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Methodology

Price–Volume Trade-off Planner methodology

This planner calculates how many units preserve baseline contribution after a proposed price change.
Duc Nguyen X.By Duc Nguyen X.· Founder, Margin101Last reviewed: View update historyMethodology

Educational only: Business decision support, not accounting, tax or legal advice.

Privacy: Calculations run locally; Margin101 does not receive your commercial inputs.

Update policy: Reviewed when formulas or official dependencies change.

Scope: Market-neutral small-business planning using your own assumptions.

1. Formulas and units

Baseline contribution
C₀ = (P₀ − V) × U₀

Where

P₀
current price excluding indirect tax (currency units/unit)Source: Business record
V
unit cost excluding indirect tax (currency units/unit)Source: Business record
U₀
current units (units/period)Source: Business record
C₀
baseline contribution (currency units/period)Source: Calculated output
Required units
U₁ = C₀ ÷ (P₁ − V)

Where

P₁
proposed price excluding indirect tax (currency units/unit)Source: User decision
V
unit cost excluding indirect tax (currency units/unit)Source: Business record
U₁
required units (units/period)Source: Calculated output
C₀
baseline contribution (currency units/period)Source: Calculated output
Operational whole units
Uw = ⌈U₁⌉

Where

U₁
required units (units/period)Source: Calculated output
Uw
operational whole units (units/period)Source: Calculated output
Required volume change
ΔU = U₁ ÷ U₀ − 1

Where

U₀
current units (units/period)Source: Business record
U₁
required units (units/period)Source: Calculated output
ΔU
required volume change (decimal)Source: Calculated output
Observed midpoint price change
ΔPm = (Pa − Pb) ÷ ((Pa + Pb) ÷ 2)

Where

Pb
before or baseline price (currency units/unit)Source: Business record
Pa
after observed price (currency units/unit)Source: Business record
ΔPm
midpoint price change (decimal)Source: Calculated output
Observed midpoint quantity change
ΔQm = (Qa − Qb) ÷ ((Qa + Qb) ÷ 2)

Where

Qb
before or baseline quantity (units/period)Source: Business record
Qa
after observed quantity (units/period)Source: Business record
ΔQm
midpoint quantity change (decimal)Source: Calculated output
Observed arc elasticity
Earc = ΔQm ÷ ΔPm

Where

ΔPm
midpoint price change (decimal)Source: Calculated output
ΔQm
midpoint quantity change (decimal)Source: Calculated output
Earc
observed arc elasticity (ratio)Source: Calculated output
Candidate price change
ΔPc = Pc ÷ Pb − 1

Where

Pb
before or baseline price (currency units/unit)Source: Business record
Pc
candidate price (currency units/unit)Source: User decision
ΔPc
candidate price change (decimal)Source: Calculated output
Conditional quantity at elasticity e
Q(e) = max(0, Qb × (1 + e × ΔPc))

Where

Qb
before or baseline quantity (units/period)Source: Business record
ΔPc
candidate price change (decimal)Source: Calculated output
e
selected user-entered elasticity (ratio)Source: User assumption
Q
conditional quantity at elasticity e (units/period)Source: Calculated output
max
maximum or non-negative floor operator (operator)Source: Calculated output
Conditional sensitivity range
Qlow = min(Q(elo), Q(ehi)); Qhigh = max(Q(elo), Q(ehi))

Where

elo
user-entered lower elasticity bound (ratio)Source: User assumption
ehi
user-entered upper elasticity bound (ratio)Source: User assumption
Q
conditional quantity at elasticity e (units/period)Source: Calculated output
Qlow
conditional quantity low (units/period)Source: Calculated output
Qhigh
conditional quantity high (units/period)Source: Calculated output
max
maximum or non-negative floor operator (operator)Source: Calculated output
min
minimum operator (operator)Source: Calculated output

Money inputs and outputs use the currency selected in the scenario without changing the canonical methodology. Rates, margins, utilisation and buffers are entered as percentages and converted to decimal values for calculation.

2. Worked example

Input assumptions

At a price of 100 currency units, a unit cost of 60 currency units and 100 units sold, baseline contribution is 4,000 currency units.

Calculation and outputs

Example

At a price of 100 currency units, a unit cost of 60 currency units and 100 units sold, baseline contribution is 4,000 currency units.

Baseline contribution
4,000.00 currency units
Whole units required
134
Required volume change
33.3%
Observed arc elasticity
-1.11
Observed midpoint price change
9.5%
Observed midpoint quantity change
-10.5%
Conditional quantity low
80 units
Conditional quantity high
95 units

At a proposed 90 currency units price, 134 whole units preserve at least that contribution.

Interpretation

Use the required-unit result to decide whether the proposed price can preserve contribution at a plausible sales volume.

3. Validation and boundary checks

  • Required mathematical units multiplied by proposed unit contribution reconciles to baseline contribution.
  • Whole units always round upward.
  • A proposed price at or below unit cost returns an unreachable target.
  • Observed arc elasticity requires different positive prices and at least one positive observed quantity.
  • Conditional sensitivity keeps elasticity bounds ordered between −10 and 10 and floors negative quantity endpoints at zero.

4. Assumptions and source classification

  • All commercial amounts exclude indirect tax.
  • The price scenarios concern the same product and planning period.
  • Unit cost remains constant.
  • Observed price and quantity pairs cover comparable periods; other conditions may still differ.
  • Elasticity bounds are entered by the user and are not provider, policy or market defaults.

This planner has no current policy-data dependency. Its commercial assumptions are user supplied. Registered family-level regression suites exercise the shared business-logic engine and worked-result reconciliation.

5. Limitations

  • Observed arc elasticity is descriptive and does not establish that price caused the quantity change.
  • The conditional quantity range is a sensitivity calculation, not a causal demand forecast, sales promise or benchmark.
  • It is educational decision support, not accounting, tax, legal or business advice.

This is educational decision support, not tax, accounting, legal or financial advice. Check the treatment of your actual transactions under the rules that apply to your business and seek qualified advice where appropriate.

6. Update and evidence policy

Registered family-level suites test formula invariants and example reconciliation; the release ledger records that coverage without claiming a separate oracle for every line of public copy. There is no official threshold or benchmark to refresh for this planner. Commercial inputs remain user-supplied because they vary by business and contract.

Change history

  1. : Initial public release of the planner and methodology after pre-launch calculation, content, source and interaction review.

Related reading

Guides to interpret the decision and its assumptions.

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