Ten years ago I did a thorough analysis:
Basic transportation (Honda Civic, Toyota Corrola): $0.20/mile
Mid size luxury sedan/wagon (BMW 5, Volvo XC70): $0.38/mile
Tahoe/Suburban, etc.: $0.50/mile
I bought a car. I drove 100,000 miles for work and then checked actual costs vs. the analysis. I was within 5% for all costs including purchase, gas, insurance, maintenance, tax, registration, and even a minor crash and a car break-in while on company business.
Since then, costs have gone up. I would project $0.25 to $0.30 for the basic transportation option today. So, you double your money with a $0.575 mileage reimbursement, and you will definitely come out ahead.