.00 $ 44,721.60 $ 57,099.90

Terminal Value $ 475,832.50

Total Cash flows $ 33,600.00 $ 36,960.00 $ 40,656.00 $ 520,554.10

Present Value of FCFs $ 30,000.00 $ 29,464.29 $ 28,938.14 $ 330,821.54

Company's Intrinsic Value

Total Present Values $ 419,223.96

Less:

Current liabilities of the firm $ (4,000.00)

Market value of preference shares $ (9,900.00)

Intrinsic Value $ 405,323.96

Shares Outstanding 20,000.00

Estimated Share price $ 20.27

Outputs of the model:

Estimated Share Price $ 20.27


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Portfolio Consisting of Assets from Procter & Gamble and Unilever

Introduction

The two assets that are selected to illustrate this model where Procter and Gamble (P&G) and

Unilever. These two companies are the leading producers in consumer goods in the world. P&G

ranks the first while Unilever is second after P&G took the peak in 2005 after acquiring Gillette

Company.

Therefore these companies are from the same industry which makes the task of comparing and

analyzing its assets less cumbersome as the nature of the markets and economy would affect both of

them in the same severity.

In this model 40% of the investment is given to Unilever while the remaining 60% is allocated in

Procter and Gamble. The data are obtained from yahoo finance website and filtered from January

2006 to June 2011.

Assets Returns

Using the data in appendix C the following statistical values were obtained for both Procter and

Gamble and Unilever.

Asset Returns

Unilever Procter & Gamble

Mean (Average) Return 0.82% 0.36%

Variance 0.00429 0.00227

Standard Deviation 6.55% 4.77%

Covariance 0.001603

Correlation Coefficient 0.513151

Mean (Average) Return:

The average return measures the return that an investor is likely to obtain by investing in each stock.

The higher the average returns the better the stock in terms of return. Despite Unilever having higher

share prices as compared to P&G; P&G has higher average return than Unilever. The figures


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obtained above show that investing in P&G is likely to provide the investors with higher rate of

return as compared to investing in Unilever since the return from P&G is more than two times than

that of Unilever.

Variance and standard deviation:

The variance and standard deviation figures measure the level of riskiness of each asset. The higher

the value the riskier the investment it is. From the figures obtained it can be concluded that P&G is a

riskier investment as compared to Unilever. Both the variance and standard deviation measures are

higher in P&G assets as compared to those in Unilever.

This result supports the theory which states that the higher the risk the higher the rate of return

also. Citation. Therefore despite P&G shares being very attractive in terms of the expected return

but also it can make the risk averse investors not to invest as a result of its riskiness.

Correlation coefficient:

Sengupta C, 2010 defines the correlation coefficient value is a statistic that measures the degree to

which two sets of data vary together. Looking at the correlation coefficient between P&G and

Unilever which is 0.51315 it suggest that the two assets are positively correlated to each other.

Moreover, the figure 0.51315 suggests that the strength of the correlation is just moderately strong.

The correlation is positive moderately correlation because the two stocks come from the same

industry. As seen earlier both P&G and Unilever are worldwide consumer goods producers. This

suggests that their exposure to risk and levels of return is likely to be very similar in the sense that if

the economy or the general conditions does not favor the demand for consumer goods in the market,both P&G and Unilever will be affected because they all produce consumer goods. On the other hand

if the market is going to favor the supply of consumer goods, the benefits are likely to be shared by

both P&G and Unilever.

This is an indication that the share prices movement for the two assets will go in the same direction

at most times. When the share price of P&G goes up so will the share price of Unilever as well.


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Covariance:

Financial-dictionary defines covariance as a measure of the degree by which the returns on two risky

assets move in tandem. A positive covariance means that the assets returns move together while a

negative covariance means the assets returns move inversely to each other. Looking at the covariance

between P&G and Unilever which is 0.001603 it suggests that the two assets are moving in the same

direction to each other in the sense that when the prices of P&G increases so does the prices of

Unilever.

This again is the result of having 2 assets in a portfolio whereby both assets are from the same

industry. This suggests that this is not a good portfolio since the portfolio holder is not able to

diversify the portfolios diversifiable risk by holding a portfolio with a positive covariance.

Therefore, using the covariance measurement one should make sure that in the portfolio held the

covariance is negative; which is a sign that the investor is able to minimize the diversifiable risks to a

possible minimum.

Portfolio Returns

Portfolio Returns

Using assets Returns Using Portfolio Return

Expected Portfolio Return 0.55% 0.55%

Portfolio Standard Deviation 4.77% 4.77%

Expected Portfolio Return:

The expected portfolio return is the return that an investor is likely to obtain when he decides to

invest in different assets at a certain weight for each. When 40% of the funds are invested in P&G

while 60% in Unilever, the Expected portfolio return will be equal to around 0.55%. This return is

significantly lower than the mean return from P&G asset itself but it is also quite high if compared to

Unilevers average return. Nonetheless, the portfolio expected return will be of different value if the

weights distributed to each stock were different.


