Finance Quiz: Sensitivity And Scenario Analysis
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Sensitivity And Scenario AnalysisQuestion 1 of 20

Break-even analysis, in the context of capital budgeting risk assessment, is a specific application of sensitivity analysis that:

determines the project's profitability under the most likely economic conditions.
calculates the value of an input variable that causes a key output metric, such as NPV, to equal zero.
combines pessimistic, base-case, and optimistic assumptions into a single expected value.
evaluates the impact of changing multiple project variables simultaneously to model a recession.
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Finance Quiz

Finance Quiz: Sensitivity And Scenario Analysis

Practice Sensitivity And Scenario Analysis in Finance with focused quiz questions that help you check what you know, review explanations, and build confidence with test-style prompts.

What this quiz covers

This quiz focuses on Sensitivity And Scenario Analysis, giving you a quick way to practice the rules, question types, and explanations that matter most for Finance.

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Try each quiz question before looking at the correct answer. Use the explanations to review missed ideas, then come back to similar questions until the pattern feels familiar.

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Question 1

Break-even analysis, in the context of capital budgeting risk assessment, is a specific application of sensitivity analysis that:

  1. determines the project's profitability under the most likely economic conditions.
  2. calculates the value of an input variable that causes a key output metric, such as NPV, to equal zero. (correct answer)
  3. combines pessimistic, base-case, and optimistic assumptions into a single expected value.
  4. evaluates the impact of changing multiple project variables simultaneously to model a recession.
Explanation: Break-even analysis is a form of sensitivity analysis focused on finding the specific value of a single input variable (e.g., sales volume, price) at which the project's NPV becomes zero or its accounting profit becomes zero. It answers the question, 'How much can this variable change before the project becomes unprofitable?'

Question 2

A firm is evaluating a project with a 4-year life. The initial investment is $400,000, depreciated straight-line to zero. Base-case annual sales are 10,000 units at a price of $50 per unit. Annual variable costs are $25 per unit, and annual fixed costs are $80,000 (excluding depreciation). The tax rate is 30%, and the required return is 10%.

If all other base-case assumptions hold, what would be the project's Net Present Value (NPV) if the variable cost per unit were 10% higher than the base-case estimate?

  1. $16,838 (correct answer)
  2. $72,310
  3. $127,783
  4. -$6,936
Explanation: First, calculate the new OCF. The new variable cost is $25 * 1.10 = $27.50. Annual depreciation is $400,000 / 4 = $100,000. New EBIT = (10,000 * $50) - (10,000 * $27.50) - $80,000 - $100,000 = $45,000. NOPAT = $45,000 * (1 - 0.30) = $31,500. OCF = NOPAT + Depreciation = $31,500 + $100,000 = 131,500.ThePVIFAfor4yearsat10131,500. The PVIFA for 4 years at 10% is 3.16987. New NPV = (131,500 * 3.16987) - $400,000 = $416,838 - $400,000 = $16,838.

Question 3

A project's tornado diagram for NPV shows that the horizontal bar for 'sales price' is the longest and positioned at the top, while the bar for 'fixed costs' is much shorter and near the bottom. What is the most accurate conclusion an analyst can draw from this?

  1. The project's NPV is more responsive to a given percentage change in sales price than to an equivalent percentage change in fixed costs. (correct answer)
  2. The sales price estimate is inherently more uncertain and has a wider range of possible outcomes than the fixed cost estimate.
  3. A decrease in sales price will have a greater absolute impact on NPV than an equivalent percentage increase in sales price.
  4. The base-case estimate for sales price is higher in absolute dollar terms than the base-case estimate for fixed costs.
Explanation: A tornado diagram ranks variables based on the sensitivity of the output (NPV) to a change in each input variable. A longer bar indicates higher sensitivity. It shows that NPV changes more for a given change in sales price than for the same proportional change in fixed costs. It does not provide information about the underlying uncertainty of the inputs themselves (B), asymmetry of impact (C), or the base-case values (D).

Question 4

An analyst determines the following sensitivities for a project's NPV:

  • For each 1% increase in sales volume, NPV increases by $50,000.
  • For each 1% increase in sales price, NPV increases by $120,000.
  • For each 1% increase in the discount rate (from a base of 10% to 10.1%), NPV decreases by $80,000.
  • For each $1 increase in variable cost per unit (base cost is $50), NPV decreases by $100,000. Which variable represents the greatest risk to the project's success?
  1. Sales volume
  2. Sales price (correct answer)
  3. Discount rate
  4. Variable cost per unit
Explanation: To compare sensitivities, they must be in equivalent terms. The sensitivity for variable cost is given per dollar, not per percentage. A $1 increase on a $50 base cost is a 1/1/50 = 2% increase. Therefore, a 1% increase in variable cost would cause an NPV decrease of $100,000 / 2 = 50,000.ComparingtheabsoluteNPVimpactsfora150,000. Comparing the absolute NPV impacts for a 1% change in each variable: Sales Volume (50k), Sales Price (120k),DiscountRate(120k), Discount Rate (80k), and Variable Cost (50k).Thesalespricehasthelargestimpact(50k). The sales price has the largest impact (120,000) and thus represents the greatest risk.

