Is it required that a company has an employee handbook what is an employer's duty to out unused vacation time

Not all employers are required to have written policies or handbooks. It depends on many factors, including the size of the company, in terms of the total number of full-time employees.

Also, whether the vacation pay calculation is legal depends on many factors, such as how other employees were paid, whether promises were made to you, whether you are represented by a collective bargaining agreement, and so forth.