Signature
X_star = D + (M - D) / c
| Inputs | Definition | Unit |
|---|---|---|
D | Annual deductible paid in full by the member | currency |
M | Annual out-of-pocket maximum | currency |
c | Share of allowed cost above the deductible paid by the member, entered as a decimal and above zero | proportion |
X_star | Annual allowed cost at which the member's cost sharing reaches the out-of-pocket maximum | currency, for example dollars |
|---|
Function
Actuarial value calculation function for health plan cost sharing
Maps a health plan's cost-sharing rules and the allowed costs of a standard population over one benefit year to the share of those costs that the plan pays. Each person's allowed cost is split into the cost sharing paid by the member and the remainder paid by the plan, and the plan's total is divided by the total allowed cost. The records follow the notation of the Actuarial Value article, where X is allowed cost, S is cost sharing and P is the plan payment. Premiums appear in neither term.
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Implementations
Excel
Out-of-pocket cap point in one cell
Excel returns the cap point from named cells holding the deductible, the out-of-pocket maximum and the member's coinsurance rate as a decimal.
=Deductible+(OOPMax-Deductible)/Coins
Assumptions
Positive member coinsurance and a single-rate plan
The plan has the structure of HE-FM-AV-002, with one deductible, one coinsurance rate and no copayments, and c is above zero. With zero coinsurance the member pays nothing after the deductible, never reaches a maximum set above it, and the formula divides by zero.
Worked examples
Cap point of the illustrative $2,000 deductible plan
With a $2,000 deductible, 20% member coinsurance and a $6,000 out-of-pocket maximum, the member reaches the maximum at an allowed cost of $22,000, as in the article.
D = 2000; M = 6000; c = 0.2; X_star = 22000
Cap point after cutting the illustrative deductible to $1,000
Cutting the deductible to $1,000 with the same coinsurance and maximum moves the cap point up to $26,000, because more of the $6,000 is now paid at the 20% rate.
D = 1000; M = 6000; c = 0.2; X_star = 26000
Common errors
Dividing the whole maximum by the coinsurance rate
Taking M divided by c as the cap point treats the deductible as if it were paid at the coinsurance rate. In the article's plan this gives $30,000 rather than $22,000.
Dividing by the plan's coinsurance share
Using the plan's share of 0.8 in place of the member's 0.2 gives a cap point of $7,000, below the $8,000 at which the article's higher spending group still pays only $3,200.
Sources
CMS 2027 AV Calculator spending level at which the MOOP applies
Centers for Medicare & Medicaid Services, Center for Consumer Information and Insurance Oversight. Final 2027 Actuarial Value (AV) Calculator Methodology. Washington, DC: CMS; 25 February 2026. Section Calculating AV, Step 5: the deductible is subtracted from the modified MOOP, the result is divided by one minus the effective coinsurance rate (the plan's share) and the adjusted deductible is added. The modified MOOP and adjusted deductible adjust for copayments, so for a plan without copayments the step reduces to this formula.
Canonical Identity
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