Charity Hospital, a not-for-profit, has a maximum capacity of 15,000 discharges per year. Variable patient service costs are $495 per discharge. Variable general and administrative costs are $5 per discharge. Fixed hospital overhead costs are $4,000,000 per year.

The current reimbursement rate is $1,000 per discharge.

a. What is Charity’s accounting breakeven volume in number of discharges?

b. Now assume that Charity’s total discharges for 2019 totaled 10,000. In late 2019, a specialty cardiac hospital opened near Charity, so discharges in 2020 will reach only 8,500.

Management is planning to cut fixed costs so that the total for 2020 will be $1,000,000 less than in 2019. Management is also considering reducing variable staffing costs to earn a target profit that will be the same dollar amount as the profit earned in 2019. Charity has already had 4,000 discharges in 2020 at a reimbursement rate of $1,000 per discharge with variable costs unchanged. What contribution margin per unit is needed on the remaining 4,500 discharges to reach the target profit?