Weighted Avg for Billable Hour

Question

I am trying to get to an avg reimbursement rate for an MD billable hour. They have different types of appointments, each receiving a different reimbursement amount. I ran an analysis which gave the historical mix of appointments across all the MDs. Looks something like this:

Appt.  % of Time Appt Occurred.  Reimb Amt.
A      30%                       $50
B      50%                       $65
C      20%                       $90

Obviously from this I could get an weighted avg reimbursement amount of $65.50 per appointment. The problem is that I need to get to an avg reimb amt per hour. Each of these appointments have varying lengths. The data set would be something like this:

Appt.  Appt Duration(Mins).  % of Time Appt Occurred.  Reimb Amt.
A      15                    30%                       $50
B      30                    50%                       $65
C      45                    20%                       $90

The added complexity of the time component has me stumped. How can I get to an avg hourly reimbursement rate?

Thank you in advance!

Answer 1

Find hourly reimbursement rate for each kind of appointment, then get the weighted average for the three kinds:

For the first kind: $\$50/(1/4) = \$200,$ etc.

Then $\$200(.3) + ?(.5) + ?(.2) = $ answer.