Technical appendix B

Model methodology and equations

This appendix describes the calculations the model uses to estimate a hospital's financial position under Medicare payment rates, from the baseline cost structure through the multiyear cash projection, and the methods used to construct hospital profiles from Medicare cost reports.

Overview

The model estimates the effect on a hospital's finances of a policy under which some or all payers pay Medicare rates. It proceeds in four stages. First, it establishes the hospital's baseline revenue and costs by payer. Second, it applies the policy scenario, repricing services for the affected payers. Third, it applies a sequence of restructuring levers that reduce costs or increase revenue. Fourth, it projects operating income and cash reserves over a 10-year horizon as payment changes phase in and restructuring takes effect.

The model is applied both to five illustrative hospitals, whose characteristics are benchmarks rather than data for actual institutions, and to individual hospitals whose financial data are drawn from the Medicare cost reports described in Appendix C. Unless otherwise noted, dollar amounts are expressed in millions of dollars per year in constant (inflation-adjusted) terms.

1. Notation

Symbol	Definition
p	Payer: Medicare, Medicaid, commercial insurance, self-pay and uninsured, or other government
mix(p)	The payer's share of the hospital's cost of care, measured as patient volume weighted by resource use rather than as a share of revenue. Shares sum to one.
PCR(p)	Payment-to-cost ratio: the payment the hospital receives from the payer for each dollar of cost incurred to treat that payer's patients
Opex₀	Operating expenses in the baseline year
Other	Other operating revenue, consisting of revenue not derived from patient care. For hospitals drawn from cost reports, this includes all other income reported, including investment income.
M	Payment rate expressed as a multiple of Medicare rates (M = 1 denotes Medicare rates)
v	Percentage change in patient volume under the policy scenario
t	Year after the payment change takes effect, from 1 to the end of the projection horizon

2. Baseline cost structure

The model represents a hospital's operating expenses as staff costs for nine occupational groups, agency (contract) labor, and eleven categories of nonlabor expense. Staff costs are the product of full-time equivalent (FTE) positions, average wages, and a benefits rate representing employee benefits and payroll taxes as a share of wages.

Staff cost(role) = FTE(role) × average wage(role) × (1 + benefits rate) Employed labor = Σ staff cost(role) Total labor = employed labor + agency labor Opex = total labor + Σ nonlabor expense(line) + turnover offset

When a policy scenario changes patient volume, each cost line changes in proportion to its variable share, defined as the portion of the line that varies with patient volume.

Cost line′ = cost line × (1 + v × variable share(line))

3. Baseline revenue and operating margin

Revenue from each payer equals the payer's share of the cost of care multiplied by its payment-to-cost ratio.

Revenue(p) = mix(p) × Opex₀ × PCR(p) Total revenue = Σ revenue(p) + Other Operating income = total revenue − Opex Operating margin = operating income ÷ total revenue

Commercial payment rates

The commercial payment-to-cost ratio is not specified directly. For illustrative hospitals, it is calculated so that the hospital's baseline operating margin equals its assumed value. For hospitals drawn from cost reports, it is calculated so that baseline patient revenue equals the net patient revenue the hospital reported.

Illustrative hospitals: Target revenue = Opex₀ ÷ (1 − baseline margin) PCR(commercial) = [target revenue − Other − Σ mix(p) × PCR(p) × Opex₀] ÷ [mix(commercial) × Opex₀] Hospitals drawn from cost reports: PCR(commercial) = [net patient revenue − Σ mix(p) × PCR(p) × Opex₀] ÷ [mix(commercial) × Opex₀] (sums are over all payers other than commercial insurance) Commercial rates as a multiple of Medicare = PCR(commercial) ÷ PCR(Medicare)

4. Payment policy scenarios

The model includes four policy scenarios, summarized in Table B1. Under each scenario, the payers subject to the policy are paid at Medicare's payment-to-cost ratio, or at a specified multiple of it.

