Study on Sensitivity Analysis and Financial Models Finance Essay

Sensitivity analysis is used to determine how "sensitive" a model is to changes in the value of the parameters of the model and to changes in the structure of the model. Inthis paper, we focus on parameter sensitivity. Parameter sensitivity is usually performedas a series of tests in which the modeller sets different parameter values to see how achange in the parameter causes a change in the dynamic behaviour of the stocks. Byshowing how the model behaviour responds to changes in parameter values, sensitivityanalysis is a useful tool in model building as well as in model evaluation. Sensitivity analysis helps to build confidence in the model by studying theuncertainties that are often associated with parameters in models. Many parameters insystem dynamics models represent quantities that are very difficult, or even impossible tomeasure to a great deal of accuracy in the real world. Also, some parameter valueschange in the real world. Therefore, when building a system dynamics model, the modelleris usually at least somewhat uncertain about the parameter values he chooses and must useestimates. Sensitivity analysis allows him to determine what level of accuracy is necessaryfor a parameter to make the model sufficiently useful and valid. If the tests reveal that themodel is insensitive, then it may be possible to use an estimate rather than a value withgreater precision. Sensitivity analysis can also indicate which parameter values arereasonable to use in the model. If the model behaves as expected from real worldobservations, it gives some indication that the parameter values reflect, at least in part, the"real world." Sensitivity tests help the modeller to understand dynamics of a system.Experimenting with a wide range of values can offer insights into behaviour of a system inextreme situations. Discovering that the system behaviour greatly changes for a change in aparameter value can identify a leverage point in the model- a parameter whose specificvalue can significantly influence the behavior mode of the system. (https://sysdyn.clexchange.org/sdep/Roadmaps/RM8/D-4526-2.pdf)

3(a) What is Sensitivity Analysis?

Sensitivity analysis is a strategy that is helpful in determining what could happen if a specific variable within a projection fails to function as originally envisioned. The idea is to identify possible deviations that could occur if one or more variables are changed or discarded, and how those changes would affect the eventual outcome. From this perspective, this type of analysis makes it possible to prepare for outcomes other than the desired goal, thus minimizing the ill effects if those variables do fail to perform or influence as anticipated. Within the process of conducting a sensitivity analysis, it is possible to look at each factor or variable that has relevance to the projected outcome. For example, if an business anticipates that launching a new product will result in an increase of twenty-five percent in annual earnings, the analysis may look at how the earnings would be affected if consumer response were only half as enthusiastic as originally predicted. As part of the development of different scenarios where a given variable failed to function as projected, the matter of an increase in the cost of raw materials may also be considered, determining what impact that increase would have on the profits earned by the new product line. While there are exceptions, a sensitivity analysis does not typically include the development of scenarios that have below a certain potential for actually coming to pass. Instead, the process focuses on identifying and projecting the outcome if certain variables that do have at least a reasonable chance of taking place should occur. For this reason, the sensitivity analysis tends to remain somewhat grounded in facts and makes use of those facts in creating the alternative scenarios. What is considered a reasonable scenario will vary somewhat from one industry to the next, and will depend a great deal on general economic conditions as well as factors that apply to the industry where the business operates and the internal function of the business itself. (https://www.wisegeek.com/what-is-sensitivity-analysis.htm)

3(b) Application of Sensitivity Analysis

Sensitivity Analysis, in other words, is a procedure that analyses how the changes of certaininput values (income, costs, value of investments, etc.),produced due to inappropriate prediction or for someother reason, influence certain criteria values and thetotal investment project evaluation. Applying thisanalysis it is possible to analyse the maximum or minimum points which one value may take while, however, still allowing an investment project to be justified andacceptable for realization. In the investment project evaluation we have at ourdisposal a set of criteria (Net Present Value, InternalRate of Return, Pay-back Period, etc.) as the basis for evaluation (set of output values), and the set of values(income, costs, discount rate, value of investments,etc.) on the basis of which we can calculate certain individual criteria (input values), as shown by the diagram. Input Values Output Values CALCULATING VALUES FOR INDIVIDUAL CRITERIA Net Present Value Internal Rate of Return Payback Period (Calculation of individual criteria using input and output values)

