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Depreciation for regulated firms given technological progress and a multi-asset setting
Depreciation for regulated firms given technological progress and a multi-asset setting Shimon Awerbuch
Depreciation allowances directly affect the economic returns of regulated firms yet are frequently based on inappropriate accounting concepts of value and obsolescence. Regulated rates are correctly set only under economic (Hotelling) depreciation which turns out to be an accelerated recovery schedule for assets with high rates of technological progress. Nonetheless, regulators widely use straight-line or even back-loaded schedules for fear that accelerated recovery will raise rates paid by consumers. Using a multiasset model it is shown that, contrary to widely held beliefs, accelerated depreciation leads to lower regulated rates for mature firms in the steady state. Keywords: Depreciation ulated firms
allowances;
Economic
returns;
Reg-
Regulated depreciation rates directly affect the economic returns of regulated firms. Regulators set arbitrary depreciation schedules using accounting based concepts of obsolescence. These schedules are frequently motivated by the view that accelerated capital recovery raises regulated prices. Assets with high rates of technological progress, such as those used in telecommunications, generate cash-flow profiles over time that are not consistent with the assumptions of the widely used straightline-depreciation (SLD). SLD has traditionally been used in financial reporting where its simplicity is highly attractive.’ Yet SLD reflects neither the underlying asset economics nor the needs of regulation, where its use can lead to sizable errors in the rate of return (ROR) computation. The depreciation practices of unregulated firms offer little gui-
Shimon Awerbuch is with the Finance Department, University of Massachusetts at Lowell, Lowell, MA 01854, USA.
228
dance towards the development of proper regulated schedules. Economic depreciation (ED) is defined as the periodic change in asset value measured by changes in the present value (PV) of future cash flows.’ When ED is used the accounting rate of return equals a project’s IRR in each period thus yielding ‘correct’ ratemaking. ED schedules are different depending on the asset’s cash flow profile and rate of return although they are often confused with annuity depreciation, an arbitrary schedule that it ‘correct’ only in the case of level cash flow~.~ This paper yields two primary results. First, correct ED schedules are developed using the approach of Anton.’ For assets with technological change these turn out to be front-loaded and regulators have shunned their use for fear of raising rates. The second result is somewhat more surprising, and contrary to conventional regulatory wisdom. Using a multi-asset model to examine depreciation,6 it turns out that ‘asymptotic” revenue requirements for regulated firms are lower with accelerated depreciation. In other words, front-loading depreciation reduces regulated rates - contrary to the widely held opposite belief. It is further possible to shows that this reduction holds for all growth rates less than the firm’s IRR - the case for most regulated utilities. Finally, although discounted cost-benefit analysis is widely used to evaluate depreciation decisions this technique must be used with extreme care since: first, depreciation is merely a cost-allocation process and not an investment; and, second, the effects of a particular depreciation policy continue in perpetuity so that finite ‘payback periods’ significantly bias the results.
Depreciation for regulated firms - steady state conditions Single asset case Regulated
revenue
0957-l 787/92/030228-l
requirements
2 0
are set so the firm
1992 Butterworih-Heinemann
Ltd
Depreciation for regulated firms Table 1. Single asset revenue requirements Revenue requirement Depreciation Year 6) w1. Sum-of-the-vear’s demeciation 1 453.33 333.33 2 346.47 266.67 3 248.00 200.00 4 157.33 133.33 5 66.67 74.67 1 000.00 Total 1 280.00 2. Straight-line depreciation 1 320.00 200.00 2 296.00 200.00 3 272.00 200.00 4 248.00 200.00 200.00 5 224.00 1 000.00 Total 1 360.00 3. Annuity depreciation 1 277.41 157.41 2 277.41 176.30 3 277.41 196.45 4 277.41 221.15 247.69 5 277.41 Total 1 387.05 1 000.00 4. Represcibed depreciation’ 1 125.00 245.00 2 225.00 150.00 277.00 190.00 3 4 235.00 299.20 300.00 5 336.00 1 412.20 1 000.00 Total
for alternative
depreciation
schedules.”
Beginning rate base ($1
Accounting net income ($)
ROR %
1 000.00 666.67 400.00 200.00 66.67
120.00 80.00 48.00 24.00 8.00
12.0 12.0 12.0 12.0 12.0
1 000.00 800.00 600.00 400.00 200.00
120.00 96.00 72.00 48.00 24.00
12.0 12.0 12.0 12.0 12.0
1 000.00 842.59 666.29 468.84 247.69
120.00 101.11 79.95 56.26 29.72
12.0 12.0 12.0 12.0 12.0
1 000.00 875.00 725.00 535.00 300.00
120.00 105.00 87.00 64.20 36.00
12.0 12.0 12.0 12.0 12.0
Notes: “Five-year asset with no taxes or retatined earnings; bThe present value is $1 000 in each case; ROR = IRR each period; ‘g-Year straight-line represcribed to 5-Year straight-line
recovers its operating expenses plus a capital charge consisting of allowed earnings and depreciation. Ignoring any operating expenses, the revenue requirement is computed as A, = r-B, + D, where: r is the allowed rate of return, B, is the periodic rate base and D, is the allowed depreciation recovery.’ Traditional regulation specifies straight-line recovery and a ratebase equal to the original cost less the accumulated depreciation. This makes the D, constant while the earnings component, r-B,, declines over time, as long as r remains relatively unchanged. For any single ratebase asset A, is therefore a decreasing function over time. This ‘frontloading’ of capital charges means that rates will rise whenever an old, fully depreciated asset is replaced with an identical new asset, even when there is no inflation. lo Moreover, if an accelerated depreciation schedule, such as sum-of-the-years digits (SYD) is used D, will initially be larger so that A, will be even higher early in the asset’s life than it would be with SLD. Table 1 illustrates the effects of depreciation on front-loading in the single asset case. Table 1 is arranged in order of decreasing acceleration: SYD
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POLICY July 1992
(Panel 1) is the most accelerated recovery schedule while Represcribed Depreciation (Panel 4) is the most decelerated (Represcribed Depreciation is further discussed later). The SLD-based revenue requirement (Panel 2) is $320.00 in Year 1 which drops to $224.00 by Year 5. The comparable cash flows for SYD are considerably more front-loaded, generating a $453.33 revenue requirement in the first year. The combined revenue requirement for Years 1 and 2 are only $616 under SLD, as compared to $800.00 for SYD which seems to support the regulator’s practice of avoiding accelerated depreciation based on the impression that it raises near-term rates. While regulated firms hold portfolios of different vintage assets, depreciation tends to be examined using single-asset models whose output should be interpreted with considerable care: researchers have long warned that depreciation is ‘far too complex’ for simple constructs” and that more realistic, multi-asset approaches are needed. The following examines the relationship between depreciation and revenue requirement for a multiasset firm.
229
Depreciation for regulated firms Table 2. Depreciation
Opening TPIS Depreciation reserve Ratebase
Depreciation Earnings” Revenue
expense”
required
and revenue requirement
Ratebase determination Year 0 Year 1 Year 2 1 000.00 3 000.00 2 000.00 0.00 200.00 600.00 1 000.00 2 400.00 1 800.00 Revenue requirements Year 1 Year 2 Year 3 200.00 400.00 600.00 120.00 240.00 288.00 320.00 640.00 888.00
Notes: “Straight-line-depreciation;
bROR
Multiple assets in steady state The rate of return (ROR) of a portfolio of fixed assets is the weighted average of the individual asset ROR’s using book value weights.‘* For a firm holding n assets, steady-state ROR is found as:
ROR
n ARR,-.B, =C j=l ZZnBj j=l
(I)
where ARRj and Bj are the rate of return and ratebase value for the j-th asset. We can easily express the periodic capital charge for any regulated firm as a function of the individual assets charges: A, = ~ [ARRj’Bj + Oj] j=l
(2)
Absent cash operating expenses, A, becomes the equivalent of the revenue requirement, (R,), and Equation (2) expresses the firm’s revenue needs in terms of its portfolio of assets. Consider a firm which makes regular annual investments in a five-year, $1 000 asset (Table 2). Total plant in service (TPIS) increases by $1 000 annually until the end of the fifth year, at which time the earliest vintage assets is retired and the firm remains in steady state, adding and retiring one new asset each year. The steady-state ratebase is $3 000, consisting of one asset of each vintage. We can now examine the steady-state revenue requirements for this firm using the previous four depreciation schedules:13 SYD, SLD, Annuity Depreciation (AD) and Represcribed Depreciation (REP), a hypothetical represcription policy under which an eight-year SLD recovery is gradually reduced to a five-year SLD recovery over the life of the asset.14 REP is the de facto depreciation policy for most telecommunications assets. Figure 1 shows
230
in a multi-asset
setting.
Year 3 4 000.00 1200.00 2 800.00
Year 4 5 000.00 2 000.00 3 000.00
Year 5 5 000.00 2 000.00 3 000.00
Year 4 800.00 336.00
Year 5 1 000.00 ~~360.00
Year 6 1 000.00 360.00
1136.00
1 360.00
1 360.00
is 12%.
the annual depreciation expense for these four schedules. The steady-state revenue requirement (R,) are computed using Equation (2). The SYD-based revenues are $1 280 (Table 3, Panel l), while the REP-based revenues are $1 412.20 per year. This clearly shows that contrary to widely held beliefs, steady-state revenue requirements are inversely related to the rate of capital recovery. The more rapidly assets are written off, the lower the perpetual annual revenue requirement.
