Uncertainty in Initial Cash Outflows

In many capital budgeting situations, the initial cost of the project, especially when occurring only at Time 0, is assumed to be known with certainty. The idea here is that in most cases bids have already been received from contractors and vendors, so the initial cost can be predicted with relative precision. However, in some circumstances, there can be substantial uncertainty in initial cost. For example, there can be a great deal of uncertainty in the cost of a building that will not be constructed for several years. Or there can be uncertainty in the cost of a major construction project that will take several years to complete.

When there is uncertainty in initial cost, how should that risk be incorporated into the analysis? If the entire cost, or even the major portion, occurs at Time 0, the discount rate is not applied to the cash flow, so the risk-adjusted discount rate method will not get the job done.

What do you think? Can the certainty equivalent method be used? Assume that Time 0 costs on a project could be $100,000 or $150,000 with equal probability, so the expected initial cost is $125,000. What is your estimate of the certainty equivalent cash flow? (Hint: Remember that risk adjustments to cash outflows are the opposite of those applied to inflows.)