A very popular method of assessing risk, sensitivity analysis has certain merits:

* It shows how robust or vulnerable a project is to changes in values of the underlying variables.

* It indicates where further work may be done. If the net present value is highly sensitive to changes in some factor, it may be worthwhile to explore how the variability of that critical factor may be contained.

* It is intuitively very appealing as it articulates the concerns that project evaluators normally have.

Not withstanding its appeal and popularity, sensitivity analysis suffers from several shortcomings:

1. It merely shows what happens to NPV (Net Present Value) when there is a change in some variable, without providing any idea of how likely that change will be.

2. Typically, in sensitivity analysis only one variable is changed at a time. In real world, however, variables tend to move together.

3. It is inherently a very subjective analysis. The same sensitivity analysis may lead one decision maker to accept the project while another may reject it.

Break even Analysis: In sensitivity analysis, we ask what will happen to the project if sales decline or costs increase or something else happens. As a project analyst, you will also be interested to know how much the project does not lose money. Such an exercise is called break even the break even point. To figure out how the break even quantity is calculated, let us look at the flour mill project for which following estimates were obtained:

Sales Rs 18 million

Variable costs 12 million

Fixed costs 1 million

Depreciation 2 million

Note that the ratio of variable costs to sales is 0.667 (12 / 18). This means that every rupee of sales makes a contribution of Rs 0.333. Put differently, the contribution margin ratio is 0.333 hence the break even level of sales wile be:

Fixed cost + Depreciation/ Contribution margin ratio

= 1 + 2 / 0.333 = Rs 9 million.

By way of confirmation you can verify that the break even level of sales is indeed Rs 9 million.

Rs in million

Sales 9

Variable costs 6

Fixed costs 1

Depreciation 2

Profit before tax 0

Tax 0

Profit after 0

Adjustment of Risk: Given the information on the risk characteristics of the project, measured in whatever way, you have to adjust for risk. You may do it by adjusting the discount rate, or the cash flows, or the payback period.

Adjusting the discount Rate:

A popular method to account for risk is to use a risk adjusted discount rate. If the risk of the project is similar to that of the existing investments of the firm use the average cost of capital of the if the firm as the discount rate; if the risk of the project is greater than the risk of the existing investments of the firm, use a discount rate grater than the average cost of capital of the firm finally, if the risks of the project is less that the risks of the existing investment of the firm, use a discount rate lower than the average cost of capital of the firm. While method is appealing, it is often applied in an ad hoc manner. The adjustment of the discount rate is done in a subjective manner.

Adjusting the cash Flows: Instead of adjusting the discount rate, one may adjust the cash flow. For example, if the expected cash flow for year 1 is say Rs 120,000 it may be adjusted downward to Rs 110,000. Doing so implies that an expected Rs 120,000 is deemed equivalent to a certain Rs 110,000. Put differently Rs 110,000 is the certainty equivalent of an expected Rs 120,000. Once the expected cash flows are converted into their certainty equivalents, the risk free discount rate is applied to compute the net present value. Remember that when the adjustment is made to the cash flows, the discount rate must be the risk free rate. If the discount rate, too, is adjusted it will tantamount to double counting of risk which is not of risk adjustment. However, it is very inconvenient to apply in practice because a certainty equivalent factor has to be specified for every cash flow – a somewhat difficult proposition.

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