Power of Incentives and Optimal Time of Investment in a Building-Blocks Approach to Regulation of an Open-Access FTTH Network

Beltrán, Fernando

doi:10.5325/jinfopoli.12.2022.0011

ABSTRACT

New Zealand’s amended Telecommunications Act, 2018 New Regulatory Framework, describes new regulations primarily based on regulation already used in electricity lines, gas pipelines, and airports. This regulatory approach, new to the telecommunications sector and known as the Building Blocks Model (BBM), seeks to determine “price-quality paths” and “information disclosure determinations” based on the condition that the present value of the firm’s allowed revenue is equal to the present value of the firm’s expenditure. This article investigates the impact of the incentive structure on the regulated firm’s investment behavior. More specifically, it models and analyses the incentive structure provided by the implementation of BBM in the wholesale fiber-based broadband market of New Zealand, as well as its effects on the timing of investment.

fiber-to-the-home, Building Blocks Model, power of incentives, time of investment

Background

The use of the forward-looking costs over the long run of the total quantity of the facilities and functions that are directly attributable to the service an efficient operator, known as TSLRIC or Total Services Long Run Incremental Cost, has been viewed as assisting the achievement of several objectives including incumbents’ decisions on technology choices and also competitors’ decisions on efficient ways to bypass the incumbent’s network.

On the other hand, common in Australia and New Zealand, the Building Blocks Model (BBM) methodology is used in regulating electricity transmission and distribution, gas transmission and distribution, railways, urban water and sewerage services, and port access. BBM is a regulatory tool that assures the regulated firm a path of revenues or prices by spreading its expenditures over time. It aims to ensure that the net present value of the firm’s cash-flow stream equals zero. BBM can be forward-looking when it contemplates expected expenditures. As long as it does not direct the firm to specific operating costs, BBM may establish a benchmark forecast that signals the efficient expenditure path.

Following suit with dissatisfaction about its practicalities, including a conclusion that the TSLRIC methodology involves too much arbitrariness at the expense of predictability, the New Zealand government’s review of its Telecommunications Act has already changed the method of regulation of fixed-line telecommunications to the BBM methodology. In New Zealand’s case, the government has introduced amendments to the Act, largely adopting existing BBM regulatory guidelines and decisions that currently apply to electricity lines and airports.

BBM is to be applied to the nationwide fiber-to-the-home (FTTH) network known as the Ultra-Fast Broadband (UFB) network, reaching 85% of premises in its tenth and final year of construction. A major fixed-line network provider and three new fiber companies, all known as Local Fiber Companies (LFCs), with the assistance of government financing, undertook the construction of the network as each company was designated as the sole government-assisted UFB fiber provider for specific, nonoverlapping geographical regions after submission of competitive bids.

Conditions imposed on the new fiber networks limit them to the wholesale market by prohibiting the sale of services to end-users. Instead, they must sell wholesale access to any service retailer that wants to operate end-user services on the UFB network. The technical and regulatory conditions imposed on the fiber networks turn them into open-access broadband platforms.

The initial pricing of wholesale services, negotiated with the LFCs and standing from 2011 up until 2020 and extended to 2021, was covered by the contracts under which financial assistance was provided. The NZ government has recently decided that after the initial period, the pricing of the fiber services by the monopoly provider in each region will be regulated by a BBM regulatory framework. In the context of such a transformed telecommunications market in which the four regional LFCs (open-access, monopolistic broadband platforms) provide access to telecommunications services by competing retailers, this article analyses the incentives provided by such a BBM regulatory methodology, using available consultation papers and some final decisions already made by New Zealand’s Commerce Commission (Commerce Commission 2020) in the process of establishing the full regulatory framework. Ultimately, this work aims to identify the conditions and regulatory decisions that lead, as claimed in the promulgation of the review of the Act, to limit the sources of uncertainty to the regulated firms and consumers.

The literature on the regulation of monopolistic utilities is extensive and well known. In their seminal article, Averch and Johnson critiqued the application of rate-of-return regulation. Train (1994, 40) establishes several results by introducing a model for the behavior of the monopolistic regulated firm that enhances the analysis and contributes several results. Among them are that the regulated firm uses more capital than the unregulated firm and that the regulated firm’s output “could be more cheaply produced with less capital and more labor than the regulated firm chooses” (40). In other words, the regulated supplier has an incentive to invest more than is socially optimal. Such investment increases the regulated asset base and thus the allowed price to provide a return on the increased base. Unless constrained by the regulator, an excess investment could continue until the price reached the level an unregulated monopolist would charge.

