Chapter 12 - If the fixed overhead rate changes the...

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If the fixed overhead rate changes, the applicable profit function depends on the cost flow assumption chosen. Two separate profit functions are provided below to illustrate the concepts involved. First, an equation is developed for the FIFO assumption, and then two equations are developed for the LIFO assumption. FIFO When the fixed overhead rate changes and FIFO is used, two rates must be included in the equation, i.e., the old rate and the new rate. In addition, the units in the beginning inventory must be kept separate from the other units that are sold during the period. The absorption costing profit function, based on a FIFO cost flow, may be stated in the following manner. [10] NIA = -TFC + (P-V)(XS) - F0(BFG) - F1(XS-BFG) + F1(XP) where: F0 = Previous period fixed overhead rate. F1 = Current period fixed overhead rate. BFG = Beginning finished goods in units. If XS<BFG, substitute XS in each place BFG appears in the equation. Observe that the adjustment for the inventory change is stated in three parts in Equation 10. The term we used in the previous equations, i.e., -F(XS-XP) is replaced by -F0(BFG) - F1(XS-BFG) + F1(XP). The term -F0(BFG) represents the prior period fixed overhead costs included in the beginning inventory that are charged to cost of goods sold. The next term, -F1(XS-BFG), represents the amount of the current period's fixed overhead costs that is charged to cost of goods sold. The last term represents the current period fixed overhead costs that were charged to the inventory. Equation 10 may be simplified by combining the last three terms and substituting NID for -TFC + (P-V)(XS). The result is Equation 11 which is easier to work with. [11] NIA = NID - (F0-F1)(BFG) - F1(XS-XP) The term -(F0-F1)(BFG) represents the effect of a fixed overhead rate change on absorption costing net income. The last term, -F1(XS-XP), represents the effect of an inventory change on absorption costing net income. Equation 11 shows that if there is no change in the fixed overhead rate, then F0 is equal to F1 and the term (F0-F1) (BFG) drops out of the equation. Then Equation 11 would provide the same results as Equations 2 and 3 presented earlier in this chapter. However, if the fixed overhead rate changes, the units in the beginning inventory will be charged into cost of goods sold at the previous period overhead rate. The usual direct/absorption costing generalizations are valid as long as the absolute amount of the first term (F0-F1)(BFG) is less than the absolute amount of the second term F1(XS-XP). The generalizations are not valid
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