*Pages 1--49 from C:\Pdf2Text\Ready4Text_in\pdf\31391.pdf* Federal Communications Commission Office of Strategic Planning and Policy Analysis 445 12th Street, SW Washington, DC 20554 OSP Working Paper Series 40 Dynamic Pricing and Investment from Static Proxy Models September 2003 David M. Mandy William W. Sharkey 1 The FCC Office of Strategic Planning and Policy Analysis Working Paper Series presents staff analysis and research in various states. These papers are intended to stimulate discussion and critical comment within the FCC, as well as outside the agency, on issues in telecommunications policy. Titles may include preliminary work and progress reports, as well as completed research. The analyses and conclusions in the Working Paper Series are those of the authors and do not necessarily reflect the views of other members of the Office of Strategic Planning and Policy Analysis, other Commission staff, or the Commission itself. Given the preliminary character of some titles, it is advisable to check with authors before quoting or referencing these Working Papers in other publications. This document is available on the FCC's World Wide Web site at http:// www. fcc. gov/ osp/. The inside back cover contains a partial list of previous titles. 2 Dynamic Pricing and Investment from Static Proxy Models † David M. Mandy * William W. Sharkey ** Abstract This paper evaluates the use of static cost proxy models in setting forward-looking prices, such as the prices set according to the FCC’s TELRIC methodology. First, it compares the time paths of prices and depreciation under traditional regulatory accounting with the prices and depreciation implied by various versions of TELRIC. When TELRIC prices are recomputed at intervals shorter than asset lives, the firm will generally not earn the target rate of return. In these cases, a correction factor must be applied to the TELRIC price path in order for revenues to exactly recover investment cost, including the target rate of return. Next, the paper considers a firm’s cost minimizing investment decisions under two different assumptions about asset obsolescence. In both scenarios, cost minimizing investment paths and implied utilization rates for the firm’s assets are derived under a variety of assumptions about the relevant input parameters. Some implications for TELRIC pricing are then derived. † The authors acknowledge helpful discussions with Jay Atkinson during preparation of this paper. We also benefited from the comments of Simon Wilkie and Donald Stockdale on an earlier draft. The views expressed in this paper, however, are those of the authors alone and do not necessarily reflect the views of the Federal Communications Commission, any Commissioners, or other staff. * Department of Economics, University of Missouri, 118 Professional Building, Columbia, MO 65211; MandyD@ missouri. edu. ** Office of Strategic Planning and Policy Analysis, Federal Communications Commission, Washington, D. C. 20554; William. Sharkey@ fcc. gov. 3 Dynamic Pricing and Investment from Static Proxy Models: Executive Summary Since release of the FCC’s Local Competition Order, 1 incumbent local exchange providers have strongly objected both to TELRIC as a methodology and to its specific implementation by state regulatory commissions. These objections generally fall into three categories. First, incumbent carriers have questioned the theoretical consistency of the TELRIC methodology itself. Specifically, they have argued that, when equipment prices are falling over time, periodic recalculation of TELRIC prices prevents them from recovering their investment costs. Second, incumbents have criticized the way in which state commissions have implemented TELRIC. They argue either that states have adopted unrealistic input values or that the cost models that were adopted contained flawed model algorithms. 2 Finally, some incumbents have argued that any forward- looking pricing methodology, including TELRIC, in which the computation of cost is not based on the incumbent’s “actual network” as a starting point, is inconsistent with the meaning of the 1996 Act. This paper addresses aspects of each of the above criticisms. Specifically, section 2 addresses the argument that periodic recalculation of TELRIC prices prevents incumbents from recovering the cost of their investment. It shows that, if investment costs are falling over time, and the period between TELRIC price adjustments is shorter than asset lives, then traditional TELRIC pricing will not permit incumbents to recover the cost of their investment. Similarly, when investment costs are rising, TELRIC pricing will result in an over- recovery of investment costs. Section 3 examines a carrier’s cost minimizing investment plan in a dynamic environment with lumpy investment costs. While not intended to recommend specific input prices for cost models, this section is directly relevant to the selection of forward- looking fill factors for such models. As such, it may partially address incumbent’s arguments that state commissions have set unrealistically high fill factors. 