Sensitivity Analysis

b) Sensitivity analysis is an extended application of SVA, which used to measure and rank value drivers according to their degree of influence. It is obtained by changing the inputs to see the corresponding changes in the dependant variable. Here the dependant variable is the share price and the inputs are sales growth, corporation tax rate and profit margin

Table1. Sensitivity Analysis of Sales growth (g), Corporation Tax rate (T) and profit Margin (m) to share price (s).


Sales Growth Rate (g)

Corporate Tax rate (T)
Operating Profit Margin (m)
Share price
(s)
Percentage Change (%) in (s)

Initial Case

4%
30%
7% increasing 2% every year
0.491
0%

Change (g) & (T)


3%
5%
7%
8%
10%
28%
31%
33%
35%
25%
No Change
No change
No Change
No Change
9% for 5years
0.4734
0.5247
0.5893
0.6077
0.2451
-4.01%
6.40%
19.5%
23.23%
-50.30%

Initial Case only (g) varied

3%
5%
7%
10%

30%
30%
30%
30%
No Change
No Change
No Change
No Change

0.4507
0.5372
0.6305
0.7836
-8.61%
8.94%
27.84%
58.89%

Back to initial case only (T) varied


4%
4%
4%
4%

25%
28%
31%
35%

No Change
No Change
No Change
No Change

0.5520
0.5169
0.4812
0.4328

11.94%
4.81%
-2.42%
-12.23%

Back to initial case only (m) is 9% for all the years

4%
30%
9%
0.0511
-89.62%

Sales Growth Rate: It is one of the value drivers in the analysis and it can be seen that a percentage change in sales growth rate is equivalent to 8.94 % increase in the share price. Sales growth rate is considered positive and is very important for a company's survival and profitability. It may result in higher dividends in shareholders and /or higher stock prices. The impact of sales growth rate on share price is more than the impact of taxation on share price.

Corporation Tax: Corporate taxes are taxes against profits by businesses during a specific taxable period. If companies are taxed less, there is possibility of increased economic production for those in favor of reduced tax. This in turn improves the business value and hence increases the share value production. An increase in corporate tax reduces the cash flow available to the fund providers and also subsidizes government spending and other programs for the nation's citizens. From the sensitivity analysis it can be seen that a percentage increase in the tax rate reduces the share price to 2.42 % whereas when the corporation tax reduced to 25%, the share price increased to almost 12 %. Thus it is proved that corporation tax is an important value driver in the Share value analysis.

Operating Profit Margin: Operating margin is defined as the ratio of operating income to revenue. It measures the profitability of the company. If we keep the profit margin same at 9 % every year and the corporation tax rate and sales growth rate at 30% and 4 % respectively, then the per cent change in share price is reduced drastically to 89.62 % .An increase in growth rate of 10% and reduction in corporation tax rate to 25 % with the profit margin at 9% for 5 years have made the reduction in share price to 50.30 %.This shows that the operating profit margin is the most powerful value driver.

'

C)Shareholder value analysis (SVA) is an approach, which depends on the net present value techniques, and is commonly used in investment appraisal purposes. The projected cash flows for each business unit has been estimated by the management for a particular planning period and for the future and this cash flows is converted into present value by discounting at the cost of capital and then it is added. The Present value obtained is then divided by the total number of shares to get the shareholder value per share, after all the debt and the marketable securities is considered. Alpha Rapaport (1998) initially proposed this technique for value measurement. The SVA approach measures the equity part of an investment and makes use of the time value of money as the standard discounted cash flow method. This technique pre assumes rational market in the economy and is based on the complete knowledge of the firm to identify true value creating investments and hence assumes the Efficient Market Hypothesis (EMH). A market that 'fully' reflect all available information is an efficient market (Fama,2001).In addition, stable and consistent sales growth, time value of money, long range time horizon, return and risk relationship and capital mix assumptions are built into the model.

