CPA Bar Quiz: Evaluate Sensitivity And Scenario Analysis

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

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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.

Question 1

1. A technique that systematically varies one or more input assumptions to measure the impact on an output variable, identifying which assumptions most influence the result (correct answer)
2. A statistical method that generates thousands of random scenarios to produce a probability distribution of outcomes
3. A process of constructing a limited number of discrete scenarios based on coherent sets of macro-economic conditions
4. A variance analysis technique for comparing actual results to budgeted results

Explanation: Sensitivity analysis examines how changes in individual input assumptions affect a model's output. By varying one assumption at a time while holding others constant, analysts identify which inputs are most influential and where errors would have the greatest consequences. Option B describes Monte Carlo simulation. Option C describes scenario analysis. Option D describes budget variance analysis.

Question 2

1. $102,000
2. $84,000 (correct answer)
3. $66,000
4. $138,000

Explanation: NPV impact = 2 x $18,000 =$36,000 reduction. NPV at higher rate = $120,000 -$36,000 = $84,000. This assumes a linear relationship between the discount rate and NPV, which sensitivity analysis typically uses for small changes around the base case. Option A applies only a 1% change. Option C applies a 3% change. Option D adds rather than subtracts the rate impact.

Question 3

1. $200,000
2. $470,000
3. $380,000 (correct answer)
4. $440,000

Explanation: 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$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.

Question 4

1. $500,000
2. $650,000
3. $425,000
4. $350,000 (correct answer)

Explanation: 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%.

Question 5

1. $2,000,000 (correct answer)
2. $2,800,000
3. $1,600,000
4. $2,200,000

Explanation: 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.

Question 6

1. $315,640
2. -$315,640
3. $138,520
4. -$138,520 (correct answer)

Explanation: PV of pessimistic cash flows = $280,000 x 3.791 =$1,061,480. NPV = $1,061,480 -$1,200,000 = -$138,520. Under the pessimistic scenario, the project does not recover its initial investment at the required rate of return. Option A is the base-case NPV (approximately$400,000 x 3.791 - $1,200,000). Option B applies the correct magnitude but wrong sign. Option C has the correct magnitude but wrong sign.

Question 7

1. $771,320 (correct answer)
2. $316,400
3. $538,280
4. $454,920

Explanation: 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.

Question 8

1. The acquisition should proceed because any positive NPV scenario justifies the investment
2. 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 (correct answer)
3. NPV is not the appropriate evaluation method for acquisitions
4. Management's confidence in the best case is sufficient justification to proceed

Explanation: 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.

Question 9

1. $40 per unit
2. $48 per unit (correct answer)
3. $52 per unit
4. $44 per unit

Explanation: 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.

Question 10

1. Project B is superior because it offers higher potential upside
2. Project A has a more resilient risk profile - its downside is limited and it stays near break-even in adverse scenarios; Project B's wider range represents significantly higher risk that may not be justified for a risk-averse organization (correct answer)
3. Both projects should be rejected because neither guarantees a positive NPV in all scenarios
4. The projects are equivalent because both have similar base-case NPVs

Explanation: Scenario analysis adds risk dimension to the NPV comparison. Project A stays close to positive NPV across all scenarios ($-50K to$+300K), indicating resilience. Project B's wide range ($-400K to$+500K) indicates much higher variance - the best case is better but the worst case is far more damaging. For risk-averse organizations or those with constrained capital, the limited downside of Project A may be more valuable than the higher upside of Project B. Option A selects based on upside alone without considering risk. Option C applies an unrealistic guarantee standard. Option D ignores the valuable information in the scenario range analysis.

Question 11

1. Sales team involvement in forecasting is required best practice for operational accuracy
2. High revenue sensitivity means the model itself is flawed and should be rebuilt
3. Forecasting bias is only a concern for companies with external reporting obligations
4. 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 (correct answer)

Explanation: 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.

Question 12

1. The project should be accepted because it is NPV-positive at the base-case 10% rate
2. The project should be rejected because it fails at the 12% rate
3. 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 (correct answer)
4. The two-way analysis is inconclusive and should be replaced with a Monte Carlo simulation

Explanation: 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.

Question 13

1. Proceed with the plan as-is because $75 oil is the most likely base-case assumption
2. Sell business units that use oil as a production input
3. Dismiss the $95 scenario as too extreme to plan for
4. 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 (correct answer)

Explanation: 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.

Question 14

1. The budget is robust because all three sensitivities are smaller than the total operating income
2. SGA reduction should be prioritized because it is the only variable management directly controls
3. Interest rate sensitivity is the most critical risk because it is an external factor outside management's control
4. 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 (correct answer)

Explanation: 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$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.

Question 15

1. +$230,000
2. -$230,000
3. -$370,000
4. -$115,000 (correct answer)

Explanation: 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.

Question 16

1. Changes only one variable at a time to isolate the effect of each assumption independently
2. Simultaneously changes multiple related variables to reflect a coherent and internally consistent set of conditions (correct answer)
3. Is used exclusively for strategic planning and has no application in capital budgeting
4. Produces a single point estimate by averaging the best, base, and worst case outcomes

Explanation: 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.

Question 17

1. 10.5%
2. 15.3%
3. 20.8% (correct answer)
4. 26.2%

Explanation: 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.

Question 18

1. $6,000,000
2. $5,800,000
3. $6,100,000 (correct answer)
4. $7,200,000

Explanation: Expected revenue = (0.25 x $8,000,000) + (0.55 x$6,000,000) + (0.20 x $4,000,000) =$2,000,000 + $3,300,000 +$800,000 = $6,100,000. The expected value exceeds the base case ($6,000,000) because the best-case upside ($8M) is larger in absolute terms than the worst-case downside ($4M), and the probabilities are not symmetric. Option A is the unweighted base case. Option B uses incorrect probability weights. Option D averages only the best and base cases.

Question 19

1. The operating leverage creates significant downside risk at lower growth rates; management should stress-test the cost structure and identify which fixed costs can be reduced if growth disappoints (correct answer)
2. The budget should be built on the 8% growth assumption because management is confident in the market outlook
3. The company should exit the market if growth is likely to fall to 0%
4. Market growth sensitivity is a routine planning consideration requiring no specific action

Explanation: The wide range of operating income outcomes ($2M profit to$400K loss) for a 8-percentage-point range in market growth reveals high operating leverage and significant structural sensitivity. The appropriate analytical response is to stress-test cost flexibility: which costs are fixed in the short term vs. reducible, and what triggers would initiate cost reduction actions? This is actionable risk management. Option B avoids the risk signal. Option C is an extreme overcorrection based on the worst-case scenario. Option D dismisses a material planning risk.

Question 20

1. The expected NPV calculation contains an arithmetic error
2. The positive expected NPV should be weighed against the 30% probability of a -$2,500,000 loss; if that downside exceeds the organization's risk tolerance or financial capacity, the positive expected value may not justify proceeding (correct answer)
3. Probability-weighted NPV is always the definitive basis for investment decisions
4. The optimistic scenario deserves more weight because management typically outperforms projections

Explanation: Expected NPV = (0.20 x $5M) + (0.50 x$1.2M) + (0.30 x -$2.5M) =$1M + $0.6M -$0.75M = $0.85M. While the expected NPV is positive, a 30$2,500,000 is a material risk. If the downside loss would cause serious financial hardship, constrain other investment options, or exceed the risk appetite of the organization, the positive expected value alone may not be sufficient justification. Risk capacity and risk tolerance matter alongside expected value. Option A is incorrect; the calculation is correct. Option C overstates expected NPV as always definitive. Option D introduces unsupported optimism.