A regulated supplier can be incentivized to constrain both operating and capital expenditure by switching to incentive regulation in which price or revenue caps are set ahead of time for a regulatory period (the caps being set at levels forecast to provide a normal return) with the supplier retaining all or part of any cost savings achieved.

The determination of the price caps under incentive regulation can be either independent of the past costs experienced by the regulated supplier for example, the regulated asset base can be TSLRIC, or based on comparators, or reflect historical costs, as is typical under the BBM approach. Price or revenue caps independent of the supplier’s actual costs (sometimes described as “price-based” incentive regulation) in principle better promote static efficiency but at the cost of potentially delaying or indeed suppressing investment and, therefore, “dynamic” efficiency. The alternative is one form or another of (historic) cost-based incentive regulation.

Since the advent of incentive regulation, several analyses have articulated critiques of price-based incentive regulation. Guthrie, Small, and Wright (2006, 1769) argue that, given demand uncertainty, forward-looking price rules or price-based incentive regulation is inferior to backward-looking price rules or cost-based incentive regulation whenever investment is desired. With telecommunication equipment costs falling rapidly, regulators favored forward-looking cost rules as likely to result in cost reductions benefiting end-users. Thus, the assessment was that argument in favor of backward-looking price rules was outweighed by the expected cost reduction benefits of forward-looking price rules (1783).

Two factors have subsequently been important in encouraging a switch from forward-looking price rules (price-based incentive regulation) toward backward-looking (historic cost-based incentive regulation). The first factor is the shift in focus to encouraging investment in fiber networks which involve very large infrastructure investments, and the second is, as noted earlier, disenchantment with the complexities and uncertainties of TSLRIC and other forward-looking price rules.

Reflecting this shift in focus, Borrmann and Brunekreeft (2020) point to the short-term, cost-reducing characteristics of price-based regulation in contrast to the current needs of firms in the electricity as well as the telecommunications sectors that face cost-increasing investments. They imply that this situation requires a renewed approach to long-run, cost-based incentive regulation.

The latter claim can be fully appreciated as one reviews the contents of two survey articles that have recently appeared in the literature on broadband investment and regulation. In their review of the literature on the regulation of broadband networks, Cambini and Jiang (2009) state their article’s commanding question: “what impacts does regulation impose on firms’ investment behavior in broadband communications, impetus or hindrance, and how should regulatory regimes be designed to foster the incentive to invest?” The second article by Briglauer et al. (2015), on the other hand, reviews the theoretical and empirical literature on alternative policies that promote the deployment of new high-speed broadband infrastructure as it is expected that investment in such networks induces substantial positive externalities. Their analysis is based on three alternative policies, particularly cost-based access regulation, among several “sector-specific” regulations.

The rest of this article unfolds as follows: section “The Ultra-Fast Broadband Network” gives a historical perspective of New Zealand’s UFB network, whereas section “New Regulatory Framework in New Zealand” provides the elements to understand the new regulatory apparatus passed as an amendment to the Telecommunications Act in 2018. Next, building on Biggar (2004), section “BBM in New Zealand” explains the foundations of the BBM, emphasizing the revenue and asset-based roll-forward equation. Section “Optimal Time of Investment” discusses the Input Methodologies (IMs), the processes determining the entries to the BBM equations mentioned above. In section “Conclusions” the article closes.

The UFB Network

Broadband access encompasses the deployment of a range of technologies. FTTH is favored by several worldwide projects whose main goal is to bring higher speed and reliability to consumers. As access to a broadband connection has been deemed essential/fundamental to citizens of a country, some governments embark on improving and expanding the reach of current communications facilities by means of regional or nationwide broadband plans. The deployment of fiber-based access networks has seen a return of the government’s role in their financing and construction. In Australia, by purchasing the network, and in New Zealand by means of a mixture of public initiative and private entrepreneurship, known as Public–Private Partnership (PPP), respective governments have stepped into the FTTH broadband markets, becoming owners or co-owners and operators of the facilities the wholesale fiber connections to retail companies serving end-users.

In 2009, New Zealand created Crown Fiber Holdings (CFH)—today known as CIP or Crown Infrastructure Partners, a company charged with managing a PPP between the government and four LFCs—Chorus, Ultrafast Fiber, Northpower and Enable Services Ltd., for the deployment of FTTH-based network to 75% of the population. This project, referred to as UFB, is complemented by the Rural Broadband Initiative (RBI). This second infrastructure project covers 22.8% of households with alternative technologies (VDSL, fixed-wireless, satellite) (Beltrán and Van der Wee 2015, 99). CFH and the LFCs signed agreements to lay a fiber backbone in urban centers across the country. The main aspects of the signed contracts can be summarized as follows (101):

LFCs must deploy a Gigabit Passive Optical Network (GPON) and offer Layer-2 bit-stream access to all service providers on equal terms.
The network should also be capable of offering Point-to-Point (P2P) access on request (albeit for a relatively high price).
Unbundling of the Layer-1 infrastructure (dark fiber access) should be possible from 2022 onwards.
Wholesale offers are fixed in terms of download and upload speed (30/10 and 100/50 Mbps) and price.
The deployment should be focused on priority users first (e.g., schools, hospitals, and large businesses); residential homes are targeted in a second stage.