The case of firm growth The results of the previous section are consistent with similar results illustrated by Fisher and McGowan15 for the growth case. They demonstrate the proposition that the ‘asymptotic’ ROR of a firm in growth increases as depreciation is accelerated, whenever the asset growth rate, g is less than the IRR. l6 Fisher and McGowan focus on the relationship between IRR and ROR and do not address regulated revenue requirements. Yet their results are applicable to the regulated case: if (as they illustrate) accelerated depreciation raises ROR while backloaded recovery lowers it, then backloaded depreciation must require more revenue for a given level of ROR. We can, therefore, extend the FisherMcGowan results to conclude that faster recovery will lower revenue requirements. This reasoning leads to the following proposition for the regulated multi-asset firm in growth: 0
Figure ciation
More rapid depreciation decreases asymptotic revenue requirements when g < IRR and increases them only in the unsustainable case of g > 1RR.l’ 2 illustrates and ROR
the relationship between depreshown by Fisher and McGowan
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POLICY July 1992
Depreciation
zw
0.35
?
0.3
0’ ‘G .; ar FL %
0.25
-! E 6
for regulated firms
0.2
0.15 0.1 0.05
I 1
2
3
4
5
Year Figure
1. Depreciation
profiles.
flow profile, so that revenues can be lowered to bring the ROR back down.” These results - that accelerating capital recovery lowers asymptotic revenue requirements - seem startling at first’” but are consistent with the weighted average relationship given in Equation (2). For example, assume that regulators use the traditional
(left hand ordinate): with g held constant, we can get ‘more’ ROR at any given level of IRR (IRR > g) by simply increasing the rate of capital recovery. The right hand ordinate of Figure 2 extends their proposition to illustrate the relationship between depreciation and the regulated revenue requirement: accelerating depreciation raises ROR for any cash Table 3. Steady rate revenue requirement Asset ARR, * vintage depreciation 1. Sum-of-the-years 1 0.12 2 0.12 3 0.12 4 0.12 5 0.12 Totals ($) 2. Straight-line depreciations 0.12 1 0.12 2 0.12 3 0.12 4 0.12 To:als ($) 3. Annuity depreciation 0.12 1 0.12 2 0.12 3 4 0.12 0.12 5 Totals ($) 4. Represcribed depreciationb 0.12 1 0.12 2 0.12 3 0.12 4 0.12 To:als ($)
for alternative
B,
POLICY July 1992
schedules.”
_
D,
R,
1 000.00 666.67 400.00 200.00 66.67 2 333.33
333.33 266.67 200.00 133.33 66.67 1 000.00
453.33 346.67 248.00 157.33 74.67 1 280.00
1 000.00 800.00 600.00 400.00 200.00 3 000.00
200.00 200.00 200.00 200.00 200.00 1 000.00
320.00 296.00 272.00 248.00 224.00 1 360.00
1 000.00 842.59 666.29 468.84 247.69 3 225.41
157.41 176.30 197.45 221.15 247.69 1 000.00
277.41 277.41 277.41 277.41 277.41 1 387.05
1 000.00 875.00 725.00 535.00 300.00 3 435.00
125.00 150.00 190.00 235.00 300.00 1 000.00
245.00 255.00 277.00 299.20 336.00 1 412.20
Notes: “Five-year asset with no taxes or retained prescribed to 5-year straight-line.
UTILITIES
+
depreciation
earnings;
‘S-Year
straight-line
re-
231
Depreciation for regulated firms Revenue requirement
ROF
Low
ligh Accelerated
)~
SLD -GF=
(economic)
IRR Annuity + Decelerated
/ g=IRR
Asset growth
Figure 2. Asymptotic
rate (g%)
ROR and revenues for various depreciation
policies.
We now develop annual revenue requirement profiles for a regulated firm in growth, given the following conditions:
typical for new firms or new asset accounts of existing firms. The revenues in Figure 3 are consistent with the results of the previous section. During the initial growth phase revenue requirements are directly related to the rate of capital recovery - SYD produces the highest rates, REP the lowest. This is expected since g > IRR. Revenue differences between the depreciation policies then dissipate as g + IRR around Year 5, also as expected. After Year 5, when the growth rate falls below the 12% IRR,*’ the ordering abruptly reverses and SYD produces the lowest revenue requirement, a result that continues in perpetuity as long as g < 12% is maintained. Further, as also suggested by the results of the previous section, the revenue advantage of REP over SYD during the initial growth phase will dissipate rapidly as initial g is reduced. This is illustrated in Figure 4, which shows the revenues for a firm in constant, 3% growth.
1.
Present value as a guide to depreciation
policy of back-loading depreciation so that individual assets generate revenue requirements that are lower than SLD early in the asset’s life and higher subsequently (Table 1, Panel 4). When growth rates are sufficiently high there is an abundance of new, ‘low-revenue’ assets with higher book-value weights relative to older ‘high-revenue’ assets. Backloading depreciation under these circumstances therefore lowers revenues. However, the presence of new, ‘low-revenue’ assets declines as the firm’s growth declines, so that eventually there are relatively more old, ‘high-revenue’ assets. Now a backloaded depreciation policy only serves to increase revenues.
Revenue requirements for different depreciation policies and growth rates
2. 3.
4. 5.
The firm makes its first investment at the end of year 0; the firm is funded entirely with equity whose cost remains invariant to depreciation policy; the firm invests in a portfolio of identical depreciable assets with a five-year life, using a pre-specified investment function; tax considerations are omitted;*a there are no operating expenses and no salvage values.
Figure 3 shows the revenue requirements, total plant in service (TPIS) and the TPIS growth rate for the case of a firm experiencing an initially high growth which is followed by lower, sustainable growth (3%/ year) beginning in Year 5. This growth pattern is
232
choice
Regulators frequently use cost-benefit analysis involving present value (PV) measures to evaluate depreciation policy. Generally speaking projects with the lowest PV revenues are desirable. Depreciation policy, however, affects only the intertemporal apportioning of costs, and is therefore not in itself an economic cost. PV measures are therefore not a meaningful decision criterion in such cases and do not help in setting depreciation. There are other reasons why PV measures should not be relied on in formulating depreciation policy. Cost-benefit analysis cannot eliminate intergenerational inequities** such as one cohort of ratepayers paying an unfairly high share of the asset
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POLICY July 1992
Depreciation for regulated firms
:ED SLD SYD
Approximate
change-over
-
3% growth
0
4
8
12
point
TPIS x x x
(g = 12%)
x
x
x
xXxX
rate
16
20
24
Years
Figure 3. Annual
revenue requirement
costs. 23 Therefore, where cohorts contributing or receiving benefits change over the life of the project it does not always provide a definitive decision criteria. For example, it cannot distinguish among two different alternatives with equal present value revenues, even though the time-shape of the benefits may be such that different cohorts prefer one alternative over the other. This has important implications in regulation where the present value of revenue requirements is, in principle, invariant with depreciation policy over the life of the asset. Given this so-called ‘Invariance Proposition’,24 cost-benefit techniques will be of limited usefulness in designing and evaluating depreciation policy. For example, if we assume that cash flows in Figure 3 are perpetual, as they would be in reality, the PV will be unaffected by depreciation choice so that by this measure we could not identify the ‘best’ choice.25 Yet any ratep a y er that begins or increases its consumption of the regulated output after Year 4 clearly prefers SYD. Indeed all ratepayer cohorts from Year 5 to perpetuity prefer SYD over less accelerated methods. This ordering of preferences is unchanged when the life of the firm is shortened to some finite period.26 The backloaded REP schedule, by constrast, is preferred only by the Year 1 - 4 cohorts, which perhaps explains its political attractiveness. It seems, therefore, that welfare criteria are not helpful in evaluating depreciation because the capital recovery rate does not affect the present value of revenues over the life of the firm. Yet this does not
UTILITIES
POLICY July 1992
for different depreciation
policies.
suggest that we should be indifferent to depreciation - only that it must be evaluated on the basis of the underlying asset economics: the time-shape of cash flows over the asset’s life. Nor does it diminish the important outcome that after the initial start-up period ends, the firm’s ratepayers enjoy a perpetuity of lower rates under an accelerated depreciation schedule.
Depreciation profiles for assets with high rates of technological progress Correct depreciation policy reflects the true costs of operation and fairly allocates it to all user cohorts.*’ The ‘correct’ depreciation policy is generally defined in the tradition of Fisher*s and Hotellingz9 as economic depreciation (ED): the annual depreciation charge which reflects the change in present value of the asset’s remaining cash flows, discounted at the asset’s IRR.‘O When depreciation is correctly specified in this manner the firm’s ROR equals its IRR and hence has economic significance. Arbitrary depreciation schedules, such as SLD or REP which generally do not reflect the economic change in asset values will distort ROR so it does not correctly reflect economic rates of return. There are potential difficulties in implementing theoretically correct ED and some researchers” feel that circularity and other problems make the effort to periodically determine economic depreciation ‘totally impractical’. Yet there are more practical approaches in the sense of Luckett3* and Kraus and Huefner3’ which conside depreciation an empirical
233
Depreciation for regulated firms
0
4
8
12
16
20
24
Years
Figure 4. Annual
revenue (constant growth rate).
