Sensitivity Analysis Explained

By Ryan O'Connell, CFA, FRM Published October 20, 2026
Table of Contents

    A forecast can look comfortable until one assumption changes. Imagine a backpack shop expecting $50,000 in annual operating profit when its owner requires at least $30,000 to renew the lease. A 5% price cut, with sales and costs otherwise unchanged, would reduce profit to $25,000. Sensitivity analysis helps identify assumptions that could change that decision and deserve closer investigation.

    What Is Sensitivity Analysis?

    Sensitivity analysis recalculates a model’s result after changing its assumptions. In operating-profit analysis, those assumptions might include selling price, units sold, variable cost per unit, or annual fixed costs.[1]

    This article uses one-at-a-time sensitivity analysis: change one input, hold the other inputs at their base values, and recalculate profit. Each separate test starts from the same base case.[3]

    The Question Behind the Calculation

    How much would the result change if this assumption changed and the others stayed at their base values? The answer helps prioritize investigation. It does not establish how likely the change is.

    Watch: Sensitivity Analysis Explained: Which Number Matters Most?

    The Operating-Profit Model

    Start with the relationship between fixed and variable costs. Subtract variable cost per unit from selling price to find contribution margin per unit. Multiply by units sold, then subtract fixed costs. Contribution covers fixed costs before any remainder becomes profit.[2]

    Single-Product Operating Profit
    Operating profit = Units sold × (Selling price − Variable cost per unit) − Fixed costs
    Use the same period throughout. Price and variable cost are per unit; fixed costs are a total for that period.
    Hypothetical Backpack Shop: Annual Base Case
    Illustrative assumptions for the coming year
    Input or decision criterion Base value
    Backpacks sold 10,000
    Selling price per backpack $50
    Variable cost per backpack $30
    Annual fixed costs: rent and staff salaries $150,000
    Owner’s minimum annual operating-profit target $30,000

    Revenue = 10,000 × $50 = $500,000. Variable expense = 10,000 × $30 = $300,000.

    Contribution per backpack = $50 − $30 = $20. Total contribution = 10,000 × $20 = $200,000.

    Operating profit = $200,000 − $150,000 = $50,000, leaving $50,000 − $30,000 = $20,000 above the owner’s target.

    All figures and ranges in this example are hypothetical. The simplified shop sells one standard product, purchasing cost is its only variable operating cost, and there are no additional operating expenses or inventory-cost complications. Assume rent and salaries remain unchanged at all sales levels used below. Operating profit is before interest and income taxes.

    One-at-a-Time Sensitivity Analysis: Price vs. Volume

    A 5% Price Cut

    Reduce selling price by 5%: $50 × 0.95 = $47.50. Keep sales at 10,000 backpacks, variable cost at $30 each, and annual fixed costs at $150,000.

    Price-Only Test
    10,000 × ($47.50 − $30) − $150,000 = $25,000
    The $17.50 contribution per backpack produces $175,000 of total contribution before fixed costs.

    The $2.50 reduction applies to every planned sale: 10,000 × $2.50 = $25,000 less profit. The profit decline is $25,000 / $50,000 = 50%, and the result falls below the owner’s $30,000 target.

    A 5% Decline in Sales Volume

    Reset to the base case, including the original $50 price. Sell 5% fewer backpacks: 10,000 × 0.95 = 9,500. Unit contribution remains $20.

    Volume-Only Test
    9,500 × ($50 − $30) − $150,000 = $40,000
    Total contribution falls to $190,000, while fixed costs remain $150,000.

    The 500 lost sales remove 500 × $20 = $10,000 of contribution, reducing profit by $10,000 / $50,000 = 20%. Unlike a price cut on existing sales, lost volume also avoids purchasing costs: $25,000 of lost revenue minus $15,000 of avoided variable expense leaves a $10,000 profit reduction.

    These percentages measure changes in profit dollars. They are different from changes in an operating profit margin, which expresses profit relative to revenue.

    How to Read a Tornado Chart

    Repeat the calculation for each input at a low and high value. A tornado chart represents each input’s resulting profit range as a horizontal bar and places the widest range at the top.[4] First, test every input 5% below and above its base value.