The RBI aims to improve the conditions of connectivity and access to broadband services for less densely populated areas. Costs incurred in deploying FTTH to each home in those areas would have been prohibitively high, so an alternative solution had to be found. CFH also negotiated with the established companies to upgrade the network in those locations. The main aspects of the deployment are (MBIE 2021):

connecting 252,000 rural households (about 90% of homes and businesses outside UFB areas),
with speeds of at least 5 Mbps by 2016 through a mix of VDSL and fixed-wireless services.

The two mobile operators, Spark and Vodafone, selected as RBI partners, deployed fiber to cabinets and improved copper-based broadband (VDSL and ADSL, respectively) and upgraded towers and transmitters to provide fixed-wireless service, respectively.

In early 2015, the UFB and RBI initiatives described above were renamed Phase 1 to distinguish them from plans to extend their scope by increasing the percentage of New Zealanders able to access fiber technologies from 75% to least 80% of households. Additional funding of up to $210 million for the UFB extension and $100 million for the RBI extension has been announced. In 2019, Phase 1 was completed.

With more than 1.19 million businesses, schools, health centers, and homes who can connect to the network as of early 2021, the UFB network is one of the largest infrastructure projects ever undertaken in New Zealand, covering over 340 towns. Completion of the whole project, including the second stage, is expected by 2022. Once completed, it is expected New Zealand will advance in the OECD country rankings for population coverage with fiber available from 14th in 2015 into the top five in the OECD for fiber availability (CIP 2021).

New Regulatory Framework in New Zealand

The government’s review of the 2001 Telecommunications Act delivered a new regulatory framework largely based on the Commerce Act of 1986, Part 4, which regulates utilities such as electricity lines, gas pipelines, and airports (NZ Government 2021). The new framework is aimed to regulate Fiber Fixed-Line Access Services FFLAS.

Technically, and according to Part 6 of the Telecommunications Act, FFLAS means “a telecommunications service that enables access to, and interconnection with, a regulated fibre service provider’s fibre network,” excluding the provision of such service by a regulated provider to itself or a related party of the provider and services provided, on any part but the end-user’s premises, over a copper line. The Commission has also stated that, in their view, FFLAS can extend “beyond the boundaries of the fibre network” but is careful to stress that “enabling access to . . . a fibre network” needs to be understood in a narrower sense than that used in the definition of telecommunication services.

Such intent on producing a balanced inclusion is visible in the Commission’s decision on services such as DFAS^¹ and ICABS^² which are both FFLAS, as well as acknowledging that the policy intent is to also include services that extend past the point of aggregation. The service candidates to be considered FFLAS are voice services, bit-stream PON services, unbundled PON services, point-to-point services, transport services, co-location and interconnection services, and connection services.

Regulation is to be achieved by using “price-quality (PQ) paths” and “information disclosure (ID) determinations.” Under PQ regulation, the regulators must determine the maximum revenue and/or prices the operator is allowed to earn from its FFLAS (known as PQ FFLAS) and the minimum quality at which they are to be provided. Under ID regulation, regulated providers must disclose the information about their FFLAS (known as ID FFLAS) that will allow the Commission to assess whether regulatory objectives are met.

Who is to be regulated by these two? Chorus, the largest telecommunications company in the country and the owner of all fixed-line copper connections, is to be regulated by both PQ and ID regulations. In contrast, the other three LFCs will be regulated through ID only.

The new framework has been introduced with several purposes in mind; they are:

promoting competition for the benefit of end-users;
promoting the legitimate commercial interests of access providers;
encouraging efficient investment;
supporting innovation in telecommunications markets or deregulation where sufficient competition exists.

The purpose of the new regulatory framework rests on two sections of Part 6: Section 162 and Section 166b. Section 162 introduces the concept of a “workably competitive market” and uses it to state that regulation must promote outcomes consistent with outcomes produced in workably competitive markets. On the other hand, Section 166 mandates that, in promoting competition, the Commission take into account the interests of end-users of telecommunications market services, directing the Commission to promote workable competition in the markets.