requirements
issue with the expectation that accuracy will improve with experience. 34 Given this app roach, ED can be set expectationally when the asset is placed in service and the cash flow estimates developed in the capital budgeting process can be used as a basis for its estimation. The initial estimates become a rate case issue with the expectation that they will be as unbiased as any other variable. In order to clearly distinguish this, more practical approach to ED it may be useful to call it Original Cost Economic Depreciation (OCED). Under OCED recovery is limited to the original cost; there are no inflation-driven asset writeups. Absent inflation and uncertainty OCED and ED are equivalent. We now explore techniques for correctly estimating OCED in assets with high rates of technological change. OCED in regulation Stauffer35 shows that for every cash flow profile (CFP) there exists one ED (Hotelling) schedule which suggests that SLD is the economic depreciation in traditional regulation. In such a traditional regulatory model, CFP is a function of depreciation and any recovery profile becomes the ED - this is the ‘Invariance Proposition’. The traditional model, however, becomes less relevant as we enter a more competitive era in telecommunications and power generation. Now the firm becomes more of a price taker, so that the CFP for a particular asset or service is set in the marketplace, independent of the inter-temporal schedule set by regulators. 36 In such a setting the traditional
234
for different depreciation
policies
‘saw-tooth’ CFP generated by SLD (Table 1, Panel 2) may be unobtainable due to market pressure. The regulatory problem is to determine the particular stream of depreciation charges which will best reflect the asset’s expected economic depreciation patterns, given market-driven cash flow expectations. In addition to equitably apportioning costs over time, the results also provide a more informative income measure which yields ROR = IRR each year as long as cash flows materialize as expected (and accountants adjust for inflation). ROR thus becomes a useful measure for testing the extent to which managerial expectations, formed at the time the asset is placed in service, are realized over time. OCED is unlike arbitrary schedules; it is a different profile for every CFP and rate of return. Ordinary SLD is the OCED schedule for the traditional ratemaking cash flow (Table 1 - Panel 2). Annuity depreciation (AD) is the OCED for a level of CFP (Panel 3). Likewise, for the front-loaded cash flow of Panel 1, SYD is the economic depreciation. Sufficient information exists at the time an asset is placed in service to allow an estimate of its expected OCED profile. Such an estimate, no matter how imprecise, is bound to be an improvement over SLD. Regulators, however, feel that this procedure is inexact and therefore default to SLD, typically selecting lives that are arbitrarily long. This, most likely represents the worst possible estimate of true depreciation for assets with high-rates of technological change. The arbitrarily long initial lives are subsequently represcribed as additional experience
UTILITIES
POLICY July 1992
Depreciation for regulated firms
Original cost economic
1 0
depreciation
I
I 2
I 4
I 6
Years
Figure 5. Economic
depreciation
and the Q-Profile.
makes the initial error obvious. The result is a backloaded depreciation schedule similar to the REP profile. Assets with high rates of technological change by definition have short economic lives with CFP’s that rise initially (after an introductory phase) and then rapidly decay as the technology matures and a subsequent vintage technology is introduced. In competitive environments, producers who lack the most efficient technology can generally lose market share to participants with newer, lower (marginal) cost technology. This market share loss results in declining net cash flows for the earlier-vintage assets _ either because sales have been lost or margins have been squeezed by newer technology.37 Figure 5 shows the ‘Q-Profile’ of cash flow’s which we use here as representative of the CFP generated in competitive environments by high technology assets. A regulated firm that employs such assets may therefore realize a CFP in the shape of the Q-Profile, independent of regulatory expectations. When SLD is used in conjunction with the Q-Profile the ROR values become uninterpretable (Table 4, Panel l), ranging from 31.7% to -60.2% over the asset’s life (IRR = 15%) and hence providing no useful information to regulators. The correct OCED schedule (Table 4, Panel 2) yields periodic ROR that meaningfuly interprets IRR. This schedule accrues depreciation most rapidly during the middle of the asset’s life, when cash flow and market power are strongest. The economics of high-technology assets quite plainly indi-
UTILITIES
POLICY July 1992
cated that depreciation must be front-loaded in this manner.40 As the traditional monopoly model of regulation erodes and firms face market-driven cash flow profiles, it becomes increasingly important for regulatorys to set depreciation correctly. Continued use of arbitrary, engineering-based schedules will yield ROR values that are increasingly unreliable as proxies of true economic profitability. Even more distortive are attempts to favour current ratepayer cohorts by instituting regulated lives that are arbitrarily long relative to expected economic usefulness. When depreciation is incorrectly specified in this manner the principal regulatory indicator - the ROR - loses all economic significance and becomes unreliable. Since correct OCED schedules are front-loaded they will lower asymptotic revenues, although this is not a sufficient reason for regulators to begin using them. On the other hand, the results clearly imply that regulators need not be afraid to use accelerated depreciation where such moves are justified on the basis of the fundamental asset economics, ie: expected life and cash flow profile.
The reality case: transitions from inefficient to efficient depreciation policies This section examines the revenue effects of transition from an existing recovery schedule such as SLD or REP, to a more efficient, accelerated schedule. This is the policy choice available for the practical
235
Depreciation for regulated firms Table 4. Income and return for the Q-profile economic depreciation.
Year 1. Straight 1 2 3 4 5 6
Cash Depreciation flow” ($) ($) line depreciation 23.76 16.67 35.79 16.67 37.83 16.67 29.27 16.67 15.70 16.67 6.63 16.67
2. Original 1 2 3 4 5 6
cost economic 23.76 35.79 37.83 29.27 15.70 6.63
100.00 depreciation 8.76 22.10 27.46 23.01 12.90 5.76
under straight-line
and original
cost
Net income (W
Beginning year ratebase RORb % (W
7.09 19.12 21.16 12.60 -0.96 - 10.04
100.00 83.33 66.67 50.00 33.33 16.67
7.1 22.9 31.7 25.2 -2.9 -60.2
15.00 13.69 10.37 6.25 2.80 0.86
100.00 91.24 69.14 41.68 18.67 5.76
15.0 15.0 15.0 15.0 15.0 15.0
100.00 Notes: “The Q-Profile 4.0%.
is adjusted
to yield
an IRR
case of an established, regulated firm which has always used SLD. Consider again the case of a new firm using SLD. Regulators then switch to OCED for all new assets placed in service after Year 8 (Figure 6). The transition from SLD to the less costly OCED is not fictionless, and regulated rates rise above what they would have been under SLD (dotted line) for about four years.4’ Indeed, a new steady-state is reached at the end of four years so that the transition requires a period equal to the average asset book life. The economic basis for the ‘bubble’ is not clear cut, although transitions from inefficient to efficient paths are often not frictionless. In this instance the
of 15%;
I
0
I 4
I
I
average
to
temporary rise in revenues can be seen as a way of balancing the benefits that SLD creates relative to OCED duirng the first four years - the Invariance Proposition requires that the area between SLD and OCED for years 1 - 4 equal the discounted area under the ‘bubble’. When initial growth is smaller (Figure 7), the transition ‘bubble’ is also smaller because there is less initial benefit to recapture. In this sense the transition ‘bubble’ becomes an investment which yields a perpetuity of correct (and lower) rates. Cost-benefit
of depreciation
The relevant
D begins for firm
01
hThe values
I 12
I
8
transitions
issues are whether
the move
from an
usi
I
I 16
I
I
I
20
I 24
Years Figure
236
6. Annual
revenue requirements:
transition
from SLD
to OCED.
UTILITIES
POLICY July 1992
Depreciation for regulated firms
Years
Figure 7. Annual revenue case of constant growth).
requirements:
SLD or REP schedule to the correct OCED is worthwhile, and the criteria by which such a judgment can be made. As previously discussed, regulators tend to examine depreciation policy over some arbitrary, finite period, and (erroneously) expect a payback during that period. But the benefits of transitioning to more efficient depreciation continue in perpetuity, and a payback over some finite period is not a valid decision criterion. Moves from a backloaded to an accelerated depreciation schedule will leave present values unaltered, eg: the Year-5 PV (Figure 6) is the same independent of whether the firm uses SLD or transitions to OCED after Year 8. Again, cost-benefit measures do not distinguish between the two alternatives and depreciation policy must be set on the basis of the underlying economics: the asset’s life and CFP. When these are properly reflected in depreciation all ratepayer cohorts automatically pay their fair share, a result well known since Baumo1.42 The move to an efficient but accelerated recovery temporarily raises rates although once the transition ends rates are perpetually reduced. In a sense the area under the bubble can be interpreted as a penalty for inefficient past recovery. It is in everyone’s interest - ratepayers and the firm - to minimize the confusing price signals created by a transition to OCED. The presence of lower growth rates, which mitigate the effects of different depreciation policies will yield smaller transition penalties - eg the bubble in Figure 7 is smaller even though the transition begins much later, in Year 16.43 Earlier transitions will yield correspondingly smaller penalinefficient
UTILITIES
POLlCY July 1992
transitions
from SLD to OCED (the
ties. Regardless of when the depreciation correction is begun, however, the initially higher rates are an efficient investment with a perpetual benefit stream.
Conclusion Depreciation can be fully understood only in terms of multi-asset models. In order for allowed rates of return to have economic meaning in the case of high-technology assets the regulatory process must move in the direction of estimating true asset depreciation rates. For most mature, regulated telecommunications companies asymptotic revenues are inversely related to the depreciation rate so that accelerated recovery yields lower revenues. This make intuitive sense: a rapidly growing firm which adds new assets at a high rate will have a preponderence of new-vintage assets so that accelerated depreciation, (which is initially higher for any given asset) will raise rates. However, when the firm grows slowly its portfolio has more older assets which have lower revenue needs under accelerated depreciation. Transitions from decelerated to accelerated depreciation do not alter the PV of revenues. This result, however, must not be allowed to overshadow the more significant outcome: that such transitions yield a perpetually reduced revenue requirement. All ratepayers are perpetually bettef off after the transition, although cohorts participating only in the transition are hurt. Cost-benefit techniques do not help us resolve this dilemma although this is not necessarily a limita-
237
Depreciation for regulated firms
tion - depreciation schedules need to be determined on the basis of the asset economics, not present value analysis. Attempts to favour one cohort over another, typically by rejecting efficient, accelerated OCED schedules on the basis that they raise nearterm rates. reduces efficiencv , and hurts the regulated firm and its ratepayers, especially in a partially competitive environment.
The author thanks Terence .I. Cooney Jr and Daniel J. Lane for their insights and comments, as well as members of the Advanced Workshop in Public Utility Economics and Regulation, Rutgers University and participants in the Symposium-on the Partially Regulated Firm, Columbia University; the support of the Institute for Tele-Information, Columbia University, is also acknowledged.