3 Dynamic Pricing of an Already- Determined Investment Section 2 is concerned with comparing alternative time paths of prices that will allow a firm to exactly recover the cost of network investments when these costs are expected to change over time. Incumbent carriers are correct to point out that, when TELRIC prices are recomputed at periodic intervals, particular care must be exercised in order to ensure that the resulting prices are consistent with the assumptions made about asset lives and the allowed rate of return. Indeed, when investment costs are falling over 1 Implementation of the Local Competition Provisions in the Telecommunications Act of 1996, First Report and Order, 11 FCC Rcd 15499, 15509 (1996). 2 For example, incumbents argue that proxy models often assume an unrealistic level of sharing of the cost of structures (i. e. poles and underground conduit facilities) with other utilities. It is also argued that cost minimization procedures in proxy models assume an unattainable level of efficiency that no real world firm could expect to emulate. The results of this paper are relevant to the setting of one input factor – the firm’s utilization rate of existing capacity (also called a fill factor). 3 The third criticism is also partially addressed at the end of Section 3. 3. 1 4 time and TELRIC price reviews are conducted at intervals shorter than expected asset lives, the firm will earn less than its target rate of return under traditional implementations of TELRIC. Specifically, a TELRIC price is traditionally computed as a constant (or levelized) price that, over the life of the asset, will earn sufficient revenue to recover the full cost of investment including the target rate of return. When TELRIC prices are recomputed at intervals shorter than these asset lifetimes, and investment costs fall between price reviews, actual revenues will not fully compensate the firm. The paper shows, however, that it is possible to compute a correction factor based on estimates of the rate of change of investment cost and the expected time between TELRIC reviews. Corrected TELRIC prices rise or fall at the same rate over time as underlying investment cost, and allow the firm to earn its target rate of return no matter how frequently price reviews are conducted. Moreover, no ad hoc adjustments of assumed asset lifetimes or depreciation schedules are needed to implement the suggested correction. These points may be illustrated in the following diagrams which represent different price paths for a hypothetical investment of $100 in an asset that is assumed to have an economic lifetime of 12 years. Figure ES1 compares price paths based on traditional regulatory accounting and levelized TELRIC pricing. Both paths assume an allowed rate of return of 11.25%, and the traditional price path (adjusted annually) assumes straight line depreciation over the 12 year life. Traditional prices fall even under straight line depreciation because price in each period reflects operating expense + depreciation expense + capital cost. The first two terms are constant by assumption, and the capital cost term declines over time at the same rate as the undepreciated balance. The levelized TELRIC price is by definition constant over the life of the asset and is set at a level such that the present value of revenues equals the investment cost of $100. 4 1 2 3 4 5 7 8 9 10 11 12 12 14 16 18 20 22 6 Figure ES1. Traditional Prices versus a Levelized TELRIC Price 4 Note that, due to levelization, a depreciation schedule does not enter in any way into the TELRIC computation in the absence of tax effects. If tax consequences are accounted for, then the TELRIC price is set at a level such that the present value of after- tax revenues is equal to the present value of after- tax investment costs, where the latter accounts for the deductibility of depreciation expense and an appropriate weighted average cost of capital is used. As a result, more accelerated tax depreciation schedules lower the levelized TELRIC price. 2 5 Figure ES1 was constructed without any reference to the rate of change of investment costs, since neither the levelized TELRIC price nor the traditional price depends on future changes in these costs. Suppose, however, that investment costs are expected to fall at a rate of 10% per year. In a competitive market, prices would also be expected to fall at a rate of approximately 10% per year, since the price at any given time would reflect the cost of newly incurred investments made at that time. In order to recover their investment costs, potential entrants therefore anticipate setting prices according to a declining price schedule, so that prices in early years recover more of the investment cost than prices in later years. If TELRIC price reviews are conducted periodically, using the current investment cost at the time of the review, then TELRIC prices will also decline over time at a rate of approximately 10%. However, since TELRIC prices were defined to allow the firm to break even assuming a levelized price schedule for the entire life of the asset, when there are periodic reviews and declining investment costs, the TELRIC prices will no longer recover the firm’s investment cost including its target rate of return. Figure ES2 compares a price schedule that allows competitive firms to earn exactly the target rate of return (dotted line) and TELRIC prices (solid line), assuming TELRIC reviews are conducted every three years. 