Dairy Premium Refund Act of 2018 This bill amends the Agricultural Act of 2014, with respect to the Dairy Margin Protection Program, to require the Department of Agriculture (USDA) to repay certain premiums to participating dairy operations. (The Dairy Margin Protection Program is a voluntary program that makes payments to participating dairy operations when a formula-based national margin [the difference between the national all milk price and the national average feed cost] falls below a producer-selected insured margin.) For 2015 and each succeeding year, USDA must repay to participating dairy operations an amount equal to the difference between: the total amount of premiums paid by participating dairy operations under the program for the year; and the sum of: (1) the total payments made to participating dairy operations under the program for the year, and (2) the costs of carrying out the program for the year. A repayment made to a participating dairy operation must be reduced by the amount of payments made to the operation under the program during the year.