Table B1. Policy scenarios

Scenario	Description	Administrative simplification	Phase-in (years)
Commercial capped at Medicare	Commercial insurers pay Medicare rates but retain their own coverage rules and administrative processes. Medicaid and uninsured patients are unaffected.	15%	1
All payers at Medicare	Commercial insurers and Medicaid pay Medicare rates under a common fee schedule. Uninsured patients are unaffected.	50%	1
All payers, 5-year phase-in	Identical to the all-payer scenario, except that payment rates decline to Medicare levels in equal steps over five years.	50%	5
Single payer at Medicare	All residents are covered, and care is paid for at Medicare rates under a single set of rules. Patient volume increases by 3 percent.	100%	1

PCR′(Medicare) = PCR(Medicare) × M PCR′(p) = PCR′(Medicare) for each payer subject to the policy PCR′(p) = PCR(p) for all other payers

The calculation of revenue under the policy depends on how the hospital is paid. Most hospitals are paid prospectively, at a fixed rate per service; critical access hospitals are paid by Medicare on the basis of their reported costs.

Prospectively paid hospitals: Revenue(p) = mix(p) × Opex₀ × (1 + v) × PCR′(p) × (1 − closed share × closure rate) × (1 + revenue increase) Critical access hospitals (Medicare and payers moved to Medicare rates): Revenue(p) = mix(p) × current Opex × PCR′(p) × (1 + revenue increase)

Because revenue for prospectively paid hospitals is based on baseline costs, payment per unit of service is fixed, and cost reductions do not reduce revenue. For critical access hospitals, Medicare payments decline when costs decline, so cost reductions improve operating income by a smaller amount. The closure terms apply only when the service line closure lever is used, and the revenue increase applies only when the denials recovery lever is used.

The annual operating loss that the hospital must close is defined as the negative of operating income under the policy before any restructuring.

Gap = −(operating income under the policy, before restructuring)

5. Hospital responses

A response scenario assigns each lever a level of none, low, base, or high. The model scales the corresponding value for insurance-related overhead levers by the policy's administrative simplification factor, and, in the sensitivity analysis, scales all levers by a realization factor representing the share of planned savings achieved.

Lever level = scenario level × administrative simplification factor (overhead levers only) × realization factor Realization factor = 1 in the main results; 0.6 and 1.15 in the sensitivity analysis

Levers are applied sequentially, each to the cost structure remaining after the previous levers.

For each lever i, in order: apply the lever's operations to the cost structure turnover offset = turnover offset + (Opex before − Opex after) × offset rate(i) operating gain(i) = operating income after lever i − operating income after lever i−1 Operating income after restructuring = operating income under the policy + Σ operating gain(i)

The operations that make up each lever, and the parameters for each, are documented in Appendix A.

6. Multiyear projections and liquidity

The projection assumes that payment changes phase in evenly over the period specified by the policy scenario, and that each lever's savings increase evenly over its ramp-up period.

Policy phase-in share: s(t) = min(1, t ÷ phase-in years) Lever ramp-up share: f(i, t) = min(1, t ÷ ramp-up years(i)) Operating income(t) = operating income₀ + s(t) × (operating income under the policy − operating income₀) + Σ operating gain(i) × f(i, t) Revenue(t) = revenue₀ + s(t) × (revenue change under the policy) + [Σ operating gain(i) × f(i, t) ÷ Σ operating gain(i)] × (revenue change from levers) One-time costs(t) = Σ max(operating gain(i), 0) × one-time multiple(i) × [f(i, t) − f(i, t−1)]

Depreciation adjusts to its post-restructuring level over five years. Capital spending is assumed to equal baseline depreciation unless reduced by the capital spending lever. Debt principal repayment is not modeled.

Depreciation(t) = depreciation₀ + (final depreciation − depreciation₀) × min(1, t ÷ 5) Capital spending = depreciation₀ × (1 − capital spending reduction) Cash₀ = days cash on hand₀ ÷ 365 × (Opex₀ − depreciation₀) Cash(t) = cash(t−1) + operating income(t) + depreciation(t) − capital spending − one-time costs(t) + investment yield × max(cash(t−1), 0) Days cash on hand(t) = cash(t) ÷ [revenue(t) − operating income(t) − depreciation(t)] × 365

The investment yield is 4 percent for illustrative hospitals. For hospitals drawn from cost reports, it is zero, because investment income is already included in other revenue.

The model reports two thresholds: the point at which days cash on hand falls below 60 days, a common liquidity covenant in hospital bond agreements, and the point at which cash is exhausted. Each is estimated by linear interpolation within the year in which it occurs.