1 2 3 4 5 6 7 8 9 10 11 12 10 15 20 25 Figure ES2. Competitive Prices versus TELRIC Prices Reviewed Every Three Years It is a simple matter, however, to define a correction factor based on: (1) the assumed rate of change of investment cost, and (2) the period between TELRIC reviews. In the current example, TELRIC prices must be increased by 35% in every year. The corrected TELRIC price path is shown in Figure ES3. By construction, corrected TELRIC prices recover the firm’s full investment costs, including its required rate of return. In addition, TELRIC prices fall at approximately the same rate as the breakeven 3 6 prices for competitive firms, with differences only in the assumed timing of the price changes. 5 1 2 3 4 5 7 8 9 10 11 12 10 12.5 15 17.5 20 22.5 25 6 Figure ES3. Competitive Prices versus Corrected TELRIC Prices Efficient Investment over Time Section 3 of the paper is concerned with deriving cost minimizing investment plans in a dynamic environment. This section of the paper seeks to address in part the second and third objections raised by incumbents to TELRIC pricing. First, by deriving an efficient forward- looking investment plan, the paper is simultaneously solving for an efficient utilization rate over time. Since assumed utilization rates are an important input to cost proxy models used to estimate TELRIC prices, these results are potentially relevant in setting appropriate utilization input rates in a forward- looking context. For example, using a cost function derived from outputs of the FCC’s Synthesis Model to represent loop investment costs, the paper demonstrates how to compute an efficient investment plan for loop plant over a 60 year time horizon. This plan is illustrated by the step function in Figure ES4. 5 Section 2 also demonstrates that when investment costs are increasing over time (e. g. due to general price inflation) then periodically reviewed TELRIC prices will lead to an over- recovery of investment cost. In this case the correction factor will lead to a reduction in TELRIC prices. 4 7 Section 3 also shows how to compute efficient investment plans based on existing capacity levels of incumbent firms. To the extent the initial capacity levels can approximate the existing investment base of incumbent carriers, these results may reconcile TELRIC price computations with “actual cost” computations favored by incumbents. 6 9 1. Introduction In February 1996 the U. S. Congress passed the Telecommunications Act of 1996, which significantly amended the Communications Act of 1934. The goals of the 1996 Act were to establish a “pro- competitive, deregulatory national policy framework” for local telephony competition. 8 Implementation of the 1996 Act by the Federal Communications Commission (FCC) included development of a new regulatory pricing standard known as “Total Element Long Run Incremental Cost” (TELRIC). 9 TELRIC has been used to price unbundled network elements and interconnection, 10 and has been widely criticized both as a conceptual framework and as actually applied by regulators. 11 An underlying current in many of these criticisms is the static nature of TELRIC pricing as implemented to date, when actual telecommunications industry costs are highly dynamic. This paper considers how TELRIC pricing can be correctly implemented in a dynamic environment. We do this by exploring first, in Section 2, how prices that are periodically reviewed can be calculated to recover the cost of a given investment in physical equipment. Second, Section 3 studies how dynamically efficient investment plans can be calculated, thereby giving the costs to be recovered via the pricing rules discussed in Section 2. Together, Sections 2 and 3 move beyond the criticisms and substantially toward theoretically sound TELRIC pricing rules that can actually be applied in practice. In contrast, the existing literature is long on criticisms of TELRIC but short indeed on suggesting rules and calculations thereof that show how TELRIC prices as currently implemented might be modified to address some of the criticisms. 12 Our contribution is to take this next step, with particular emphasis on correctly capturing the dynamics of the industry and the sense in which costs and prices should be forward-looking. One way to view TELRIC is as a new form of incentive regulation. Traditional incentive regulation tries to induce socially efficient behavior from a franchise monopolist. The traditional approach was precluded by the 1996 Act, however, which nullified the state and local statutes that historically granted franchise monopoly status to 8 See Joint Managers’ Statement, S. Conf. Rep. No. 104- 320, 104 th Cong., 2d Sess. 113 (1996) at 1. 9 See Implementation of the Local Competition Provisions of the Telecommunications Act of 1996 (hereinafter Local Competition Order), 11 FCC Rcd 15499, 15509, and 15812- 15922 (1996). 10 The 1996 Act envisioned three alternative methods for competitive entry: construction of new network facilities, resale of the incumbent firm’s retail services, and leasing of unbundled network elements from the incumbent. The 1996 Act also required incumbents to provide interconnection. See 47 U. S. C. §§ 251( c)( 4) and 252( d)( 3). 11 See, for example, Hausman (1997); Kahn (1998, 2001); Sidak and Spulber (1998); Alleman (1999); Kahn, Tardiff, and Weisman (1999); Salinger (1999); Weisman (2000); Mandy (2002); Tardiff (2002); Weisman (2002), and Weingarten and Stuck (2003). Although these studies differ in their points of emphasis, all are critical of at least some aspects of TELRIC in theory or practice. 