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Accounting theory and practice, Volume 2 (of 3) : a textbook for colleges and…

2. VARIABLE PERCENTAGE METHODS

1050 words  |  Chapter 56

The second main classification of methods, called for want of a better title, “Variable Percentage” methods, differs from the proportional methods in that either the base or the percentage rate varies for each estimate of depreciation. The various proportional methods can all be expressed as percentages but their base remains fixed and is always the total amount of depreciation to be charged off. Under the variable percentage methods, if the percentage is fixed, the base varies; and if the base is fixed, the percentage varies. The subclasses here are: (a) Fixed Percentage of Diminishing Value Method (b) “Changing Percentage of Cost Less Scrap” Method (sometimes known as the “Sum of Expected Life-Periods” Method) (c) Arbitrary with Increasing Amounts (d) Arbitrary with Decreasing Amounts (a) Fixed Percentage of Diminishing Value Method The “Fixed Percentage of Diminishing Value” method estimates the periodic depreciation as a fixed percentage of the appraised or book value of the asset as at the time of the last appraisal. Thus, if the asset cost $1,000 and the fixed rate is 10%, the first depreciation estimate is $100 (10% of $1,000) giving an appraised value of $900; the second depreciation estimate is $90 (10% of $900), with a new appraised value of $810; the third estimate is $81 (10% of $810), with an appraisal of $729 for the asset; and so on. It is evident that a final zero valuation can never be reached (although it may be approximated) as the series becomes an indefinite or indeterminate series. If there is any scrap value, and there usually is, the series becomes determinate. From the standpoint of calculation the problem here is the determination of the fixed rate necessary to reduce the asset value to residual or scrap value in the given life-term. Using the standard notation, we may formulate the following equations: V₁ = V(1 - d); V₂ = V₁(1 - d) = V(1 - d)(1 - d); V₃ = V₂(1 - d) = V(1 - d)(1 - d)(1 - d); whence Vₙ = V(1 - d)ⁿ, which solved for 1 - d gives ______ 1 - d = ⁿ√Vₙ/V) , and, solving for d, we get _____ (2) d = 1 - ⁿ√(Vₙ/V) While complex, the formula is readily solvable by means of logarithms. For an asset costing $150 with a service life of 5 years and a scrap value of $50, the rate is found by the above formula to be approximately 19.726%. _______ d = 1 - ⁵√(50/150) = .19726 The appraisal schedule is, therefore, as follows: =======+==============+============+=================+============== | Fixed | | | Total Age in | Depreciation | Periodic | Depreciated or | Accumulated Periods| Rate % |Depreciation| Appraised Value | Depreciation -------+--------------+------------+-----------------+-------------- 0 | ..... | $ ..... | $150.00 | $ ..... 1 | 19.726 | 29.59 | 120.41 | 29.59 2 | 19.726 | 23.75 | 96.66 | 53.34 3 | 19.726 | 19.07 | 77.59 | 72.41 4 | 19.726 | 15.32 | 62.27 | 87.73 5 | 19.726 | 12.27 | 50.00 | 100.00 | | ------ | | | | 100.00 | | -------+--------------+------------+-----------------+-------------- The following chart shows graphically the appraised values and the accumulated depreciation: [Illustration: _Graphic Chart—Fixed Percentage of Diminishing Value Method_] (b) Changing Percentage of Cost Less Scrap Method Similar in effect to the method just explained is the “Changing Percentage of Cost Less Scrap” or the “Sum of Expected Life-Periods” method. Here, the base remains fixed, but the periodic depreciation rates change. Each depreciation rate is a fraction the common denominator of which is the sum of the expected life-periods as viewed from the beginning of each successive period, and the numerator of which is the expected life for the period in question. For example, an asset of which the expected life is 5 periods has at the beginning of each successive period expected life-terms of 4, 3, 2, and 1 periods respectively, making a total of 15 which becomes the common denominator of the fractions whose numerators are 5, 4, 3, 2, and 1 respectively; i.e., the changing depreciation rates are ⁵/₁₅, ⁴/₁₅, ³/₁₅, ²/₁₅, and ¹/₁₅. For an asset costing $150 with expected life of 5 periods and scrap value of $50, the appraisal schedule would be as follows: =========+==============+==============+==============+============= Age | Changing | | Depreciated | Total in | Depreciation | Periodic | or Appraised | Accumulated Periods | Rate % | Depreciation | Value | Depreciation ---------+--------------+--------------+--------------+------------- 0 | ..... | $ ..... | $150.00 | $ ..... 1 | 33⅓ | 33.33 | 116.67 | 33.33 2 | 26⅔ | 26.67 | 90.00 | 60.00 3 | 20 | 20.00 | 70.00 | 80.00 4 | 13⅓ | 13.33 | 56.67 | 93.33 5 | 6⅔ | 6.67 | 50.00 | 100.00 ---------+--------------+--------------+--------------+------------- A comparison of this appraisal schedule with that of the fixed percentage of diminishing value method shows that this method charges more depreciation during the early life-periods and less during the later periods. The general effect of this method and its significance are discussed in Chapter X where the relative merits of the various methods are considered. The graph for the sum of expected life-periods method is not shown as it differs little from that of the fixed percentage of diminishing value method on page 158. (c, d) Arbitrary Methods The two other arbitrary types of this variable percentage method are hardly to be classed as methods as they do not rest on any law according to which they may be operated. Under them arbitrary amounts are charged to depreciation each period, the only controlling principle being that in the one case these periodic amounts increase from period to period, while in the other case they decrease. In the one case, therefore, the appraisal schedule would be similar as to its “Periodic Depreciation” column to those of the two methods just explained, excepting that the column must be reversed, i.e., read from the bottom upward. In the other case, the appraisal schedule would be exactly similar to those just shown. Within the restriction that they must be increasing or decreasing amounts for succeeding periods and that the total depreciation must be charged off within the estimated life-period of the asset, the periodic depreciation charges are, under these methods, purely arbitrary, neither based on fact nor logic.
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Chapters