Value drivers are those factors that have a very strong influence on the business value and on the equity stake of the investors and in turn have the greatest influence on the shareholder value. They are the following
' Sales Growth
' Operating Profit Margin
' Cash Tax Rate
' Fixed Assets
' Working Capital
' Cost of Capital
' Growth Duration Period (planning horizon)

Value drivers track the effects of each variable on the maximization of the shareholder value. The variables can also be used to analyse the sensitivity of shareholder value to changes in one or more of the drivers. Value drivers can be expressed in terms of their constituents and this decomposition will assist managers to identify roots of critical factors in the process of maximizing shareholder value. Free Cash flows are evaluated by the first five value drivers and is assessed over the growth duration period and then using the cost of capital, discounted to a present value. One of the main benefits of the SVA approach is that it helps the managers to focus on value creating activities like acquisition and divestment strategies, capital structure and dividend policies, performance measures, transfer pricing, executive compensation etc. Management will have a better idea of what to focus on by understanding the exact drivers the shareholder value. To find the shareholder value we need to know the business value. From business value to calculate the shareholder value we need to do the following
' Calculate Business value by adding the present values from the planning period
' Add the marketable securities to obtain the corporate value
' Deduct the market value of external debts to obtain the shareholder value
' Divide by the total number of issued ordinary shares to get the estimated shareholder value per share.

The main advantage of SVA is that it avoids many inadequacies of the usage of accounting for valuation purposes and this is done by focussing on the short-term profitability, neglecting risk, ignoring cost of equity and by ignoring the fixed and working capital requirements. However the drawbacks are while the SVA avoids the problem related to the accounting measures, the value drivers are based on the accounting data and also there is problems due to the overvaluation of stocks by the analysts .The two drawbacks are discussed below

' The relevance of accounting measure: Value is defined as the Net Present value of all future cash flows discounted at a rate that takes into account the risk involved in the investment. As the estimation of all future cash flows may not be acceptable, we take into account the historical cost information. As identified by Rees, if a potential problem arises,' Consequently it is accepted that accounting information is valuable as an input to the valuation process of individuals who wish to value firms, but not as a measure of these factors'. SVA when used properly has a number of benefits in such a way that it directs attention to fixed and working capital investment for future growth. These have to be estimated for the understanding of the technical, resourcing and logistical requirements to produce the sales growth required.
' Analysts' overvaluations: Recent studies have shown that analysts over-value the past sales growth and margins. This is due to the fact that SVA is totally dependant on the input assumptions and this results in the over estimation of the inputs and hence on overall overvaluations.

Steps involved in SVA and its importance

' Calculation of Weighted Average Cost of Capital
Cost of capital plays a very important role on the calculation of the SVA especially when a perpetuity calculation is required to determine the residual value. Calculating the WACC is not important on the current capital structure but important on the relative weights that the company targets for the future planning period .The calculation of WACC is done in the following 3 steps;
Determine the respective costs of debts and equity that the company will need to pay the investor
Find out the target percentage of debt and equity in the capital structure
Determine the weighing cost of equity and cost of debt by the relative proportion of debt and equity in the overall capital structure

To determine the cost of equity we use the CAPM model with an underlying motive that higher the risk that an investor is will to take, higher will his return be. We calculate CAPM cost of equity using the following formula;

Cost of Equity=Risk free Rate+ Equity risk premium
Where the risk premium is measured by beta and the risk involved here is the systematic or market risk and is caused by macroeconomic factors such as inflation, which in turn may affect the returns of the companies and the risk free rate is the most secure return that can be obtained

The future cost of debt to the company is the market rate required by investors less any tax benefit to the company. Higher the cost of debt higher will be the risk involved in the company.

' Calculation of future sales
It is important as the level of sales determines the profit and the growth of sales determines how the corporation is growing. An estimate of the expected sales is calculated by;

Future Sales=Previous year end sales *sales growth rate

' Calculation of after tax cash inflow
Every firm is subject to taxation of income. The rate of taxation varies between countries and has other factors that govern them. After cash inflow is calculated by;

After tax cash inflows=Increased sales* operating margin*(1-Tax rate)

' Calculation of Incremental Investment needs
With growth of a firm, there is increasing need to expand, invest and diversify. There is need of resources for incremental investment. This is in addition to the capital expenditure that the firm already incurs for the existing sustenance of its productivity. This will include up gradation of organization or network, including software, acquisition either in form of land or other firms and diversification into newer fields. The Incremental investment is calculated by;

Incremental investment = Capital expenditure - Depreciation expense

' Calculation of Cumulative Present value
When a company is expecting cash flows in the future, then they can estimate how much the future cash flows are worth at the current time. This is because of the difference in the value of money at different periods of time. When the company is invested for several years, it can add the present value of each cash flow to calculate the cumulative present value

