Evaluate Sensitivity And Scenario Analysis
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CPA Business Analysis and Reporting (BAR) › Evaluate Sensitivity And Scenario Analysis
Sensitivity analysis in financial modeling is best described as which of the following?
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
A process of constructing a limited number of discrete scenarios based on coherent sets of macro-economic conditions
A statistical method that generates thousands of random scenarios to produce a probability distribution of outcomes
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.
A project's base-case NPV is $120,000. Sensitivity analysis shows that each 1% increase in the discount rate reduces NPV by $18,000. What is the NPV if the discount rate increases by 2 percentage points?
$66,000
$138,000
$102,000
$84,000
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.
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?
$440,000
$200,000
$380,000
$470,000
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% 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.
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?
$650,000
$425,000
$500,000
$350,000
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%.
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?
$2,200,000
$1,600,000
$2,000,000
$2,800,000
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.
A project requires an initial investment of $1,200,000 and generates annual cash flows for 5 years. The PV annuity factor at 10% for 5 years is 3.791. Under a pessimistic scenario, annual cash flows are $280,000. What is the NPV under the pessimistic scenario?
-$138,520
-$315,640
$138,520
$315,640
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.
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?
$771,320
$538,280
$454,920
$316,400
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.
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?
The acquisition should proceed because any positive NPV scenario justifies the investment
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
NPV is not the appropriate evaluation method for acquisitions
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.
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?
$40 per unit
$52 per unit
$48 per unit
$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.
Two capital projects have similar base-case NPVs. Across all scenarios tested, Project A's NPV ranges from -$50,000 to +$300,000. Project B's NPV ranges from -$400,000 to +$500,000. Which conclusion best incorporates the scenario analysis results?
Both projects should be rejected because neither guarantees a positive NPV in all scenarios
Project B is superior because it offers higher potential upside
The projects are equivalent because both have similar base-case NPVs
Project A has a more resilient risk profile - its downside is limited and it stays near break-even in adverse scenarios; Project B's wider range represents significantly higher risk that may not be justified for a risk-averse organization
Explanation
Scenario analysis adds risk dimension to the NPV comparison. Project A stays close to positive NPV across all scenarios ($-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.