When implementing PQ paths and ID determinations, the Commission will follow the BBM approach. The next two sections discuss, in general terms and as intended to be applied in New Zealand, the elements, components, and incentives in the BBM approach.

BBM in New Zealand

Biggar (2004) defines the BBM approach to regulation as “a tool for spreading (or amortizing) the expenditure of the regulated firm over time so as to ensure a path of revenue or prices which has the property that the present value of the firm’s allowed revenue is equal to the present value of the firm’s expenditure.”

BBM regulation is based on the valuation of the asset base by assessment of the actual historic costs incurred by the regulated operator upon deployment of its network. The resulting value of the asset base is usually referred to as the Regulatory Asset Base (RAB).

The BBM regulation is a form of “incentive regulation” in which the regulated entity is constrained by requiring that either its weighted average price or revenue complies with a cap specified by the regulator and that quality requirements are met. In New Zealand, the regulatory constraints are referred to as PQ (or path-quality) paths, as introduced in section “New Regulatory Framework in New Zealand”.

Biggar summarizes BBM in two equations: the Revenue equation and the Asset-based Roll-forward equation.

The Revenue equation can be stated as follows:

R_{t} = r_{t} K_{t - 1} + O_{t} + D_{t}

[1]

while the Asset-based Roll-forward equation is written as:

K_{t} = K_{t - 1} + I_{t} - D_{t}

[2]

where—the subscript t refers to the current period (say, a given year); R is the maximum allowed revenue; r is the rate of return on capital; K is the RAB (at the end of the period); O is the operating expenditure, and D is the depreciation or “return of capital.” In addition, I is the capital expenditure. The equations are complemented with a boundary condition that states that if at period T the firm ceases to exist, the RAB at the end of that period is zero, that is, K_T = 0.

As can be appreciated, once one path is determined, that is, either $K_{t}, D_{t},$ or $R_{t}$ ⁠, Equations [1] and [2] and the boundary conditions can be used to find the other two. The latter allows us to see how a regulator using a BBM approach would set the revenue path so that, in particular, incentives are built into the resulting investment path that determines the future asset base.

A crucial component of this estimation is the determination of the asset base on which a normal return will be calculated. Under BBM regulation, investment undertaken by the regulated entity during the regulatory period is added to the RAB at the beginning of the next regulatory period (subject to a test of the efficacy of that investment in some types of BBM regulation).

The redetermination of the PQ path for the next regulatory period provides for a normal return on the RAB, including the addition corresponding to investment during the previous period and taking into account a forecast of operational expenditure (and in the case of a weighted average price path a forecast of demand).

Biggar’s work develops a framework for incentive regulation under BBM, which is aimed to gather ad-hoc approaches to incentive regulation adopted by regulators around Australia under a single conceptual umbrella. The framework is intended to provide insights into the role of the Asset-based Roll-forward method in determining incentives and the distinction between recurrent expenditure and nonrecurrent expenditure—as opposed to the traditional view of operational costs and investment expenditures.

The incentive characteristic of this type of regulation is that the regulated entity retains part or all of any cost savings it achieves relative to the price or revenue caps. Thus, the management of the regulated entity has an incentive to seek efficiency gains by way of cost savings. The implementation of such savings reveals to the regulator the extent of achievable efficiency improvements. This can then be taken into account when the PQ price is redetermined. The redetermination of the PQ path is based on an estimation of the price or revenue path that would provide the regulated entity with a normal return taking into account the forthcoming regulatory period and the expected future PQ path in future periods.

BBM in New Zealand: The IMs

The New Zealand Commerce Commission New Regulatory Framework (Commerce Commission 2020) adopts the BBM approach already used in the regulation of electricity lines, gas pipelines, and airports. In such sectors, notably, the regulator is required to develop and publish full details of the specifics of its BBM methodologies, also known as IMs, introduced in section “New Regulatory Framework in New Zealand”, as a preliminary step in applying regulation.

In essence, setting a maximum revenue allows the provider subject to regulation to ex-ante earn its allowed return. This is the best estimate of a normal return, that is, an estimate of the return that an efficient operator has the opportunity to earn in a workably competitive environment. Higher efficiencies will allow the provider to earn higher profits, which will be shared with end-users as lower prices in the next regulatory period.

Part 6 of the Telecommunications Act has determined that a revenue cap will apply for the first two regulatory periods. The first regulatory period will last for 3 years. Part 6 also commands the Commission to perform a PQ review and make recommendations not before three years after the new regulatory framework is first implemented on January 1, 2022. Any determination on maximum prices will only be made as early as some time during the second regulatory period, which means that price regulation of FFLAS will only start in the third regulatory period.