12 Exceptions are Hausman (1997), Mandy (2002), Tardiff (2002) and Weingarten and Stuck (2003). However, even these papers do not calculate prices and costs under the variety of possible assumptions considered herein, and only Mandy (2002) presents evidence on dynamic and forward- looking price and cost paths that might form a conceptually sound basis for revisions to TELRIC pricing as currently practiced. 7 10 incumbents, and charged the FCC and state regulators with creating rules under which new competition would operate. 13 Under the “incentive regulation” view, by adopting TELRIC, the FCC tried to create a market structure in a highly concentrated industry that provides incentives for efficient investment decisions similar to those present in competitive industries with many small suppliers. Under this view, TELRIC tries to induce socially efficient behavior from firms that may have significant market power, thereby sharing the same goal as traditional incentive regulation. But unlike traditional incentive regulation, TELRIC must pursue this goal outside of the franchise monopoly market structure. TELRIC therefore tries to induce efficient investment decisions, including efficient entry and exit, in an industry that, because of high concentration and substantial scale economies, might experience very little (efficient) entry and exit without such inducement. There is substantial disagreement over whether TELRIC succeeds in promoting efficient investment by both entrants and incumbents, or whether it is even possible for price regulation to achieve this objective. 14 However, even those most critical of the TELRIC methodology agree that the 1996 Act “… asks regulators to create prices that will induce appropriate new entry.” 15 In other words, Congress charged the FCC and state regulators with incentive regulating entry and exit, and doing so via price regulation. The strong objections of some writers, as well as incumbent local exchange carriers (ILECs), to TELRIC as a methodology and to its specific implementation by state regulatory commissions fall into three categories. First, some have questioned the theoretical consistency of the TELRIC methodology itself. Specifically, ILECs have argued that, when equipment prices are falling over time, periodic recalculation of TELRIC prices prevents them from recovering their investment costs. Second, some have criticized the way state commissions have implemented TELRIC. They argue either that states have adopted unrealistic input values or that the cost models adopted contained flawed model algorithms. 16 Finally, some have argued that any forward- looking pricing methodology, including TELRIC, in which the computation of cost is not based on the incumbent’s “actual network” as a starting point, is inconsistent with the meaning of the 1996 Act. This paper examines these claims. 17 Section 2 studies whether TELRIC, as implemented, permits cost recovery of investments in physical equipment. We show that the claim of potential under- recovery is correct. When investment costs are falling over time and TELRIC price reviews are conducted at intervals shorter than expected asset 13 47 U. S. C. § 253. 14 See the references cited in footnote 9. 15 Justice Breyer (Verizon v. FCC, Dissent: 22), as quoted by Weisman (2002). 16 For example, ILECs argue that proxy models often assume an unrealistic level of sharing of the cost of structures (i. e. poles and underground conduit facilities) with other utilities. They also argue that cost minimization procedures in proxy models assume an unattainable level of efficiency that no real world firm could expect to emulate. The results of this paper are relevant to the setting of one input factor – the firm’s utilization rate of existing capacity (also called a fill factor). 17 We do not, however, evaluate the realism of proxy model algorithms or attempt to recommend specific input values for use in proxy model computations. In addition, we do not specifically consider the conditions under which unbundled network elements should be offered under TELRIC prices. 8 11 lives, a firm will earn less than its target rate of return under the TELRIC methodology as generally implemented. A TELRIC price is usually computed as a constant (or levelized) price that, over the life of the asset, will earn sufficient revenue to recover the full cost of investment including the target rate of return. This paper shows that, when TELRIC prices are recomputed at intervals shorter than these asset lifetimes, and investment costs fall between price reviews, actual revenues will not fully compensate the firm. The paper further shows that it is possible to compute a correction factor based on estimates of the rate of change of investment cost and the expected time between TELRIC reviews. Corrected TELRIC prices rise or fall at the same rate over time as underlying investment cost, and allow the firm to earn its target rate of return no matter how frequently price reviews are conducted. Moreover, no ad hoc adjustments of assumed asset lifetimes or depreciation schedules are needed to implement the suggested correction. Section 3 of the paper partially addresses the second and third objections raised to TELRIC pricing. We consider two stylized assumptions about asset replacement. Under one scenario, which we call “expected innovation date