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Evaluate Sensitivity And Scenario Analysis - CPA Bar

  1. The one-at-a-time method in sensitivity analysis is least able to:
    Answer: Show input interactions One-at-a-time changes one input at a time, so it cannot detect joint effects of multiple inputs. Thus it is least able to show input interactions. It can still rank inputs by impact, set break-even values by finding an input that makes NPV zero, and reveal the NPV sign in the base case. The tempting wrong answer is ranking inputs by impact, but that is a strength, not a limitation.
  2. A model's base-case NPV is $1,800,000. A 5% revenue decline reduces NPV by $900,000 (50%), while a 1% discount rate increase reduces NPV by only $120,000 (6.7%). Which risk management conclusion is most appropriate?
    Answer: Revenue is the critical assumption - a modest revenue miss cuts NPV in half, making revenue projection accuracy and contingency planning far more important than discount rate precision The sensitivity analysis clearly indicates revenue as the dominant driver: a 5% revenue shortfall is seven times more impactful than a 1% discount rate change. Risk management resources should be concentrated on the highest-impact assumptions. This means greater scrutiny of the revenue forecast, stronger monitoring of market signals, and contingency plans for revenue downside scenarios. Option B incorrectly elevates controllability over impact magnitude in risk prioritization. Option C incorrectly treats both as equal when the data shows a 7:1 impact ratio. Option D treats high sensitivity as a model flaw rather than an insight.
  3. Changing several variables to model a recession, then varying only volume to find break-even, are best described as:
    Answer: Scenario; sensitivity Changing several variables together to model a recession is scenario analysis: you set a coherent alternative set of assumptions. Varying only volume to find break-even is sensitivity analysis: you change one driver at a time to see its impact. Simulation is the tempting distractor for the first step, but it relies on random inputs and repeated trials, not a fixed recession scenario.
  4. A pricing sensitivity analysis (variable cost $30/unit, fixed costs $90,000) shows: at $40/unit with 10,000 units sold, contribution margin $100,000; at $44/unit with 9,000 units sold, $126,000; at $48/unit with 7,500 units sold, $135,000; at $52/unit with 6,000 units sold, $132,000. Which price maximizes operating income?
    Answer: $48 per unit Operating income = Contribution margin - Fixed costs. At $40: $100,000 - $90,000 = $10,000. At $44: $126,000 - $90,000 = $36,000. At $48: $135,000 - $90,000 = $45,000. At $52: $132,000 - $90,000 = $42,000. The $48 price maximizes operating income at $45,000 because it achieves the highest total contribution margin ($135,000). Pricing sensitivity analysis of this type shows that the optimal price is not the highest price (which loses too much volume) nor the lowest (which sacrifices contribution margin per unit). Option A produces the lowest operating income ($10,000). Option D produces lower operating income ($36,000) than the maximum. Option C produces slightly lower operating income ($42,000) than the maximum.
  5. A 5% price cut reduces NPV by $20,000; a 10% volume cut reduces NPV by $20,000. More sensitive to:
    Answer: Price; smaller % change A 5% price cut costs $20,000, so every 1% price cut costs $4,000. A 10% volume cut also costs $20,000, so every 1% volume cut costs only $2,000. The same dollar impact from a smaller percentage change means price sensitivity is higher. Don't choose equal just because the dollar losses match; compare the size of the change.
  6. A two-way sensitivity table shows: NPV = $850,000 at a 10% discount rate and 5% revenue growth; NPV = $620,000 at a 12% discount rate and 5% revenue growth. What is the estimated impact on NPV of a 1-percentage-point increase in the discount rate, holding revenue growth constant?
    Answer: -$115,000 The sensitivity table moves from a 10% to a 12% discount rate - a 2-percentage-point change, not 1. Total NPV impact over 2 points = $620,000 - $850,000 = -$230,000. Impact per 1 percentage point = -$230,000 / 2 = -$115,000. Higher discount rates reduce the present value of future cash flows, lowering NPV. Option A incorrectly states the direction as positive. Option B applies the full 2-point NPV change (-$230,000) to a 1-point question, overstating the impact by a factor of two. Option C overstates the impact further beyond the total 2-point change.
  7. An acquisition model shows positive NPV only in the best-case scenario. Both the base-case and worst-case NPVs are negative. Management argues the acquisition should proceed because the best case is achievable. Which concern is most significant?
    Answer: The decision depends entirely on achieving the best-case outcome; both the most likely and adverse scenarios produce value destruction, meaning the most probable outcomes are unfavorable When a positive NPV appears only in the best-case scenario while both the base case and worst case are negative, the investment creates value only under the most optimistic assumptions. The base case typically represents the most likely outcome; if it shows negative NPV, the expected outcome of the investment is value destruction. Management's confidence does not change the probability structure of the scenarios. Option A sets an inappropriately low bar by requiring only one positive scenario. Option C is incorrect; NPV is the standard method for acquisition evaluation. Option D treats subjective management confidence as an analytical substitute.