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Standard Deviation of Portfolio:

The portfolio standard deviation is the level of riskiness that an investor is likely to face when he

decides to invest in different assets at a certain given weight for each asset. When an investor decides

to invest 40% of his funds in P&G and the remaining in Unilever the standard deviation will be

4.77%. This level of riskiness is very low as compared to that of P&G which was 6.55%; but it is the

same level of riskiness as that of Unilever. This implies that when an investor decides to invest in

two different assets his risk will definitely reduce.

Again these findings support the idea of holding a portfolio rather than holding one stock only. The

portfolio theory suggests that by holding a portfolio an investor is entitled to an average return of the

component stocks but a lower than average risk level. As seen from the scenario; by investing in a

portfolio consisting of assets from both Unilever and P&G the expected return is lowered to only0.55% but the level of risk is also lowered to 4.77%. Therefore one will enjoy an average amount of

return at a lower risk level when he decides to hold a portfolio instead of holding only one stock.

Conversely, if the correlation coefficient between P&G and Unilever was negative the impact of the

portfolio would have been more profitable. If the correlation was negative the average return would

decrease to just average but the standard deviation (which measures the risk level) would reduce to a

figure way below any of the stocks level of risk.

Therefore, the best idea of investing in a portfolio is to ensure that the two portfolios are from two

different industries (such as one from banking and another one from consumer goods) which ensure

that the correlation between the two sides is negative or positively weak and the level of risk will

reduce tremendously once the portfolio theory is applied. Investing in a portfolio with a high positive

correlation will just ensure that the investor gains an average return at a slightly lower level of risk.

Construction of an Efficient Frontier

The efficient frontier was constructed by altering the proportion of funds that was invested in the two

portfolios. By changing the weight of Procter and Gamble, which automatically changes that of

Unilever by (1 weight of P&G), the efficient frontier below was obtained using the new portfolio

standard deviation and the portfolio expected return.


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The efficient frontier above shows the trend of both the level of risk and return at different levels of

weights investments in the portfolio. The frontier shows that by increasing investment in Procter and

Gambles assets and reducing that in Unilever will lead to a decrease in the level of portfolio risk at

first while the returns will be growing up; however in the future the level of portfolio risk will start

going up while still maintaining an increase in the expected portfolio return level.

The efficient frontier helps to describe what combination of assets several people will consider

taking into consideration their perception towards risk.

An investor who is a risk averse person will consider investing at point A in the efficient frontier

whereby the portfolio will have 20% of funds in Procter and Gamble while the remaining 80% in

Unilever. At this combination the investor will bear the lowest possible risk level of 4.63% while

accepting an average return of only 0.46%. Since the person is very risk conscious he will be happy

investing at this point since it allows him to incur a very low amount and rate of risk.

Conversely, if an investor is an average risk taker he will invest at point B. An average risk taker is

an investor who can bear a higher risk only if it promises a higher return. Investing at point B means

having 40% of the funds in Procter and Gamble whilst the remaining 60% in Unilevers assets. At

point B, an investor will incur a risk level of 4.77% which is exactly the same as if he only investedin Unilever only but the return will be higher as compared to the later scenario. If an investor puts all

0.30%

0.40%

0.50%

0.60%

0.70%

0.80%

0.90%

4.00% 4.50% 5.00% 5.50% 6.00% 6.50% 7.00%

PortfolioExpectedReturn

Portfolio standard Deviation

Efficient Frontier

Wp = 0.0Wu = 1.0

Wp = 1.0

Wu = 0.0

A

B


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his funds in Unilever he will gain a return of 0.36% but at point B the expected return is 0.55%.

Therefore as an average risk taker since there is a higher return at point B but the same risk level, he

will definitely consider investing 40% in P&G.

On the other hand if an investor is a high risk taker he will consider investing at any point after point

B in the efficient frontier. At this region the amount invested in Procter and Gamble will be higher as

compared to that invested in Unilever. After point B the level of riskiness of the portfolio increases at

an increasing rate and so does the expected rate of return. Therefore an investor who is quite a risk

taker will consider investing his portfolio at this region bearing in mind that the expected return on

the portfolio will be higher also.

Estimation of Beta and Intercept

By comparing P&Gs return and Unilevers return against the SP 500 return, the scatter diagrams

below were drawn to portray the relationship between the two stocks returns with that of the market.

On the scatter diagrams seen below the trend lines are drawn in the form of Y = a + bX, whereby by

a is the intercept and b is the beta of the stock.