replacement,” we assume the physical life of an asset is effectively infinite, in the sense that technical advances make it obsolete before it suffers substantial physical deterioration, so that assets are eventually replaced due to technological advances. In the second scenario, which we call “light bulb performance,” we assume each asset has a fixed lifetime. In both scenarios, we derive cost minimizing investment plans over assumed planning horizons. These results are relevant to TELRIC cost studies and cost models generally in that they provide a method by which forward- looking capacity utilization factors (an important input in cost models) can be derived. Section 3 also shows how to compute efficient investment plans starting from existing capacity levels of an incumbent firm. To the extent that initial capacity levels can approximate the existing investment base of ILECs, these results may reconcile TELRIC price computations with “actual cost” computations favored by ILECs and some writers. Based on our derivation of efficient investment plans in the light bulb performance scenario, we also compare TELRIC pricing rules, as generally implemented, with prices defined by an efficient contestable entry criterion. This paper does not address the criticism, raised by some observers and ILECs, concerning the appropriate cost of capital to be used in calculations like those performed herein. Specifically, some 18 have argued that a competitive environment exposes ILECs to more risk than the former franchise monopoly environment. They argue that higher risk, including the risk associated with foregone option value when an investment is made, must be compensated through higher input values for the firm’s cost of capital. The analysis herein makes no judgments regarding these arguments. Throughout, we treat the cost of capital as an exogenous input that has been derived via some other analysis. Both sections 2 and 3 are based on extensive computations using Mathematica™, and details of the relevant programming code are available from the authors upon request. Some of the results of section 2 have appeared elsewhere in the academic literature, 19 18 See Hausman (1997). 19 See, for example, Biglaiser and Riordan (2000), Mandy (2002) and Salinger (1998). 9 12 Figure 4 compares TELRIC prices reviewed every three years with traditional prices based on straight- line depreciation. As Figure 4 indicates, TELRIC prices subject to three- year reviews understate traditional prices in every year. Note that neither traditional prices nor TELRIC prices computed at each review period account for the rate of decline of investment cost in future years. While this does not create a problem in the case of traditional pricing, since it is designed to recover the historical cost of the asset over its lifetime, it creates a problem for TELRIC computations subject to a three- year review. More specifically, the TELRIC computation ignores the impact of future cost reviews on prices during the life of the asset, instead incorrectly assuming the initial levelized TELRIC price will continue to be received for the entire life of the asset. Thus, while the TELRIC price computed in year 0 was computed to fully compensate the firm for its investment costs made in year 0, it does so only if maintained throughout the life of the asset. If prices are reduced in future years due to the lower investment costs at future TELRIC cost reviews, then the resulting price schedule no longer fully compensates the firm. 1 2 3 4 5 6 7 9 10 11 12 13 14 15 16 2.5 5 7.5 10 12.5 15 8 Figure 4. Traditional and Triennially Reviewed TELRIC Prices: Case of Decreasing Investment Cost Figure 5 compares TELRIC economic depreciation and straight- line depreciation. While in the benchmark analysis, depreciation under TELRIC pricing was increasing over time (see Figure 3), the economic depreciation identity (1) now reveals a secularly decreasing depreciation schedule under TELRIC that increases only within each review cycle. This is because the periodic reviews with decreasing investment cost produce TELRIC prices that fall fast enough in this example to more than offset the decelerated depreciation caused by levelization. 17 20 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 5 10 15 20 25 30 Figure 6. Traditional and Triennially Reviewed TELRIC Prices: Case of Increasing Investment Cost The economic depreciation implied by TELRIC, as shown in Figure 7, is now severely decelerated, to the point that it is negative in the early years after the investment. This is because the deceleration caused by levelization is reinforced by the decelerating effects of rising prices. Rising prices decelerate economic depreciation for two reasons. First, other things constant, economic depreciation is higher when prices are higher. Recall that economic depreciation is simply the change in the value of the asset from one period to the next. As equation (1) indicates, however, the drop in the value of the asset is equal to the revenue received in the period. 