Friday, January 10, 2020

Net Present Value

Critics to DCF methods Ducht an UK companies * However, it is found inappropriate to use DCF methods for investments that have got strategic implications. * There are various reasons for the use of open approach. Since the outcomes of these projects are highly unforeseen, according one interviewee, the application of quantitative tools is not plausible. Therefore, companies tend to apply the rule of thumb methods rather than standardized quantitative models. The justification for not applying quantitative models is some times attributed to the nature of a project. Capital inv appraisal of new technologies: Problems, misconceptions and research directions Specifically, it has been alleged that the traditional appraisal methods of payback, discounted net present value (NPV) and internal rate of return (IRR) undervalues the long-term benefits; that traditional financial appraisals assume a far too static view of future industrial activity, under-rating the effects and pace of technological change; that there are many benefits from investments in new technology which are difficult to quantify and are often ignored in the appraisal process; and lastly, it is claimed that the systems of management control often employed by large organizations compound the bias against those investments which, although expensive, reap rewards vital for lon g-term viability. The first issue is a criticism of financial technique; the next two are criticisms of the way in which business operations are modelled; and the last is an issue of organizationalc ontrol and behavior. * We show that the criticisms directeda traditional appraisal methods may to some extent be based on misconceptions of the financial models and the ways in which they are best used * A similar objection is raised to the use of NPV and IRR. The claim is that discounting future cash benefits under-emphasizes the future benefits of new technology. This problem may be exacerbated by the application of risk premia to the discount rate. New echnology is assumed to be riskier than that which has been well established, Why DCF are bad for business and why business schools should stop using it * The assumptions related to DCF are increasingly becoming so disconnected from business reality that its continued use should come with the following warning, ‘This financial man agement technique is hazardous to your business. ’ * DCF as a capital investment appraisal tool suffers from a number of major limitations. These limitations include its narrow perspective, exclusion of non-financial benefits, overemphasis on the short-term, faulty assumptions about the status quo, inconsistent treatment of inflation, and promotion of dysfunctional/cheating behaviour. Previous authors, including Hastie (1974); Ramasesh and Jayakumar (1993); and Adler (2000) have enumerated and discussed the various sins of DCF. * The objections against the use of DCF for capital investment appraisal have often been objected to themselves. Kaplan (1986), for example, feels that the supposed limitations of DCF are in truth a limitation of the user and not of the technique. For example, the selection of a static discount rate is a failure of the user and not of the technique itself. Likewise, the inconsistent treatment of inflation, the overemphasis on the short-term, faulty assumptions about the status quo alternative, the adoption of a narrow organisational perspective, and manipulative and cheating behaviour are again all mistakes of the user. Even the difficulty of including non-financial benefits is seen as a lack of the financial analyst’s imagination rather than an inherent shortcoming of the technique. To help overcome the problems of DCF for capital investment decision-making, proponents of real options theory have argued for the tandem use of the Black and Scholes’ (1973) model and DCF. – The problem with DCF, and which cannot be overcome by its real options complement, occurs when data is not accessible or quantifiable. Not only do these occasions happen quite frequently, but also they become increasingly common as the decision moves from the operationally mundane to the strategically critical. The missapplication of capital investment appraisal techniques * Surveys of capital budgeting practices in the UK and USA reveal a trend towards the increased use of more sophisticated investment appraisals requiring the application of discounted cash flow (DCF) techniques. Several writers, however, have claimed that companies are underinvesting because they misapply ormisinterpret DCF techniques. * the only justification we can think of for using the accounting rate of return method is because top management believe that reported profits have an impact on how financial markets evaluate a company. This is further reinforced in many companies by linking management rewards to short-term financial accounting measures. Thus a project’s impact on the financial accounting measures used by financial markets would appear to be a factor that is taken into account within the decision-making process. Dimson and Marsh (1994) have expressed concern that many UK companies may be using exces sively high discount rates to appraise investments and, as a result, these companies are in danger of underinvesting. In the USA it has also been alleged that firms use discount rates to evaluate investment projects that are higher than their estimated cost of capital (Porter, 1992). Conclusions: Ducht an UK companies * All the UK case study companies apply combined methods of investment appraisal and most of them combine the DCF techniques with the