    Equal-5% tests, sorted in tornado order; every row holds the other inputs at base values
    Input Low to high input Profit at low input Profit at high input Full profit swing
    Selling price $47.50 to $52.50 $25,000 $75,000 $50,000
    Variable cost per backpack $28.50 to $31.50 $65,000 $35,000 $30,000
    Annual sales volume 9,500 to 10,500 $40,000 $60,000 $20,000
    Annual fixed costs $142,500 to $157,500 $57,500 $42,500 $15,000

    For example, the unit-cost endpoints come from 10,000 × ($50 − $28.50) − $150,000 = $65,000 and 10,000 × ($50 − $31.50) − $150,000 = $35,000. The fixed-cost endpoints are $200,000 − $142,500 = $57,500 and $200,000 − $157,500 = $42,500.

    To draw the chart, put annual operating profit on the horizontal axis and mark the $50,000 base case. Draw price’s bar from $25,000 to $75,000, unit cost’s from $35,000 to $65,000, volume’s from $40,000 to $60,000, and fixed costs’ from $42,500 to $57,500.

    Price ranks first under these equal-percentage tests. Notice that higher costs produce lower profit, so input direction reverses for the cost rows. Also, the full bar width differs from the downside loss: price’s $50,000-wide bar includes a $25,000 decline and a $25,000 increase from base.

    Choose Realistic Ranges Before Ranking Assumptions

    An equal 5% test offers a consistent comparison, but it does not establish that every input could realistically move by the same percentage. For a business decision, document ranges supported by the business’s circumstances:

    • Price: realized selling prices, planned promotions, discount history, and customer response.
    • Volume: comparable-period sales, seasonality, customer commitments, and changes in competition.
    • Unit costs: supplier quotes, contract coverage, shipping charges, and purchase quantities.
    • Fixed costs: lease terms, salary commitments, and staffing or capacity changes at different activity levels.

    Ranges can be asymmetric. Distinguish an ordinary planning range from a deliberately severe stress, and avoid treating an old sales pattern as automatically applicable to a changed business.

    Why the Ranking Can Change

    For illustration, narrow the price range to plus/minus 2% and widen the volume range to plus/minus 15%. Keep the two cost ranges at plus/minus 5%. These revised ranges are invented for teaching; they are not estimates from actual backpack-shop records.

    Price now runs from $50 × 0.98 = $49 to $50 × 1.02 = $51. The endpoints are 10,000 × ($49 − $30) − $150,000 = $40,000 and 10,000 × ($51 − $30) − $150,000 = $60,000.

    Volume runs from 10,000 × 0.85 = 8,500 to 10,000 × 1.15 = 11,500. Profit becomes 8,500 × $20 − $150,000 = $20,000 at the low end and 11,500 × $20 − $150,000 = $80,000 at the high end.

    Revised tornado ranking with different illustrative input ranges
    Rank and input Tested input range Profit range Full profit swing
    1. Sales volume 8,500 to 11,500 $20,000 to $80,000 $60,000
    2. Unit variable cost $28.50 to $31.50 $35,000 to $65,000 $30,000
    3. Selling price $49 to $51 $40,000 to $60,000 $20,000
    4. Annual fixed costs $142,500 to $157,500 $42,500 to $57,500 $15,000

    Volume now ranks first. The profit equation has not changed. The wider volume range creates a $60,000 profit swing, while the narrower price range creates a $20,000 swing. A ranking therefore needs its input ranges and base case alongside it.

    A Tested Range Does Not Supply a Probability

    These calculations do not say that sales have any particular chance of falling to 8,500. Sensitivity analysis alone does not supply the likelihood of a change.[7] The selected ranges are not confidence intervals or guarantees that every possible profit outcome lies inside them.

    Find the Inputs That Would Miss the Profit Target

    A ranking shows the size of a tested effect. A decision threshold shows how far an input could move before the result falls below the owner’s criterion. For a positive unit contribution, the volume needed to earn a target profit is:[5]

    Sales Volume Needed for Target Profit
    Required units = (Fixed costs + Target profit) / (Selling price − Variable cost per unit)
    ($150,000 + $30,000) / ($50 − $30) = 9,000 backpacks per year.

    At 9,000 sales, profit is 9,000 × $20 − $150,000 = $30,000. That is a (10,000 − 9,000) / 10,000 = 10% volume decline. Lower volume misses the target if the other inputs remain at base values.

