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SENSIVITY ANALYSIS
In the evaluation of an investment project, we work with the forecasts of cash flows. Forecasted cash flow depends on the expected revenue and costs. Further, expected revenue is a function of sales volume and unit selling price. Similarly, sales volume depends on the market size and the firm‘s market share. Costs include variable costs, which depend on sales volume and unit variable cost and fixed costs. Costs include variable costs, which depend on sale volume, and unit variable cost and fixed cost. The net present value or the internal rate of return of a project is determined by analyzing the after-tax cash flows arrived at by combining forecasts of various variables. It is difficult to arrive at an accurate and unbiased forecast of each variable. We can‘t be certain about the outcome of any of these variables. The reliability of the NPV or Internal Rate of Return (IRR), we can work out how much difference it makes if any of these forecasts goes wrong. We can change each of the forecast, on at a time, to atleast three values: Pessimistic, Expected, and Optimistic. The NPV of the project is recalculated
under these different assumptions. This method of recalculating NPV or IRR by changing each forecast is call sensitivity analysis.
Sensitivity analysis is a way of analyzing change in the project‘s NPV (or IRR) for a given change in one of the variables. It indicates how sensitive a project‘s NPV (or IRR) is to changes in particular variables. The more sensitive the NPV, the more critical is the variable. The following three steps are involved in the use of sensitivity analysis: F 0A 7 Identification of all those variables, which have an influence on the
project‘s NPV (or IRR).
F 0A 7 Definition of the underlying (mathematical) relationship between the
variables. F 0A 7 Analysis of the impact of the change in each of the variables on the
project‘s NPV.
The decision-maker, while performing sensitivity analysis, computes the project‘s NPV (or IRR) for each forecast under three assumptions: (a) pessimistic; (b) expected, and (c) optimistic. It allows him to ask ‗what if 2 01 6questions. For example, what (is the NPV) if the volume increases or decreases? What (is the NPV) if variable cost or fixed cost increases or decreases? What (is the NPV) if the selling price increases or decreases? What (is the NPV) if the project is delayed or outlay escalates or the project‘s life is more or less than anticipated? A whole range of question can be answered with the help of sensitivity analysis. It examines the sensitivity of the variables underlying the computation of NPV or IRR, rather than attempting to quantify risk. It can be applied to any variable, which is an input for the after-tax cash flows. Let us consider an example.
How confident is the financial manger about his forecasts of various variables? Before he takes a decision, he may like to know whether the NPV changes, if any, of the forecast goes wrong. A sensitivity analysis can be conducted with regard to volume, price costs etc. In order to do so, we must obtain pessimistic and optimistic estimates of the underlying variables. Let us assume the following pessimistic and optimistic values for volume, price and costs.
FORECASTS UNDER DIFFERENT ASSUMPTIONS
S.No. Variable Pessimistic Expected Optimistic 1 Volume (Units ‗000) 750 1000 1250 2 Units selling price (Rs) 12.750 15.00 16. 3 Units variable cost (Rs) 7.425 6.75 6. 4 Annual fixed cost (Rs ‗000) 4800 4000 3200 If we change each variable (others holding constant), the project‘s NPV are
recalculated in the following Table (detailed calculations are not shown)
SENSIVITY ANALYSIS UNDER DIFFERENT ASSUMPTINS
S.No. Variable Pessimistic Expected Optimistic 1 Volume (1289) 4,829 10, 2 Units selling price (1,845) 4,829 9, 3 Units variable cost 2,827 4,829` 6, 4 Annual fixed cost 2,456 4,829 7, The above Table shows that the project‘s NPV when each variable is set to its pessimistic and optimistic values. The project does not seem to be that attractive with change in assumptions. The most critical variables is sales volume, followed by the units selling price. If the volume declines by 25 per cent (to 7,50, units), NPV of the project becomes negative (-Rs.12,89,000). Similarly, if the unit selling price falls by 15 per cent (to Rs.12.75), NPV IS –Rs.1,84,500.
Sensitivity Analysis: Pros and Cons
Sensitivity analysis has the following advantages:
F 0A 7 It compels the decision maker to identify the variables, which affect the cash
flow forecasts. This helps him in understanding the investment project in totality. F 0A 7 It indicates the critical variables for which additional information may be
obtained. The decision maker can consider actions, which may help in strengthening the ‗weak spots‘ in the project. F 0A 7 It helps to expose inappropriate forecasts, and thus guides the decision maker to
concentrate on relevant variables.
Let us emphasize that sensitivity analysis is not a panacea for a project‘s all uncertainties. It helps a decision maker to understand the project better. It has the flowing limitations: F 0A 7 It does not provide clear-cut results. The terms ‗optimistic‘ and
pessimistic‘ could mean different things to different persons in an organization. Thus, the rage of values suggested may be inconsistent.
It fails to focus on the interrelationship between variables. For example, sale volume may be related to price and cost. A price cut may lead to high sales and low operating cost.
Example:
Assume that the financial manager made pessimistic, most likely, and o ptimistic estimates of the cash flows for each project. The cash inflow estimates and resulting, NPVs in each case are summarized in the following table. Comparing the rages of cash inflows ($1,000 for project A and $4,000 for B0 and, more important, the ranges of NPVs ($7, for project A and $30,424 for B) makes it clear that project A is less risky than Project B. Given that both projects have the same most likely NPV of $5,212, the assumed risk-averse decision maker will take project A because it has less risk and no possibility of loss.
