Project analysis and risk
Forecasts are uncertain. Sensitivity analysis, scenarios, break-even analysis, and real options help managers understand project risk.
Forecasting risk
NPV depends on forecasts of sales, prices, costs, and timing, which are uncertain. Optimistic forecasts, a common bias, can make bad projects look good. Analysts test how results change when assumptions change.
Sensitivity analysis
Sensitivity analysis changes one input at a time, such as sales volume or unit cost, to see how much NPV changes. Inputs that cause large NPV swings deserve the most attention and better forecasting.
Scenario analysis
Scenario analysis examines combinations of changes: a best case, a base case, and a worst case, each with consistent assumptions. If NPV is negative even in a plausible bad scenario, managers might reduce the project's scale or seek ways to cut risk.
Simulation
Monte Carlo simulation assigns probability distributions to uncertain inputs and runs thousands of trials, producing a distribution of possible NPVs. It shows the probability that a project loses money, though results depend on the assumptions built into the model.
Break-even analysis
Break-even analysis finds the sales level at which a project's NPV (or accounting profit) is zero. Accounting break-even covers costs including depreciation; cash break-even covers cash costs; financial break-even gives zero NPV, usually requiring higher sales. Managers judge whether expected sales comfortably exceed break-even.
Real options
Real options are choices managers have to adapt projects as information arrives: the option to expand if successful, abandon if unsuccessful, delay until conditions are clearer, or switch inputs or outputs. Standard NPV may undervalue projects with valuable flexibility. Pilot projects and staged investments create such options.
Capital budgeting in practice
Large projects often go through stages of approval, with post-audits comparing actual results with forecasts to improve future estimates and discourage over-optimism. Strategic considerations, such as entering a new market or defending against competitors, also influence decisions alongside NPV.
Worked example
A new product's base-case NPV is 2 million dollars. Sensitivity analysis shows that if sales are 10% lower than forecast, NPV falls to 0.5 million; if unit costs are 10% higher, NPV falls to 1.6 million. Sales volume is the critical variable, so the firm commissions more market research and launches a smaller pilot first, creating an option to expand.
Key takeaways
NPV depends on uncertain forecasts, often biased toward optimism. Sensitivity analysis tests one input at a time; scenario analysis tests consistent combinations; Monte Carlo simulation produces distributions of outcomes. Break-even analysis finds the sales needed for zero profit or NPV. Real options to expand, abandon, delay, or switch add value that basic NPV may miss. Post-audits and staged approvals improve capital budgeting.
Flashcard
Uncertainty in projected cash flows
Check your understanding
Why might a firm launch a small pilot of a new product before a full launch?