    Each boundary produces exactly $30,000 annual profit, with all other inputs at base values
    Input boundary Calculation Target is missed when
    Minimum price: $48 $30 + ($150,000 + $30,000) / 10,000 = $48 Price falls below $48
    Minimum volume: 9,000 ($150,000 + $30,000) / $20 = 9,000 Annual sales fall below 9,000
    Maximum unit variable cost: $32 $50 − ($150,000 + $30,000) / 10,000 = $32 Unit cost rises above $32
    Maximum annual fixed cost: $170,000 10,000 × $20 − $30,000 = $170,000 Fixed costs rise above $170,000

    The price boundary is a ($50 − $48) / $50 = 4% decline. The opening 5% price cut crosses it. Each boundary is conditional: remaining above the price boundary does not protect the target if volume also falls.

    Also distinguish the owner’s target from zero-profit break-even. At the base price and costs, break-even sales are $150,000 / $20 = 7,500 backpacks. Selling 8,500 produces a positive $20,000 profit, yet still misses the owner’s $30,000 requirement.

    Sensitivity vs. Scenario and Variance Analysis

    One-at-a-Time Sensitivity

    • Changes one assumption per test.
    • Isolates the model’s response to that assumption.
    • Example: price falls to $49 while sales remain 10,000.

    Scenario Analysis

    • Combines assumptions into a specified business situation.
    • Examines the result of those changes together.
    • Example: a competitor reduces both the shop’s achievable price and sales.

    Both approaches can use the same profit model. Moving from a single-variable test to multiple simultaneous changes answers a different question.[1] Broader applications are covered in stress testing and scenario analysis.

    When Price and Sales Both Fall

    Suppose the shop sells only 8,500 backpacks at $49 each. Keep unit variable cost at $30 and annual fixed cost at $150,000:

    Combined Downside Case

    Unit contribution = $49 − $30 = $19.

    Total contribution = 8,500 × $19 = $161,500.

    Operating profit = $161,500 − $150,000 = $11,500.

    This result is below either separate downside: $40,000 from testing the $49 price alone or $20,000 from testing 8,500 sales alone. A two-input table makes the combinations visible:

    Annual operating profit at selected price-volume combinations; unit cost $30 and fixed costs $150,000 throughout
    Annual backpacks sold Price $49 Price $50 Price $51
    8,500 $11,500 $20,000 $28,500
    10,000 $40,000 $50,000 $60,000
    11,500 $68,500 $80,000 $91,500

    Every cell uses units × (price − $30) − $150,000. For example, 8,500 × ($51 − $30) − $150,000 = $28,500. At that sales level, even the highest price in this grid does not meet the target.

    The grid does not predict how many customers would buy at each price. A discount might attract buyers, while a higher price might lose them. Investigate price elasticity of demand and model an evidence-based volume response when evaluating an actual pricing change.

    Variance Analysis Examines Results Against a Plan

    Budget variance analysis compares actual performance with a budget or standard and investigates the differences.[8] Sensitivity analysis here asks what profit would be under changed assumptions. A future volume test is not evidence that the shop has already missed its sales budget.

    How to Use Sensitivity Analysis for a Decision

    1. Define the criterion. Name the output, period, and threshold. Here they are annual operating profit and a $30,000 minimum.
    2. Check the base model. Reconcile units, unit economics, and total expenses before testing variations.
    3. Document the ranges. Record the evidence behind each low and high input and any contractual or capacity limits.
    4. Run separate tests and compare thresholds. Reset the base case each time. Keep both the profit swing and the distance to the decision boundary.
    5. Test important combinations. Include linked changes such as price and demand, or higher volume and additional staffing.
    6. Investigate before committing. Check the credibility of the downside and the available responses, then update the model when evidence changes.

    For this shop, the revised 8,500-sales downside deserves attention because it produces only $20,000 at the original $50 price. That result prompts a closer demand investigation before renewing the lease; it does not automatically establish that closing the shop is the best alternative.

    Common Mistakes in Sensitivity Analysis

    • Failing to reset the base case. Changing price and then reducing volume without resetting creates a combined test rather than two isolated tests.
    • Using revenue to measure the volume effect on profit. Lost sales also avoid variable costs. Use the contribution lost, with fixed costs held unchanged.
    • Calling the widest bar the most likely risk. Bar width measures an output swing under chosen inputs, not the probability of those inputs.
    • Omitting the ranges from a ranking. Price leads under equal 5% tests; volume leads under the revised ranges. Both descriptions need their conditions.
    • Adding isolated effects without recalculating. Subtracting the separate $10,000 price loss and $30,000 volume loss from $50,000 gives $10,000. The actual combined result is $11,500 because the $1 price reduction applies to 8,500 sales rather than 10,000.
    • Mixing units or periods. A monthly rent figure, annual sales count, and total purchasing expense cannot be inserted as though they were annual fixed cost, annual units, and variable cost per unit.