Brigham, E., Houston J, (2010) defines beta as a metric that shows the extent to which a given

stocks returns move up and down with the stock market. Beat thus measures market risk. The slope

of the lines drawn on each of the scatter diagrams is the beta for each stock. The higher beta value or

the steeper the slope of the trend line the riskier the stock is since a stocks beta reflects its

contribution to the riskiness of a portfolio. Therefore, because a stocks beta coefficient determines

how stock affects the riskiness of a diversified portfolio, beta is the relevant measure of a stocks

risk.

On the other hand, the intercept measures the alpha coefficient of the investment. Financial-dictionary elaborates alpha as the mathematical estimate of the return on the security when the

market return as a whole is zero. Furthermore, the alpha value measures the performance of the

portfolio after adjusting for risk. Therefore, it has been cited out by several researchers and authors

that the alpha coefficient is normally zero in an efficient market; however when the value is less than

zero it signifies that investment has earned too little for its risks whilst when the value is positive it

means the investment has a higher return than the investment risk.


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From the figures above the following estimates were obtained:

Estimated Beta (b) for Procter and Gamble = 0.484

Intercept (a) for Procter and Gamble = - 0.0036%

Estimated Beta (b) for Unilever = 0.587

Intercept (a) for Unilever = - 0.0017%

Y = 0.484X - 0.0036R = 0.393

-20.00%

-16.00%

-12.00%

-8.00%

-4.00%

0.00%

4.00%

8.00%

12.00%

-24.00% -14.00% -4.00% 6.00% 16.00% 26.00%

PnG Return vs SP 500, 2006 - 2011

Y = 0.587X - 0.0017R = 0.307

-20.00%

-15.00%

-10.00%

-5.00%

0.00%

5.00%

10.00%

15.00%

-15.00% -10.00% -5.00% 0.00% 5.00% 10.00% 15.00%

Unilever Return vs SP 500, 2006 - 2011


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Based on the findings from the two scatter diagrams earlier it can be seen that the changes of Procter

and Gambles stock is less dependent on the market movement as compared to the stocks of

Unilever. Therefore Unilevers stock will be regarded to be riskier as compared that of Procter and

Gamble since the beta value of Unilevers stock of 0.587 is larger as compared to that of P&G which

is only 0.484. If the market return falls by lets say 10% due several economic factors such asinflation, the return of Unilever will fall by 5.87% whilst the return of Procter and Gamble will fall

by only 4.84%; which means the fall of Unilevers return will be higher as compared to P&Gs

returns fall. On the other hand if there is a rise in the market return during the boom period,

Unilevers return will rise by 5.87% while that of P&G will rise by only 4.84%. This indicates that

Unilevers stock is more volatile as compared to P&Gs hence Unilever will be riskier.

Conversely the intercepts for both stocks indicate that the performance of the stock has been poor to

date. The intercept for P&G is -0.0036 while that of Unilever is -0.0017 which are all less than zero

which suggests a poor performance of the stocks. In other words the investment in both P&G and

Unilever is very risky whilst their returns are not sufficient to compensate the investor for the risk

assumed. In conclusion, despite the good levels of expected returns that can be seen from each stock

and together in a portfolio, the risk position for each stock is very much in excess hence making the

stocks unattractive to risk-averse investors.

Moving averages & Technical analysis

References

http://financial-dictionary.thefreedictionary.com/Covariance

http://financial-dictionary.thefreedictionary.com/Alpha

http://stockcharts.com/school/doku.php?id=chart_school:technical_indicators:moving_averages
http://financial-dictionary.thefreedictionary.com/Covariancehttp://financial-dictionary.thefreedictionary.com/Covariancehttp://financial-dictionary.thefreedictionary.com/Alphahttp://financial-dictionary.thefreedictionary.com/Alphahttp://stockcharts.com/school/doku.php?id=chart_school:technical_indicators:moving_averageshttp://stockcharts.com/school/doku.php?id=chart_school:technical_indicators:moving_averageshttp://stockcharts.com/school/doku.php?id=chart_school:technical_indicators:moving_averageshttp://financial-dictionary.thefreedictionary.com/Alphahttp://financial-dictionary.thefreedictionary.com/Covariance


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Brigham, E., Houston J, (2003), Fundamentals of Financial Management, 10th Edition, Thompson

South Western, United States of America

Brigham, E., Houston J, (2010),Essentials of Financial Management, 2nd Edition, Cengage Learning

Asia Pte Ltd, Singapore

http://www.stock-market-strategy.com/education/technical-analysis/moving-averages-ma/

http://www.learn-stock-options-trading.com/moving-average-analysis.html
http://www.stock-market-strategy.com/education/technical-analysis/moving-averages-ma/http://www.stock-market-strategy.com/education/technical-analysis/moving-averages-ma/http://www.learn-stock-options-trading.com/moving-average-analysis.htmlhttp://www.learn-stock-options-trading.com/moving-average-analysis.htmlhttp://www.learn-stock-options-trading.com/moving-average-analysis.htmlhttp://www.stock-market-strategy.com/education/technical-analysis/moving-averages-ma/


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