Article ID: | iaor200128 |
Country: | United Kingdom |
Volume: | 10 |
Issue: | 1 |
Start Page Number: | 1 |
End Page Number: | 14 |
Publication Date: | Jan 1999 |
Journal: | IMA Journal of Mathematics Applied in Business and Industry |
Authors: | Lane John A., Willett Roger J. |
Keywords: | accounting |
Accountants seeking to estimate the profitability of a firm via the calculation of earnings utilize information about the number and current lifespan of unfinished activities by incorporating a smoothing device – depreciation – into their calculations. This paper considers a firm in steady state, carrying out a large number of similar activities with random starts and completion dates. By developing a stochastic model for the firm's activities, a difference equation for the minimum-variance smoothing function is obtained. This can be solved explicitly in the case of a periodic Poisson process of start times and independent exponential durations and is a variant of declining-balance depreciation.