Standard Deviation and Coefficient of variation:
Assigning probabilities to cash flow estimates represents a further improvement over sensitivity analysis. But it suffers from a limitation to the extent that it does not provide the decision maker with a concrete value indicative of vartability and therefore, risks. The Standard Deviation (S.D.) and the coefficient of variation (CV) are two such measures, which tell us about the variability associated with the expected cash flow in terms of degree of risk.
Standard Deviation is an absolute measure, which can be applied when the projects are giving same NPV. If the projects to be compared involve different NPVs, the coefficient of variation is the correct choice being a relative measure. Higher degree of S.D. and CV means project is more risky and vice versa. Calculation of S.D. involves two steps:
(A) S.D. for each particular period is calculated with the help of following formula:
S.D.(t1) = 
(B) After that a consolidated S.D. for the project will be calculated. Calculation of consolidated SD for the project depends on pattern of cash flows over the period. Cash flows can be independent over the period or dependent over the period. If cash flows are dependent over the period, it can be perfectly correlated or moderately correlated over the period.
(i) Independence of cash flows overtime
It means that the probability distribution over the period is not dependent on each other. In this situation Project's S.D. is calculated as below:
S.D. = 
(ii) Dependence of cash flows overtime
It means that cash flows are dependent over the time. T-he favorable or unfavorable outcome in the earlier periods is generally accompanied by the favorable or unfavorable outcome in the later periods. When cash flows are dependent over the time, the SD will be larger than what it would be under the assumption of independence of cash flows. The greater the degree of correlation between cash flows, the larger will be SD. Dependent cash flows over the time can be perfectly correlated or moderately correlated over time.
Perfect Correlation
Cash flows are perfectly correlated over time if they deviate in exactly the same relative manner. In other words, the cash flows in the next period depend entirely on what happened in previous period. In this SO will be calculated as follows:
Moderate Correlation
When the cash flows of the firm are neither independent nor perfectly correlated over time, they are rather moderately correlated. This problem can be handled by utilizing the concept of conditional probabilities-and/or decision tree. In this situation, correlation of cash flow over the time is not perfect. With a given cash flow in perioat1 the cash flow in period t2 can vary within a range and so on. To find out ENPV and SD of project, we will proceed in following manner:
(a) First step is to determine cash flows series on the basis of initial probability and conditional probabilities.
(b) For each cash flow series, NPV is calculated on the basis of outflow of project and cash inflows of that series.
(c) For each cash flow series, Joint probability (JP) is calculated by multiplying the initial probability and conditional probabilities of that series. The sum of JPs of all cash flow series should be equal to 1.
(d) NPV of each cash flow series is multiplied by JP of that series and added. Result is ENPV or NPV of the project.
(e) After that using following formula, SD of project will be calculated:
SDp = [NPV1 - ENPV)2 × JP1 + …………. ]
(i) NPV1 = NPV of a particular cash flow series
(ii) JP1 = Probability of a particular cash flow series
Calculation of Coefficient of Variation:
