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1 Chapter 8: Sensitivity and Breakeven Analysis Analyzing project risks by making mechanical trial and error changes to forecast values of selected variables.

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2 Handling Risk Measuring the risk associated with the expected cash flows of the project and incorporating this risk into the determination of the net present value (NPV) is essential for any real world project evaluation. There are various ways in which risk can be incorporated into the NPV computation and capital budgeting decision support. These include : –The risk-adjusted discount rate, –The certainty equivalent, –Sensitivity and break-even analysis –Simulation.

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3 Introduction Analyzing the risks of investment projects, by changing the values of forecasted variables. Finding the values of particular variables which give the project a Breakeven NPV of zero.

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4 Terminology used within sensitivity analysis Sensitivity analysis : The process of analyzing risky projects by estimating a net present value for each of the pessimistic, most likely and optimistic values for each variable under consideration. Only one variable at a time is analyzed, and all other variables are held at their most likely value whilst this one variable is analyzed. The process is designed to separate those variables which have material impacts on the project’s estimated net present value.

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5 Terminology used within sensitivity analysis Sensitive variables: Variables which return wide ranges of estimated net present values, or which return negative net present values, and hence are those most likely to receive management’s attention. Since all variables are forecast variables, all will have some impact on the project’s estimated net present value. Those which have the largest relative impacts are known as the sensitive variables.

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6 Terminology used within sensitivity analysis Optimistic, most likely and pessimistic values : These are estimated values at three identified points along the range of possible forecast values for the variables under consideration. The terms, ‘optimistic’ and ‘pessimistic’ are used in the context of impact on net cash flows and the positive wealth of the firm. For example, an optimistic unit sales price will be above the most likely unit sales price, whilst an optimistic unit production cost will be below the most likely unit production cost.

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7 Terminology used within sensitivity analysis Best case result : the name of net present value estimate when the optimistic forecast value for an individual variable is used in calculation. Base case result : the name of net present value estimate when the most likely forecast value for an individual variable is used in calculation. Worst case result: the name of net present value estimate when the pessimistic forecast value for an individual variable is used in calculation. The term ‘result’ here encompasses other common, like terms such as ‘scenario’, ‘outcome’, ‘output’ and ‘solution’.

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8 Process of Analysis 1.Calculate the project’s NPV using the most likely value estimated for each variable. 2.Select from the set of uncertain variables those which management feels may have an important bearing on predicted project performance (may be sensitive variable). 3.Forecast pessimistic, most likely and optimistic values for each of these variables over the life of the project.

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9 Process of Analysis 4.Recalculate the project’s NPV for each of the three levels of each variable. While each particular variable is stepped through each of its three values, all other variables are held at their most likely values.

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10 Process of Analysis 5.Calculate the change in NPV for the pessimistic to optimistic range of each variable. 6.Identify the sensitive variables. 7.The most sensitive variables are further investigated by management.

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11 Management Use of Sensitivity and Breakeven Analysis Sensitive variables are investigated and managed in two ways: (1) Ex ante; in the planning phase; more effort is used to create better forecasts of future values. If management decides the project is too risky, it is abandoned at this stage. Using Sensitivity:

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12 Management Use of Sensitivity and Breakeven Analysis (2) Ex post; in the project execution phase; management monitors the forecasted values. If the project is performing poorly, it is abandoned or sold off prior to its planned termination. Using Sensitivity: Sensitive variables are investigated and managed in two ways:

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13 Selection Criteria For Variables in the Analysis There are five characteristics which management could consider in choosing a set of variables for analysis. –Degree of management control. –Management's confidence in the forecasts. –Amount of management experience in assessing projects. –Extrinsic variables more problematic than intrinsic variables. –Time and cost of analysis.

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14 Selection Criteria For Variables in the Analysis Degree of management control. Management may feel confident of controlling variations in some variables but not in others –Internal variables Vs external variables –Monopoly supply situation Vs Perfectly competitive market. Sensitivity analysis would then be undertaken only on the uncontrollable variables, because management can usually respond positively ex post to changes in levels of the controllable variables.

