Signature
Q_star = F / (P - V); MS = (Q_e - Q_star) / Q_e
| Inputs | Definition | Unit |
|---|---|---|
F | Fixed cost of the service for the period, within the capacity considered | money per period |
P | Price or tariff paid to the service per unit of activity | money per unit, above V |
V | Cost that varies with each unit of activity, such as consumables | money per unit |
Q_e | Expected activity for the period | units of activity per period, above zero |
Q_star | Volume of activity at which income equals fixed plus variable costs | units of activity per period |
|---|---|---|
MS | Expected activity less the break-even volume, as a share of expected activity | proportion, negative when expected activity is below break-even |
Function
Break-even price, cost-neutral price and service volume function
Solves for the value of one input at which a decision criterion is exactly zero, holding every other input at its base-case value. For a new health technology the input is the unit price and the criterion is incremental net monetary benefit at a stated threshold (the break-even price) or incremental cost alone (the cost-neutral price). For a service paid per unit of activity the input is volume and the criterion is the surplus of income over fixed and variable costs (the break-even volume). The records follow the notation of the Break-Even Analysis article. NICE's manual (PMG36) calls the general calculation threshold analysis and its result a switching value; the switching value of a non-linear input by interpolation is HE-FM-OWSA-002, and the payer's maximum price per patient in price negotiation is HE-FM-BARG-002.
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Implementations
Excel
Break-even volume from named fixed cost, tariff and variable cost cells
Excel divides the named cell holding the fixed cost for the period by the tariff less the variable cost per unit.
=FixedCost/(Tariff-VariableCost)
Excel
Margin of safety from named expected activity and break-even cells
Excel subtracts the named break-even volume from the expected activity and divides by the expected activity.
=(ExpectedActivity-BreakEvenVolume)/ExpectedActivity
Assumptions
Costs linear and fixed or variable within the relevant range
Fixed costs stay fixed in total and variable costs stay fixed per unit over the range of activity considered, and the price per unit does not change with volume.
Fixed costs constant only up to capacity
Above the capacity of the current fixed resources, fixed costs step up, and a new break-even volume applies to each block of capacity. Decisions about extra activity within a block rest on marginal cost, not on an average cost that includes a share of fixed costs.
Worked examples
Day unit break-even at 3,000 attendances
In the article's illustrative day unit, paid £160 per attendance with variable costs of £70 and fixed costs of £270,000 a year, the contribution is £90 and the break-even volume is 3,000 attendances. With 3,600 attendances expected the margin of safety is about 0.167, or 17%, and the surplus is £54,000.
F = 270000; P = 160; V = 70; Q_e = 3600; Q_star = 3000; MS = 0.1667
Day unit break-even with a second team above 4,000 attendances
If growth beyond a capacity of 4,000 attendances needs a second team costing £120,000 a year, fixed costs become £390,000 and the break-even volume is about 4,333.3, so the unit only covers its costs again at 4,334 attendances. With 4,500 attendances expected the margin of safety would be about 0.037 (computed here for illustration).
F = 390000; P = 160; V = 70; Q_e = 4500; Q_star = 4333.33; MS = 0.037
Common errors
Rounding a fractional break-even volume down
With two teams the day unit makes a loss of £30 at 4,333 attendances and a surplus of £60 at 4,334, so a fractional break-even volume is rounded up (computed here for illustration).
Ignoring a step in fixed costs above capacity
Using the one-team cost structure for 4,500 attendances suggests a surplus of £135,000, but the second team's £120,000 leaves £15,000 (computed here for illustration). The article shows that expansion beats staying at 4,000 attendances, with its £90,000 surplus, only above 5,333 attendances.
Judging extra activity against average cost
At 3,600 attendances the average cost per attendance, including a share of fixed costs, is £145, so an extra contract paying £120 per attendance looks loss-making, yet within capacity each extra attendance adds £50 to the surplus because only the £70 variable cost changes (computed here for illustration).
Sources
Break-even point in units from fixed costs and contribution margin
Franklin M, Graybeal P, Cooper D. Principles of Accounting, Volume 2: Managerial Accounting. Houston, TX: OpenStax; 2019. Section 3.2, Calculate a Break-Even Point in Units and Dollars: the break-even point in units equals total fixed costs divided by the contribution margin per unit, with costs assumed linear and either fixed or variable over the relevant range.
Margin of safety as a share of budgeted or actual sales
Franklin M, Graybeal P, Cooper D. Principles of Accounting, Volume 2: Managerial Accounting. Houston, TX: OpenStax; 2019. Section 3.5, on the margin of safety: the margin of safety is the difference between current and break-even sales, expressed as a percentage by dividing it by budgeted or actual sales (inference: with a fixed price per unit the same share applies to units of activity).
Canonical Identity
Stable URI · Machine-readable · Resolvable · CC BY 4.0