PQ regulation is a revenue cap with a “wash-up” mechanism for the first period. Individual caps will apply to anchor services and DFAS (Layer 1 point-to-point lines). Anchor services, the basic services Chorus provides, are 100/20 Mbps broadband and voice, and their maximum prices or the maximum revenue generated for Chorus, as well as the quality, are determined by the Commission.

The IMs are regulatory rules, requirements, and processes that support the Commission’s specific choice of regulation of FFLAS. One of the most important aspects of the introduction of IMs is their intended role in promoting certainty for regulated fiber service providers, access seekers, and end-users. The IMS are applied when the Commission makes its PQ and ID determinations. The IMs determined by the Commission and their intended use are:

the cost of capital, which defines how the WACC will be determined;
the asset valuation, which dictates how to value the regulated provider’s assets used to provide FFLAS;
the cost allocation, which determines how asset values and operating expenses are allocated between regulated and nonregulated services;
tax;
Chorus capex, which defines requirements and processes supporting the evaluation of Chorus’ capital expenditure projects; and
regulatory processes and rules, which specify and define the revenues.

Components of the BBM

In New Zealand, the Commerce Commission released its proposed PQ-path approach that would start to be applied from January 1, 2022 (Commerce Commission 2021). Figure 1 shows the current Commerce Commission’s proposed components (blocks) to be included in its calculation of RAB and the BBM revenue applicable to Chorus.

The Commission released several determinations, which refer to decisions on the values of specific blocks for the first PQ regulatory period, PQP1. Figure 1 shows explicitly the components of the two regulatory foundational equations as well as the way the return on capital is calculated. For PQP1, since Chorus did not forecast any asset disposal, the value of Disposed Assets is zero. Also, on the BB revenue equation, Revenue Smoothing will only be applied on period PQP1, consisting of increases by forecasts of weighted average demand growth (proposed by Chorus) and the latest Consumer Price Index by the Reserve Bank.^³ Also, Tax Allowance has been set to zero for every year of the period PQP1.

FIGURE 1

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Calculation of the revenue cap using the BBM approach (Source: Commerce Commission 2021).

Some assets used in the production of digital telecommunications services are at risk of suffering from unanticipated or premature devaluations, which are usually caused by technology upgrades. This type of risk is considered non-systematic as it relates to technological change and asymmetric due to the operator’s inability to set a floor that responds to the decrease in value of the asset. The Commission has signalled its intention to provide some mode of compensation to the operator. The compensation is intended to be a combination of retaining the stranded assets in the RAB and allowing for the possibility of shortening the economic lives of assets. The compensation also combines an ex-ante allowance to be implemented through cash flows at the time of setting the PQ path. However, in consideration of the Commission, the regulated provider will have to bear some of the risk associated with the stranded assets.

A Model to Estimate the Power of an Incentive Under BBM

In the context of a 1-year regulatory period, we start off from a scenario where incentives are absent, known as the Financial Capital Maintenance (FCM) scenario, defined as the situation where the net present value of the operator’s revenue stream is equal to that of its expenditure stream.

What is then the scope for incentive regulation within the constraints provided by applying the BBM methodology? The regulator needs to establish opex and capex forecasts and the revenue cap. It then uses the forecast revenue to roll forward the RAB and determine the closing RAB at the end of a period accounting for the deviations introduced by the difference between forecasts and out-turns.

Consequently, if the regulator estimates forecast levels of opex ${\hat{O}}_{t}$ and capex ${\hat{I}}_{t}$ at the beginning of the regulatory period, and a forecast level of depreciation ${\hat{D}}_{t}$ that depends on the forecast capex, to determine the forecast maximum revenue ${\hat{R}}_{t}$ ⁠, Equation [1] becomes:

{\hat{R}}_{t} = r_{t} K_{t - 1} + {\hat{O}}_{t} + {\hat{D}}_{t}

[3]

Likewise, when the regulator learns the actual levels of opex $O_{t}$ and capex $I_{t}$ ⁠, the RAB is rolled forward to determine the closing RAB for the period. Thus, Equation [2] turns into:

K_{t} = K_{t - 1} + I_{t} - {\hat{D}}_{t} + (O_{t} - {\hat{O}}_{t}) + (R_{t} - {\hat{R}}_{t})

[4]

Some regulators may decide to “carry over” any gains the firm may have realized from the previous period onto the next one. On the other hand, the discrepancies incurred between the forecast capex and the realized capex may have to be accounted for somehow by the regulator. The former can be represented by an additive term in Equation [3], whereas the latter can be accounted for as an additive term of the asset-based roll-forward Equation [4]. