Funding cash reserves with capitation payments - Managed Care

Healthcare Financial Management, May, 1995 by J. Bruce Ryan, Scott B. Clay

The March 1995 Managed Care column in HFM ("How to Determine Financial Reserves for Capitated Contracts," p. 18) described a method to determine the reserves an organization would be required to maintain to absorb the financial effect of service fluctuations in a capitated contract at an acceptable level of risk. These reserves consist Of two components: funds held to cover incurred-but-not-reported (IBNR) liabilities and a cash cushion (CC).

The analysis introduced in that Managed Care column can be extended to show the conditions under which a capitated contract would generate monies to fund the cash cushion, as opposed to having to fund these reserves from other sources within the organization. (The contract is assumed to generate cash to fund the IBNR.) This analysis also can help determine how quickly an organization can be expected to generate funds from the capitated contract to fund the required reserves.

Assumptions

As in the previous column, this discussion is based on a hypothetical hospital and assumes that the hospital's average cost per case (C) is $6,597 and the standard deviation (SD) per case is $5,492. The example also assumes that the hospital's expected age/sex/health-status-adjusted rate (U) is 0.04781 (ie, 47.81 admissions per 1,000 enrollees). The example assumes that management wants to be 99 percent sure that it will not run out of cash during the course of the contract (ie, a Z factor of 2.33). For the sake of simplicity, the example also assumes that the number of covered lives (M) is constant throughout the period of the contract.

Number of covered lives

The cash cushion amount is:

CC = Z x SD x [(M x U).sup.1/2]

To determine the extent to which profits from the contract will be sufficient to fund the cash cushion, it is necessary to subtract the cash cushion amount from the contract's net cash flows (NCF). NCF is defined as:

NCF = L x C x U x M

where L is the safety loading factor or profit margin on the contract (assumed to be 4 percent). The difference between the net cash flows and the cash cushion is the net equity cushion (NEC):

NEC = NCF - CC = [L x U x C x M] - [Z x SD x [(M x U).sup.1/2]]

Solving this equation for M, the break-even volume of covered lives ([M.sup.*]) to fund the CC is:

[M.sup.*] = (1/U) [(Z x SD/L x C).sup.2]

Using the values specified above, the break-even volume is:

[M.sup.*] = (1/0.04781)[(2.33 x $5,492/0.04 x $6,597).sup.2] = 49,186 covered lives

This equation serves as the basis for understanding several critical points regarding funding of the cash cushion (see Exhibit 1):

* Break-even volume increases as the safety loading factor decreases (assuming L[greater than]0).

* Break-even volume decreases as Z (level of certainty) decreases.

* If the safety loading factor is less than or equal to zero, cash to fund the cash cushion would have to be funded totally from external sources.

* The minimum net equity cushion for a contract (or maximum need for external funding) occurs when the number of covered lives equals one-fourth the break-even volume ([M.sup.1]). This is a mathematical constant and should be considered when determining the minimum number of lives to capitate:

[M.sup.1] = [M.sup.*]/4

[M.sup.1] = 49,186/4

= 12,296 covered lives

The amount of external funding (EF) required for this volume (ie, the maximum amount of external funds required to fund the cash cushion) is:

EF = (1/4)([Z.sup.2] x [SD.sup.2]/L x C)

= (1/4) ([2.33.sup.2] x [$5,492.sup.2]/0.04 x $6,597)

= $155,134

This amount is always equal to one-half of the cash cushion for [M.sup.1] covered lives.

The cash cushion of [M.sup.1] is: (2.33) x ($5,492) x [(0.04781 x 12,296).sup.1/2] = $310,264. The cash cushion would be fully funded in two years. See Exhibit 2.

Required duration

Assuming the safety loading factor is greater than zero, the next question is how quickly the contract will generate funds to cover the required reserves. This duration in years (Y) is found by solving the following formula:

Y = (Z x SD/L x C)[(1/U x M).sup.1/2]

As shown below, 3.14 years would be necessary for the capitated contract to fund the cash cushion for 5,000 covered lives.

Y = (2.33 x $5,492/0.04 x $6,597) [(1/.04781 x 5,000).sup.1/2] = 3.14 years

Exhibit 2 shows the relationship between the number of covered lives and the number of years required to fund the cash cushion from profits on the capitated contract in this example.

The duration equation allows analysts to make the following observations regarding the time required to fund the cash cushion from contract net cash flows. Specifically, the number of years:

* Increases as the organization's risk aversion (as measured by the Z factor) increases;

* Decreases as the safety loading factor increases; and

* Decreases as the number of covered lives increases.

Conclusion

Understanding the financial commitment an organization makes when accepting capitation is critical to ensuring success under these contracts. Although this analysis employs a number of simplifying assumptions (such as a fixed number of covered lives over the contract period and only a single contract), the observations made are valid and can serve as a basis for understanding these financial commitments.