28 Thus, if prices rise, revenue will rise, which will increase depreciation. Second, as time passes discounting takes a progressively lighter toll on the present value of the as- yet unrealized relatively high late- life prices. Even with only 3 percent growth and triennial reviews, prices are so high at the end of thirty years compared to the initial prices (over twice as high) that the value- enhancing effect of moving them one year closer in time can be larger than the revenue actually received in an early year. Hence value can actually increase over time. An increase in value that occurs without additional investment is negative economic depreciation. This second factor is responsible for the negative economic depreciation observed in Figure 7. 28 Prior to time t, the revenue pt qt is in the asset’s future and therefore contributes to its value. After time t, however, the revenue pt qt is no longer in the asset’s future, so the asset must lose value pt qt at time t. 19 22 incumbent firm to recoup its costs and earn the target rate of return on a forward looking basis. Figure 8 illustrates both corrected (solid line) and uncorrected (dashed line) TELRIC prices compared to traditional prices (dotted line). The corrected TELRIC prices begin above but quickly fall below traditional prices, reflect the difference in three year versus one- year review, and have the same pattern as the uncorrected TELRIC prices. 1 2 3 4 5 6 7 9 10 11 12 13 14 15 16 5 10 15 20 8 Figure 8. Traditional versus Corrected and Uncorrected Triennially Reviewed TELRIC Prices: Case of Decreasing Investment Cost By construction, the corrected TELRIC prices also deliver the regulator's target cost of capital, equal to 11.25% in the present case. 2.7.2 Increasing Initial Investment Cost These same comparisons between traditional and TELRIC prices can be made when investment cost is increasing, using the parameter values in section 2.6. The TELRIC correction factor is now 0.802743. That is, assuming the parameter values in scenario 3 and a three year review period, TELRIC loop prices should be reduced by approximately 20% in order to allow the incumbent firm to recoup its cost and earn the target rate of return on a forward looking basis. The corrected TELRIC prices, again shown as a solid line in Figure 9, begin below but rise above traditional prices after less than one- third of the life, again reflect the difference between three- year versus one- year reviews, and again have the same pattern as the uncorrected TELRIC prices. 21 24 1 2 3 4 5 6 7 9 10 11 12 13 14 15 16 5 10 15 20 8 Figure 10. Contestable versus Corrected Triennially Reviewed TELRIC Prices: Case of Decreasing Investment Cost 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 12.5 15 17.5 20 22.5 25 27.5 Figure 11. Contestable versus Corrected Triennially Reviewed TELRIC Prices: Case of Increasing Investment Cost 2.8 Variable Utilization Rates All computations up to this point have assumed a constant utilization rate. If demand is growing, a cost- minimizing firm may make investments in anticipation of future growth, in which case utilization rates will increase as the asset ages. All of the definitions of previous sections are valid under these conditions, although the specific time paths of price and depreciation will change when utilization rates are not constant. However, when utilization rates are not constant, a discrepancy emerges between the TELRIC pricing rule (5) and the TELRIC prices actually calculated by cost proxy models, such as the FCC’s synthesis model. Specifically, the Synthesis Model uses average utilization to calculate the TELRIC price, rather than anticipating that utilization will change over the life of the asset. In addition, the size of the investment F0 is assumed 24 27 to be sufficient to satisfy current demand divided the utilization factor. These issues will be explored further in the following section. 31 In this section, we assume increasing investment cost using the same parameter values as in section 2.6, except that we assume a growing utilization rate given by qt = .40 + .55 t / (L- 1) for t = 0, … , L- 1. This utilization path models loops that are used at 40% of capacity when installed but whose usage increases linearly to 95% at the end of the thirty year life. Figure 12 below compares three separate price paths: traditional prices (solid line), contestable prices (dotted line), and TELRIC prices reviewed every three years (dashed line). The traditional prices still fall, as when the utilization rate is constant, but now they begin much higher and decrease faster. This is because the traditional rule only uses utilization in period t to calculate the price in period t, so the price must drop to offset growing quantity. This effect reinforces the downward slope caused by straight-line depreciation. In contrast, the contestable and TELRIC prices still increase over time because they take account of the entire utilization path to calculate the price at each time (see equations 5 and 7). Hence their dynamics are driven entirely by the growth rate of initial investment cost. Both paths are higher than under scenario 3, where utilization rates are constant, reflecting the fact that average utilization over the life of the asset is about the same as scenario 3 but revenues are delayed because utilization is initially low. 