Time of crossing = (t − 1) + [value(t−1) − threshold] ÷ [value(t−1) − value(t)]

7. Supplementary analyses

Decomposition of the payment change

The change in operating income under the policy is attributed to each payer by applying the change in its payment-to-cost ratio to baseline volume. Any remaining difference is attributed to the change in patient volume.

Change attributable to payer p = mix(p) × Opex₀ × [PCR′(p) − PCR(p)] Change attributable to volume = total change in operating income − Σ change attributable to payer p (For critical access hospitals, the change attributable to each payer is calculated as the difference in revenue.)

Single-measure equivalents

To illustrate the scale of the gap, the model calculates the change that would be required if a single measure were used to close it.

Uniform reduction in pay and benefits = gap ÷ employed labor Equivalent reduction in staff (FTE) = gap ÷ (employed labor ÷ total FTE) Gap as a multiple of physician costs = gap ÷ physician staff costs Gap as a multiple of management costs = gap ÷ management staff costs Required reduction in purchase prices = gap ÷ (drugs + devices + supplies + purchased services + billing vendors)

A multiple of physician or management costs greater than one indicates that eliminating that group's compensation entirely would not close the gap.

Break-even payment rate

The break-even payment rate is the multiple of Medicare rates at which the hospital's operating margin after restructuring equals zero. The single-hospital reports solve for this rate numerically; the national analysis uses the fact that operating income is a linear function of the payment rate.

Single-hospital reports: solve margin(M) = 0 by bisection over M from 0.5 to 3.0 (50 iterations) National analysis: M* = 1 − OI(1) ÷ [OI(2) − OI(1)], where OI(M) is operating income at rate M

Sensitivity analysis

The sensitivity analysis varies one input at a time and recalculates the operating margin after an aggressive restructuring, in which all levers are applied at their base levels.

Table B2. Inputs varied in the sensitivity analysis

Input	Lower value	Higher value
Medicare payment-to-cost ratio	−0.04	+0.04
Payment rate as a multiple of Medicare	0.95	1.15
Realization of planned lever savings	60%	115%
Uninsured share of the cost of care (offset by Medicare share)	+4 percentage points	−4 percentage points
Administrative simplification	None (0)	Complete (1)
Patient volume	−3%	+5%
Turnover offset rates	Doubled	None
Commercial share of the cost of care (offset by Medicare share)	+5 percentage points	−5 percentage points

Probabilistic analysis

The probabilistic analysis draws the level of each lever independently from a triangular distribution bounded by its low and high levels, with its mode at the base level, and adds normally distributed variation to the Medicare payment-to-cost ratio. The model is run 3,000 times with a fixed random seed, and the share of runs in which the hospital reaches a nonnegative operating margin is reported. A second set of runs holds all compensation levers at zero.

Lever level(i) ~ Triangular(low(i), base(i), high(i)), then adjusted for administrative simplification PCR(Medicare) ~ PCR(Medicare) + Normal(0, 0.02) P(break-even) = share of runs with operating margin ≥ 0

8. Construction of hospital profiles from cost reports

Hospital profiles are constructed from the CMS Hospital Provider Cost Report¹ using the procedures below, implemented in model/hcris.py. The cost report variables used are listed in Appendix C.

Inclusion criteria

The analysis includes short-term acute care hospitals and critical access hospitals that meet all of the following criteria: revenue, operating expenses, salaries, FTEs, and charges are reported and positive; the cost reporting period is between 330 and 400 days; operating expenses are at least $5.0 million and staffing is at least 10 FTEs; the estimated commercial share of the cost of care is at least 3 percent; labor and depreciation account for no more than 90 percent of operating expenses; and the implied commercial payment rate is between 0.7 and 6 times the Medicare rate. Hospitals that do not meet these criteria are excluded, and the reason for exclusion is recorded.

Payer mix

The cost report identifies traditional Medicare discharges but not Medicare Advantage discharges. The Medicare share is therefore estimated by increasing the traditional Medicare share by an assumed ratio of Medicare Advantage to traditional Medicare discharges of 0.8 (0.4 for critical access hospitals). Inpatient days are used when discharges are not reported. The Medicaid share is estimated from charges, the uninsured share from the reported cost of uncompensated care, and the commercial share as the remainder.