‘Shimon Awerbuch, ‘Accounting rates of return’, American Economic Review, Vol 78, No 3, June 1988, pp 581-87. *Hector A. Anton, ‘Depreciation, cost allocation and investment decisions’, Accounting Research, Vol 7, April 1956, pp 117-34; Franklin M. Fisher and J.J. McGowan, ‘On the misuse of accounting rates of return to infer monopoly profits’, American Economic Review. Vol73. No 1. DD 82-97. March 1983. esoeciallv pp 92-93; Richard S. Bower, ‘The capital recovery’question’, Resources and Energy, Vol 7, No 1, 1985, pp 7-42; Sidney S. Alexander, ‘Income measurement in a dynamic economy’, (revised by David Solomons) in, W.T. Baxter, and S. Davidson, eds, Studies in Accounting Theory, Homewood, Irwin, USA, 1962; Edgar, 0. Edwards and P.W. Bell, Theory and Measurement of Business Income, University of California Press, Berkeley, CA, USA, 1961. ‘The term ‘correct ratemaking’ is used in the sense of Baumol (William J. Baumol, ‘Optimal depreciation policy: pricing the products of durable assets’, Bell Journal of Economics and Management Science, Vol 2, No 2, Autumn 1971, pp 638-656) who showed that ED yields the correct time-pattern of prices for the underlying asset. See also, Miles 0. Bidwell, ‘Optimal prices, economic depreciation, and regulated utilities’, 23rd Annual Regulatory Conference, Ames, IO, USA, 1985; and Bower, Ibid. “Awerbuch, op tit, Ref 1. ‘Anton, op tit, Ref 2. 6As suggested by Gabriel A.D. Preinreich, ‘The principles of public utility depreciation’, Accounting Review, Vol 13, No 2, June 1938, pp 149-165, p 149. ‘The term is used after Fisher and McGowan, op tit, Ref 2, p 86, to mean annual revenue and requirement in the steady-state. 8Theorem I, Ibid. ‘Under perfect regulation this becomes Turvey’s amortization (Ralph Turvey, ‘Marginal costs’, Economic Journal, Vol79, June 1979, pp 282-300). “‘This so called ‘rate shock’ becomes sizable whenever the firm places into service an asset, such as a nuclear plant, which represents a significant percentage of existing ratebase. Inflation aggravates the situation by raising the cost of new capacity as compared to older capacity. “Preinreich, op tit, Ref 6, p 149. “See, J.A. Kay, ‘Accountants, too, could be happy in a golden age: the accountant’s ratet of profit and the internal rate of return’, Oxford Economic Pappers, Vol 28, November 1976, pp 447-60: Richard Brealev and S.C. Mvers. Principle of Corporate Finance, 2nd ed, McGraw Hill, New York, 1984: chapter l!2; and Fisher and McGowan, op tit, Ref 2. i3This paper addresses depreciation only insofar as it affects ratemaking; tax depreciation remains unaffected and the firm is free to use any appropriate method for financial reporting. 14When compared to some actual results this schedule seems quite
238
conservative: telephone switching equipment in some jurisdictions, originally allowed a 40-year life, was ultimately represcribed to under 20 years. “Fisher and McGowan: op tit, Ref 2. “The relationship reverses when g > IRR, although such growth rates are not sustainable without negative dividends. (Gerald L. Salamon. ‘Models of the relationshiu between the accountine and internal rate of return: an examination of the methodoibgy’, Journal of Accounting Research, Vol 11, Autumn 1973,-pp 296303.) We therefore limit the discussion to the region of g > IRR. Fisher and McGowan’s finding for unregulated-firm’s G in contrast to widely held beliefs to the contrary - ie it is usually felt by accountants that accelerated depreciation serves to reduce the accounting return. For the case of g = IRR, varying the depreciation leaves ROR unaltered (Fisher and McGowan’s Theorem 1, op tit, Ref 12, pp 91-92). Solomon (Ezra Solomon, ‘Alternative rate of return concepts and their implications for utility regulation’, Bell Journal of Economics and Management Science, Vol 1, No I, Spring 1970, pp 65-81, especially pp 75-76) obtains similar results although they are not discussed. “The region g < IRR covers most practical situations involving mature regulated firms. Certain situations such as lumpy additions caused by nuclear plant completions may temporarily result in g > IRR. Under such circumstances more rapid depreciation indeed increases regulated revenues until the growth rate diminishes again. ‘XObserve that the acclerated schedule yields ROR values that overstate the true IRR which is correctly given only by the economic depreciation - in this case SLD. “Similar results were shown 50 years ago by Preinreich, op tit, Ref 6, although the presentation is complex and does not note the significance - which perhaps explains why regualators seem unaware of it. ‘(This simplifies without distorting outcomes (Shimon, Awerbuch, ‘Depreciation for high technology assets’, The Partially Regulated Firm and Accounting Based Regulation: Issue in Capital Budgeting and Technology Adoption, Columbia University, November 1989, pp 45-46). Regulated depreciation alters revenue requirements but tax depreciation remains unchanged and hence has a constant effect on pretax cash flow. *iDiscrete time is used. The firm’s growth rate is 25% in year 4 and 3% in Year 5 and thereafter. “Robert C. Lind, Discounting for Time and Risk in Energy Policy, Resources for the Future, Johns Hopkins University Press, Baltimore, NE, USA, 1982, p 457. “This is precisely what happens with SLD and arbitrarily long asset lives: ratepayer cohorts near the end of an asset’s life pay the same annual depreciation charge as earlier cohorts even where obsolescence has diminished the asset’s value. “See, Richard Schmalensee, ‘An expository note on depreciation and profitability under rate of return regulation’, Journal of Regulatory Economics, Vol 1, No 3, September 1988, pp 293-298; Kay, op tit, Ref 12; and, Bruce Greenwald, ‘Rate base selection and the structure of regulation’, Rand Journal of Economics, Vol 15, Spring 1984, pp 85-95. The Invariance Proposition is illustrated bv Table 1. Observe that the PV of cash flows is $1 000 independent of depreciation choice. This demonstration ignores taxes, debt retirement, regulatory lag and numerous other practical problems and should therefore not be interpreted to imply that ROR = IRR in practice; see, Shimon Awerbuch, ‘Depreciation and rate of return’, Journal of Regulatory Economics, 1991 (forthcoming). ‘sHowever, an analysis that is arbitrarily limited to some finite period, say the first eight years, will show that REP is the most ‘desirable’ and possibly this is why regulators favour it. The result is obviously incorrect because it ignores subsequent cash flows. *6PV computations for the case of a finite-lived firm, or where the analysis has been arbitrarily limited to some finite ‘payback’ period will be in error unless ending asset values (which equal the present value of remaining cash flows) are included. See, Awerbuch, op tit, Ref 24. “Baumol, op tit, Ref 3.
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Depreciation for regulated firms ‘sIrving Fisher, The Nature of Capital and Income, MacMillan, New York, USA, 1906. 29Harold Hotelling, ‘A general mathematical theory of depreciation’, Journal of American Statistics Association, Vol 20, September 1925, pp 34@53. ‘“For example see, Bower, op tit, Ref 2; Bidwell, op tit, Ref 3; Saully Hunt Streiter, ‘Avoiding the ‘money saving rate increase’, Public Utilities Fortnightly, Vol 109, No 13, 24 June 1982, pp 18-22. ‘For example, Franklin M. Fisher, ‘On the misuse of accounting rates of return: reply’, American Economic Review, Vol74, No 3, June 1984, pp 509-517, p 510. “Peter F. Luckett, ‘ARR vs. IRR: a review and an analysis’, Journal of Business Finance and Accounting, Vol 11, No 2, Summer 1984, pp 213-231. “Alan Kraus and Ronald J. Huefner, ‘Cash-flow patterns and the choice of a depreciation method’, Bell Journal of Economics and Management Science, No 3, Spring 1972, pp 316334. s4Lawrence A. Gordon, ‘Accounting rate of return vs. economic rate of return’, Journal of Business Finance & Accounting, Vol 1, Spring 1974, pp 343-X ‘“Thomas R. Stauffer, ‘The measurement of corporate rates of return’, Bell Journal of Economics and Management Science, No 2, Autumn 1971, pp 434-469. ?Shimon Awerbuch, ‘Efficient income measures and the partially regulated firm’, in Michael Crew, ed, Deregulation and Diversification of Utilities, Kluwer Academic Publishers, Norwell, MA, USA, 1989. 37For an ingenious example of technology costs to market entrants see Bower, op tit, Ref 2; additional discussion of the
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economics of changing technologies can be found in Michael Crew and P. Kleindorfer, Capital Recovery and the FCC’s Price Cap Proposal, Center for Regulated Industries, Graduate School of Management, Rutgers University, Newark, NJ, USA, 1988. ssFisher and McGowan, op cit. Ref 12. “The Q-Profile is an outgrowth of the IBM anti-trust case although the issue of whether it accurately represents the experience of IBM’s System 360 was disputed (See Franklin M. Fisher, J.J. McGowan and Joen Greenwood, Folded, Spindled and Mutilated: Economic Analysis and U.S. vs. lBM, MIT Press, Cambridge, MA, USA). ““Michael A. Crew and Paul B. Kleindorfer, ‘Depreciation and resource allocation in the regulated firm: a dynamic analysis with technological change’, Advanced Workshop in Public Utility Economics and Regulation, Rutgers University, Fifth Annual Conference, 1986, and others have argued for accelerated capital recovery on the basis of increasing competitive pressures which limit future recovery. The results herein are independent of those arguments. Charles Hulten and Frank Wykoff, in ‘The measurement of economic depreciation’ in, Charles Hulten, ed, Depreciation, InfZation and the Taxation of Income from Capital, The Urban Institute, Washington, DC, USA, 1981, and others also find that true depreciation is accelerated for many types of assets. 4’The rate ‘bubble’ is formed because the first asset to be placed in service in Year 9 requires more revenue, with the offsetting benefit of lower revenues not available until the end of this asset’s life three or four years later. 4ZBaumol, op tit, Ref 3. 4’Transition costs can be managed in a number of other ways. See, Awerbuch, op tit, Ref 20.