' Growth Duration Period and calculation of residual value
A very important determinant of the value of a commodity is the time period taken into consideration. The importance of the time period is understood if we consider two simple statistics ' the P/E multiple and the planning periods. The managers have to plan for the time periods involved and the difference in value called 'value gap' . To overcome this, the shareholder value analysis (SVA) includes the predicted value beyond the planning periods, known as residual or terminal value.
When identifying an appropriate valuation period, businesses try to identify 2 time periods; a planning period, which extends till where the competitive advantage fades and the continuing period beyond it. The value creating potential is thus achieved in two time frames, value in the planning period and the value for the continuing period (residual value). The value of these two parts is estimated using principles of net present value analysis. The net present value is estimated by calculating free cash flows, which are discounted at the cost of capital and then added. To this result, the residual value is added. The residual value is estimate by calculating value of the assumed free cash flow beyond the planning period. Economic theory states that the earning of the positive NPVs is tantamount to supernormal profits. This will attract other firms into the industry. At the end of the planning period the company will achieve no more growth and will earn zero NPV into perpetuity. Michael Porter's five forces model is highly relevant here.
Porter's five forces
Michael Porter identified five forces that can estimate planning period
1. Rivalry among existing firms
2. Threat of new entrants
3. Threat of substitute products or services
4. Bargaining power of suppliers
5. Bargaining power of buyers
All these factors have a bearing on the planning period and businesses take their decisions based on these factors
Core competencies
Newer strategic thinking is towards relative performance within the industry itself, to outline what makes one firm different from others. Those firms that focus on relative performance will be able to generate most value. These companies enjoy a competitive advantage, ie, long planning period having good sales growth potential and free cash flows. This advantage is a consequence of core competencies that are nurtured by the company. This includes collective learning of the organisation, coordination of diverse production skills and integration of different technologies. The sole aim of such competencies is to build distinctive skills and capabilities that it set it apart from other organisations.
' Calculation of Business value
This estimates the total value of the business, including debt.. It is calculated by adding cumulative present value of cash flows to the residual value.

' Calculate Share price
This is the final step in Share value analysis. It is derived from the business value after eliminating debt, liabilities, etc.

Shareholder value determines whether the firm has invested sensibly and have made strategic decisions and in doing so, generated a positive return on money invested. Hence it is evident that each step of Share value analysis has a role to play in the final outcome. The presence of numerous steps in assessment of SVA may be cumbersome. When each step individually is considered, it may not have a direct bearing on SVA. The cumulative effect of each step is to be taken into consideration.

D) Genetic Algorithm

Man has always been fascinated by nature. There are various natural sciences that explain how nature functions. A key natural science is the study of evolution and genetics. Darwin, Mendel and other pioneers have laid the foundations of evolution. Their theories of natural selection and 'survival of the fittest' have helped explain the development and evolution of higher species and the extinction of species that lack a special advantage.

The science of genetics has proved that the better adapted species survive and the lesser adapted one fade away. This model has been incorporated into the financial world as a method of adapting to the economic situation. This programming technique that mimics biological evolution and natural selection as a problem-solving strategy is called Genetic Algorithm or GA. It involves using techniques such as inheritance, mutation, natural selection and cross over, which are inherent factors of evolutionary biology.

Genetic algorithms and their application in financial situations and markets were the brainchild of John Holland in the 1960s and were developed by Holland and his students, notably Goldberg, and colleagues at the University of Michigan in the 1960s and 70s. Around the same time, researchers such as G.E.P. Box, G.J. Friedman, W.W. Bledsoe and H.J. Bremermann, each had independently worked on algorithms inspired by evolution, but their work had little following. In 1965, Ingo Rechenberg from the Technical University of Berlin, introduced evolution strategy which was to develop better offspring by inducing mutation in the parent The newer, better offspring would then be induced mutation to enhance the next offspring and so forth. There was no cross over or study population.(Haupt and Haupt 1998). Later population started to be introduced as a parameter. In 1966, L.J. Fogel, A.J. Owens and M.J. Walsh from America applied the same principle to develop a technique called evolutionary programming, which involved randomly mutating one of a pair of simulated machines and keeping the better one (Mitchell 1996). The importance of cross over in these studies was still not recognized.

John Holland's work in 1962, was the first to propose crossover and recombination techniques to enhance problem solving. In 1975, Holland and colleagues published;' Adaptation in Natural and Artificial Systems' which was a landmark in GA. The book covered adaptive digital systems using mutation, selection and crossover, and put forth the idea of simulating evolutionary processes in nature as a problem-solving strategy. (Mitchell 1996);(Haupt and Haupt 1998). Kenneth De Jong, in the same year published a dissertation that GAs had the potential of performing a wide variety of test functions. Following these studies, by the 80s, GAs were being applied in various mathematical problems like bin-packing and graph coloring and in engineering issues such as pattern recognition and classification, pipeline flow control, and structural optimization (Goldberg 1989) .

