Skip to main content
Sign in Create a free account
Varsity Tutors
Sign in

Sensitivity & Scenario Analysis - Finance

  1. A key limitation of traditional one-variable sensitivity analysis is that it often:
    Answer: provides an incomplete assessment of risk by ignoring the effects of variable interdependencies. 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.
  2. 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?
    Answer: Lower-than-expected regional GDP growth, a weaker local currency (vs. USD), and higher-than-expected tariffs on imported raw materials. 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).
  3. An analyst is constructing a tornado diagram to illustrate the sensitivity of a project's NPV to several key variables. A fundamental step in this process is to:
    Answer: calculate the effect on NPV by moving each variable to its upper and lower bound, one at a time, while holding all others at their base-case values. The construction of a tornado diagram is the visual output of a one-variable sensitivity analysis. The core methodology involves systematically changing one variable at a time between a low and high estimate (its range) while all other variables remain constant at their base-case values. The resulting impact on NPV is calculated for each variable, and the results are then plotted. The other options describe Monte Carlo simulation (A), scenario analysis (B), or a prerequisite for a more complex simulation (D).
  4. 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?
    Answer: $16,838 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. The PVIFA for 4 years at 10% is 3.16987. New NPV = ($131,500 * 3.16987) - $400,000 = $416,838 - $400,000 = $16,838.
  5. 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?
    Answer: The project's NPV is more responsive to a given percentage change in sales price than to an equivalent percentage change in fixed costs. 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).
  6. Break-even analysis, in the context of capital budgeting risk assessment, is a specific application of sensitivity analysis that:
    Answer: calculates the value of an input variable that causes a key output metric, such as NPV, to equal zero. 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?'
  7. What is the project's expected Net Present Value (NPV)?
    Answer: $1.2 million 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) = -$0.5M + $0.5M + $1.2M = $1.2 million.
  8. A firm has a project with a base-case NPV of $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?
    Answer: $1,760,000 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.
  9. Under which of the following conditions might a standard one-variable sensitivity analysis provide a misleadingly optimistic view of a project's risk?
    Answer: When the project's most sensitive variables are positively correlated. Sensitivity analysis tests how changes in individual variables affect a project's NPV, but it can create a false sense of security when you don't consider how variables interact. The key insight is understanding when one-variable analysis masks the true risk profile. When a project's most sensitive variables are positively correlated (Answer D), they tend to move in the same direction simultaneously. This creates a compounding effect that makes the project much riskier than individual sensitivity tests suggest. For example, if both sales volume and selling price are highly sensitive variables that typically rise and fall together due to market conditions, a downturn could devastate both simultaneously. One-variable analysis would show each risk in isolation, missing the amplified impact of their combined movement. Answer A is incorrect because negatively correlated variables actually provide natural hedging—when one moves unfavorably, the other tends to move favorably, reducing overall risk rather than creating misleading optimism. Answer B represents a limitation of sensitivity analysis but doesn't specifically create misleadingly optimistic results—it simply means you're working with incomplete information. Answer C describes a situation where standard sensitivity analysis would actually reveal high risk accurately, since discount rate sensitivity is precisely what one-variable analysis is designed to capture. Remember this pattern: sensitivity analysis becomes dangerously misleading when it fails to capture correlation effects. Always ask yourself whether the key risk variables in a project are likely to move together—if so, scenario analysis or Monte Carlo simulation will give you a more realistic risk assessment than isolated sensitivity testing.
  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?
    Answer: -$49,489 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 = -$59,250. Since EBIT is negative, there is a tax shield: Tax = -$59,250 * 0.25 = -$14,812.50. Net Operating Profit After Tax (NOPAT) = EBIT - Tax = -$59,250 - (-$14,812.50) = -$44,437.50. OCF = NOPAT + Depreciation = -$44,437.50 + $100,000 = $55,562.50. Finally, calculate NPV: NPV = -$100,000 + ($55,562.50 / 1.10) = -$100,000 + $50,511.36 = -$49,489.
  11. Which statement best describes a key difference between sensitivity analysis and Monte Carlo simulation?
    Answer: Monte Carlo simulation provides a distribution of possible NPV outcomes, while sensitivity analysis typically provides a discrete set of point estimates. The core difference lies in their outputs. Sensitivity analysis provides a limited number of outcomes (e.g., 'What is NPV if sales are 10% lower?'). Monte Carlo simulation, by contrast, uses probability distributions for inputs and runs thousands of trials to generate a full probability distribution of potential outcomes (e.g., 'There is a 25% probability that NPV will be negative'). Both tools are quantitative, and simulation is superior at handling correlations if they are programmed into the model.
  12. 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?
    Answer: Analysis A is sensitivity analysis, and Analysis B is scenario analysis. 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.
  13. What is the annual sales quantity at which the project's Net Present Value (NPV) is zero?
    Answer: 16,647 units 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 = [($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.
  14. Based on this analysis, what is the standard deviation of the project's NPV?
    Answer: $17.85 M First, calculate the expected NPV: E(NPV) = (0.25 -$10M) + (0.50 $20M) + (0.25 * $40M) = -$2.5M + $10M + $10M = $17.5M. Next, calculate the variance: Var(NPV) = Σ[PiP_i (NPV_i - E(NPV))^2] = 0.25(−10−17.5)2(-10 - 17.5)^2 + 0.50*(20−17.5)2(20 - 17.5)^2 + 0.25*(40−17.5)2(40 - 17.5)^2 = 0.25*(−27.5)2(-27.5)^2 + 0.50*(2.5)2(2.5)^2 + 0.25*(22.5)2(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.
  15. 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?
    Answer: Investigate strategies to mitigate the specific risks identified in the pessimistic scenario before making a final decision. 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.
  16. 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?
    Answer: Scenario analysis 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.
  17. The primary advantage of using scenario analysis over standard sensitivity analysis when evaluating project risk is its ability to:
    Answer: analyze the combined effect of several interrelated economic variables changing at the same time. Scenario analysis allows for changing multiple input variables simultaneously in an internally consistent way. This addresses the main weakness of sensitivity analysis by allowing analysts to model the effects of correlations between variables, such as what might occur in a recession or an economic boom.
  18. 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?
    Answer: Sales price 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/$50 = 2% increase. Therefore, a 1% increase in variable cost would cause an NPV decrease of $100,000 / 2 = $50,000. Comparing the absolute NPV impacts for a 1% change in each variable: Sales Volume ($50k), Sales Price ($120k), Discount Rate ($80k), and Variable Cost ($50k). The sales price has the largest impact ($120,000) and thus represents the greatest risk.
  19. 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:
    Answer: a significant portion of the project's total cash flows occurs far in the future. 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.
  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?
    Answer: $93,138 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.

Start this quiz