239
Depreciation allowances directly affect the economic returns of regulated firms yet are frequently based on inappropriate accounting concepts of value and obsolescence. Regulated rates are correctly set only under economic (Hotelling) depreciation which turns out to be an accelerated recovery schedule for assets with high rates of technological progress. Nonetheless, regulators widely use straight-line or even back-loaded schedules for fear that accelerated recovery will raise rates paid by consumers. Using a multiasset model it is shown that, contrary to widely held beliefs, accelerated depreciation leads to lower regulated rates for mature firms in the steady state. Keywords: Depreciation ulated firms
allowances;
Economic
returns;
Reg-
Regulated depreciation rates directly affect the economic returns of regulated firms. Regulators set arbitrary depreciation schedules using accounting based concepts of obsolescence. These schedules are frequently motivated by the view that accelerated capital recovery raises regulated prices. Assets with high rates of technological progress, such as those used in telecommunications, generate cash-flow profiles over time that are not consistent with the assumptions of the widely used straightline-depreciation (SLD). SLD has traditionally been used in financial reporting where its simplicity is highly attractive.’ Yet SLD reflects neither the underlying asset economics nor the needs of regulation, where its use can lead to sizable errors in the rate of return (ROR) computation. The depreciation practices of unregulated firms offer little gui-
Shimon Awerbuch is with the Finance Department, University of Massachusetts at Lowell, Lowell, MA 01854, USA.
228
dance towards the development of proper regulated schedules. Economic depreciation (ED) is defined as the periodic change in asset value measured by changes in the present value (PV) of future cash flows.’ When ED is used the accounting rate of return equals a project’s IRR in each period thus yielding ‘correct’ ratemaking. ED schedules are different depending on the asset’s cash flow profile and rate of return although they are often confused with annuity depreciation, an arbitrary schedule that it ‘correct’ only in the case of level cash flow~.~ This paper yields two primary results. First, correct ED schedules are developed using the approach of Anton.’ For assets with technological change these turn out to be front-loaded and regulators have shunned their use for fear of raising rates. The second result is somewhat more surprising, and contrary to conventional regulatory wisdom. Using a multi-asset model to examine depreciation,6 it turns out that ‘asymptotic” revenue requirements for regulated firms are lower with accelerated depreciation. In other words, front-loading depreciation reduces regulated rates - contrary to the widely held opposite belief. It is further possible to shows that this reduction holds for all growth rates less than the firm’s IRR - the case for most regulated utilities. Finally, although discounted cost-benefit analysis is widely used to evaluate depreciation decisions this technique must be used with extreme care since: first, depreciation is merely a cost-allocation process and not an investment; and, second, the effects of a particular depreciation policy continue in perpetuity so that finite ‘payback periods’ significantly bias the results.
Depreciation for regulated firms - steady state conditions Single asset case Regulated
revenue
0957-l 787/92/030228-l
requirements
2 0
are set so the firm
1992 Butterworih-Heinemann
Ltd
Depreciation for regulated firms Table 1. Single asset revenue requirements Revenue requirement Depreciation Year 6) w1. Sum-of-the-vear’s demeciation 1 453.33 333.33 2 346.47 266.67 3 248.00 200.00 4 157.33 133.33 5 66.67 74.67 1 000.00 Total 1 280.00 2. Straight-line depreciation 1 320.00 200.00 2 296.00 200.00 3 272.00 200.00 4 248.00 200.00 200.00 5 224.00 1 000.00 Total 1 360.00 3. Annuity depreciation 1 277.41 157.41 2 277.41 176.30 3 277.41 196.45 4 277.41 221.15 247.69 5 277.41 Total 1 387.05 1 000.00 4. Represcibed depreciation’ 1 125.00 245.00 2 225.00 150.00 277.00 190.00 3 4 235.00 299.20 300.00 5 336.00 1 412.20 1 000.00 Total
for alternative
depreciation
schedules.”
Beginning rate base ($1
Accounting net income ($)
ROR %
1 000.00 666.67 400.00 200.00 66.67
120.00 80.00 48.00 24.00 8.00
12.0 12.0 12.0 12.0 12.0
1 000.00 800.00 600.00 400.00 200.00
120.00 96.00 72.00 48.00 24.00
12.0 12.0 12.0 12.0 12.0
1 000.00 842.59 666.29 468.84 247.69
120.00 101.11 79.95 56.26 29.72
12.0 12.0 12.0 12.0 12.0
1 000.00 875.00 725.00 535.00 300.00
120.00 105.00 87.00 64.20 36.00
12.0 12.0 12.0 12.0 12.0
Notes: “Five-year asset with no taxes or retatined earnings; bThe present value is $1 000 in each case; ROR = IRR each period; ‘g-Year straight-line represcribed to 5-Year straight-line
recovers its operating expenses plus a capital charge consisting of allowed earnings and depreciation. Ignoring any operating expenses, the revenue requirement is computed as A, = r-B, + D, where: r is the allowed rate of return, B, is the periodic rate base and D, is the allowed depreciation recovery.’ Traditional regulation specifies straight-line recovery and a ratebase equal to the original cost less the accumulated depreciation. This makes the D, constant while the earnings component, r-B,, declines over time, as long as r remains relatively unchanged. For any single ratebase asset A, is therefore a decreasing function over time. This ‘frontloading’ of capital charges means that rates will rise whenever an old, fully depreciated asset is replaced with an identical new asset, even when there is no inflation. lo Moreover, if an accelerated depreciation schedule, such as sum-of-the-years digits (SYD) is used D, will initially be larger so that A, will be even higher early in the asset’s life than it would be with SLD. Table 1 illustrates the effects of depreciation on front-loading in the single asset case. Table 1 is arranged in order of decreasing acceleration: SYD
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(Panel 1) is the most accelerated recovery schedule while Represcribed Depreciation (Panel 4) is the most decelerated (Represcribed Depreciation is further discussed later). The SLD-based revenue requirement (Panel 2) is $320.00 in Year 1 which drops to $224.00 by Year 5. The comparable cash flows for SYD are considerably more front-loaded, generating a $453.33 revenue requirement in the first year. The combined revenue requirement for Years 1 and 2 are only $616 under SLD, as compared to $800.00 for SYD which seems to support the regulator’s practice of avoiding accelerated depreciation based on the impression that it raises near-term rates. While regulated firms hold portfolios of different vintage assets, depreciation tends to be examined using single-asset models whose output should be interpreted with considerable care: researchers have long warned that depreciation is ‘far too complex’ for simple constructs” and that more realistic, multi-asset approaches are needed. The following examines the relationship between depreciation and revenue requirement for a multiasset firm.
229
Depreciation for regulated firms Table 2. Depreciation
Opening TPIS Depreciation reserve Ratebase
Depreciation Earnings” Revenue
expense”
required
and revenue requirement
Ratebase determination Year 0 Year 1 Year 2 1 000.00 3 000.00 2 000.00 0.00 200.00 600.00 1 000.00 2 400.00 1 800.00 Revenue requirements Year 1 Year 2 Year 3 200.00 400.00 600.00 120.00 240.00 288.00 320.00 640.00 888.00
Notes: “Straight-line-depreciation;
bROR
Multiple assets in steady state The rate of return (ROR) of a portfolio of fixed assets is the weighted average of the individual asset ROR’s using book value weights.‘* For a firm holding n assets, steady-state ROR is found as:
ROR
n ARR,-.B, =C j=l ZZnBj j=l
(I)
where ARRj and Bj are the rate of return and ratebase value for the j-th asset. We can easily express the periodic capital charge for any regulated firm as a function of the individual assets charges: A, = ~ [ARRj’Bj + Oj] j=l
(2)
Absent cash operating expenses, A, becomes the equivalent of the revenue requirement, (R,), and Equation (2) expresses the firm’s revenue needs in terms of its portfolio of assets. Consider a firm which makes regular annual investments in a five-year, $1 000 asset (Table 2). Total plant in service (TPIS) increases by $1 000 annually until the end of the fifth year, at which time the earliest vintage assets is retired and the firm remains in steady state, adding and retiring one new asset each year. The steady-state ratebase is $3 000, consisting of one asset of each vintage. We can now examine the steady-state revenue requirements for this firm using the previous four depreciation schedules:13 SYD, SLD, Annuity Depreciation (AD) and Represcribed Depreciation (REP), a hypothetical represcription policy under which an eight-year SLD recovery is gradually reduced to a five-year SLD recovery over the life of the asset.14 REP is the de facto depreciation policy for most telecommunications assets. Figure 1 shows
230
in a multi-asset
setting.
Year 3 4 000.00 1200.00 2 800.00
Year 4 5 000.00 2 000.00 3 000.00
Year 5 5 000.00 2 000.00 3 000.00
Year 4 800.00 336.00
Year 5 1 000.00 ~~360.00
Year 6 1 000.00 360.00
1136.00
1 360.00
1 360.00
is 12%.
the annual depreciation expense for these four schedules. The steady-state revenue requirement (R,) are computed using Equation (2). The SYD-based revenues are $1 280 (Table 3, Panel l), while the REP-based revenues are $1 412.20 per year. This clearly shows that contrary to widely held beliefs, steady-state revenue requirements are inversely related to the rate of capital recovery. The more rapidly assets are written off, the lower the perpetual annual revenue requirement.