1. Chapter 1 2. Introduction of System 3. 1. PROPORTIONAL METHODS 4. 2. VARIABLE PERCENTAGE METHODS 5. 3. COMPOUND INTEREST METHODS 6. 4. MISCELLANEOUS METHODS 7. 1. PROPORTIONAL METHODS 8. 2. VARIABLE PERCENTAGE METHODS 9. 3. COMPOUND INTEREST METHODS 10. 4. MISCELLANEOUS METHODS 11. Introduction 12. Introduction 13. CHAPTER I 14. 5. Debenture 15. CHAPTER II 16. Introduction of System 17. Chapter XXXVI, a cash discount is usually treated as a financial 18. 6. Indexing vouchers. 19. 4. It localizes responsibility by showing authority for 20. 5. It secures a receipted bill for all disbursements of cash. 21. 1. Clumsy provision for returns and allowances, partial 22. 3. The giving out of information about the business 23. CHAPTER III 24. CHAPTER IV 25. 2. Deferred Charges to | 2. Deferred Income 26. 5. Fixed Assets | 27. 4. For publication or report to regulating or 28. 6. For advertising purposes to float new issues 29. CHAPTER V 30. 12. Liquidation or forced-sale value, etc. 31. 1. For the current assets, the principle of valuation may be stated 32. 2. The principle of valuation involved in deferred charges to operation 33. 3. For the fixed assets, the principle of valuation generally 34. CHAPTER VI 35. 2. The managerial policy as to repairs, maintenance, 36. 3. The past performance and expected future performance 37. 4. All other factors locally present which may affect 38. Chapter XIII.) 39. CHAPTER VII 40. 5. Crystallization[25] 41. CHAPTER VIII 42. 2. Rates of depreciation and their relation to repairs, 43. 5. Financing depreciation and some related problems. 44. Chapter IX. 45. 4. Normal climatic conditions. 46. 5. Probable misuse and neglect brought about by the 47. 6. Probable change in ownership and consequent 48. 7. Probable change in the requirements of the market, 49. 2. Installed operating and generating machinery 50. 3. Fixed equipment including boilers and piping 51. Chapter X of the effect of the various methods used for calculating 52. CHAPTER IX 53. 4. Miscellaneous Methods 54. 4. Under some methods, an arbitrary interest rate 55. 1. PROPORTIONAL METHODS 56. 2. VARIABLE PERCENTAGE METHODS 57. 3. COMPOUND INTEREST METHODS 58. 4. MISCELLANEOUS METHODS 59. CHAPTER X 60. 2. Inadequacy, which is lack of capacity to do the 61. 3. Obsolescence, which represents the inability to 62. 1. PROPORTIONAL METHODS 63. 2. VARIABLE PERCENTAGE METHODS 64. 3. COMPOUND INTEREST METHODS 65. 4. MISCELLANEOUS METHODS 66. Chapter XI. 67. CHAPTER XI 68. 2. Estimate of life in periods, working hours, service 69. 5. Periodic appraisal value. 70. 3. Profits of the past may be reserved in the business 71. CHAPTER XII 72. Introduction 73. 4. Bank 74. 1. Cash deposited to cover breakage or damage to 75. 2. Moneys advanced to subsidiaries, salesmen, and other 76. 3. Claims against creditors for returned or damaged 77. 4. Prepayments on purchase or expense contracts, as 78. 5. Unpaid calls or instalments on stock subscription 79. 6. Claims against absconding officers for property 80. 1. In the case of a new concern where there is no past 81. 2. In the case of an outsider—a professional auditor 82. 3. Periodically, in any business, as a check on the 83. 1. The amount of outstanding trade debt at the time 84. 2. The amount of sales on credit made during the 85. 3. The total sales, both cash and credit, for the present 86. CHAPTER XIII 87. 1. Carry the market valuation, whether more or less 88. 2. In case market value is less than cost, set up a reserve 89. 3. Carry in an inner column in the body of the balance 90. Chapter XXVI of this book, where a full presentation of the case for 91. CHAPTER XIV 92. CHAPTER XV 93. 1. By practically full ownership of the subsidiary 94. 3. Through the agency of advances, particularly when, 95. CHAPTER XVI 96. Chapter IX, is the one most widely employed. It is to be preferred to 97. CHAPTER XVII 98. 