Medicare share = min[Medicare discharges ÷ total discharges × (1 + 0.8), 0.75] Medicaid share = min(Medicaid charges ÷ total charges, 0.80) Uninsured share = min(cost of uncompensated care ÷ total costs, 0.40) Commercial share = 1 − Medicare share − Medicaid share − uninsured share

Payment-to-cost ratios

The Medicare payment-to-cost ratio is assumed to be 0.84 for prospectively paid hospitals and 0.99 for critical access hospitals. The Medicaid ratio is calculated from each hospital's reported Medicaid revenue and charges, converted to costs using the hospital's cost-to-charge ratio; where any of these values is missing, a ratio of 0.80 is assumed. The uninsured ratio is zero because the reported cost of uncompensated care is already net of patient payments. The commercial ratio is calculated as described in section 3.

PCR(Medicaid) = Medicaid net revenue ÷ (Medicaid charges × cost-to-charge ratio), limited to 0.3–1.3

Published payer mix

Where a hospital's audited financial statements report net patient revenue by payer, those shares, denoted R(p), replace the estimates above. These values are recorded in assumptions/overrides.yaml.

mix(Medicare) = R(Medicare) × net patient revenue ÷ [PCR(Medicare) × Opex] mix(commercial) = 1 − mix(Medicare) − mix(Medicaid) − mix(uninsured) PCR(p) = R(p) × net patient revenue ÷ [mix(p) × Opex], for Medicaid, uninsured, and commercial

Cost structure

Total salaries, FTEs, benefits, agency labor, and depreciation are taken from the cost report. Because the cost report does not report staffing or wages by occupation, these totals are distributed across occupational groups and nonlabor categories in the same proportions as the model's template hospital.

Benefits rate = wage-related costs ÷ salaries (if between 8% and 50%; otherwise 0.24) FTE(role) = reported FTE × template share of FTE(role) Wage(role) = template wage(role) × k, where k = reported salaries ÷ Σ [FTE(role) × template wage(role)] Agency labor = reported contract labor for direct patient care (if under 30% of Opex; otherwise template share) Depreciation = reported depreciation (if under 25% of Opex; otherwise template share) Nonlabor(line) = [Opex − salaries × (1 + benefits rate) − agency labor − depreciation] × template share(line) Days cash = (cash + temporary investments + investments) ÷ [(Opex − depreciation) ÷ 365]

Hospital categories

Critical access hospitals are identified by facility type. Other hospitals are classified as major teaching hospitals if they have at least 0.25 residents per bed, as other teaching hospitals if they have any residents, and otherwise as rural or urban nonteaching hospitals according to the cost report's geographic designation.

National estimates

National estimates are reported as medians, percentiles, and shares of hospitals meeting specified conditions. Hospitals are not weighted by size, so each hospital contributes equally regardless of its number of beds or its expenses.

9. Limitations

The results should be interpreted in light of several limitations.

For hospitals drawn from cost reports, the Medicare payment-to-cost ratio is a single assumed value rather than a hospital-specific measure. Because this ratio determines the hospital's financial position after the policy takes effect, it is the largest single source of uncertainty in hospital-level results.
The Medicare and commercial shares of the cost of care are estimated from discharge data and an assumed Medicare Advantage ratio, except where a published payer mix is available.
Staffing by occupation and nonlabor spending by category follow a single template, scaled to each hospital's reported totals. Results by occupational group are therefore indicative.
The model does not estimate the effects of restructuring on quality of care, patient outcomes, or patient volume.
Labor market responses are represented by fixed turnover offsets rather than by a model of labor supply.
Supplier responses to lower hospital revenue, which could affect purchasing savings, are not modeled.
Projections are in constant dollars and exclude debt principal repayment, philanthropy, and investment portfolio policies.
Supplemental payment programs, including 340B, disproportionate share hospital payments, graduate medical education payments, and Medicaid supplemental payments, are reflected in payment-to-cost ratios rather than modeled separately.
Medicare Advantage is treated as equivalent to traditional Medicare.

Note: This appendix is generated from the model's assumption files (assumptions/*.yaml) and source code (model/) by run.py --docs, and reflects the parameter values in effect on November 12, 2026.