Net Present Value

The Net Present Value criterion is defined as a sum ofpresent values of annual net incomes earned in theperiod of the project exploitation. Mathematical expression of this criterion is: NPV= value (1+rate) value - net cash flow occurs at the end of each period i rate - discount rate used to discount the cashflow n - time period of the projectA The word "net" in "net present value" indicates that our calculationA includes the initial costs as well as the subsequent profits. It also remindsA us that all the amounts in the income stream are net profits, revenuesA minus cost. In other words, "net" means the same as "total" here. (https://hadm.sph.sc.edu/courses/econ/invest/invest.html)

Internal Rate of Return

one of the uses of IRRA is byA corporations that wishA to compare capital projects.A For example, a corporation will evaluate an investment in a new plant versus anextension of an existing plant based on the IRR of each project. In such a case, each new capital project must produce anA IRR that isA higher than the company'sA cost of capital. Once this hurdle is surpassed, the project with the highest IRR would be the wiser investment, all other things being equal (includingA risk). IRR is also useful for corporations in evaluating stockA buybackA programs. Clearly, if a company allocates a substantial amount to a stock buyback, the analysis must show that the company's own stock is a better investment (has a higher IRR) than any other use of the funds for other capital projects, or than any acquisition candidate at current market prices. Calculating IRR The simplest example of computing an IRR is by using the example of a mortgage with even payments. Assume an initial mortgage amount of £200,000 and monthly payments of £1,050 for 30 years. The IRR (or impliedA interest rate) on this loan annually is 4.8%. A Because the a stream ofA paymentsA is equal and spaced at even intervals, an alternative approach is to discount these payments at a 4.8% interest rate, which will produce a net present value of £200,000. Alternatively, if the payments are raised to, say £1,100, the IRR of that loan will rise to 5.2%. The formula for IRR, using this example, is as follows: Where the initial payment (CF1) is £200,000 (a positive inflow) Subsequent cash flows (CFA 2, CFA 3, CF N) are negative £1050 (negative because it is being paid out) Number of payments (N) is 30 years times 12 = 360 monthly payments Initial Investment is £200,000 IRR is 4.8% divided by 12 (to equate to monthly payments) = 0.400%

A A A A A A A A A A A A A A A A

Payback Period(PBP)

Payback PeriodA is a financial metric that answer the question: How long does it take forA an investment to pay for itself? Or, how long does it take for incoming retuns to cover costs? Or, put still another way: How longA does it take forA the investment toA break even? Like other financial metrics such asA A internal rate of return (IRR)A and return on investment (ROI),A payback periodA takes essentially an "Investment" view of the action, plan, or scenario and its estimatedA cash flowA stream.A Each of these metrics compares investment costs to investment returns in one way or another.A Payback period is the length of time required for cumulative incoming returns to equal the cumulative costs of an investment (e.g. purchase of computer software or hardware, training expenses, or new product development), usually measured in years. Other things being equal, the investment with the shorter payback period is considered the better investment.A The shorter payback period is preferred because:A The investment costs are recovered soonerA and are available againA for further use.A AA shorter payback period is viewed asA less risky. It is usually assumed that the longer the payback period, the more uncertain are the positive returns. For this reason, payback period is often used as a measure of risk, or a risk-related criterion that must be met before funds are spent. A company might decide, for instance, to undertake no major investments or expenditures that have a payback period over, say, 3 years.A

Conclusion

There is clearly much more to the use of a decision support model than finding a single optimal solution. That solution should be viewed as the starting point for a wide ranging set of sensitivity analyses to improve the decision maker's knowledge and understanding of the system's behaviour. Even without undertaking the relatively complex procedures which explicitly involve probabilities in the sampling of scenarios or interpretation of results, sensitivity analysis is a powerful and illuminating methodology. The simple approach to sensitivity analysis is easy to do, easy to understand, easy to communicate, and applicable with any model. As a decision aid it is often adequate despite its imperfections. Given its ease and transparency, the simple approach to SA may even be the absolute best method for the purpose of practical decision making. Sensitivity analysis is an important tool in the model building process. By showingthat the system does not react greatly to a change in a parameter value, it reduces themodeler's uncertainty in the behavior. In addition, it gives an opportunity for a betterunderstanding of the dynamic behavior of the system. Sensitivity analysisA investigates what happens to the NPV and IRR of the project when one or more variables change. The idea is that we freeze all the variables except the one(s) analyzed and check how sensitive the NPV and/or the IRR are to changes in that variable. (https://cyllene.uwa.edu.au/~dpannell/dpap971f.htm)

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