Functioning as Director of Finance Department for a private hospital, was approached by Dr$.$ Michael Carroll, the hospital owner, whereby he expressed an interest in estimating the volume of patient$-$days to make profit under a newly proposed capitation contract. The hospital is considering a new capitation contract with a major MHO. Dr$.$ Carroll was interested in learning above what number of patient$-$days the hospital will risk losing money. He also needed the supporting rationale to make a decision whether or not the hospital should accept this capitation contract under the proposed terms. Under the contract, the hospital would agree to provide all inpatient hospital services to $10,000$ covered lives of the HMO plan. The hospital would receive $$38$ per$-$member$-$per$-$month $($PMPM$)$ to cover all inpatient services. It is anticipated that the hospital will incur fixed costs, or readiness to serve costs, of $$1,860,000$ for these $10,000$ covered lives. Variable costs per patient$-$day are expected to be $$600.$ Calculate the break$-$even point in patient$-$days under this contract.

Based on historical data collected by the hospital, it is anticipated that $93$ admissions per $1,000$ covered members of this HMO will be provided with an average length of stay equal to $5\mathrm{.}0,$ or $465$ days per $1,000.$

Taking into consideration the questions expressed by Dr$.$ Carroll and based on information presented in the mini$-$case, information obtained from credible outside sources, and your professional experience, prepare a memorandum addressing the number of patient$-$days, under which the hospital will make profit, and above which the hospital will risk losing money under the proposed capitation agreement. Further, based on the historical data collected by the hospital, determine anticipated patient$-$days of this HMO covered membership and explain whether the hospital should accept this capitation contract under the proposed terms.