The approximate contribution quoted by the board and the actual contribution to be made if a contract results shall be determined by actuarial valuations by the actuary of the prior and future service liability under this system, on account of the employees involved in the computation, in the same manner as the contribution required of the state on account of its employees was originally determined, except that in consideration of the number of employees of the agency or other circumstances, a different manner of determining the contribution may be adopted by the board, upon recommendation of the actuary.