Continuous and Consistent Depreciation Formulas. - Thomsen, C. Torben (The Accounting Review, 1970)
Abstract This article applies some elementary principles of mathematics and statistics to a discussion of depreciation, and in the process casts light on several problem areas. New formulas are suggested for sum of the year's digits and double declining balance methods of depreciation. Finally, the assignment of cost to depreciation is examined using the tools developed in the first part of the article. This discourse seeks to supplement the presentation of depreciation for students who have some quantitative background, since most students appreciate finding applications of mathematical concepts, which by them may seem esoteric or irrelevant. A depreciation density twice lion is a real-valued, non-negative, continuous function. Depreciation depends on a multitude of factors. Since consistent methods of depreciation depend only on the fraction of total life exhausted and not on the total lifetime of an asset, it is possible to compare different methods of depreciation on one graph. The analogy between depreciation and a probability distribution was exploited in the article. It was shown how some problem areas were illuminated using the tools developed. But in a discussion of accounting that makes use of any concepts of mathematics or statistics, it should be remembered that mathematical niceties or rigor can never be substituted for what is economically relevant.