---
title: "Methods for assessing risk and uncertainty"
subject: "Engineering Economics"
chapter: 6
key: "semester_6/engineering_economics:methods-assessing-risk-uncertainty"
source: https://www.bctengineer.com/q/semester_6/engineering_economics/methods-assessing-risk-uncertainty
site: BCT Engineering
---

# Methods for assessing risk and uncertainty

Engineering Economics · Chapter 6: Risk Analysis

- Asked in: 2068 Jestha, 6 marks
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_6/engineering_economics/methods-assessing-risk-uncertainty
- Whole chapter: https://www.bctengineer.com/md/semester_6/engineering_economics/chapter-6

## Question

Explain the methods for assessing risk/uncertainty.

## Short answer

Methods: break-even analysis, sensitivity analysis, scenario analysis, expected value analysis, decision tree analysis, Monte Carlo simulation, risk-adjusted discount rate, reduced useful life/payback cut-off, certainty equivalent. Break-even and sensitivity are simplest and most used; others require probability estimates.

## Answer

Risk and uncertainty arise because cash flows, lives and interest rates used in an analysis are estimates of the future. The common methods to assess their effect are:

#### 1. Break-even analysis
Finds the value of one variable (for example annual output, price or life) at which PW or AW becomes zero, i.e. income equals cost. If the expected value is well above the break-even point, the risk is small. It is simple but treats one variable at a time.

#### 2. Sensitivity analysis
One factor (investment, annual revenue, life, MARR) is changed over a range (for example ±30%) while others stay fixed, and the change in PW, AW or IRR is recorded.
- Results are shown in a **sensitivity diagram**: the steeper the line, the more sensitive the decision is to that factor.
- It shows which estimate must be made most carefully, but gives no probabilities and ignores the link between factors.

#### 3. Scenario analysis
Three sets of estimates (optimistic, most likely, pessimistic) are assumed and the project value is computed for each. It shows the range of outcomes and the downside.

#### 4. Expected value analysis
When probabilities are known, the expected value is E(X) = Σ pᵢXᵢ. For PW, E(PW) = Σ p × PW(outcome). The alternative with the highest expected PW (or lowest expected cost) is chosen. The variance or standard deviation, σ² = Σ pᵢ(Xᵢ − E)², measures the risk: a larger spread means higher risk.

#### 5. Decision tree analysis
Used for sequential decisions with chance events. The tree is rolled back from the end: expected values at chance nodes and best choice at decision nodes.

#### 6. Monte Carlo simulation
Probability distributions are given to the uncertain variables; many random trials are run by computer and the distribution of PW or IRR is built. It gives the probability that PW < 0 and is suitable for complex projects.

#### 7. Other approaches
- **Risk-adjusted discount rate:** a higher MARR for riskier projects.
- **Reduction of useful life / payback cut-off:** accept only projects that recover investment quickly.
- **Certainty equivalent:** replace uncertain cash flows by sure equivalents.

**Summary:** break-even and sensitivity analyses are the simplest and are most used in practice; expected value, decision trees and simulation need probability estimates.

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. Break-even analysis finds:
   A. The probability of each outcome
   B. The value of a variable at which PW or AW becomes zero (income equals cost)
   C. The largest possible PW
   D. The MARR to be used
   Answer: B. It treats one variable at a time and is simple; a value far above break-even means low risk. (Key point: Break-even analysis)

2. In a sensitivity diagram, a steeper line indicates:
   A. The decision is less sensitive to that factor
   B. The factor has no effect
   C. The probability is higher
   D. The decision is more sensitive to that factor
   Answer: D. A steeper line shows PW changes more for the same % change, so that estimate must be made carefully. (Key point: Sensitivity analysis)

3. Which measure indicates the risk (spread) of outcomes in expected value analysis?
   A. Variance or standard deviation
   B. The sum of probabilities
   C. The first cost
   D. The payback period
   Answer: A. sigma^2 = sum p(X - E)^2; a larger spread means higher risk. (Key point: Expected value and risk)

4. What does Monte Carlo simulation give that sensitivity analysis does not?
   A. A single deterministic PW
   B. The break-even life only
   C. The distribution of PW or IRR, including the probability that PW < 0
   D. A lower MARR
   Answer: C. Uncertain variables get probability distributions, many random trials are run, and the distribution of PW is built. (Key point: Monte Carlo simulation)

## Related in Engineering Economics

- [Define certainty, uncertainty and risk](https://www.bctengineer.com/question.md?key=semester_6%2Fengineering_economics%3Acertainty-uncertainty-risk-define) — Engineering Economics, chapter 6