Question 5

A sensitivity analysis for a 20-year infrastructure project reveals that its NPV is extremely sensitive to small changes in the discount rate but relatively insensitive to moderate changes in annual maintenance costs. This most likely suggests that:

  1. the project's cash flows are heavily weighted toward the early years of its life.
  2. the project has a very high internal rate of return (IRR).
  3. the base-case estimate for maintenance costs is likely inaccurate.
  4. a significant portion of the project's total cash flows occurs far in the future. (correct answer)
Explanation: The present value of cash flows is more sensitive to the discount rate the further into the future those cash flows are expected to occur. Therefore, high sensitivity to the discount rate implies that the project's value is derived from cash flows that are many years away. Conversely, if cash flows were front-loaded (A), the discount rate would have less of an impact. The IRR (B) and accuracy of cost estimates (C) are not directly addressed by this specific sensitivity pattern.

Question 6

A project's scenario analysis provides the following data:

  • Pessimistic Scenario: NPV = -$10M, Probability = 25%
  • Base-Case Scenario: NPV = $20M, Probability = 50%
  • Optimistic Scenario: NPV = $40M, Probability = 25%

Based on this analysis, what is the standard deviation of the project's NPV?

  1. $17.50 M
  2. $17.85 M (correct answer)
  3. $25.00 M
  4. $318.75 M
Explanation: First, calculate the expected NPV: E(NPV) = (0.25 * -$10M) + (0.50 * $20M) + (0.25 * 40M)=−40M) = -2.5M + $10M + $10M = $17.5M. Next, calculate the variance: Var(NPV) = Σ[P_i * (NPV_i - E(NPV))^2] = 0.25*(-10 - 17.5)^2 + 0.50*(20 - 17.5)^2 + 0.25*(40 - 17.5)^2 = 0.25*(-27.5)^2 + 0.50*(2.5)^2 + 0.25*(22.5)^2 = 0.25*(756.25) + 0.50*(6.25) + 0.25*(506.25) = 189.0625 + 3.125 + 126.5625 = 318.75. Finally, the standard deviation is the square root of the variance: SD = √318.75 ≈ $17.85 M.

Question 7

A company is launching a new product that requires an initial outlay of $1,500,000. The project has a 5-year life and will be depreciated straight-line to zero. The product will sell for $100 per unit. Variable costs are $60 per unit, and fixed costs are $200,000 per year. The company's tax rate is 30% and its cost of capital is 12%.

What is the annual sales quantity at which the project's Net Present Value (NPV) is zero?

  1. 11,647 units
  2. 12,500 units
  3. 16,647 units (correct answer)
  4. 19,861 units
Explanation: To have an NPV of zero, the present value of the operating cash flows (OCFs) must equal the initial investment. The PVIFA for 5 years at 12% is 3.60478. The required annual OCF is $1,500,000 / 3.60478 = $416,115. The OCF formula is OCF = [(Price - VC)*Q - FC - Dep](1 - T) + Dep. Annual depreciation is $1,500,000 / 5 = 300,000.So,OCF=[(300,000. So, OCF = [(100 - $60)*Q - $200,000 - $300,000](1 - 0.30) + $300,000 = (40Q - 500,000)(0.7) + 300,000 = 28Q - 350,000 + 300,000 = 28Q - 50,000. Set this equal to the required OCF: $416,115 = 28Q - 50,000. Solving for Q: 28Q = $466,115, so Q = 16,647 units.

Question 8

A company's scenario analysis for a new project yields the following potential NPVs and associated probabilities:

  • Pessimistic Scenario: NPV = -$2.5 million, Probability = 20%
  • Base-Case Scenario: NPV = $1.0 million, Probability = 50%
  • Optimistic Scenario: NPV = $4.0 million, Probability = 30%

What is the project's expected Net Present Value (NPV)?

  1. $1.2 million (correct answer)
  2. $0.83 million
  3. $1.0 million
  4. $1.7 million
Explanation: The expected NPV is the weighted average of the possible NPV outcomes, where the weights are the probabilities of each scenario. Expected NPV = Σ(Probability_i * NPV_i) = (0.20 * -$2.5M) + (0.50 * $1.0M) + (0.30 * 4.0M)=−4.0M) = -0.5M + $0.5M + $1.2M = $1.2 million.