  8. Using the same base case (revenue $3,000,000, fixed costs $700,000), if the variable cost ratio increases from 60% to 65% while all other assumptions remain constant, what is operating income?
    Answer: $350,000 Variable costs at 65% = $3,000,000 x 0.65 = $1,950,000. Operating income = $3,000,000 - $1,950,000 - $700,000 = $350,000. The 5-percentage-point increase in the variable cost ratio costs $3,000,000 x 5% = $150,000, reducing operating income from $500,000 to $350,000. Option A is the unchanged base case. Option B is incorrect - higher variable costs reduce, not increase, operating income. Option C uses a 4.5% change rather than 5%.
  9. A Monte Carlo simulation of a business plan runs 10,000 iterations and shows: 70% probability of positive operating income, 15% probability of operating income exceeding $1,000,000, and 30% probability of an operating loss. Management concludes the plan is sound because most outcomes are positive. Which caution is most analytically relevant?
    Answer: Management should also evaluate the magnitude of the 30% loss scenarios - a meaningful probability of loss with potentially large downside can represent significant expected loss even when most scenarios are profitable Probability alone is an incomplete measure of risk. A 30% probability of operating loss is material and should be examined for the severity of the downside outcomes. If those losses are large, the expected loss from the 30% of negative scenarios could overwhelm the expected profit from the 70% positive scenarios, resulting in a negative overall expected value. Management should examine the full distribution, particularly the lower tail, not just the percentage of positive outcomes. Option A is incorrect; Monte Carlo simulation is a well-established analytical method. Option B accepts the majority probability without examining the downside. Option D is incorrect; 10,000 iterations is generally considered sufficient for most business simulations.
  10. A company's base-case operating income is $500,000 (revenue $3,000,000, variable cost ratio 60%, fixed costs $700,000). If revenue declines 10% while all other assumptions remain constant, what is operating income?
    Answer: $380,000 New revenue = $3,000,000 x 0.90 = $2,700,000. Variable costs = $2,700,000 x 60% = $1,620,000. Operating income = $2,700,000 - $1,620,000 - $700,000 = $380,000. The $120,000 decline in operating income ($500,000 - $380,000) reflects the contribution margin lost on the $300,000 revenue decline: $300,000 x 40% CM ratio = $120,000. Option A applies a much larger impact. Option B deducts only the revenue decline without applying the variable cost offset. Option D uses an incorrect variable cost calculation.
  11. Base annual cash flow is $80,000; zero NPV occurs at $60,000. Maximum cash-flow decrease is:
    Answer: 25% The cash flow can fall from $80,000 to $60,000, a decrease of $20,000. Divide that decrease by the base cash flow: 20,000 / 80,000 = 25%. A common error is dividing by the $60,000 zero-NPV amount, which gives 33%, but the base is the original $80,000.
  12. A tornado chart shows the following NPV impact from a plus-or-minus 10% change in each variable: unit volume plus-or-minus $240,000; selling price plus-or-minus $180,000; variable cost plus-or-minus $120,000; discount rate plus-or-minus $90,000; fixed cost plus-or-minus $60,000. Which variable has the greatest influence on NPV and should receive priority attention?
    Answer: Unit volume Unit volume produces the largest NPV swing of plus-or-minus $240,000, making it the most sensitive assumption. In a tornado chart, bars are arranged from longest to shortest, with the longest bar at the top representing the assumption with the greatest impact. Uncertainty in unit volume carries the highest consequence for project viability. Selling price (Option A) is second at $180,000. Options B, C, and E have progressively smaller impacts.
  13. Sensitivity analysis reveals that revenue is the most important NPV driver (a 10% shortfall reduces NPV by 65%). The revenue forecast was prepared by the same sales team that will be evaluated on achieving those targets. Which concern does this raise?
    Answer: The most sensitive assumption may contain optimistic bias if prepared by those with a personal stake in the outcome; independent review or additional scenario testing of the revenue assumption is warranted Combining high sensitivity with a potential source of bias creates elevated model risk. When the assumption that most affects the outcome is prepared by individuals who benefit from optimistic targets, the forecast may be systematically overstated - not necessarily through dishonesty but through natural optimism bias. The appropriate response is an independent review, comparison to market data, or deliberate downside scenario testing of the revenue assumption. Option A correctly notes operational relevance but ignores the bias risk. Option B treats high sensitivity as a model defect. Option C incorrectly limits the concern to publicly reporting companies.
  14. A DCF model produces an NPV of $2,400,000 at a 10% discount rate. NPV changes by $200,000 for each 1-percentage-point change in the discount rate. What is the NPV at a 12% discount rate?
    Answer: $2,000,000 NPV at 12% = $2,400,000 - (2 x $200,000) = $2,400,000 - $400,000 = $2,000,000. Each percentage-point increase in the discount rate reduces NPV by $200,000; a 2-point increase reduces it by $400,000. Option B adds instead of subtracts. Option C applies a $400,000 reduction per percentage point rather than the stated $200,000. Option D applies only a 1-point reduction.
