Chapter 11: Adjustment of Risk and Uncertainty in Capital Budgeting Decision (CAIIB – Paper 3)
1. Which of the following is the primary source of risk in capital budgeting decisions?
A. Fixed cost of the project
B. Discounting method used
C. Uncertainty in future cash flows
D. Depreciation method chosen
The primary source of risk in capital budgeting is the uncertainty of future cash inflows and outflows, as they directly impact project viability.
2. Sensitivity Analysis in capital budgeting is primarily used to:
A. Assess the effect of changes in key variables on project outcomes
B. Measure the probability distribution of returns
C. Eliminate risk entirely from decision-making
D. Adjust the discount rate for inflation
Sensitivity analysis tests how changes in one or more variables (sales, costs, discount rate) affect project outcomes like NPV or IRR.
3. A project has an NPV of ₹10,00,000 at expected sales of 50,000 units. If sales fall by 10%, the NPV decreases to ₹6,00,000. What does this indicate?
A. Project is not profitable
B. Project is risk-free
C. Sales volume is not a critical factor
D. NPV is highly sensitive to sales volume
A large reduction in NPV due to a small fall in sales volume shows that the project outcome is highly sensitive to sales changes.
4. Which of the following best differentiates Risk from Uncertainty in financial decisions?
A. Both involve unknown outcomes but probabilities are not relevant
B. In risk, probabilities of outcomes are known; in uncertainty, probabilities are not known
C. Risk always leads to losses, uncertainty does not
D. There is no difference between the two
Risk implies that the probabilities of different outcomes can be estimated, while uncertainty means outcomes are not measurable in terms of probability.
5. In Sensitivity Analysis, the variable that causes the largest change in NPV when altered is known as:
A. Independent variable
B. Control variable
C. Critical factor
D. Opportunity cost variable
The most influential variable in sensitivity analysis is called the critical factor, as it determines project feasibility under uncertainty.
6. Case Study: A company is evaluating a project. The expected NPV is ₹5,00,000. If raw material cost increases by 15%, NPV falls to ₹1,00,000. Which of the following is correct?
A. Project’s NPV is highly sensitive to raw material cost
B. Project is risk-free
C. Sensitivity analysis is not applicable here
D. Discount rate should be reduced
Since a change in raw material cost drastically reduces NPV, the project’s viability is very sensitive to cost fluctuations.
7. Scenario analysis in capital budgeting involves:
A. Changing only one variable at a time
B. Ignoring the worst-case situation
C. Analyzing projects without considering uncertainty
D. Evaluating project outcomes under different assumptions such as best case, worst case, and most likely
Scenario analysis examines the impact of different possible future situations (best, worst, most likely) on project outcomes like NPV or IRR.
8. Which of the following is a limitation of scenario analysis?
A. It considers only a few discrete outcomes and ignores probabilities
B. It eliminates risk completely
C. It always gives a single deterministic answer
D. It cannot be used in capital budgeting
Scenario analysis is limited because it only looks at selected cases (best, worst, likely) and does not incorporate full probability distributions.
9. Hillier’s Model in capital budgeting is primarily concerned with:
A. Adjusting discount rate for inflation
B. Incorporating probability distribution of cash flows into project risk assessment
C. Only comparing IRR and NPV
D. Eliminating uncertainty through diversification
Hillier’s Model introduces probability distributions of cash flows into capital budgeting, allowing expected value and variance of NPV to be computed.
10. According to Hillier’s Model, the risk of a project is generally measured by:
A. Accounting rate of return
B. Payback period
C. Standard deviation of NPV
D. Internal rate of return
In Hillier’s Model, risk is measured by the standard deviation of NPV, which indicates variability in project returns due to uncertain cash flows.
11. Case Study: A project has three possible NPVs – ₹12 lakh (probability 0.2), ₹8 lakh (probability 0.5), and ₹2 lakh (probability 0.3). What is the expected NPV?
12. The key difference between sensitivity analysis and scenario analysis is:
A. Sensitivity changes one variable at a time, while scenario changes several variables together
B. Both methods change only one variable at a time
C. Scenario is deterministic, sensitivity is probabilistic
D. There is no difference between the two
Sensitivity analysis tests the effect of changing one variable, while scenario analysis evaluates multiple variables changing simultaneously.
13. Simulation analysis in capital budgeting is mainly used to:
A. Eliminate all risk factors from projects
B. Generate a probability distribution of project outcomes by testing thousands of possible scenarios
C. Replace scenario analysis completely
D. Compute IRR using shortcuts
Simulation analysis (e.g., Monte Carlo) generates probability distributions for NPV/IRR by running multiple iterations with varying input assumptions.
14. Which of the following best describes Monte Carlo Simulation in project appraisal?
A. It compares only the best and worst case
B. It focuses only on sensitivity of sales volume
C. It assumes a single fixed cash flow value
D. It uses random sampling of input variables to estimate probability distribution of outcomes
Monte Carlo Simulation assigns probability distributions to inputs (sales, cost, interest rate) and uses random sampling to estimate possible NPVs.
15. Which of the following is an advantage of simulation analysis compared to sensitivity analysis?
A. It ignores probability distributions
B. It can test only one variable at a time
C. It incorporates the simultaneous variability of multiple input variables
D. It provides a single deterministic NPV value
Unlike sensitivity analysis, simulation allows multiple variables to vary simultaneously, giving a more realistic probability distribution of outcomes.
16. Limitation of simulation analysis in capital budgeting is that:
A. It requires complex computation and reliable probability data for inputs
B. It eliminates the role of risk completely
C. It cannot be applied in project finance
D. It always gives incorrect results
Simulation needs advanced tools, large data, and probability assumptions. Its accuracy depends on the quality of input data and model.
17. Case Study: A project’s NPV depends on two major uncertain factors – sales growth rate and raw material cost. To capture the combined effect of both simultaneously, which technique should be used?
A. Sensitivity Analysis
B. Scenario Analysis
C. Hillier’s Model
D. Simulation Analysis
Simulation is most suitable when multiple uncertain variables interact, as it models joint probability effects on NPV or IRR.
18. Decision Tree Analysis in capital budgeting is most useful when:
A. Only one certain outcome exists
B. All cash flows are risk-free
C. Projects involve sequential decisions with uncertain future outcomes
D. There are no probabilities to assign
Decision tree analysis is used when investment decisions are made in stages and each stage depends on uncertain future outcomes.
19. In Decision Tree Analysis, the value at each decision node is obtained by:
A. Taking only the maximum possible return
B. Calculating the expected monetary value (EMV) by multiplying payoffs with their probabilities
C. Choosing the least risky branch only
D. Ignoring probabilities and using average returns
At chance nodes, the expected monetary value (EMV) is computed by multiplying each possible outcome with its probability and summing the results.
20. Case Study: A project requires an initial investment of ₹50 lakh. There is a 60% chance of NPV = ₹30 lakh and 40% chance of NPV = –₹10 lakh. What is the Expected Monetary Value (EMV)?
A. It considers the effect of a project on the overall firm’s risk profile rather than in isolation
B. It ignores the firm’s capital structure
C. It assumes the project has no impact on shareholder wealth
D. It excludes correlation between projects
Corporate risk analysis measures how a project affects the overall firm’s risk-return, considering diversification and correlation among projects.
22. Which of the following tools is often used in corporate risk analysis to measure the impact of projects on shareholders?
A. Payback period
B. Accounting Rate of Return
C. Beta and CAPM-based analysis
D. Random guessing
Corporate risk analysis often uses Beta (systematic risk) and CAPM to assess how a project impacts the firm’s cost of equity and shareholder value.
23. Case Study: A bank is evaluating two projects. Project A has high standalone risk but low correlation with existing projects. Project B has moderate risk but strong positive correlation with existing projects. Which is preferable in terms of corporate risk?
A. Project B, because it has moderate risk
B. Both projects equally preferable
C. Project A is always inferior due to higher risk
D. Project A, because diversification reduces overall corporate risk
In corporate risk analysis, diversification matters. Even though Project A has higher standalone risk, its low correlation with other projects reduces overall firm risk.
24. Which of the following is a technique commonly used to manage project risk?
A. Ignoring uncertainty in forecasts
B. Relying only on accounting profits
C. Diversification of projects
D. Selecting projects randomly
Diversification helps spread risk across multiple projects, reducing the impact of failure in any one project.
25. In capital budgeting under risk, the “certainty equivalent approach” involves:
A. Adjusting expected cash flows by a risk factor
B. Increasing discount rate for all risky projects
C. Ignoring risk premiums in cash flows
D. Using nominal interest rate for discounting
The certainty equivalent approach converts risky cash flows into risk-free equivalents by adjusting them with a certainty factor.
26. Project selection under risk often relies on:
A. Book value of assets
B. Historical profits only
C. Tax shield benefits exclusively
D. Probability-adjusted NPV
Probability-adjusted NPV incorporates likelihood of outcomes, making it more reliable for decision-making under uncertainty.
27. Which of the following best describes risk-adjusted discount rate (RADR)?
A. A discount rate based only on the time value of money
B. A discount rate increased to account for project risk
C. A rate lower than the risk-free rate
D. A fixed rate applied to all projects regardless of risk
RADR incorporates both time value of money and risk premium, making it higher than the risk-free rate for riskier projects.
28. When selecting projects under risk, the “risk-return tradeoff” implies:
A. Higher return always leads to lower risk
B. Projects with higher risk should always be rejected
C. Higher risk should be justified by higher expected returns
D. Risk is irrelevant if NPV is positive
The risk-return tradeoff highlights that investors and managers accept higher risks only if there is a potential for higher rewards.
29. In practice, risk analysis in capital budgeting is primarily used to:
A. Eliminate all uncertainties in project cash flows
B. Replace management judgment with mathematical models
C. Ensure projects have guaranteed returns
D. Assess the impact of uncertainty on project viability
Risk analysis does not remove uncertainty but helps managers evaluate how risks affect project outcomes and decisions.
30. Which of the following tools is most frequently used in practice for risk analysis of projects?
A. Decision tree analysis
B. Sensitivity analysis
C. Hillier model
D. Simulation analysis
Sensitivity analysis is widely used in practice because of its simplicity and ability to show how changes in key variables affect outcomes.
31. A major limitation of risk analysis in practice is that:
A. It completely ignores probability distribution of cash flows
B. It guarantees removal of uncertainty
C. Results often depend on assumptions and quality of input data
D. It can only be applied to small-scale projects
Risk analysis outcomes are only as good as the assumptions and input data; poor data quality can lead to misleading results.
32. Which of the following is considered a qualitative aspect of risk analysis in practice?
A. Management perception of industry risk
B. Monte Carlo simulation results
C. Probability-adjusted NPV
D. Certainty equivalent coefficients
Practical risk analysis often includes qualitative judgments like management experience, competitive environment, and industry outlook.
33. In practice, why is simulation analysis not used as frequently as sensitivity analysis?
A. It ignores correlation among variables
B. It produces less reliable results
C. It does not allow multiple scenarios
D. It is more complex and resource-intensive
Although powerful, simulation analysis requires advanced tools, data, and time, making sensitivity analysis more popular in day-to-day practice.
Caselet (Questions 34–36):
A company is evaluating a project requiring an initial investment of ₹10,00,000.
There are three possible outcomes for annual cash inflows over 5 years:
• Best Case: ₹3,50,000 (Probability 0.3)
• Most Likely Case: ₹3,00,000 (Probability 0.5)
• Worst Case: ₹2,00,000 (Probability 0.2)
The discount rate is 10%.
34. What is the expected annual cash inflow (EACF)?