Question 9

A project has a base-case NPV of $150,000. The analyst performs a sensitivity analysis on the sales price. The project's life is 5 years, the tax rate is 25%, and the discount rate is 10%. The base-case assumption is 10,000 units sold per year. If the sales price is reduced by $2.00 from the base case, what will be the new project NPV?

  1. $93,138 (correct answer)
  2. $74,184
  3. $75,000
  4. $50,000
Explanation: The change in sales price affects the annual after-tax cash flow. The annual before-tax revenue reduction is 10,000 units * $2.00/unit = $20,000. The annual after-tax reduction in cash flow is $20,000 * (1 - 0.25) = $15,000. This reduction is an annuity for 5 years. The present value of this reduction must be calculated using the PVIFA at 10% for 5 periods, which is 3.7908. PV of reduction = $15,000 * 3.7908 = $56,862. The new NPV is the base-case NPV minus this reduction: $150,000 - $56,862 = $93,138.

Question 10

A firm has a project with a base-case NPV of 2million.ThesensitivityoftheNPVtochangesinsalesvolumeis−2 million. The sensitivity of the NPV to changes in sales volume is -400,000 for every 1,000-unit decrease in annual sales. The firm's management believes there is a 30% chance that annual sales will be 2,000 units lower than the base case. Assuming sales volume is the only variable that changes, what is the expected NPV of the project considering this possibility?

  1. $1,760,000 (correct answer)
  2. $1,600,000
  3. $1,200,000
  4. $2,000,000
Explanation: First, determine the NPV in the low-sales state. A 2,000-unit decrease is two 'blocks' of 1,000 units. The NPV will decrease by 2 * $400,000 = $800,000. The NPV in this state is $2,000,000 - $800,000 = $1,200,000. This state has a 30% probability. The base-case state (NPV = $2M) has the remaining probability of 1 - 0.30 = 70%. The expected NPV is the probability-weighted average of the two outcomes: E(NPV) = (0.30 * $1,200,000) + (0.70 * $2,000,000) = $360,000 + $1,400,000 = $1,760,000.

Question 11

A financial analyst is evaluating a capital project and performs two distinct types of risk analysis. Analysis A calculates the project's NPV by individually changing the sales volume assumption to a high and low estimate while keeping all other variables at their expected values. Analysis B calculates the project's NPV under a 'recession' framework where sales volume is low, variable costs are high, and the project's required return is increased. Which statement correctly identifies these analyses?

  1. Analysis A is scenario analysis, and Analysis B is sensitivity analysis.
  2. Analysis A is sensitivity analysis, and Analysis B is scenario analysis. (correct answer)
  3. Both Analysis A and Analysis B are forms of sensitivity analysis.
  4. Both Analysis A and Analysis B are forms of scenario analysis.
Explanation: Sensitivity analysis involves changing one variable at a time to see its effect on an outcome like NPV, which is what Analysis A does. Scenario analysis involves changing multiple, typically correlated, variables simultaneously to model a particular outcome or 'scenario,' such as a recession, which is what Analysis B does.

Question 12

A firm is developing a pessimistic scenario for a new consumer product launch in Europe, and the firm reports its earnings in U.S. dollars. Which of the following sets of assumptions is the most internally consistent for such a scenario?

  1. Lower-than-expected regional GDP growth, a stronger local currency (vs. USD), and lower-than-expected raw material costs.
  2. Higher-than-expected consumer demand, higher inflation, and a lower-than-expected market share for the product.
  3. Lower-than-expected regional GDP growth, a weaker local currency (vs. USD), and higher-than-expected tariffs on imported raw materials. (correct answer)
  4. Stable regional GDP growth, a stable currency, and higher-than-expected variable costs due to operational inefficiencies.
Explanation: A consistent pessimistic scenario involves multiple, related variables moving in an adverse direction. Lower GDP growth suggests a weak economy, which would likely lead to a weaker local currency. A weaker local currency means that revenues translated back to USD will be lower. Higher tariffs represent an additional external negative shock. This combination is internally consistent and uniformly negative. The other options contain inconsistencies (e.g., lower GDP growth but a stronger currency, or higher demand in a pessimistic scenario).

Question 13

A scenario analysis for a strategic project reveals an expected NPV of $500,000, but a 40% probability of a significant negative NPV in the pessimistic 'recession' scenario. The project is not deferrable. What is the most appropriate action for management to take based on this information?

