Optimal smoothing of account earnings

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.