Difference between Cost Allocation and Profit Allocation

2325  Internal rate is 10. Vatter 1966, 689 explained the difference between the straight line method which is consistent with cost allocation and the compound interest method which is consis tent with profit allocation as follows. ―In the straight-line case, depreciation is computed and deducted in calculating the annual income from cash inflow while the compound interest model reverses the process －first computing income, which when subtracted from cash revenue, yields the amortization figure.‖ Parentheses added by authors. See Figure 2 On the basis of Vatter‘s statement, the characteristics of the cost allocation straight line method can be clarified in that income 2nd period 21 is calculated ex post as the difference between realized cash inflow 2nd period 121 and the matching cost deferred cost from the 1st period 50 plus depreciation cost at the 2nd period 50. On the other hand, the ch aracteristics of the profit allocation compound interest method can be found in that profit in each period 1st period 10 and 2nd period 11 is allocated created through the 2326 process of discount and premium of the expected cash inflow 2nd period 121 at the internal rate of 10. From above, the decisive difference between them can be found in whether the realization concept or matching concept functions or not, even though both fall under allocation basis. This difference can also be found in that the former presupposes actual cash flow ex post cash flow and the latter presupposes estimated cash flow ex ante cash flow. F i g u r e 2 C o s t Al l o c a t i o n a n d P r of i t Al l o c a t i o n T i m e N e t C I F Co s t Al l o c a t i o n : S t r a i g h t Li n e Me t h o d Profit Allocation: Compound Interest Method 1 Ca r r yi n g a m o u n t 2 A m o r t i za t i o n 100’βyear 3 I n c o m e R e a l i z e d CI F － E xpe ns es 1 Ca r r yi n g a m o u n t 2 I n c o m e B e g i n n i n g o f 1×10％ 3 A m o r t i za t i o n E xp e c t e d N e t CI F － 2 1 2 - - - - - - 1 2 1 1 0 0 5 0 - - - 5 0 5 0 - - 2 1 1 0 0 1 1 0 - - 1 0 1 1 - - - △ 10 1 1 0 T o t a l s 1 2 1 - - - 1 0 0 2 1 - - - 2 1 1 0 0 ＊ S i n c e a m o r t i z a t i o n 5 0 i s d e f e r r e d t o t h e 2 n d y e a r , t h e e xp e n s e s o f t h e 1 s t y e a r b e c o m e ze r o , t h e r e f o r e income a l s o b e c o m e s z e r o . 3. The Feature of Cost Allocation Approach [Form 1] Compared with Profit Allocation Approach [Form 2] In this Section, we introduce the cost allocation approach [Form 1] in the line of following three steps, and then try to clarify the feature of Form 1 compared with Form 2. 2327 First step is to identify the straight line method. Vatter recognized the straight line method as a procedure that allocates a fixed amount to each period without regard of future cash flow patterns. In second step, the cost allocation which takes into account future cash flow patterns will be developed. When annual cash inflow is constant, the straight line method will be s elected See Figure 3, Case 1. If the cash inflow is assumed to diminish, the decreasing charge method sum-of-the-years-digits method, etc. will be selected Case 2. The third step considers time value. In this step, the straight line method can be justified when future cash inflow is estimated to diminish linearly Case 3. The decreasing charge method can be justified when future cash inflow is estimated to diminish rapidly Case 4. After all, the cost allocation approach [Form 1] starts from the first step and considers cash flow patterns and time value in selection of the depreciation method. Such ideas can be found in Anton 1956, 117-134 and Beaver 1989, chap.3, which clarified the relationship between cash flow patterns and appropriate depreciation patterns. 2328 F i g u r e ３Cost Allocation and Cash Flow Patterns Case 1: Straight Line Method 1,000 2,000 3,000 1 2 3 4 5 6 7 8 9 10 Case 2: Decreasing Line Method 1,000 2,000 3,000 1 2 3 4 5 6 7 8 9 10 Case 3: Straight Line Method 1,000 2,000 3,000 1 2 3 4 5 6 7 8 9 10 Case 4: Decresing Line Method 1,000 2,000 3,000 1 2 3 4 5 6 7 8 9 10 Notes ・Investment Amount: 10,000 Useful Life: 10 years Salvage Value: 0 ・Dotted line: Cash Flow Patterns Solid Line: Depreciation Cost The above methods are based on the retroactive income calculation as the difference of revenues realized cash inflow and expenses depreciation cost etc.. While in the profit allocation approach, income is determined at first, and depreciation is subordinated to it See Figure 2. This approach sets artificial allocation creation of profit above realization and matching. The intension of this approach is the ex ante allocation creation of profits. 2329 4. Present Value with the Restriction of Cost: [Form 1], [Form 2] and [Form 3] This section compares market value approach with the restriction of cost [Form 3] to cost allocation approach [Form 1] and profit allocation approach [Form 2], and clarify the similarity of these forms and three methods which are relating to estimation change. Example 2 will show this case. [Example 2]  At the beginning of the first period, equipment was purchased at 300. Its useful life is three years and the salvage value is zero.  Initially, it was expected that net cash inflow accrues 130 at the end of the first period, 120 at the end of the second period and 110 at the end of the third period.  Internal rate is 10.  Net cash inflow at the end of the first period was realized as estimated. However at the end of the first period, the estimation was adjusted 2330 downward at the end of the second and third periods due to lowered profitability, as 90 and 70 respectively.  Fair value of the equipment was 120 at the end of the first period. If market participants estimate fair value of the equipment, they would predict net cash inflow from its asset at the end of the second and third periods, as 72 and 62 respectively Discount rate is 8. Figure 4 shows the calculation result and graph of the prospective method and the catch-up method, which have been the two main methods for impairment of a loan. F i g u r e 4 Prospective Method a n d Catch-up Method T i m e Re a l i z e d CI F Prospective Method 1 Catch-up Method 2 Ca r r yi n g a m o u n t A m o r t i za t i o n I n c o m e Ca r r yi n g a m o u n t A m o r t i za t i o n I n c o m e 1 2 3 - - - 130 90 70 3 0 0 1 6 0 7 0 - - - - - - 1 4 0 9 0 70 - - △ 10 - -- 0 0 ％ 0 0 ％ 3 0 0 1 4 0 6 4 - - - - - - 1 6 0 7 6 64 - - △ 30 - -- - - 14 10 ％ 6 10 ％ T o t a l s 2 9 0 - - - 3 0 0 △ 10 - - - 3 0 0 △ 10 Notes In the parentheses, the rate of return are shown. Impairment loss is included in amortization. 1 ・Here, a zero rate is applied, because the revised rate r that fills the following formula is neg ative. 300 = 130 1+r - 1 + 90 1+r - 2 + 70 1+r - 3 ・Impairment loss 10 =300-290 is included in amortization 140. ・In the 2nd period, it is calculated as follows. 1 Modified Carrying amount at the Impairment: 90 + 70 = 160 2 Carrying amount at the end: 70 3 Amortization difference between 1 and 2: 160 - 70 = 90 4 Income realized CIF - amortization: 90 - 90 = 0 2 ・Here, the revised balance is calculated with a discount rate 10％ as follows. 130 1+0.1 - 1 + 90 1+0.1 - 2 + 70 1+0.1 - 3 = 245 ・Impairment loss 55 =300-245 is included in amortization 160.