value based management methods, such as SVA and EVA. The combination among the Netherlands companies, however, is mostly with the accounting based measures. Project decision-making in most of the case study companies is found decentralized, which provides the benefits of teamwork in project management. * In terms of appraisal model selection, however, the result is heterogeneous. Most companies prefer to apply combined methods of appraisal. Uniform methods of evaluation are no applied across all stages of a project, which will make diffi cult the comparison of project values at different stages. Although research in capital budgeting suggests the use of quantitative models for R&D and ICT projects, the application is not found in practice. In contrary, firms are relying on qualitative and non-standard approaches. This does not have rigorous theoretical basis, and hence, the decision-making process may not get an acceptable yardstick for its rationality. Capital inv appraisal of new technologies: Problems, misconceptions and research directions * Payback methods are inadequate appraisal techniques and should never be used alone. NPV and IRR are appropriate ways of valuing future cash-flows. Any bias in their application will be due to a systematic use of too high a discount rate, but this can be avoided by correct analysis. Assumptionsa bout the futurec an lead to bias if an over-optimisticp ictureo f the no-investment position is taken, but again this is an avoidable pitfall. As for the benefits ignored, many of these can be quantifieda nd broughtf ormallyi nto the analysis. W hereb enefitsc annot be quantifiedt, hey shouldn everthelessb e stateds o that they can be givenp roperc onsiderationw hena finalj udgement is made. The bias due to the use of short-term financial criteria can be removed by the use of measures reflecting the longer-term benefits of present investments. In principle, then, the biases of capital-investment appraisals are avoidable, but one difficulty remains. New technology invariably leads to greater complexity, and any unwillingness to face this complexity in the capital-investment process is likely to lead to bias against change. * NPV, IRR and PB undervalue long term benefits * Benefits from investing in technology very difficult to quantify and often are ignored in the appraisal process. DCF analysis places too little weight on the future due to the magnitude of the discount rate (too high). Reasons for a too high discount rate: 1. 2. to compensate non-profit projects 3. – To calculate the required rate of return we use t he CAPM – Managers? interests different from shareholders? ones so higher rate or return determined. Then, again, the critic/problem is not of the appraisal method but of its application or understanding Theory-practice gap in .. : UK The survey results indicate that UK corporations have increasingly adopted prescribed textbook financial analysis. The stage has now been reached where only a small minority do not make use of discounted cash flows, formal risk analysis, ppropriate inflation adjustment and post-auditing. However, managers continue to employ simpler rules-of-thumb techniques. There has not, in general, been a replacement of one set of methods with another, but rather, a widening of the range of ways of analysing a financial decision. Why DCF are bad for business and why business schools should stop using it It has been said, ‘Life must be lived forward but can only be understood backwards. ’ There is no denying that DCF is wonderful at looking backwa rds and calculating, for example, the actual NPV a project has earned. Sometimes, generally when commonplace, operational decisions are involved, DCF can even work as a forward-looking tool. To work in this manner, however, requires the relevant cash flow data to be either present or, perhaps with a bit of work, discoverable. DCF does not work well when the decision at hand is strategic in nature. In these situations, the data is often neither present nor discoverable in time for an ex ante evaluation. Only after the decision is made does useful data likely become available. The condition described here is well captured in the lyrics of the Rolling Stones’ song ‘You Can’t Always Get What You Want’: You can’t always get what you want But if you try sometimes, well you might find You get what you need. When it comes to matters that really matter, DCF and real options theory fail to enlighten us. Instead, they sap managers’ energy by focusing their attention on Pareto’s trivial many at the expense of his vital few. In the end, managers end up missing the forest in their search for the non-existent trees. It is time that as educators, we rediscovered the vital few and culled out the trivial many topics that have crept into our course outlines. DCF should be one of the first topics we drop or at a minimum drastically prune back. It is not only a prime example of the trivial many, but it is a potential hazard to firms that use it for decisions that affect firm strategy. Do I hear any other offers? The missapplication of capital investment appraisal techniques The use of conservative cash flow forecasts, combined with the incorrect treatment of nflation and excessive discount rates observed in the survey suggests that many UK organizations may be rejecting profitable investments. Given these problems it could be argued that DCF procedures should be abandoned or give n little weight in long-term investment decisions. We strongly disagree. DCF procedures should not be ignored or relegated in importance merely because they might be used incorrectly. Instead, decisionmakers should recognize potential problems and be careful to ensure that the financial appraisal is performed correctly. CRITICS TO PAYBACK PERIOD Capital inv appraisal of new technologies: Problems, misconceptions and research directions The objection to payback methods is that they ignore all cash flows after the desired payback period, which may be as short as 2 or 3 years. Thus they take no account of the long-term advantages that many large investments in new process technology bring, so the use of payback criteria is worthy of comment. 