  15. A break-even sensitivity analysis shows the project becomes unviable (NPV = 0) when annual cash flows fall to $316,840. The base-case annual cash flow is $400,000. What is the maximum percentage decline in cash flows the project can sustain before it becomes unviable?
    Answer: 20.8% Maximum decline = (Base case - Break-even) / Base case = ($400,000 - $316,840) / $400,000 = $83,160 / $400,000 = 20.8%. This metric tells management how much cushion exists between the expected cash flow and the minimum required for the project to break even on a present value basis. Option A uses an incorrect numerator. Option B and D result from different base amounts.
  16. Sensitivity analysis of an annual budget (operating income $800,000) shows: a 1% gross margin decline reduces operating income by $400,000; a 5% SGA reduction increases it by $300,000; a 10% interest rate increase raises interest expense by $150,000. Which conclusion best integrates these findings for risk management prioritization?
    Answer: Gross margin is the most sensitive driver - a 1% decline eliminates half of budgeted operating income; monitoring and contingency planning should focus on revenue mix, pricing discipline, and COGS control A 1% gross margin decline reduces operating income by $400,000 - half the total budget of $800,000. This is the highest-impact sensitivity in the analysis. By comparison, a 5% SGA reduction generates $300,000, and a 10% interest rate increase costs only $150,000. Risk management resources should be directed proportionally to impact: gross margin deserves the most attention, with pricing, product mix, and COGS all key monitoring areas. Option A dismisses all three sensitivities as acceptable without noting the gross margin's disproportionate impact. Option B is incorrect; gross margin is also partially controllable through pricing and cost management. Option C incorrectly ranks interest rate sensitivity above the more impactful gross margin sensitivity.
  17. A two-way sensitivity analysis of a DCF model shows NPV is positive in all 9 cells at a 10% discount rate, but negative in 6 of 9 cells at a 12% discount rate. What is the most analytically appropriate conclusion?
    Answer: The project's viability is highly sensitive to the discount rate assumption; a 2-percentage-point increase in the cost of capital would make the project value-destructive under most revenue and growth scenarios, warranting careful scrutiny of whether 10% accurately reflects current risk The two-way analysis reveals that the project's positive NPV depends heavily on the discount rate assumption. A relatively modest change from 10% to 12% - plausible if interest rates rise or the project's risk is reassessed - flips 6 of 9 scenarios from positive to negative. This is precisely the kind of insight scenario analysis is designed to provide: the project is not robustly positive but conditionally positive depending on a key assumption. The appropriate response is to carefully validate whether 10% is the right rate and understand what could cause it to change. Option A accepts the base-case result without acknowledging the identified sensitivity. Option B overreacts to a stress test. Option D dismisses valuable findings without justification.
  18. A company's five-year plan assumes oil prices of $75 per barrel. Sensitivity analysis shows that $95 per barrel oil would increase annual operating costs by $8,000,000, eliminating the projected operating income of $6,000,000 and creating a $2,000,000 operating loss. Which risk management response is most appropriate?
    Answer: The oil price assumption creates material plan risk; management should evaluate hedging strategies, identify cost reduction levers, and develop a contingency response plan for scenarios of significantly higher oil prices A $20 per barrel increase in oil price (a plausible market movement) completely eliminates operating income and creates a loss. This is a material, plan-threatening sensitivity that demands a formal risk management response. Hedging through commodity futures or options can lock in a portion of oil costs; cost reduction programs can partially offset exposure; and contingency plans specify what management will do if prices rise. Proceeding without a response plan would leave the company exposed to a foreseeable and potentially severe disruption. Option A ignores the sensitivity finding. Option B is a disproportionate response to a commodity price risk. Option C dismisses a plausible scenario.
  19. Using the same project data (initial investment $1,200,000, PV annuity factor 3.791 at 10%), what is the NPV under an optimistic scenario where annual cash flows are $520,000?
    Answer: $771,320 PV of optimistic cash flows = $520,000 x 3.791 = $1,971,320. NPV = $1,971,320 - $1,200,000 = $771,320. Option B is the base-case NPV ($400,000 x 3.791 - $1,200,000 = $316,400). Option C applies an incorrect annuity factor. Option D uses a different cash flow figure.
  20. Scenario analysis differs from one-way sensitivity analysis in that scenario analysis:
    Answer: Simultaneously changes multiple related variables to reflect a coherent and internally consistent set of conditions Scenario analysis develops complete, internally consistent pictures of the future by simultaneously adjusting multiple interdependent variables. For example, a recession scenario would lower revenue, reduce margins, and increase borrowing costs together - a combination that reflects how the world actually works. Sensitivity analysis isolates one variable at a time to measure its individual impact. Option A describes sensitivity analysis. Option C is incorrect; scenario analysis is widely used in capital budgeting. Option D describes expected value calculation, not scenario analysis.

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