The reasonable cost of routine services furnished during any calendar year by a hospital under an agreement under this section is equal to the product of—
the number of patient-days during the year for which the services were furnished, and
the average reasonable cost per patient-day, such average reasonable cost per patient-day being the average rate per patient-day paid for routine services during the most recent year for which cost reporting data are available with respect to such services (increased in a compounded manner by the applicable increase for payments for routine service costs of skilled nursing facilities under subsections (a) through (d) of
section 1395yy of this title for subsequent cost reporting periods and up to and including such calendar year) under this subchapter to freestanding skilled nursing facilities in the region (as defined in
section 1395ww(d)(2)(D) of this title) in which the facility is located.