5 Payback can be insensitive to considerable variation among projects (in terms of their cash flows). 6 Payback methods are simple rules of thumb. Their attraction is their simplicity, and robustness for making judgements on possibly optimistic costings and uneasily quantified business risks. However, they do ignore medium- and long-term cash flows, and it is perhaps surprising that they seem to be regarded as serious tools of financial analysis. Net present value Firms generally have many investment opportunities available.   Some of these investment opportunities are valuable and others are not. The essence of successful financial management is identifying which opportunities will increase shareholder wealth. There are three basic and related concepts that form the very foundation of modern day finance: present value, net present value (NPV) and opportunity cost. Present value gives the value of cash flows generated by an investment and NPV gives the effective net benefit from an investment after subtracting its costs. Opportunity cost represents the rate of return on investments of comparable risk. Application of these concepts enables us to value different kinds of assets, especially those which are not commonly traded in well-functioning markets. NPV of an asset or investment is the present value of its cash flows less the cost of acquiring the asset. Smart investors will only acquire assets that have positive NPVs and will attempt to maximize the NPV of their investments. The rate of return received from an investment is the profit divided by the cost of the investment. Positive NPV investments will have rates of return higher than the opportunity cost. This gives an alternate investment decision rule. Good investments are those that have rates of return higher than the opportunity cost. This opportunity cost can be inferred from the capital market and is based on its risk characteristics of the investment. To assess why Net Present Value leads to better investment decisions than other criteria, let us start with a review of the NPV approach to investment decision making and then present four other widely used measures. These are: the payback period, the book rate of return, the internal rate of return (IRR) and profitability index. The measures are inferior to the NPV and should not, with the qualified exception of the IRR, normally be relied upon to provide sound investment decisions. These measures are commonly used in practice. The NPV represents the value added to the business by the project or the investment. It represents the increase in the market value of the stockholders’ wealth. Thus, accepting a project with a positive NPV will make the stockholders better off by the amount of its NPV. The NPV is the theoretically correct method to use in most situations. Other measures are inferior because they often give decisions different from those given by following the NPV rule. They will not serve the best interests of the stockholders (Brealey, 2002). To calculate NPV we should firstly forecast the incremental cash flows generated by the project and determine the appropriate discount rate, which should be the opportunity cost of capital. Then calculate the sum of the present values (PV) of all the cash flows generated by the investment. NPV = PV of cash inflows – initial investment. To make decision on investment, we should accept projects with NPV greater than zero and for mutually exclusive projects, accept the project with the highest NPV, if the NPV is positive. The NPV represents the value added to the stockholders’ wealth by the project. The discount rate should reflect the opportunity cost of capital or what the stockholders can expect to earn on other investments of equivalent risk (Brealey, 2002). The NPV approach correctly accounts for the time value of money and adjusts for the project’s risk by using the opportunity cost of capital as the discount rate. Thus, it clearly measures the increase in market value or wealth created by the project. The NPV of a project is not affected by â€Å"packaging† it with another project. In other words, NPV(A+B) = NPV(A) + NPV(B). The NPV is the only measure that provides the theoretically correct measure of a project’s value (Ross, 2002). Payback Period. The payback period is simply the time taken by the project to return your initial investment. The measure is very popular and is widely used; it is also a flawed and unreliable measure. It is simple to calculate and easy to comprehend. However, payback period has very limited economic meaning because it ignores the time value of money and the cash flows after the payback period. It can be inconsistent and the ranking of projects may be changed by packaging with other projects. Discounted payback is a modified version of the payback measure and uses the discounted cash flows to compute payback. This is an improvement over the traditional payback in that the time value of money is recognized. A project, which has a measurable discounted payback, will have a positive NPV. However, the other disadvantages of payback still apply. It is