Estimating for a small project

Lets say we have a test automation sprint. The sprint has 12 stories out of which 8 will be in the first sprint(4-weeks) and the remaining 4 will be in the second sprint(2-Week). For the first sprint, the total story points are 38 and for the 2nd one, there are 11 story points. The first sprint is to be completed with 5 people and the second sprint is to be completed with a reduced set of 3 people. Here are my calculations.

First Sprint

The total story points come to 38. Considering a team of 5 with 6 hours of effective work per day(2 hours daily spent in meetings, timesheets,discussions,issue resolutions etc. This is the fixed overhead). Let’s consider a 4 weeks of sprint to start with. So we have 4*5*5*6=600 person hours of work. Say for example, the hourly rate is 15$ per person, so the total cost billed to the customer is 9000 for the entire 4 weeks of effort.

Second Sprint

The pending 11 story points can be covered in a 2 weeks sprint with 3 people. The person hours for this sprint will be 2*5*3*6=180. The total cost to be billed to the customer is 15*180=2700 for 2 weeks of effort. The total automation cost with an agile approach is 11700 USD.

Here I have not accounted for variable overhead and resource downtime (People being sick, personal emergencies, leaves etc). It has been assumed that there are no planned leaves.

Please let me know whether this calculation is correct.