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 10 20 30 40 Figure 12. Traditional, Contestable, and Triennially Reviewed TELRIC Prices: Case of Increasing Investment Cost and Increasing Utilization As before, the TELRIC prices can be corrected so that they yield the same rate of return as the traditional and contestable prices. The correction factor in this case is 0.761538, which is not much different from scenario 3. The corrected TELRIC prices 31 In the present section, the function q has served both as a utilization rate and as a proxy for potentially varying demand conditions. When an efficient investment plan requires repeated investments made over a planning horizon, there is no longer a simple relationship between utilization rates and aggregate demand. In section 3, these issues are treated in a more general framework in which demand is the exogenous variable and utilization rates are determined through cost minimization. 25 28 (solid line) again track the contestable prices (dotted line), as shown in Figure 13, and as expected, the corrected prices yield the target rate of return of 11.25%. 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 15 20 25 30 Figure 13. Contestable and Corrected Triennially Reviewed TELRIC Prices: Case of Increasing Investment Cost and Increasing Utilization We note in conclusion that these results demonstrate that demand growth as well as changing investment cost must be considered when setting a time path of prices. 32 Generally, a firm’s utilization rate at any point in time is determined by a solution to a cost minimization problem. The cost minimum determines the time and level of investments needed to satisfy demand at every future point in time. It may very well involve intentional under- utilization that varies over time. We consider some of these issues in the next section in a framework in which efficient investment decisions can be determined when the rate of demand growth is explicitly modeled, and a more general investment cost function is introduced. 3. Efficient Dynamic Investment Section 2 was concerned with the time path of TELRIC prices that could be used to recover the cost of an arbitrary investment F0 that has an arbitrary utilization path qt. There, it was assumed the investment cost and utilization path had already been determined. Actual investment cost and utilization of assets subject to TELRIC pricing result from decisions made by incumbent suppliers. An efficient supplier makes such decisions to minimize the cost of serving an evolving expected demand, given the expected costs of raw inputs, the expected evolution of those costs, the expected performance of the assets over time, the cost of capital and other input prices. These are dynamic cost- minimizing investment decisions. 32 While the asset’s utilization rate has been allowed to vary in the present section, the aggregate level of capacity has remained constant at a normalized value of one unit. 26 29 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 t 20000 21000 22000 23000 24000 25000 26000 27000 Capacity Figure 15. Demand and Efficient Capacity, Benchmark Case Switching Scenario 2.5 5 7.5 10 12.5 15 t 0.02 0.04 0.06 0.08 0.1 0.12 0.14 Percent Excess Capacity Figure 16. Percent Excess Capacity, Benchmark Case Switching Scenario Table 1 summarizes the results for various parameterizations. The benchmark parameterization is in row 1. Subsequent rows report only those parameters that differ from the benchmark. The second row, which may be interpreted as an incremental cost calculation, shows the optimal investment plan if initial demand is only 80% of initial capacity. This initial excess capacity is adequate to satisfy demand until year 11.2, at which time efficient investment installs exactly enough capacity to satisfy demand through the end of the horizon. Costs are much lower than in the benchmark plan, because the initial excess capacity both reduces the need for new investment and forestalls the time of that investment. The third row examines the effect of a change in the cost of capital. It shows that the optimal plan places heavier emphasis on delaying investment costs rather than exploiting scale economies when the cost of capital is higher. This delaying tactic, along with the pure discounting effects of a lower discount factor, reduces the present value of the plan compared with the benchmark even though the total cash outlay is higher. The fourth row shows how a 50% delay in the innovation date affects the optimal investment plan. The second investment is accelerated slightly and a 31 34 10 20 30 40 50 60 t 0. 05 0.1 0. 15 0.2 0. 25 0.3 Percent Excess Capacity Figure 19. Percent Excess Capacity, Benchmark Case Loop Scenario Table 2 presents results when some of the benchmark assumptions are modified. 43 As the cost of capital rises, it becomes more expensive to have units of unused capacity and the present value of future investment costs is reduced. As a result, there is a reduction in the size of the initial investment and a corresponding acceleration in the time that subsequent investments are made. When investment costs are assumed constant, instead of increasing at the benchmark rate of 3% per year, the size of the initial investment is again reduced modestly. If the life of the asset is 15 years, substantially less than in the benchmark case, it is efficient to invest as infrequently as possible under the light bulb replacement scenario. The cost minimizing investment plan then consists of investments made at 15 year intervals with no intermediate investments. If there is existing capacity from previous investments at time t = 0, then the time of initial investment is delayed until demand growth exhausts the initial capacity. In this situation, the cost minimizing investment plan of an efficient firm should take account of these initial investments. However, the timing of subsequent investment decisions will not, in general, have a simple relationship to the time that existing investments were made. 44 The last row of Table 2 and Figure 20 describe the efficient investment program for one possible set of initial conditions. 