also not simple anymore (Investment Criteria). Book Rate of Return (BRR). This is a rate of return measure based on accounting earnings and is defined as the ratio of book income to book assets. Accounting earnings are reported by firms to the stockholders and the book return measure fits in with the reported earnings and the accounting procedures used by firms. However, the measure suffers from the serious drawback that it does not measure the cash flows or economic profitability of the project. It does not consider the time value of money and gives too much weight to distant earnings. The measure depends on the choice of depreciation method and on other accounting conventions. BRR can give inconsistent ranking of projects and rankings may be altered by packaging. There is very little relationship between the book return and the IRR. (Brealey, 2002). Internal Rate of Return (IRR). IRR is defined as the discount rate at which the NPV equals zero. Used properly, the IRR will give the same result as the NPV for independent projects and for projects with normal cash flows. As long as the cost of capital is less than the IRR, the NPV for the project will be positive. IRR can rank projects incorrectly, and the rankings may be changed by the packaging of the projects. For mutually exclusive projects, IRR can give incorrect decisions and should not be used to rank projects. If one must use IRR for mutually exclusive projects, it should be done by calculating the IRR on the differences between their cash flows (Ross, 2002). Profitability Index. Occasionally, companies face resource constraint or capital rationing. The amount available for investment is limited so that all positive NPV projects cannot be accepted. In such cases, stockholder wealth is maximized by taking up projects with the highest NPV per dollar of initial investment. This approach is facilitated by the profitability index (PI) measure. Profitability index is defined as: NPV/Investment. The decision rule for profitability index is to accept all projects with a PI greater than zero. This rule is equivalent to the NPV rule. The modified rule applied in the case of capital rationing is to accept projects with the highest profitability index first, followed by the one with next highest, and so on till the investment dollars are exhausted. This rule will maximize the NPV and stockholder wealth. If the resource constraint is on some other resources, the profitability index needs to be modified to measure the NPV per unit of the resource that is rationed. The profitability index cannot cope with mutually exclusive projects or where one project is contingent on another (Brealey, 2002). Thus, comparing NVP with other criteria we can assert that NPV is superior to other criteria. First, it is the only measure, which considers the time value of money, properly adjusting for the opportunity cost of capital. Second, it gives consistent measures of the project’s value (i.e. not affected by packaging with other projects). Third, it clearly measures the value added to the stockholders’ wealth. The only exception to the superiority of NPV is when the firm is constrained by capital rationing. This implies that the firm cannot finance all positive NPV projects and should therefore choose projects that give the highest NPV for each dollar of investment. The profitability index that is defined as the ratio of NPV to the investment amount is used to achieve this selection. However, the other criteria for the evaluation of projects are found to be popular in practice. If using them, we should make sure we use them in the best possible way and understand the limitations of them. For example, we should always compare mutually exclusive projects on the basis of the difference between their cash flows, because that it is the cash flows that determine the value of a project. Inadequate forecast of the cash flows can be far more disastrous than using the wrong appraisal technique. Cash flow forecasts are difficult to make and can be expensive. It does not make sense to waste the forecasts by using an inferior method of evaluation. References: Brealey, Richard A. & Myers, Stewart C. (2002). Principles of Corporate Finance, 7th ed. Chapters 5 – 6. Irwin/McGraw-Hill Book Co. Investment Criteria, Chapter 9. Introduction to Finance. COMM 203 Homepage. College of Commerce, University of Saskatchewan, 2004 from http://www.commerce.usask.ca/faculty/loescher/Commerce203/CapitalBudgeting/Investment_Criteria.ppt Ross, S., Westerfield, R., Jordan, B. & Roberts, G. (2002). Fundamentals of Corporate Finance, 4th Edition. McGraw-Hill Ryerson Limited. Net Present Value Critics to DCF methods Ducht an UK companies * However, it is found inappropriate to use DCF methods for investments that have got strategic implications. * There are various reasons for the use of open approach. Since the outcomes of these projects are highly unforeseen, according one interviewee, the application of quantitative tools is not plausible. Therefore, companies tend to apply the rule of thumb methods rather than standardized quantitative models. The justification for not applying quantitative models is some times attributed to the nature of a project. Capital inv appraisal of new technologies: Problems, misconceptions and research directions Specifically, it has been alleged that the traditional appraisal methods of payback, discounted net present value (NPV) and internal rate of return (IRR) undervalues the long-term benefits; that traditional financial appraisals assume a far too static view of future industrial activity, under-rating the effects and pace of technological change; that there are many benefits from investments in new technology which are difficult to quantify and are often ignored in the appraisal process; and lastly, it is claimed that the systems of management control often employed by large organizations compound the bias against those investments which, although expensive, reap rewards vital for lon g-term viability. The first issue is a criticism of financial technique; the next two are criticisms of the way in which business operations are modelled; and the last is an issue of organizationalc ontrol and behavior. * We show that the criticisms directeda traditional appraisal methods may to some extent be based on misconceptions of the financial models and the ways in which they are best used * A similar objection is raised to the use of NPV and IRR. The claim is that discounting future cash benefits under-emphasizes the future benefits of new technology. This problem may be exacerbated by the application of risk premia to the discount rate. New echnology is assumed to be riskier than that which has been well established, Why DCF are bad for business and why business schools should stop using it * The assumptions related to DCF are increasingly becoming so disconnected from business reality that its continued use should come with the following warning, ‘This financial man agement technique is hazardous to your business. ’ * DCF as a capital investment appraisal tool suffers from a number of major limitations. These limitations include its narrow perspective, exclusion of non-financial benefits, overemphasis on the short-term, faulty assumptions about the status quo, inconsistent treatment of inflation, and promotion of dysfunctional/cheating behaviour. Previous authors, including Hastie (1974); Ramasesh and Jayakumar (1993); and Adler (2000) have enumerated and discussed the various sins of DCF. * The objections against the use of DCF for capital investment appraisal have often been objected to themselves. Kaplan (1986), for example, feels that the supposed limitations of DCF are in truth a limitation of the user and not of the technique. For example, the selection of a static discount rate is a failure of the user and not of the technique itself. Likewise, the inconsistent treatment of inflation, the overemphasis on the short-term, faulty assumptions about the status quo alternative, the adoption of a narrow organisational perspective, and manipulative and cheating behaviour are again all mistakes of the user. Even the difficulty of including non-financial benefits is seen as a lack of the financial analyst’s imagination rather than an inherent shortcoming of the technique. To help overcome the problems of DCF for capital investment decision-making, proponents of real options theory have argued for the tandem use of the Black and Scholes’ (1973) model and DCF. – The problem with DCF, and which cannot be overcome by its real options complement, occurs when data is not accessible or quantifiable. Not only do these occasions happen quite frequently, but also they become increasingly common as the decision moves from the operationally mundane to the strategically critical. The missapplication of capital investment appraisal techniques * Surveys of capital budgeting practices in the UK and USA reveal a trend towards the increased use of more sophisticated investment appraisals requiring the application of discounted cash flow (DCF) techniques. Several writers, however, have claimed that companies are underinvesting because they misapply ormisinterpret DCF techniques. * the only justification we can think of for using the accounting rate of return method is because top management believe that reported profits have an impact on how financial markets evaluate a company. This is further reinforced in many companies by linking management rewards to short-term financial accounting measures. Thus a project’s impact on the financial accounting measures used by financial markets would appear to be a factor that is taken into account within the decision-making process. Dimson and Marsh (1994) have expressed concern that many UK companies may be using exces sively high discount rates to appraise investments and, as a result, these companies are in danger of underinvesting. In the USA it has also been alleged that firms use discount rates to evaluate investment projects that are higher than their estimated cost of capital (Porter, 1992). Conclusions: Ducht an UK companies * All the UK case study companies apply combined methods of investment appraisal and most of them combine the DCF techniques with the value based management methods, such as SVA and EVA. The combination among the Netherlands companies, however, is mostly with the accounting based measures. Project decision-making in most of the case study companies is found decentralized, which provides the benefits of teamwork in project management. * In terms of appraisal model selection, however, the result is heterogeneous. Most companies prefer to apply combined methods of appraisal. Uniform methods of evaluation are no applied across all stages of a project, which will make diffi cult the comparison of project values at different stages. Although research in capital budgeting suggests the use of quantitative models for R&D and ICT projects, the application is not found in practice. In contrary, firms are relying on qualitative and non-standard approaches. This does not have rigorous theoretical basis, and hence, the decision-making process may not get an acceptable yardstick for its rationality. Capital inv appraisal of new technologies: Problems, misconceptions and research