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Unfortunately, employees must be paid for all "on the job" travel time, regardless of whether they are riding in a company car or their own personal vehicle. The only travel time which is not compensable is the employer's initial commute to the employer's principle place of business. Employers never have to pay for that, but once an employee is working--and they would be if they were driving to a particualr job site--they are entitled to be paid for that time.
The travel time should be paid at the employee's regular rate of pay. However, it is generally permissible to have a wage agreement whereby employees are paid at a lower rate
not to fall below minimum wage for compensable travel time and other types of non-productive work time, as noted in 29 C.F.R. 778.318(b) and a DOL administrative opinion letter dated January 22, 1999 (BNA, WHM 99:8211).
Note well, however, that any such agreement should be clearly expressed in a written wage agreement signed by the employee, and the time distinguished as travel time must be carefully and precisely recorded. Further, if such travel time results in overtime hours, the overtime pay must be calculated according to the weighted average method of computing overtime pay, as provided in 29 C.F.R. 778.115.
With regard to your second question about liability, if an employee is involved in an accident in their personal vehicle while driving to a job site, the company would be liable for any damages pursuant to the legal theory of "respondeat superior." Respondeat superior holds that liability for any on the job conduct that occurs in the ordinary course and scope of the employee's employment automatically transfers to the employer. There is no way to avoid respondeat superior liability, regardless of whether the employee drives a company or personal vehicle.
Finally, though you did not specifically ask about this, I feel obliged to mention that Labor Code 2802 requires employers to reimburse employees for all expenses necessarily incurred in the course of discharging their duties. This would include gas expenses and "wear and tear" on any personal vehicle they use to perform company work.
The total mileage reimbursement (aking into account both gas and wear and tear) recommended under the IRS rules is .56.5 cents per mile for 2013. See here for more information: http://www.calchamber.com/headlines/pages/11272012-irsannounces2013mileagereimbursementrates.aspx
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