# DEFINITIONSum of the Digitsas defined in Glossary of Termsby The Association of Corporate Treasurers

"Sum of the digits": (SOD). 1. A basis of allocating total costs or income across successive time periods, so as to 'front-end load' them. In other words, a systematically greater proportion of the total cost or income is allocated to the earlier periods. For example, a fixed asset has a cost of \$12m, an expected disposal value of \$2m and an expected useful life of 4 years. The total expected accounting cost for the 4 year period = \$12m - \$2m = \$10m. The 'sum of the digits' of the expected holding Years 1 to 4 inclusive = 1 + 2 + 3 + 4 = 10. The allocation proportions (for the total depreciation charges of \$10m) are calculated as follows: Year 1: 4/10 (x \$10m = \$4m). Year 2: 3/10 (x \$10m = \$3m). Year 3: 2/10 (x \$10m = \$2m). Year 4: 1/10 (x \$10m = \$1m). The net book value of the fixed asset - applying the depreciation charges calculated above - would be (at the end of each year) : Year 1 = 12 - 4 = \$8m. Year 2 = 8 - 3 = \$5m. Year 3 = 5 - 2 = \$3m. Year 4 = 3 - 1 = \$2m. 2. Sum of the digits methods are sometimes used to allocate total finance charges - for example under IAS 17 - as a simpler alternative to the Implied rate of interest (or Actuarial) method.