    Limitations of Sensitivity Analysis

    The Result Depends on the Model

    One-at-a-time tests omit joint input movements, and their conclusions depend on the base case.[6] Use the results with evidence about customer behavior, costs, and operating constraints.

    Fixed costs may rise when the shop needs another employee or more space. Unit costs may change with purchasing quantities, and multiple products may have different contributions. Revise the cost and product-mix model when these conditions matter.[5]

    In this example, testing each input’s endpoints identifies its lowest and highest isolated profit because the model moves in one direction with that input. A nonlinear model can turn within the tested interval, so its endpoints may miss an important result.[4]

    Finally, annual operating profit does not establish cash availability. Inventory purchases, customer collections, payment timing, and capital spending need separate analysis.[9] Consider working capital management and, for an investment commitment, capital budgeting and free cash flow alongside the profit forecast.

    Frequently Asked Questions

    Use the formula for the output you are testing, then recalculate it with changed inputs. Here, operating profit equals units sold multiplied by the difference between selling price and variable cost per unit, less fixed costs. Compare each recalculated result with the same base case. The underlying formula changes when the subject is a different output, such as project cash flow.

    The price cut removes $2.50 from each of 10,000 sales, reducing profit by $25,000. Losing 500 sales instead removes $20 of contribution per sale, reducing profit by $10,000, because the shop also avoids each missing backpack’s $30 purchasing cost. These results depend on the example’s unchanged remaining inputs.

    It identifies the input producing the widest output swing under the selected range and base case. It does not identify the most likely change. In this example, price leads when all ranges are plus/minus 5%, but volume leads when its range expands to plus/minus 15% and price narrows to plus/minus 2%.

    Start with evidence relevant to the forecast period: sales and discount records, supplier quotes, contracts, and operating capacity. Document what the endpoints represent. Different inputs can use different or asymmetric ranges. A convenient percentage is useful for a standardized test, but it does not become a realistic forecast merely because it is easy to calculate.

    These deterministic tests do not. They show the profit produced by specified inputs, without estimating how likely those inputs are. A probability claim needs separate evidence and a method that models likelihoods and relevant dependencies. Neither the tornado ranking nor the two-input grid supplies that probability.

    Break-even means zero operating profit in this model. The owner’s target is $30,000. At the base price and costs, 7,500 backpacks cover fixed expenses, while 9,000 are required to earn the target profit. Sales between those levels can leave the shop profitable while still falling short of the owner’s requirement.

    Sources

    Sources accessed October 20, 2026. All backpack-shop figures, targets, and tested ranges are hypothetical; calculations use the model stated above.

    1. OpenStax, Perform Break-Even Sensitivity Analysis for a Single Product Under Changing Business Situations, especially Changing a Single Variable and Changing Multiple Variables.
    2. OpenStax, Contribution Margin, especially relevant range, Unit Contribution Margin, and Total Contribution Margin.
    3. Oracle, Measuring Variable Effects with the Tornado Analysis Tool, explanation of one-at-a-time tests with other inputs at base values.
    4. Oracle, Tornado Chart, output swings, ordering, and non-monotonic relationships.
    5. ACCA, Cost-volume-profit analysis, especially Ascertaining the Sales Volume Required to Achieve a Target Profit and Limitations of Cost-volume Profit Analysis.
    6. Oracle, Limitations of the Tornado Chart Tool, input correlations and base-case dependence.
    7. ACCA, Financial Management: June 2015 Answers, question 5(b), printed page 19, distinction between sensitivity and probability analysis.
    8. OpenStax, Explain How and Why a Standard Cost Is Developed, variance definitions and Ethical Variance Analysis.
    9. OpenStax, Prepare Financial Budgets, especially Cash Budget and the timing of receipts and payments.
    Disclaimer

    This article is for educational purposes. The hypothetical example simplifies a business’s costs and operations. Business decisions require reliable records, appropriate forecasts, and consideration of alternatives and cash needs.

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