The case of firm growth The results of the previous section are consistent with similar results illustrated by Fisher and McGowan15 for the growth case. They demonstrate the proposition that the ‘asymptotic’ ROR of a firm in growth increases as depreciation is accelerated, whenever the asset growth rate, g is less than the IRR. l6 Fisher and McGowan focus on the relationship between IRR and ROR and do not address regulated revenue requirements. Yet their results are applicable to the regulated case: if (as they illustrate) accelerated depreciation raises ROR while backloaded recovery lowers it, then backloaded depreciation must require more revenue for a given level of ROR. We can, therefore, extend the FisherMcGowan results to conclude that faster recovery will lower revenue requirements. This reasoning leads to the following proposition for the regulated multi-asset firm in growth: 0
Figure ciation
More rapid depreciation decreases asymptotic revenue requirements when g < IRR and increases them only in the unsustainable case of g > 1RR.l’ 2 illustrates and ROR
the relationship between depreshown by Fisher and McGowan
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Depreciation
zw
0.35
?
0.3
0’ ‘G .; ar FL %
0.25
-! E 6
for regulated firms
0.2
0.15 0.1 0.05
I 1
2
3
4
5
Year Figure
1. Depreciation
profiles.
flow profile, so that revenues can be lowered to bring the ROR back down.” These results - that accelerating capital recovery lowers asymptotic revenue requirements - seem startling at first’” but are consistent with the weighted average relationship given in Equation (2). For example, assume that regulators use the traditional
(left hand ordinate): with g held constant, we can get ‘more’ ROR at any given level of IRR (IRR > g) by simply increasing the rate of capital recovery. The right hand ordinate of Figure 2 extends their proposition to illustrate the relationship between depreciation and the regulated revenue requirement: accelerating depreciation raises ROR for any cash Table 3. Steady rate revenue requirement Asset ARR, * vintage depreciation 1. Sum-of-the-years 1 0.12 2 0.12 3 0.12 4 0.12 5 0.12 Totals ($) 2. Straight-line depreciations 0.12 1 0.12 2 0.12 3 0.12 4 0.12 To:als ($) 3. Annuity depreciation 0.12 1 0.12 2 0.12 3 4 0.12 0.12 5 Totals ($) 4. Represcribed depreciationb 0.12 1 0.12 2 0.12 3 0.12 4 0.12 To:als ($)
for alternative
B,
POLICY July 1992
schedules.”
_
D,
R,
1 000.00 666.67 400.00 200.00 66.67 2 333.33
333.33 266.67 200.00 133.33 66.67 1 000.00
453.33 346.67 248.00 157.33 74.67 1 280.00
1 000.00 800.00 600.00 400.00 200.00 3 000.00
200.00 200.00 200.00 200.00 200.00 1 000.00
320.00 296.00 272.00 248.00 224.00 1 360.00
1 000.00 842.59 666.29 468.84 247.69 3 225.41
157.41 176.30 197.45 221.15 247.69 1 000.00
277.41 277.41 277.41 277.41 277.41 1 387.05
1 000.00 875.00 725.00 535.00 300.00 3 435.00
125.00 150.00 190.00 235.00 300.00 1 000.00
245.00 255.00 277.00 299.20 336.00 1 412.20
Notes: “Five-year asset with no taxes or retained prescribed to 5-year straight-line.
UTILITIES
+
depreciation
earnings;
‘S-Year
straight-line
re-
231
Depreciation for regulated firms Revenue requirement
ROF
Low
ligh Accelerated
)~
SLD -GF=
(economic)
IRR Annuity + Decelerated
/ g=IRR
Asset growth
Figure 2. Asymptotic
rate (g%)
ROR and revenues for various depreciation
policies.
We now develop annual revenue requirement profiles for a regulated firm in growth, given the following conditions:
typical for new firms or new asset accounts of existing firms. The revenues in Figure 3 are consistent with the results of the previous section. During the initial growth phase revenue requirements are directly related to the rate of capital recovery - SYD produces the highest rates, REP the lowest. This is expected since g > IRR. Revenue differences between the depreciation policies then dissipate as g + IRR around Year 5, also as expected. After Year 5, when the growth rate falls below the 12% IRR,*’ the ordering abruptly reverses and SYD produces the lowest revenue requirement, a result that continues in perpetuity as long as g < 12% is maintained. Further, as also suggested by the results of the previous section, the revenue advantage of REP over SYD during the initial growth phase will dissipate rapidly as initial g is reduced. This is illustrated in Figure 4, which shows the revenues for a firm in constant, 3% growth.
1.
Present value as a guide to depreciation
policy of back-loading depreciation so that individual assets generate revenue requirements that are lower than SLD early in the asset’s life and higher subsequently (Table 1, Panel 4). When growth rates are sufficiently high there is an abundance of new, ‘low-revenue’ assets with higher book-value weights relative to older ‘high-revenue’ assets. Backloading depreciation under these circumstances therefore lowers revenues. However, the presence of new, ‘low-revenue’ assets declines as the firm’s growth declines, so that eventually there are relatively more old, ‘high-revenue’ assets. Now a backloaded depreciation policy only serves to increase revenues.
Revenue requirements for different depreciation policies and growth rates
2. 3.
4. 5.
The firm makes its first investment at the end of year 0; the firm is funded entirely with equity whose cost remains invariant to depreciation policy; the firm invests in a portfolio of identical depreciable assets with a five-year life, using a pre-specified investment function; tax considerations are omitted;*a there are no operating expenses and no salvage values.
Figure 3 shows the revenue requirements, total plant in service (TPIS) and the TPIS growth rate for the case of a firm experiencing an initially high growth which is followed by lower, sustainable growth (3%/ year) beginning in Year 5. This growth pattern is
232
choice
Regulators frequently use cost-benefit analysis involving present value (PV) measures to evaluate depreciation policy. Generally speaking projects with the lowest PV revenues are desirable. Depreciation policy, however, affects only the intertemporal apportioning of costs, and is therefore not in itself an economic cost. PV measures are therefore not a meaningful decision criterion in such cases and do not help in setting depreciation. There are other reasons why PV measures should not be relied on in formulating depreciation policy. Cost-benefit analysis cannot eliminate intergenerational inequities** such as one cohort of ratepayers paying an unfairly high share of the asset
UTILITIES
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Depreciation for regulated firms
:ED SLD SYD
Approximate
change-over
-
3% growth
0
4
8
12
point
TPIS x x x
(g = 12%)
x
x
x
xXxX
rate
16
20
24
Years
Figure 3. Annual
revenue requirement
costs. 23 Therefore, where cohorts contributing or receiving benefits change over the life of the project it does not always provide a definitive decision criteria. For example, it cannot distinguish among two different alternatives with equal present value revenues, even though the time-shape of the benefits may be such that different cohorts prefer one alternative over the other. This has important implications in regulation where the present value of revenue requirements is, in principle, invariant with depreciation policy over the life of the asset. Given this so-called ‘Invariance Proposition’,24 cost-benefit techniques will be of limited usefulness in designing and evaluating depreciation policy. For example, if we assume that cash flows in Figure 3 are perpetual, as they would be in reality, the PV will be unaffected by depreciation choice so that by this measure we could not identify the ‘best’ choice.25 Yet any ratep a y er that begins or increases its consumption of the regulated output after Year 4 clearly prefers SYD. Indeed all ratepayer cohorts from Year 5 to perpetuity prefer SYD over less accelerated methods. This ordering of preferences is unchanged when the life of the firm is shortened to some finite period.26 The backloaded REP schedule, by constrast, is preferred only by the Year 1 - 4 cohorts, which perhaps explains its political attractiveness. It seems, therefore, that welfare criteria are not helpful in evaluating depreciation because the capital recovery rate does not affect the present value of revenues over the life of the firm. Yet this does not
UTILITIES
POLICY July 1992
for different depreciation
policies.
suggest that we should be indifferent to depreciation - only that it must be evaluated on the basis of the underlying asset economics: the time-shape of cash flows over the asset’s life. Nor does it diminish the important outcome that after the initial start-up period ends, the firm’s ratepayers enjoy a perpetuity of lower rates under an accelerated depreciation schedule.
Depreciation profiles for assets with high rates of technological progress Correct depreciation policy reflects the true costs of operation and fairly allocates it to all user cohorts.*’ The ‘correct’ depreciation policy is generally defined in the tradition of Fisher*s and Hotellingz9 as economic depreciation (ED): the annual depreciation charge which reflects the change in present value of the asset’s remaining cash flows, discounted at the asset’s IRR.‘O When depreciation is correctly specified in this manner the firm’s ROR equals its IRR and hence has economic significance. Arbitrary depreciation schedules, such as SLD or REP which generally do not reflect the economic change in asset values will distort ROR so it does not correctly reflect economic rates of return. There are potential difficulties in implementing theoretically correct ED and some researchers” feel that circularity and other problems make the effort to periodically determine economic depreciation ‘totally impractical’. Yet there are more practical approaches in the sense of Luckett3* and Kraus and Huefner3’ which conside depreciation an empirical
233
Depreciation for regulated firms
0
4
8
12
16
20
24
Years
Figure 4. Annual
revenue (constant growth rate).
