Per-unit net salvage estimation.

INTRODUCTION

Regulated public utilities are generally allowed to collect revenue from customers using a formula called the revenue requirement equation. For any accounting interval, the equation can be expressed as:

RR = OE + TAX + [D.sub.x] + ROR(RB), (1)

where RR is the revenue to be collected, OE is the operating expense covering such costs as fuel, salaries, pension accruals, and advertising, TAX is the amount of tax expense, [D.sub.x] is the depreciation expense allocable to the interval, and ROR is the rate of return allowed on the rate base, RB. A comprehensive discussion of the elements of equation (1) can be found in Garfield and Lovejoy [3]. For the purposes of this paper, however, it is important to note that [D.sub.x] is reflective of the change (normally a decline) during an accounting interval, in the present value of the future net revenue stream associated with physical assets such as production plant and equipment.

This paper focuses on an element of the depreciation accrual component called net salvage. Although much of the literature and discussion on net salvage is associated with regulated industries, the need for net salvage analysis and estimation extends to non-regulated firms as well. Regulated or non-regulated, firms are expected to allocate capital costs to advantaged periods in order to achieve the goal of depreciation accounting which is to charge to operations an amount proportional to the service capacity of capital assets expended during an accounting interval.

Although depreciation accruals can be computed in different ways under different assumptions of the amounts and the pattern of the future net revenue stream, a general form of the accrual equation for the straight line method under original cost valuation is:

[D.sub.x] = [B.sub.x](1 - [S.sub.a])/[L.sub.a] (2)

where [B.sub.x] is the plant in service during the interval, i.e., at time x, [S.sub.a] is an estimate of the average net salvage ratio and represents average gross salvage less average costs of removal as a proportion of the plant in service, and [L.sub.a] is an estimate of the average service life of the equipment or plant account of interest. Both [S.sub.a] and [L.sub.a] are defined relative to the original installation vintages contributing to the surviving plant. The equation is equally applicable to a specific vintage, a group of vintages within an account, or a whole account with minor modifications. Its similarity, excluding the averaging process, to the familiar item depreciation accrual, should be apparent. The equation is developed for the whole life technique which assumes that estimates will be operative throughout the life of the assets and that the parameters are estimated correctly. In most situations, however, that assumption is overly restrictive. The parameters are, therefore, re-estimated periodically and accruals computed using the remaining-life technique with the equation:

[D.sub.x] = [B.sub.x](1 - [R.sub.x] - [S.sub.f])/[L.sub.x], (3) where [R.sub.x], [L.sub.x] and [S.sub.f] are the recorded reserve ratio, the estimated remaining life, and an estimate of the future net salvage rate respectively. Unlike [S.sub.a] and [L.sub.a] which are associated with the original vintage installations, [S.sub.f] and [L.sub.x] are associated with the surviving investment at time x. The development of [S.sub.a] and [S.sub.f] are discussed later in this paper and equations for [L.sub.a] and [L.sub.x] can be obtained using the probabilistic frequency distribution best descriptive of the plant life characteristics under study such as a member of the Iowa Curves [11][18], Gompertz-Makeham Curves [4][10], h-Curves [8], or Weibull distribution [6][7][16].

Unlike the estimation of life characteristics [L.sub.a] and [L.sub.x], which draws on a rich reservoir of mathematical and actuarial statistics, the estimation of net salvage has only recently started to attract literary, conceptual, and theoretical development. It is perhaps a reflection of the cursory attention depreciation professionals and analysts have in the past placed on net salvage parameters as a component of depreciation accrual computations. …