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15 In the Delta Project, the controllable variables would include: –Initial outlay, upgrade cost, project life, outlays of working capital and the other costs. The uncontrollable variables might include: –Total asset salvage value, tax depreciation rate, forecast unit sales, required rate of return and the company tax rate. Since management might feel comfortable in exercising control over the controllable variables whatever the future brings, sensitivity analysis would be conducted on the uncontrollable variables only. Selection Criteria For Variables in the Analysis Degree of management control.

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16 Selection Criteria For Variables in the Analysis Management's trust in the forecasts. If management is confident that forecasts for some variables are reasonably reliable, then these variables could be left out of the analysis –Initial outlay (probably an agreed contract price) –Tax depreciation rate (historically relatively stable) –Unit production cost (the engineering costs and labor costs for physical production are generally well known from experience, or from engineering studies.)

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17 Selection Criteria For Variables in the Analysis Historical experience held by management Management may know that cash flow forecasts for elements of production such as unit costs for physical facilities and outlays of working capital are not as important as forecasts of unit sales and unit selling prices. With the benefit of such experience, management might judge that the only variables that it is necessary to test are: – initial outlay – forecast sales – unit selling price

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18 Selection Criteria For Variables in the Analysis Variables which give rise to extrinsic project benefits Income from private sector projects is taxable. Tax savings against this income are available in the form of plant and equipment depreciation, and plant and equipment salvage value tax adjustments. Whilst these are beneficial to the project, the project ought not to rely on them for viability. One way of testing this attribute is to remove or reduce these tax savings by setting their benefits at a pessimistic level.

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19 Selection Criteria For Variables in the Analysis Time available for analysis and cost of analysis In an ideal world, all forecast variables in a project would be subject to sensitivity analysis. With practical constraints on time and cost, only those variables which can be investigated quickly and cheaply will be investigated. While the actual mechanical analysis using a spreadsheet is relatively trivial, the time and effort involved in establishing pessimistic and optimistic values for some variables is not. This constraint might rule out variables such as forecast unit sales and forecast unit selling price, as these may require extensive empirical data-gathering and detailed economic analysis. Unfortunately, these may also turn out to be the critical variables.

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20 Management Use of Sensitivity and Breakeven Analysis Using Breakeven: Forecasted calculated Breakeven values of variables are continuously compared against actual outcomes during the execution phase.

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21 Terminology Within the Analysis Point values of forecasts are known as: ‘optimistic’, ‘most likely’, and ‘pessimistic’. Respective calculated NPVs are known as: ‘best case’, ‘base case’ and ‘worst case’. Variables giving a ‘breakeven’ value, return an NPV of zero for the project.

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22 Sensitivity analysis example: Delta Project In Chapter 7, the Delta Project proposal was evaluated using the most likely values for all variables. The resulting net present value was $1,008,457. This project is now subjected to sensitivity analysis. The variables In this project the forecast variables, expressed at their most likely values, are: –Initial outlay: $1,000,000 & Upgrade cost: $500,000 at the end of year 3 –Various outlays of working capital after year 0 –Total asset salvage value: $16,000 at the end of year 8

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23 –Tax depreciation rate: 12.5% per annum –Time-trend forecast of sales volume: an upward trend beginning with 691,106 units in the first year of operations, plus an additional 500,000 units per year following the upgrade –Predicted selling price: $0.50 per unit, rising to $0.75 per unit after the first five years. –Predicted production cost: $0.10 per unit –Predicted other costs: $50,000 per annum, rising to $55,000 per annum after five years. –Company tax rate: 30% per annum & Project life: eight years –Estimated required rate of return: 5.37% per annum. Sensitivity analysis example: Delta Project

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24 The actual choice of variables for sensitivity analysis The choice of variables should be based on mature and experienced judgment combined with a knowledge of the sensitivity analysis process. The choice ought to be made by management in conjunction with the project analyst. Sensitivity analysis example: Delta Project