requirements
issue with the expectation that accuracy will improve with experience. 34 Given this app roach, ED can be set expectationally when the asset is placed in service and the cash flow estimates developed in the capital budgeting process can be used as a basis for its estimation. The initial estimates become a rate case issue with the expectation that they will be as unbiased as any other variable. In order to clearly distinguish this, more practical approach to ED it may be useful to call it Original Cost Economic Depreciation (OCED). Under OCED recovery is limited to the original cost; there are no inflation-driven asset writeups. Absent inflation and uncertainty OCED and ED are equivalent. We now explore techniques for correctly estimating OCED in assets with high rates of technological change. OCED in regulation Stauffer35 shows that for every cash flow profile (CFP) there exists one ED (Hotelling) schedule which suggests that SLD is the economic depreciation in traditional regulation. In such a traditional regulatory model, CFP is a function of depreciation and any recovery profile becomes the ED - this is the ‘Invariance Proposition’. The traditional model, however, becomes less relevant as we enter a more competitive era in telecommunications and power generation. Now the firm becomes more of a price taker, so that the CFP for a particular asset or service is set in the marketplace, independent of the inter-temporal schedule set by regulators. 36 In such a setting the traditional
234
for different depreciation
policies
‘saw-tooth’ CFP generated by SLD (Table 1, Panel 2) may be unobtainable due to market pressure. The regulatory problem is to determine the particular stream of depreciation charges which will best reflect the asset’s expected economic depreciation patterns, given market-driven cash flow expectations. In addition to equitably apportioning costs over time, the results also provide a more informative income measure which yields ROR = IRR each year as long as cash flows materialize as expected (and accountants adjust for inflation). ROR thus becomes a useful measure for testing the extent to which managerial expectations, formed at the time the asset is placed in service, are realized over time. OCED is unlike arbitrary schedules; it is a different profile for every CFP and rate of return. Ordinary SLD is the OCED schedule for the traditional ratemaking cash flow (Table 1 - Panel 2). Annuity depreciation (AD) is the OCED for a level of CFP (Panel 3). Likewise, for the front-loaded cash flow of Panel 1, SYD is the economic depreciation. Sufficient information exists at the time an asset is placed in service to allow an estimate of its expected OCED profile. Such an estimate, no matter how imprecise, is bound to be an improvement over SLD. Regulators, however, feel that this procedure is inexact and therefore default to SLD, typically selecting lives that are arbitrarily long. This, most likely represents the worst possible estimate of true depreciation for assets with high-rates of technological change. The arbitrarily long initial lives are subsequently represcribed as additional experience
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Depreciation for regulated firms
Original cost economic
1 0
depreciation
I
I 2
I 4
I 6
Years
Figure 5. Economic
depreciation
and the Q-Profile.
makes the initial error obvious. The result is a backloaded depreciation schedule similar to the REP profile. Assets with high rates of technological change by definition have short economic lives with CFP’s that rise initially (after an introductory phase) and then rapidly decay as the technology matures and a subsequent vintage technology is introduced. In competitive environments, producers who lack the most efficient technology can generally lose market share to participants with newer, lower (marginal) cost technology. This market share loss results in declining net cash flows for the earlier-vintage assets _ either because sales have been lost or margins have been squeezed by newer technology.37 Figure 5 shows the ‘Q-Profile’ of cash flow’s which we use here as representative of the CFP generated in competitive environments by high technology assets. A regulated firm that employs such assets may therefore realize a CFP in the shape of the Q-Profile, independent of regulatory expectations. When SLD is used in conjunction with the Q-Profile the ROR values become uninterpretable (Table 4, Panel l), ranging from 31.7% to -60.2% over the asset’s life (IRR = 15%) and hence providing no useful information to regulators. The correct OCED schedule (Table 4, Panel 2) yields periodic ROR that meaningfuly interprets IRR. This schedule accrues depreciation most rapidly during the middle of the asset’s life, when cash flow and market power are strongest. The economics of high-technology assets quite plainly indi-
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cated that depreciation must be front-loaded in this manner.40 As the traditional monopoly model of regulation erodes and firms face market-driven cash flow profiles, it becomes increasingly important for regulatorys to set depreciation correctly. Continued use of arbitrary, engineering-based schedules will yield ROR values that are increasingly unreliable as proxies of true economic profitability. Even more distortive are attempts to favour current ratepayer cohorts by instituting regulated lives that are arbitrarily long relative to expected economic usefulness. When depreciation is incorrectly specified in this manner the principal regulatory indicator - the ROR - loses all economic significance and becomes unreliable. Since correct OCED schedules are front-loaded they will lower asymptotic revenues, although this is not a sufficient reason for regulators to begin using them. On the other hand, the results clearly imply that regulators need not be afraid to use accelerated depreciation where such moves are justified on the basis of the fundamental asset economics, ie: expected life and cash flow profile.
The reality case: transitions from inefficient to efficient depreciation policies This section examines the revenue effects of transition from an existing recovery schedule such as SLD or REP, to a more efficient, accelerated schedule. This is the policy choice available for the practical
235
Depreciation for regulated firms Table 4. Income and return for the Q-profile economic depreciation.
Year 1. Straight 1 2 3 4 5 6
Cash Depreciation flow” ($) ($) line depreciation 23.76 16.67 35.79 16.67 37.83 16.67 29.27 16.67 15.70 16.67 6.63 16.67
2. Original 1 2 3 4 5 6
cost economic 23.76 35.79 37.83 29.27 15.70 6.63
100.00 depreciation 8.76 22.10 27.46 23.01 12.90 5.76
under straight-line
and original
cost
Net income (W
Beginning year ratebase RORb % (W
7.09 19.12 21.16 12.60 -0.96 - 10.04
100.00 83.33 66.67 50.00 33.33 16.67
7.1 22.9 31.7 25.2 -2.9 -60.2
15.00 13.69 10.37 6.25 2.80 0.86
100.00 91.24 69.14 41.68 18.67 5.76
15.0 15.0 15.0 15.0 15.0 15.0
100.00 Notes: “The Q-Profile 4.0%.
is adjusted
to yield
an IRR
case of an established, regulated firm which has always used SLD. Consider again the case of a new firm using SLD. Regulators then switch to OCED for all new assets placed in service after Year 8 (Figure 6). The transition from SLD to the less costly OCED is not fictionless, and regulated rates rise above what they would have been under SLD (dotted line) for about four years.4’ Indeed, a new steady-state is reached at the end of four years so that the transition requires a period equal to the average asset book life. The economic basis for the ‘bubble’ is not clear cut, although transitions from inefficient to efficient paths are often not frictionless. In this instance the
of 15%;
I
0
I 4
I
I
average
to
temporary rise in revenues can be seen as a way of balancing the benefits that SLD creates relative to OCED duirng the first four years - the Invariance Proposition requires that the area between SLD and OCED for years 1 - 4 equal the discounted area under the ‘bubble’. When initial growth is smaller (Figure 7), the transition ‘bubble’ is also smaller because there is less initial benefit to recapture. In this sense the transition ‘bubble’ becomes an investment which yields a perpetuity of correct (and lower) rates. Cost-benefit
of depreciation
The relevant
D begins for firm
01
hThe values
I 12
I
8
transitions
issues are whether
the move
from an
usi
I
I 16
I
I
I
20
I 24
Years Figure
236
6. Annual
revenue requirements:
transition
from SLD
to OCED.
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POLICY July 1992
Depreciation for regulated firms
Years
Figure 7. Annual revenue case of constant growth).
requirements:
SLD or REP schedule to the correct OCED is worthwhile, and the criteria by which such a judgment can be made. As previously discussed, regulators tend to examine depreciation policy over some arbitrary, finite period, and (erroneously) expect a payback during that period. But the benefits of transitioning to more efficient depreciation continue in perpetuity, and a payback over some finite period is not a valid decision criterion. Moves from a backloaded to an accelerated depreciation schedule will leave present values unaltered, eg: the Year-5 PV (Figure 6) is the same independent of whether the firm uses SLD or transitions to OCED after Year 8. Again, cost-benefit measures do not distinguish between the two alternatives and depreciation policy must be set on the basis of the underlying economics: the asset’s life and CFP. When these are properly reflected in depreciation all ratepayer cohorts automatically pay their fair share, a result well known since Baumo1.42 The move to an efficient but accelerated recovery temporarily raises rates although once the transition ends rates are perpetually reduced. In a sense the area under the bubble can be interpreted as a penalty for inefficient past recovery. It is in everyone’s interest - ratepayers and the firm - to minimize the confusing price signals created by a transition to OCED. The presence of lower growth rates, which mitigate the effects of different depreciation policies will yield smaller transition penalties - eg the bubble in Figure 7 is smaller even though the transition begins much later, in Year 16.43 Earlier transitions will yield correspondingly smaller penalinefficient
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POLlCY July 1992
transitions
from SLD to OCED (the
ties. Regardless of when the depreciation correction is begun, however, the initially higher rates are an efficient investment with a perpetual benefit stream.
Conclusion Depreciation can be fully understood only in terms of multi-asset models. In order for allowed rates of return to have economic meaning in the case of high-technology assets the regulatory process must move in the direction of estimating true asset depreciation rates. For most mature, regulated telecommunications companies asymptotic revenues are inversely related to the depreciation rate so that accelerated recovery yields lower revenues. This make intuitive sense: a rapidly growing firm which adds new assets at a high rate will have a preponderence of new-vintage assets so that accelerated depreciation, (which is initially higher for any given asset) will raise rates. However, when the firm grows slowly its portfolio has more older assets which have lower revenue needs under accelerated depreciation. Transitions from decelerated to accelerated depreciation do not alter the PV of revenues. This result, however, must not be allowed to overshadow the more significant outcome: that such transitions yield a perpetually reduced revenue requirement. All ratepayers are perpetually bettef off after the transition, although cohorts participating only in the transition are hurt. Cost-benefit techniques do not help us resolve this dilemma although this is not necessarily a limita-
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Depreciation for regulated firms
tion - depreciation schedules need to be determined on the basis of the asset economics, not present value analysis. Attempts to favour one cohort over another, typically by rejecting efficient, accelerated OCED schedules on the basis that they raise nearterm rates. reduces efficiencv , and hurts the regulated firm and its ratepayers, especially in a partially competitive environment.
The author thanks Terence .I. Cooney Jr and Daniel J. Lane for their insights and comments, as well as members of the Advanced Workshop in Public Utility Economics and Regulation, Rutgers University and participants in the Symposium-on the Partially Regulated Firm, Columbia University; the support of the Institute for Tele-Information, Columbia University, is also acknowledged.