Holland's original goal was to study the phenomenon of adaptation in nature and to develop ways in which these processes might be imported into everyday computations. The problem arising would be the evolutionary process, and the strategies would be the different chromosomal combinations. The best combination or strategy would give the best suited solution to the problem, just as natural selection would aid in evolution. GA is useful in the financial sector in finding the best strategy in trading, fitness functions, functional optimization, problems in budget, minimizing costs, etc. In recent years there has been increased interaction between GA, evolutionary programming and evolution strategies in the various evolutionary computation methods that the true concept for which GA was developed has been challenged. Similar methods of optimization are the fuzzy logic model and neural network model.

Genetic algorithms have been applied to a number of real life and complex situations, because they adapt to the situation and environment in which they are applied, just like live organisms adapt to their natural environment. GAs has been used in economics, bioinformatics, operational optimization, robotics and scheduling. A common problem being solved by GA is the 'travelling salesman'. In this situation, the starting point and different cities and their distances are used in a GA to find the shortest distance covering all the cities and back to the starting point (Reeves, Rowe 2003). The study of GA can also be used to generate an optimal ecosystem and in the future, it will also become more prominent in artificial life systems.

Traditionally GA has been used for optimization in machine learning and classification. Mahfoud and Mani (1996) presented a new system that utilizes GA to predict future performances of individual stocks. They studied the utility of GA on time-series forecasting. For this, they compared GA predictions with neural network system on around 5000 stock prediction experiments. Their findings showed that both methods outperformed the markets with GA performing better. Their study also showed that a combined approach of the two methods were better than either one individually.

In Economics, the ability of GAs to represent individuals as part of a population with differing strategy is used to process information in parallel for a problem solution or for better performing strategies (Dawid and Kopel 1998). They are also used in studies of strategic decision making, resolving conflicts or stalemates and for exploring the possibility of developing cooperation between firms. Wong and Bodnovich in their study in 2008 of 97 genetic algorithms showed that GAs are being utilized for a wide range of corporate functional activities like areas of production/operation and information systems. In a study by Kapoor, Dey and Khurana, published in 2011, used the power of genetic algorithms to adjust technical trading rules parameters in financial markets. Their findings showed that optimization using GA increased the profit significantly when compared to traditional financial modifications in trading.

Operations of GA
The following mathematical features are used for the purpose of optimization in GA
1) Binary Representation: By using binary digits 0 and 1in vectors, GA helps to determine solutions. Other ways of representation are by using integers or decimals or by using strings of letters representing each element.

2) Objective Function: An objective directed function helps GA models to arrive at optimal or near optimal solutions in the quickest possible way with minimal cost. The generation of a GA also depends on a value called the

3) fitness function. A fitness function is a figure of merit that determines how close the solution is to the desired goal.

4) Genetic Operations: Robert Pereira in 2000, explained the process by which genetic operations function. He suggests that an initial sample of randomly generated solutions to a problem is evolved and in successive generations, a final sample consisting of optimal or near-optimal solution is generated. The factors that determine the solutions of a GA are;

i. Selection: The elements of the problem that may determine a solution are selected. These elements may undergo mutation (changes) or may cross-over (recombination). They are selected by various processes like elitist selection, roulette wheel selection, tournament selection, scaling selection, steady-state selection, hierarchical selection rank selection or generational selection methods.

ii. Crossovers: The solution elements that are better performing, and those that are likely to be part of the solution are combined through binary recombination called cross-overs. Recombination in the direction of the solution ensures that they are not random and yield the best results.

iii. Mutation: Solutions to a problem may involve incorporating innovative ideas and new strategies just like how mutation introduces new genetic material into the population. These new properties enhance the efficiency and functionality. In exploring new terrain, it may however, lead to areas f solution that may not be relevant to the problem at hand. Measures are taken to maintain the search and mutation to be directed at the problem and thus discard suboptimal solutions.


Advantages of Using GA
One has to understand the advantages of using GA in computation of solutions when compared to other forms of optimization. These advantages are;
' GA are intrinsically parallel. This means that they can explore multiple possible solutions at once and eliminate the ones that do not yield a suitable solution, thus reducing time wasted in exploring options with dead ends.
' They can be applied to solve problems where potential solutions and possibilities are large, eg. Non-linear problems that is too vast to search completely within the time frame.
' By crossover, GA may be able to address problems with functions that are not related or are discontinuous or situations where the elements and variables are complex or when the parameter may change over time..
' GA can be used to manipulate many parameters at the same time. This helps generate more than one optimal solutions rather than a single one.
' GA may also encode the variables so that solution is derived not with the true variables but with encoded variables. The optimization so derived may also be used to derive solutions for experimental, numerical or analytical functions.
' During each possible solution derivation, using fitness function, the GA makes random changes and analyses the performance of the new change. In the event of non-functionality, it can start from scratch.

