The previous chapter discussed project analysis under certainty, i.e. in a no-risk situation. In reality, however, the future cash flows of a project are not certain. Cash flows cannot be forecast with absolute accuracy. These are estimates of what is expected in the future, not necessarily what will be realized in the future. Sometimes, even the initial capital outlay can be uncertain and subject to high estimation errors. For example, in 1987 the cost of the Channel Tunnel (between Britain and France) was estimated to be $12 billion, but later this was increased to about $22 billion. The Sydney Opera House is another famous example of a large cost increase over the initial estimate.

In the previous chapter, one single series – the best estimate of the project's future cash flows – was used to compute the net present value. This series may be viewed as the best estimate of a range of possible outcomes. For example, in Chapters 2 and 6, the Delta Project was considered and its first year's sales were expected to be $345,553. This was the best estimate. But this amount could eventually prove to have been under or over the actual sales that the project generated. This sales forecast was arrived at by estimating the sales units on the basis of past sales and assuming a unit selling price of $0.50. However, the actual selling price might be different to this forecast value.