‘Shimon Awerbuch, ‘Accounting rates of return’, American Economic Review, Vol 78, No 3, June 1988, pp 581-87. *Hector A. Anton, ‘Depreciation, cost allocation and investment decisions’, Accounting Research, Vol 7, April 1956, pp 117-34; Franklin M. Fisher and J.J. McGowan, ‘On the misuse of accounting rates of return to infer monopoly profits’, American Economic Review. Vol73. No 1. DD 82-97. March 1983. esoeciallv pp 92-93; Richard S. Bower, ‘The capital recovery’question’, Resources and Energy, Vol 7, No 1, 1985, pp 7-42; Sidney S. Alexander, ‘Income measurement in a dynamic economy’, (revised by David Solomons) in, W.T. Baxter, and S. Davidson, eds, Studies in Accounting Theory, Homewood, Irwin, USA, 1962; Edgar, 0. Edwards and P.W. Bell, Theory and Measurement of Business Income, University of California Press, Berkeley, CA, USA, 1961. ‘The term ‘correct ratemaking’ is used in the sense of Baumol (William J. Baumol, ‘Optimal depreciation policy: pricing the products of durable assets’, Bell Journal of Economics and Management Science, Vol 2, No 2, Autumn 1971, pp 638-656) who showed that ED yields the correct time-pattern of prices for the underlying asset. See also, Miles 0. Bidwell, ‘Optimal prices, economic depreciation, and regulated utilities’, 23rd Annual Regulatory Conference, Ames, IO, USA, 1985; and Bower, Ibid. “Awerbuch, op tit, Ref 1. ‘Anton, op tit, Ref 2. 6As suggested by Gabriel A.D. Preinreich, ‘The principles of public utility depreciation’, Accounting Review, Vol 13, No 2, June 1938, pp 149-165, p 149. ‘The term is used after Fisher and McGowan, op tit, Ref 2, p 86, to mean annual revenue and requirement in the steady-state. 8Theorem I, Ibid. ‘Under perfect regulation this becomes Turvey’s amortization (Ralph Turvey, ‘Marginal costs’, Economic Journal, Vol79, June 1979, pp 282-300). “‘This so called ‘rate shock’ becomes sizable whenever the firm places into service an asset, such as a nuclear plant, which represents a significant percentage of existing ratebase. Inflation aggravates the situation by raising the cost of new capacity as compared to older capacity. “Preinreich, op tit, Ref 6, p 149. “See, J.A. Kay, ‘Accountants, too, could be happy in a golden age: the accountant’s ratet of profit and the internal rate of return’, Oxford Economic Pappers, Vol 28, November 1976, pp 447-60: Richard Brealev and S.C. Mvers. Principle of Corporate Finance, 2nd ed, McGraw Hill, New York, 1984: chapter l!2; and Fisher and McGowan, op tit, Ref 2. i3This paper addresses depreciation only insofar as it affects ratemaking; tax depreciation remains unaffected and the firm is free to use any appropriate method for financial reporting. 14When compared to some actual results this schedule seems quite
238
conservative: telephone switching equipment in some jurisdictions, originally allowed a 40-year life, was ultimately represcribed to under 20 years. “Fisher and McGowan: op tit, Ref 2. “The relationship reverses when g > IRR, although such growth rates are not sustainable without negative dividends. (Gerald L. Salamon. ‘Models of the relationshiu between the accountine and internal rate of return: an examination of the methodoibgy’, Journal of Accounting Research, Vol 11, Autumn 1973,-pp 296303.) We therefore limit the discussion to the region of g > IRR. Fisher and McGowan’s finding for unregulated-firm’s G in contrast to widely held beliefs to the contrary - ie it is usually felt by accountants that accelerated depreciation serves to reduce the accounting return. For the case of g = IRR, varying the depreciation leaves ROR unaltered (Fisher and McGowan’s Theorem 1, op tit, Ref 12, pp 91-92). Solomon (Ezra Solomon, ‘Alternative rate of return concepts and their implications for utility regulation’, Bell Journal of Economics and Management Science, Vol 1, No I, Spring 1970, pp 65-81, especially pp 75-76) obtains similar results although they are not discussed. “The region g < IRR covers most practical situations involving mature regulated firms. Certain situations such as lumpy additions caused by nuclear plant completions may temporarily result in g > IRR. Under such circumstances more rapid depreciation indeed increases regulated revenues until the growth rate diminishes again. ‘XObserve that the acclerated schedule yields ROR values that overstate the true IRR which is correctly given only by the economic depreciation - in this case SLD. “Similar results were shown 50 years ago by Preinreich, op tit, Ref 6, although the presentation is complex and does not note the significance - which perhaps explains why regualators seem unaware of it. ‘(This simplifies without distorting outcomes (Shimon, Awerbuch, ‘Depreciation for high technology assets’, The Partially Regulated Firm and Accounting Based Regulation: Issue in Capital Budgeting and Technology Adoption, Columbia University, November 1989, pp 45-46). Regulated depreciation alters revenue requirements but tax depreciation remains unchanged and hence has a constant effect on pretax cash flow. *iDiscrete time is used. The firm’s growth rate is 25% in year 4 and 3% in Year 5 and thereafter. “Robert C. Lind, Discounting for Time and Risk in Energy Policy, Resources for the Future, Johns Hopkins University Press, Baltimore, NE, USA, 1982, p 457. “This is precisely what happens with SLD and arbitrarily long asset lives: ratepayer cohorts near the end of an asset’s life pay the same annual depreciation charge as earlier cohorts even where obsolescence has diminished the asset’s value. “See, Richard Schmalensee, ‘An expository note on depreciation and profitability under rate of return regulation’, Journal of Regulatory Economics, Vol 1, No 3, September 1988, pp 293-298; Kay, op tit, Ref 12; and, Bruce Greenwald, ‘Rate base selection and the structure of regulation’, Rand Journal of Economics, Vol 15, Spring 1984, pp 85-95. The Invariance Proposition is illustrated bv Table 1. Observe that the PV of cash flows is $1 000 independent of depreciation choice. This demonstration ignores taxes, debt retirement, regulatory lag and numerous other practical problems and should therefore not be interpreted to imply that ROR = IRR in practice; see, Shimon Awerbuch, ‘Depreciation and rate of return’, Journal of Regulatory Economics, 1991 (forthcoming). ‘sHowever, an analysis that is arbitrarily limited to some finite period, say the first eight years, will show that REP is the most ‘desirable’ and possibly this is why regulators favour it. The result is obviously incorrect because it ignores subsequent cash flows. *6PV computations for the case of a finite-lived firm, or where the analysis has been arbitrarily limited to some finite ‘payback’ period will be in error unless ending asset values (which equal the present value of remaining cash flows) are included. See, Awerbuch, op tit, Ref 24. “Baumol, op tit, Ref 3.
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Depreciation for regulated firms ‘sIrving Fisher, The Nature of Capital and Income, MacMillan, New York, USA, 1906. 29Harold Hotelling, ‘A general mathematical theory of depreciation’, Journal of American Statistics Association, Vol 20, September 1925, pp 34@53. ‘“For example see, Bower, op tit, Ref 2; Bidwell, op tit, Ref 3; Saully Hunt Streiter, ‘Avoiding the ‘money saving rate increase’, Public Utilities Fortnightly, Vol 109, No 13, 24 June 1982, pp 18-22. ‘For example, Franklin M. Fisher, ‘On the misuse of accounting rates of return: reply’, American Economic Review, Vol74, No 3, June 1984, pp 509-517, p 510. “Peter F. Luckett, ‘ARR vs. IRR: a review and an analysis’, Journal of Business Finance and Accounting, Vol 11, No 2, Summer 1984, pp 213-231. “Alan Kraus and Ronald J. Huefner, ‘Cash-flow patterns and the choice of a depreciation method’, Bell Journal of Economics and Management Science, No 3, Spring 1972, pp 316334. s4Lawrence A. Gordon, ‘Accounting rate of return vs. economic rate of return’, Journal of Business Finance & Accounting, Vol 1, Spring 1974, pp 343-X ‘“Thomas R. Stauffer, ‘The measurement of corporate rates of return’, Bell Journal of Economics and Management Science, No 2, Autumn 1971, pp 434-469. ?Shimon Awerbuch, ‘Efficient income measures and the partially regulated firm’, in Michael Crew, ed, Deregulation and Diversification of Utilities, Kluwer Academic Publishers, Norwell, MA, USA, 1989. 37For an ingenious example of technology costs to market entrants see Bower, op tit, Ref 2; additional discussion of the
UTILITIES
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economics of changing technologies can be found in Michael Crew and P. Kleindorfer, Capital Recovery and the FCC’s Price Cap Proposal, Center for Regulated Industries, Graduate School of Management, Rutgers University, Newark, NJ, USA, 1988. ssFisher and McGowan, op cit. Ref 12. “The Q-Profile is an outgrowth of the IBM anti-trust case although the issue of whether it accurately represents the experience of IBM’s System 360 was disputed (See Franklin M. Fisher, J.J. McGowan and Joen Greenwood, Folded, Spindled and Mutilated: Economic Analysis and U.S. vs. lBM, MIT Press, Cambridge, MA, USA). ““Michael A. Crew and Paul B. Kleindorfer, ‘Depreciation and resource allocation in the regulated firm: a dynamic analysis with technological change’, Advanced Workshop in Public Utility Economics and Regulation, Rutgers University, Fifth Annual Conference, 1986, and others have argued for accelerated capital recovery on the basis of increasing competitive pressures which limit future recovery. The results herein are independent of those arguments. Charles Hulten and Frank Wykoff, in ‘The measurement of economic depreciation’ in, Charles Hulten, ed, Depreciation, InfZation and the Taxation of Income from Capital, The Urban Institute, Washington, DC, USA, 1981, and others also find that true depreciation is accelerated for many types of assets. 4’The rate ‘bubble’ is formed because the first asset to be placed in service in Year 9 requires more revenue, with the offsetting benefit of lower revenues not available until the end of this asset’s life three or four years later. 4ZBaumol, op tit, Ref 3. 4’Transition costs can be managed in a number of other ways. See, Awerbuch, op tit, Ref 20.
239