6.4 Risk Analysis in Capital Budgeting

Sensitivity and Scenario Analysis

Capital budgeting forecasts are uncertain, so risk analysis asks how robust the NPV decision is.

Sensitivity Analysis

Sensitivity analysis changes one input at a time (sales volume, price, cost, salvage) while holding others constant, recomputing NPV to see which variable moves it most. The variable that produces the largest NPV swing is the project's key risk driver and deserves the most forecasting care. Its weakness: it ignores correlations between variables.

For example, if a 10% drop in unit volume cuts NPV by $40,000 but a 10% rise in variable cost cuts it by only $8,000, NPV is far more sensitive to volume, so management should validate the sales forecast above all else. The output is often shown as a tornado diagram ranking variables by impact.

Scenario Analysis

Scenario analysis improves on this by changing several variables together in internally consistent bundles — typically a best case, base case, and worst case. For instance, a recession scenario lowers price and volume simultaneously. It captures the combined effect of related variables but examines only a few discrete outcomes.

A worked illustration: base-case NPV is +$50,000. The worst case (low volume, low price, high cost) gives −$30,000 and the best case +$140,000. If managers attach probabilities of 25% / 50% / 25%, the expected NPV is 0.25(−$30,000) + 0.50($50,000) + 0.25($140,000) = $52,500, and the negative worst case flags the downside the firm must be able to absorb.

Monte Carlo Simulation

Monte Carlo simulation is the most sophisticated technique. The analyst assigns a probability distribution to each uncertain input, then the computer draws thousands of random combinations and computes NPV for each. The output is a full probability distribution of NPV — its mean, standard deviation, and the probability that NPV is negative. This reveals the likelihood of outcomes rather than a handful of cases, but it requires defensible distributions and correlation assumptions.

Real Options

Traditional NPV assumes a project is locked in once started. In reality, managers can react to new information, and that flexibility has value. Real options include:

• Option to expand: scale up if early results are strong.
• Option to abandon: exit and recover salvage if results disappoint.
• Option to defer (delay): wait for uncertainty to resolve before committing.
• Option to switch: change inputs, outputs, or processes as conditions change.

Because flexibility only adds value, a project's true worth = static NPV + value of its real options. Ignoring real options understates the value of uncertain projects. Real-option value is greatest when uncertainty is high and the manager can wait for or react to new information — for example, deferring a mine until commodity prices clarify, or staging an expansion in phases that can be abandoned cheaply.

Adjusting for Risk

Two formal methods incorporate risk into the discount calculation:

• Risk-adjusted discount rate (RADR): raise the hurdle rate above WACC for riskier projects, increasing the denominator so risky cash flows are discounted harder. Simple, but it compounds the penalty over time.
• Certainty equivalents: instead of raising the rate, shrink each risky cash flow to the smaller certain amount a decision-maker would accept in its place, then discount at the risk-free rate. This separates risk adjustment from time value, the theoretically cleaner approach.

The RADR is the more common method in practice because divisional hurdle rates are easy to assign, but it implicitly assumes risk grows at a constant rate over time. The certainty-equivalent method is more flexible because the equivalent factor can differ year by year, letting a manager penalize distant, more uncertain cash flows more heavily than near-term ones.

Inflation in Cash Flows

Inflation must be treated consistently. Discount nominal cash flows (which include expected inflation) at a nominal discount rate, or discount real cash flows at a real rate. Mixing a real rate with nominal cash flows overstates NPV — a classic exam trap. A common error is to inflate revenues and costs each year but forget that the depreciation tax shield is fixed in nominal dollars (depreciation is based on historical cost), so inflation erodes its real value and slightly lowers a project's real return.

Post-Audit of Capital Projects

The post-audit (or post-implementation review) compares a project's actual cash flows and results against the original forecast after it is operating.

The post-audit closes the capital budgeting loop and feeds lessons back into the next round of project selection.

Two cautions apply. First, a post-audit should be conducted after the project has run long enough for results to stabilize, not at the first sign of teething problems. Second, results must be interpreted in light of conditions that were genuinely unforeseeable at approval — a recession that no one could predict should not be charged against the sponsor's forecasting skill, whereas optimistic sales estimates should. Used well, the post-audit improves discipline without discouraging managers from proposing sound but uncertain projects.