Investment Analysis Using the Probability Distribution of the Internal Rate of Return

The probability distribution of the internal rate of return of an investment is derived under conditions where uncertainty in costs and returns can be described by a multi-variate normal distribution. The paper sketches the derivation of the exact probability distribution for the rate of return and gives the normal approximation to this distribution when variances of period costs and returns are small. A number of typical normal probability models are discussed in order to demonstrate the flexibility of the approach. An extended application of the analysis is presented using a World Bank appraisal of a hydroelectric power investment in Argentina.