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25 In the Delta Project example, any suite of variables could be chosen. The following set has been chosen : –Initial outlay: $1,000,000 –Total asset salvage value: $16,000 at the end of year 8 –Time-trend forecast of sales volume: an upward trend beginning with 691,106 units in the first year of operations, plus an additional 500,000 units per annum following the upgrade –Predicted selling price: $0.50 per unit, rising to $0.75 per unit after the first five years –Predicted production cost: $0.10 per unit –Predicted other costs: $50,000 per annum, rising to $55,000 per annum after five years –Estimated required rate of return: 5.37% per annum. Sensitivity analysis example: Delta Project The actual choice of variables for sensitivity analysis

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26 Sensitivity analysis example: Delta Project Initial outlay, for the fixed asset: Pessimistic $1,200,000; optimistic $800,000. With a fixed asset, the initial outlay is usually a fixed contractual amount, and there should not be much variation in its value. The value can vary when there are time delays in delivery, or in the construction of specialized equipment which has not been proven. Management experience with projects similar to the Delta Project suggests that this range should incorporate most foreseeable values. The actual choice of variables for sensitivity analysis

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27 Sensitivity analysis example: Delta Project Total asset salvage value : Pessimistic $0; optimistic $32,000. The most likely value has been estimated at $16,000. This is a forecast for eight years forward for an asset depreciating at 12.5% per annum. It is highly unlikely that any such forecast figure could be regarded as ‘reliable’, particularly in a world where technology is changing so rapidly. A wide variation, of plus or minus 100%, has been chosen to demonstrate this point. Again, this adjustment is based on management experience. In this particular project, given an initial outlay of $1,000,000, a salvage value of only $16,000 is immaterial. The salvage value has been included in the analysis to demonstrate testing of salvage values generally. A pessimistic value of $0 has been chosen to emphasize the point that any project should not rely on a salvage value for its viability. The actual choice of variables for sensitivity analysis

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28 Time-trend sales volume: Pessimistic: minus one standard error of the regression; optimistic: plus one standard error of the regression. This adjustment, of 16,701 per annum, is applied to the sales forecast given by the regression equation. The adjustment amount of plus or minus one standard deviation has been chosen because management is confident the trend will fall within this range. Sensitivity analysis example: Delta Project The actual choice of variables for sensitivity analysis

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29 The sales forecast of an extra 500,000 units for year 4 onwards This should be adjusted also. This sales forecast is only a management expectation and is not supported by any formal analysis. In the absence of a formal forecast, management feels that a variation of plus or minus 20% around the most likely value should cover all foreseeable variations. This variation will be equal to plus or minus 100,000 units per year. As a comparison, the standard error of the regression for the original sales units is 16,701 units, which is only 2.4% of the forecast value of 691,106 units for the first year. Sensitivity analysis example: Delta Project The actual choice of variables for sensitivity analysis

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30 Unit selling price : In many capital budgeting analyses, this variable will be the one of most concern. It represents the firm’s interactive face with the consumer, is not subject to management control and is at the mercy of competitors. Initial product pricing is a decision of management in consultation with the production and marketing departments, and will always be a difficult figure to determine. Additionally, it is this estimate which is most likely to vary in response to changes in the market-place. For these reasons, the figure should be carefully tested for sensitivity Sensitivity analysis example: Delta Project The actual choice of variables for sensitivity analysis

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31 The lowest price which can be set is equal to the direct costs of production. This value allows production to proceed by covering merely the direct costs of labor and materials, without contributing to fixed costs. Obviously, this is a figure which can be maintained only over the shortest possible term. In the example, this figure is $0.10. However, this is not a sensible value for a sensitivity test because it cannot be maintained over the full life of the project. An alternative value of $0.30 per unit is chosen as the pessimistic value for the test, because it can be assumed to represent the lowest price a competitor could set to drive the product from the market. Sensitivity analysis example: Delta Project The actual choice of variables for sensitivity analysis

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32 The highest (or optimistic) figure which can be set is the price which the market will bear. There is no direct information about this value in the example. In practice, it could be equal to the highest price being charged by a competing product. A value of $0.90 is assumed for the analysis. Sensitivity analysis example: Delta Project The actual choice of variables for sensitivity analysis

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33 Unit production cost : The figure given as the most likely value ($0.10 per unit) should be reasonably stable because it represents the consensus of production and cost accounting opinion. It should be reasonably accurate. As extremes around this value, it is assumed that the accounting and engineering staff have arrived at a pessimistic value of $0.13 and an optimistic value of $0.08 per unit. These are changes of +30% and −20% respectively. Sensitivity analysis example: Delta Project The actual choice of variables for sensitivity analysis

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34 Other costs : The values here, $50,000 per annum rising to $55,000 per annum after five years, are probably global values representing ‘overhead’. The amounts should be reasonably accurate since they are engineering/production oriented. Again, it is assumed that the relevant professionals have developed a forecast pessimistic value of $70,000 per annum, and a forecast optimistic value of $35,000 per annum, over the project’s life. These figures represent a rise of 40% and a fall of 30% respectively. These values are held constant over the whole life of the project, and are assumed to encompass the step increase at year 6. Sensitivity analysis example: Delta Project The actual choice of variables for sensitivity analysis

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35 Estimated required rate of return of 5.37% per annum : In addition to sales volume and sales price, this variable is subject to considerable change due to macro-economic influences. It is usually well tested in sensitivity analyses because of the traditional belief that the firm should have an expected upward shifts in the required yield. Management feels that current interest rates are at a historically low value, and that interest rates are likely to rise. To accommodate these changes, the interest rates chosen for the sensitivity analysis are an optimistic value of 4% per annum and a pessimistic value of 12% per annum. The pessimistic level is relatively high compared to the most likely rate. However, management feels that it is a valid expectation. Sensitivity analysis example: Delta Project The actual choice of variables for sensitivity analysis

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36 Sensitivity analysis example: Delta Project The actual choice of variables for sensitivity analysis

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37 Sensitivity analysis example: Delta Project Results of sensitivity tests

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38 Identification of the sensitive variables Naturally, all the variables will have some impact on the project’s net present value. Management is concerned with those having the largest impacts. The sensitivity test results show that the rank ordering of these by the dollar size of the range is: – forecast unit selling price – required rate of return – initial outlay. Other variables such as the sales forecast (in units) and the unit production cost are also important. Sensitivity analysis example: Delta Project Sensitivity test results

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39 Real Life Examples of Forecast Errors Large blowouts in initial construction costs for Sydney Opera House, Montreal Olympic Stadium. Big budget films are shunned by critics and public alike; e.g ‘Waterworld’: whilst cheap films become classics; eg.‘Easy Rider’. High failure rate of rockets used to launch commercial satellites.

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40 Developing Optimistic and Pessimistic Forecasts ( a) Use forecasting –error information from the forecasting methods: eg - upper and lower bounds; prediction interval; expert opinion; physical constraints, are applied to the variables. This method is formalized, but arguable, slow and expensive.

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41 Developing Optimistic and Pessimistic Forecasts (b) Use ad hoc percentage changes: a fixed percentage, such as 20%,or 30%, is added to and subtracted from the most likely forecast value. This method is vague and informal, but fast, popular, and cheap. ? +20% -20%

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42 Outputs and Uses Each forecast value is entered into the model,and one solution is given. Solutions can be summarized automatically, or individually by hand. Variables are ranked in order of the monetary range of calculated NPVs. Management investigates the sensitive variables. More forecasting is done, or the project is accepted or rejected as is.

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43 Strengths and Weaknesses of Analysis Easy to understand. Forces planning discipline. Helps to highlight risky variables. Relatively cheap. --------- --------- --------- Relatively unsophisticated. May not capture all information. Limited to one variable at a time. Ignores interdependencies.

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