Test of Condition Per Cent
At the time of reappraisal the estimated condition per cent or the expectancy as to remaining service life are the points most to be considered. C. E. Grunsky has made an interesting contribution to the study of expectancy—theoretical, it is true, in the sense that it is based on assumed hypotheses, but nevertheless of value as calling attention to a phase of the subject that presents large possibilities. He takes 10,000 similar articles, all of probable life-terms of 10 years, and all simultaneously installed. Assuming that of these 10,000, 100 will fail or go out of service at the end of the first year, 200 at the end of the second year, that the largest numbers will fail in the years just before and just after the expected life-term of 10 years, and from then on, that there will be a gradual decrease in the number of failures until the 20th year, beyond which time (double the estimated life-period) none will remain in service—the following table is shown, which gives in the last column at the right the life expectancy of all remaining articles as at the beginning of a given year.
It will thus be seen that an article which has survived its 5th year, has at the beginning of its 6th an expectancy, not of 5 years but of 6.12 years; an article which has lived its allotted 10 years has an expectancy of 3.67 years; and so on. Certainly Mr. Grunsky’s study, if it serves no other purpose, at least draws attention to possible lines of development and, read in connection with facts as to the known length of life of many assets which have outlived their expected terms, it draws strong attention to the need of very careful use of any so-called mortality tables. These life history tables for assets are similar to the mortality tables used by life insurance companies.
Table of Expectancy[37]
The probable life of each article is 10 years or periods. For terms other than 10 years, each year in the table may be regarded as a period equal to one-tenth of the probable life-term.
(Based on the special hypothesis of failures as explained in the text)
| Year or Period | For 10,000 Articles | Single Article | ||
|---|---|---|---|---|
| Number of Failures | Remaining Number of Articles at Beginning of Year | Remaining Service at Beginning of Year | Expectancy at Beginning of Year or Period | |
| 1 | 100 | 10,000 | 100,000 | 10.00 |
| 2 | 200 | 9,900 | 90,000 | 9.00 |
| 3 | 300 | 9,700 | 80,100 | 8.27 |
| 4 | 400 | 9,400 | 70,400 | 7.46 |
| 5 | 500 | 9,000 | 61,000 | 6.77 |
| 6 | 600 | 8,500 | 52,000 | 6.12 |
| 7 | 700 | 7,900 | 43,500 | 5.51 |
| 8 | 800 | 7,200 | 35,600 | 4.95 |
| 9 | 900 | 6,400 | 28,400 | 4.44 |
| 10 | 1,000 | 5,500 | 22,000 | 4.00 |
| 11 | 900 | 4,500 | 16,500 | 3.67 |
| 12 | 800 | 3,600 | 12,000 | 3.33 |
| 13 | 700 | 2,800 | 8,400 | 3.00 |
| 14 | 600 | 2,100 | 5,600 | 2.67 |
| 15 | 500 | 1,500 | 3,500 | 2.33 |
| 16 | 400 | 1,000 | 2,000 | 2.00 |
| 17 | 300 | 600 | 1,000 | 1.67 |
| 18 | 200 | 300 | 400 | 1.33 |
| 19 | 100 | 100 | 100 | 1.00 |
| 20 | 0 | 0 | 0 | 0 |
Composite and Group Rates
In the practical application of the depreciation rate in a large plant, every separate piece of property is not, of course, considered by itself. The plant is divided into groups of similar assets, determined roughly on the basis of life expectancy, conditions of service, etc. Using these groups it is possible to find the rate of composite depreciation—a figure which serves as a check over the group depreciation. This is also sometimes called the “mean life” of the plant. It is determined by two methods—one called the direct, the other the dollar-year method. Assuming groups of assets of varying life lengths and costs, the following examples show the manner of estimating the amount of depreciation for the whole plant and also composite life; that is, the mean average life of the individual assets when viewed not as units but as a composite whole:
Mean Life
Direct Method