1. If the building is purchased outright for cash, whatever costs 99. 2. If the building is bought by the issue of stocks or bonds, the 100. 3. When buildings are put up by the concern itself, full cost may 101. Chapter XVI, any increase or decrease in the value of the land cannot 102. CHAPTER XVIII 103. 1. _Time Lapse._ There is no such thing as wear and tear on a patent 104. 2. _Supersession._ If no other causes than time lapse were operative, 105. 3. _Obsolescence._ Akin to the element of supersession is that of 106. 1. Lump sum payments to the state or some division 107. 2. The full purchase price paid another company for 108. 3. Legal and other fees in connection with securing 109. 4. Any other legitimate expenses, such as the cost of 110. CHAPTER XIX 111. 6. Merchandise Inventory 112. Chapter XX, in the discussion of the liability, bonds. 113. CHAPTER XX 114. 1. The character of the issuing corporation under 115. 2. The security of the bonds under which come: 116. 3. The purpose of the issue, as: 117. 4. The conditions incident upon payment of principal 118. 4. A bond sold at par to be redeemed at a premium on maturity. 119. CHAPTER XXI 120. CHAPTER XXII 121. 2. Profits realized on sales of fixed assets should be first applied 122. 3. A sufficient surplus should be accumulated (in addition to the 123. CHAPTER XXIII 124. Chapter XXII, have their proper place of record direct into some margin 125. Chapter XXV on sinking funds for a full discussion of the merits and 126. 2. Reserves created to provide an additional capital 127. 3. Reserves created to provide for equalizing dividends 128. 1. Valuation Reserves 129. 5. Market Fluctuations Reserves, etc. 130. 2. Proprietorship Reserves 131. 3. Reserves for Working Capital, etc. 132. CHAPTER XXIV 133. Introduction 134. CHAPTER XXV 135. 1. The sinking fund, then, under suitable title, may appear only among 136. 2. The balance sheet may record the sinking fund status among the 137. 3. There may appear on the balance sheet as the only evidence of a 138. 4. There may be no record of the sinking fund transactions shown on 139. 1. Those dealing with the original and subsequent 140. 2. Those required to book the trustee’s periodic 141. 3. Those to show the redemption of the debt and the final 142. CHAPTER XXVI 143. 1. The difficulty of determining the rate at which 144. 2. Inasmuch as the amount of investment in current 145. 3. If interest is to be charged, how shall the offsetting 146. 4. The introduction in production costs of a more or 147. 5. As the business world is accustomed to consider 148. CHAPTER XXVII 149. Chapter XXIII on “Reserves and Surplus.” There the illegitimate use of 150. CHAPTER XXVIII 151. 1. To convey, transfer, conceal, or remove, or to permit 152. 2. To transfer while insolvent any portion of the property 153. 3. To make a general assignment for the benefit of 154. 4. For the debtor to admit in writing his inability to 155. 5. To suffer or permit, while insolvent, any creditor to 156. 1898. The courts of the Federal Government have jurisdiction in these 157. CHAPTER XXIX 158. 1. Agreement by the directors of the various companies 159. 2. Assent of the stockholders of each company to the 160. 3. Filing of certified copies of the agreement, with the 161. 4. The exchange and issuance of new stock for the 162. 1. A uniform accounting system for all the companies 163. 2. The reserves for depreciation should be based on 164. 3. Costs should be determined in the same way if the 165. 4. The apportionment of labor, factory expense, and 166. 5. Only real items of cost should be included under the 167. 6. The same methods of inventory-taking, both of 168. 7. The amount of orders on hand should be considered. 169. CHAPTER XXX 170. 2. A proper rate of turnover on the merchandise 171. 3. Economical management. 172. 3. Facilities for centralizing and comparing such

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