43 In this table only we use the notation F j = F( Ij , Tj). 44 Note that the optimal investment plan illustrated in Figure 20 has existing assets retired at times t = 10, 15, 25, and even as late as year 55, without any corresponding new investments at those times. Thus, initial capacities can have a substantial impact on the firm’s capital stock even after many years have elapsed. 36 39 10 20 30 40 50 60 t 10000 15000 20000 25000 30000 35000 Capacity Figure 20. Demand and Efficient Capacity, Loop Scenario With Initial Installed Capacity at Time t = 0 3.4 Implications for TELRIC Pricing Let us now consider some implications of the “light bulb” efficient investment results for TELRIC pricing. TELRIC pricing rules have traditionally been defined in an environment in which little or no account is taken of market dynamics. In particular, current TELRIC pricing rules are generally defined without reference to either expected changes in future investment cost or expected changes in future demand (or utilization rates). In section 2.7 we illustrated how a simple multiplicative correction factor could be defined to take proper account of changing investment cost. Under corrected TELRIC pricing, a regulated firm would exactly recover its forward looking investment cost, even if TELRIC price reviews occur at intervals shorter than assumed asset lifetimes. In section 2.8, it was similarly demonstrated that varying utilization rates, which could result from cost minimizing decisions made in the face of growing demand, could be easily incorporated into the TELRIC pricing rule. Sections 3.2 and 3.3 have focused on another aspect of efficient investment planning in a dynamic environment. In these sections, a cost minimizing investment program was explicitly calculated in a variety of circumstances. In order to complete our analysis, it only remains to demonstrate how these cost minimizing investment decisions can be used as inputs into a fully efficient forward looking pricing regime. In the case of assets having light bulb performance characteristics this process is relatively straightforward. The TELRIC prices for a sequence of investments made as part of an optimal investment plan now depend on the demand conditions at the time at which the investment occurs. 45 With this modification, equation (5) of section 2 is repeated using notation of the current section as equation (10): 45 In section 2, utilization rates, which play the same role as aggregate demand in section 3, were generally assumed to be constant. In the case of growing utilization rates discussed in section 2.8, the utilization rate path was assumed to be based on the time of investment rather than calendar time. 38 41 under a previous regulatory compact. Details of possible additions for embedded costs, that preserve incentives for efficient entry and exit, are left for future research. 4. Concluding Comments The objective of this paper has been to evaluate the use of static cost proxy models in setting forward- looking prices such as the prices set according to TELRIC. Section 2 compared the time paths of prices and depreciation under traditional regulatory accounting with the prices and depreciation implied by various versions of TELRIC. Under levelized TELRIC pricing, where prices are assumed to remain constant for the entire economic life of an asset, both prices and implied depreciation schedules follow significantly different trajectories than under traditional regulation. Under both pricing rules, however, the firm earns revenues that fully recover investment costs and a target rate of return. When TELRIC prices are recomputed at intervals shorter than asset lives and investment costs change over time, however, the firm will generally not earn the target rate of return. In these cases, a correction factor must be applied to the TELRIC price path in order for revenues to exactly recover investment cost, including the target rate of return. When investment costs are falling by 11% per year (as is assumed for switching assets in the FCC Synthesis Model), the TELRIC correction factor is approximately 50%. That is, switching prices should be increased by 50% from those suggested by Synthesis Model runs. When investment costs are rising at the rate of inflation, assumed to equal 3% per year, the TELRIC correction factor is -20%. In this case, TELRIC prices should be reduced by 20% from those suggested by model outputs. Section 3 of the paper considered a firm’s cost minimizing investment decisions over time. Two different assumptions about asset lives were analyzed. Under one scenario, characterized as “light bulb” performance, assets have a fixed and known physical life. In a second scenario the assets last forever, but due to technological change it is assumed that they will be replaced by a new generation of assets regardless of the date at which the original assets were put into service. 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