directions * Payback methods are inadequate appraisal techniques and should never be used alone. NPV and IRR are appropriate ways of valuing future cash-flows. Any bias in their application will be due to a systematic use of too high a discount rate, but this can be avoided by correct analysis. Assumptionsa bout the futurec an lead to bias if an over-optimisticp ictureo f the no-investment position is taken, but again this is an avoidable pitfall. As for the benefits ignored, many of these can be quantifieda nd broughtf ormallyi nto the analysis. W hereb enefitsc annot be quantifiedt, hey shouldn everthelessb e stateds o that they can be givenp roperc onsiderationw hena finalj udgement is made. The bias due to the use of short-term financial criteria can be removed by the use of measures reflecting the longer-term benefits of present investments. In principle, then, the biases of capital-investment appraisals are avoidable, but one difficulty remains. New technology invariably leads to greater complexity, and any unwillingness to face this complexity in the capital-investment process is likely to lead to bias against change. * NPV, IRR and PB undervalue long term benefits * Benefits from investing in technology very difficult to quantify and often are ignored in the appraisal process. DCF analysis places too little weight on the future due to the magnitude of the discount rate (too high). Reasons for a too high discount rate: 1. 2. to compensate non-profit projects 3. – To calculate the required rate of return we use t he CAPM – Managers? interests different from shareholders? ones so higher rate or return determined. Then, again, the critic/problem is not of the appraisal method but of its application or understanding Theory-practice gap in .. : UK The survey results indicate that UK corporations have increasingly adopted prescribed textbook financial analysis. The stage has now been reached where only a small minority do not make use of discounted cash flows, formal risk analysis, ppropriate inflation adjustment and post-auditing. However, managers continue to employ simpler rules-of-thumb techniques. There has not, in general, been a replacement of one set of methods with another, but rather, a widening of the range of ways of analysing a financial decision. Why DCF are bad for business and why business schools should stop using it It has been said, ‘Life must be lived forward but can only be understood backwards. ’ There is no denying that DCF is wonderful at looking backwa rds and calculating, for example, the actual NPV a project has earned. Sometimes, generally when commonplace, operational decisions are involved, DCF can even work as a forward-looking tool. To work in this manner, however, requires the relevant cash flow data to be either present or, perhaps with a bit of work, discoverable. DCF does not work well when the decision at hand is strategic in nature. In these situations, the data is often neither present nor discoverable in time for an ex ante evaluation. Only after the decision is made does useful data likely become available. The condition described here is well captured in the lyrics of the Rolling Stones’ song ‘You Can’t Always Get What You Want’: You can’t always get what you want But if you try sometimes, well you might find You get what you need. When it comes to matters that really matter, DCF and real options theory fail to enlighten us. Instead, they sap managers’ energy by focusing their attention on Pareto’s trivial many at the expense of his vital few. In the end, managers end up missing the forest in their search for the non-existent trees. It is time that as educators, we rediscovered the vital few and culled out the trivial many topics that have crept into our course outlines. DCF should be one of the first topics we drop or at a minimum drastically prune back. It is not only a prime example of the trivial many, but it is a potential hazard to firms that use it for decisions that affect firm strategy. Do I hear any other offers? The missapplication of capital investment appraisal techniques The use of conservative cash flow forecasts, combined with the incorrect treatment of nflation and excessive discount rates observed in the survey suggests that many UK organizations may be rejecting profitable investments. Given these problems it could be argued that DCF procedures should be abandoned or give n little weight in long-term investment decisions. We strongly disagree. DCF procedures should not be ignored or relegated in importance merely because they might be used incorrectly. Instead, decisionmakers should recognize potential problems and be careful to ensure that the financial appraisal is performed correctly. CRITICS TO PAYBACK PERIOD Capital inv appraisal of new technologies: Problems, misconceptions and research directions The objection to payback methods is that they ignore all cash flows after the desired payback period, which may be as short as 2 or 3 years. Thus they take no account of the long-term advantages that many large investments in new process technology bring, so the use of payback criteria is worthy of comment. 5 Payback can be insensitive to considerable variation among projects (in terms of their cash flows). 6 Payback methods are simple rules of thumb. Their attraction is their simplicity, and robustness for making judgements on possibly optimistic costings and uneasily quantified business risks. However, they do ignore medium- and long-term cash flows, and it is perhaps surprising that they seem to be regarded as serious tools of financial analysis.

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