  1. Reject the project immediately because the risk of a loss is unacceptably high.
  2. Accept the project because its expected NPV is positive, which is the sole criterion for investment.
  3. Investigate strategies to mitigate the specific risks identified in the pessimistic scenario before making a final decision. (correct answer)
  4. Rerun the analysis using sensitivity analysis instead, as its results are more precise for decision-making.
Explanation: Scenario analysis is a tool for understanding and managing risk, not just for making a binary accept/reject decision. A positive expected NPV with significant downside risk suggests that management should explore ways to mitigate that risk (e.g., hedging, changing operational plans, insurance). Rejecting (A) or blindly accepting (B) ignores the nuances of the analysis. Switching to sensitivity analysis (D) would be a step backward, as it would ignore the variable correlations that the recession scenario correctly captures.

Question 14

A project manager is concerned that in an economic downturn, raw material costs will rise due to supply chain issues at the same time that consumer demand for the finished product falls. Which capital budgeting risk analysis tool is best suited to evaluate this specific concern?

  1. Sensitivity analysis
  2. Payback period analysis
  3. Break-even analysis
  4. Scenario analysis (correct answer)
Explanation: When evaluating capital budgeting risks, you need to match the analysis tool to the specific type of uncertainty you're facing. This question tests your understanding of when multiple variables change simultaneously and interact with each other. Scenario analysis (D) is the best choice because it's specifically designed to evaluate situations where multiple variables change together in realistic combinations. The project manager's concern involves two interconnected changes happening simultaneously during an economic downturn: rising raw material costs AND falling consumer demand. Scenario analysis allows you to model this complete "downturn scenario" as one cohesive situation, capturing how these variables interact and compound each other's effects on project returns. Sensitivity analysis (A) examines how changes in one variable at a time affect project outcomes, keeping other variables constant. This misses the crucial interaction between rising costs and falling demand that defines the manager's specific concern. Payback period analysis (B) simply measures how long it takes to recover the initial investment, but doesn't help evaluate different risk scenarios or changing economic conditions. Break-even analysis (C) identifies the sales level needed to cover costs, but it's a static calculation that doesn't model how multiple changing variables might affect that break-even point over time. Remember this distinction: use sensitivity analysis when you want to isolate the impact of individual variables, but choose scenario analysis when you need to evaluate realistic situations where multiple factors change together. Economic conditions like recessions, booms, or industry disruptions typically affect several variables simultaneously, making scenario analysis the superior tool for these comprehensive risk assessments.

Question 15

A company is considering a single-year project with an initial investment of $100,000, which will be fully depreciated in the first year. Base-case assumptions are: 5,000 units sold at $30/unit, variable costs of $15/unit, and fixed operating costs of $20,000. The tax rate is 25% and the required rate of return is 10%.

In a pessimistic scenario, sales volume is 10% lower than the base case and variable cost per unit is 10% higher than the base case. What is the project's Net Present Value (NPV) in this pessimistic scenario?

  1. -$39,773
  2. -$44,886
  3. -$49,489 (correct answer)
  4. -$62,955
Explanation: First, calculate the operating cash flow (OCF) for the pessimistic scenario. New sales units = 5,000 * 0.9 = 4,500. New variable cost/unit = $15 * 1.1 = $16.50. Revenue = 4,500 * $30 = $135,000. Total VC = 4,500 * $16.50 = $74,250. Depreciation = $100,000. EBIT = $135,000 - $74,250 - $20,000 - 100,000=−100,000 = -59,250. Since EBIT is negative, there is a tax shield: Tax = -59,250∗0.25=−59,250 * 0.25 = -14,812.50. Net Operating Profit After Tax (NOPAT) = EBIT - Tax = -59,250−(−59,250 - (-14,812.50) = -44,437.50.OCF=NOPAT+Depreciation=−44,437.50. OCF = NOPAT + Depreciation = -44,437.50 + $100,000 = 55,562.50.Finally,calculateNPV:NPV=−55,562.50. Finally, calculate NPV: NPV = -100,000 + (55,562.50/1.10)=−55,562.50 / 1.10) = -100,000 + 50,511.36=−50,511.36 = -49,489.

Question 16

A financial analyst is evaluating a capital project and performs two distinct types of risk analysis. Analysis A calculates the project's NPV by individually changing the sales volume assumption to a high and low estimate while keeping all other variables at their expected values. Analysis B calculates the project's NPV under a 'recession' framework where sales volume is low, variable costs are high, and the project's required return is increased. Which statement correctly identifies these analyses?

  1. Analysis A is scenario analysis, and Analysis B is sensitivity analysis.
  2. Analysis A is sensitivity analysis, and Analysis B is scenario analysis. (correct answer)
  3. Both Analysis A and Analysis B are forms of sensitivity analysis.
  4. Both Analysis A and Analysis B are forms of scenario analysis.
Explanation: Sensitivity analysis involves changing one variable at a time to see its effect on an outcome like NPV, which is what Analysis A does. Scenario analysis involves changing multiple, typically correlated, variables simultaneously to model a particular outcome or 'scenario,' such as a recession, which is what Analysis B does.

Question 17

A company is considering a single-year project with an initial investment of $100,000, which will be fully depreciated in the first year. Base-case assumptions are: 5,000 units sold at $30/unit, variable costs of $15/unit, and fixed operating costs of $20,000. The tax rate is 25% and the required rate of return is 10%.

In a pessimistic scenario, sales volume is 10% lower than the base case and variable cost per unit is 10% higher than the base case. What is the project's Net Present Value (NPV) in this pessimistic scenario?

  1. -$39,773
  2. -$44,886
  3. -$49,489 (correct answer)
  4. -$62,955
Explanation: First, calculate the operating cash flow (OCF) for the pessimistic scenario. New sales units = 5,000 * 0.9 = 4,500. New variable cost/unit = $15 * 1.1 = $16.50. Revenue = 4,500 * $30 = $135,000. Total VC = 4,500 * $16.50 = $74,250. Depreciation = $100,000. EBIT = $135,000 - $74,250 - $20,000 - 100,000=−100,000 = -59,250. Since EBIT is negative, there is a tax shield: Tax = -59,250∗0.25=−59,250 * 0.25 = -14,812.50. Net Operating Profit After Tax (NOPAT) = EBIT - Tax = -59,250−(−59,250 - (-14,812.50) = -44,437.50.OCF=NOPAT+Depreciation=−44,437.50. OCF = NOPAT + Depreciation = -44,437.50 + $100,000 = 55,562.50.Finally,calculateNPV:NPV=−55,562.50. Finally, calculate NPV: NPV = -100,000 + (55,562.50/1.10)=−55,562.50 / 1.10) = -100,000 + 50,511.36=−50,511.36 = -49,489.

Question 18

A key limitation of traditional one-variable sensitivity analysis is that it often:

  1. fails to identify the break-even points for key project variables.
  2. provides an incomplete assessment of risk by ignoring the effects of variable interdependencies. (correct answer)
  3. requires complex statistical software to determine probability distributions for inputs.
  4. is less effective than scenario analysis for identifying the single most critical variable affecting project outcomes.
Explanation: The primary weakness of one-variable sensitivity analysis is that it assumes variables are independent. In reality, economic variables are often correlated (e.g., in a recession, sales volume and prices may both fall). By changing only one variable at a time, it ignores these interdependencies, potentially understating total project risk.

Question 19

A company's scenario analysis for a new project yields the following potential NPVs and associated probabilities:

  • Pessimistic Scenario: NPV = -$2.5 million, Probability = 20%
  • Base-Case Scenario: NPV = $1.0 million, Probability = 50%
  • Optimistic Scenario: NPV = $4.0 million, Probability = 30%

What is the project's expected Net Present Value (NPV)?

  1. $1.2 million (correct answer)
  2. $0.83 million
  3. $1.0 million
  4. $1.7 million
Explanation: The expected NPV is the weighted average of the possible NPV outcomes, where the weights are the probabilities of each scenario. Expected NPV = Σ(Probability_i * NPV_i) = (0.20 * -$2.5M) + (0.50 * $1.0M) + (0.30 * 4.0M)=−4.0M) = -0.5M + $0.5M + $1.2M = $1.2 million.

Question 20

A project has a base-case NPV of $150,000. The analyst performs a sensitivity analysis on the sales price. The project's life is 5 years, the tax rate is 25%, and the discount rate is 10%. The base-case assumption is 10,000 units sold per year. If the sales price is reduced by $2.00 from the base case, what will be the new project NPV?

  1. $93,138 (correct answer)
  2. $74,184
  3. $75,000
  4. $50,000
Explanation: The change in sales price affects the annual after-tax cash flow. The annual before-tax revenue reduction is 10,000 units * $2.00/unit = $20,000. The annual after-tax reduction in cash flow is $20,000 * (1 - 0.25) = $15,000. This reduction is an annuity for 5 years. The present value of this reduction must be calculated using the PVIFA at 10% for 5 periods, which is 3.7908. PV of reduction = $15,000 * 3.7908 = $56,862. The new NPV is the base-case NPV minus this reduction: $150,000 - $56,862 = $93,138.