Limitations of GA

Although GA is extremely useful in optimization, they have their limitations;

' One important limitation is that the generation of solution through GA requires proper representation of problems. The language used should be sturdy, and should be able to tolerate random changes like fatal errors etc.
' The fitness function of the solution proves to be a determinant of the outcome. If the fitness function is poorly chosen, then a wrong solution or no solution at all may be generated.
' The parameters like the elemental population size, the crossover and mutation parameters, the type and quality of selection should be carefully estimated.
' GA cannot analyze fitness functions that are misleading (Mitchell 1996), where incomplete information or data for a problem may be given, such as market predictability.
' The most common problem with GA is premature convergence. GA may ignore the global optimum, as it analyses all possible solutions without bias and is ignorant to any favoring outcomes. If in the early course of its run, the GA identifies an element that is better than its competitors, then it reproduces that element to such an extent that it undermines the diversity of the initial population in the derivation of the solution This can even lead to failure to converge with the population.

These few disadvantages do not limit the utility of GA. It still remains a vital solution provider to various problems that arise in financial markets and economic scenarios. At a management level, GA is an inevitable tool in quick decision making and managerial responses to expected and unexpected problems that arise in the markets.

References

1. Adam, M, April 23, 2004, 'Genetic Algorithm and Evolutionary Computation', Article in 'The Talk Origins Archive'.

2. Akalu, M M (2008). Projects for Shareholder value: a Capital budgeting perspective. Amsterdam: Erasmus University. 37-47.

3. Bodnovich, T A et al (1996), A Bibliography of Genetic Algorithm, Business Application Research,15(2),75-82

4. Colin, R et al (2002). Genetic Algorithms: Principles and Perspectives-A Guide to G A Theory. U S A: Kluwer Academic Publisher. 19-60.

5. Dawid, H et al. (1998). On economic applications of the Genetic Algorithm: a model of the cobweb type. Journal of Evolutionary Economics. 8 (3), 297-315.

6. Dimitris, N C (1994), Chaos Theory in the Financial Markets: Applying Fractals, Fuzzy Logic, Genetic Algorithms, Swarm Simulation & Monte Carlo Method to Manage Market chaos & Volatility, Probus Publishing Company, 128-129

7. Fama, E F. (2001). Efficient capital markets: A Review of theory and empirical work. Journal of finance. 1 (3), 283-415

8. Goldberg, D E (1989). Genetic Algorithms in Search, Optimization, and Machine Learning. Boston: Addison-Wesley Longman Publishing Co. 47-51.

9. Kapoor, V et al (2011), Genetic Algorithm: An Application to Technical Trading System Design, International Journal of Computer Applications 36(5), 44-50.

10. Mahfoud, S et al. (1996). Financial Forecasting using Genetic Algorithms. Applied Artificial Intelligence. 10 (5), 545-563.

11. Malkiel, B G. (2003). The Efficient Market Hypothesis and its critics. Journal of economic perspectives. 17 (1), 59-82.

12. Mitchelle, Melanie, 'An Introduction to Genetic Algorithms', MIT Press, 1996.

13. Pilkington, M (2005). Financial Information Systems. Harlow: Pearson Education Limited. 3-38.

14. Rappaport, A (1998). Creating Shareholder Value: A guide for Managers and Investors. 2nd ed. New York: The Free Press. 32-73.

15. Randy, L H et al (2004). Practical Genetic Algorithms. 2nd ed. Pennsylvania: John Wiley and sons. 22-23.

16. Richard Pike and Bill Neale, fifth edition, "Corporate Finance and Investment: Decisions & Strategies", FT Prentice Hall, 278-280

17. Roger W. Mills, 1998, "The Use of Shareholder Value Analysis in Acquisition and Divestment Decisions by Large UK Companies", published by CIMA, 41-53

18. Robert P, (2000), Genetic Algorithm Optimization for Finance and Investment, Discussion Paper, Series A00.02, 2-18

19. Sudarsanam, S (2010). Creating Value From Mergers and Acquisitions. 2nd ed. Essex: Pearson Education Limited. 1-11.

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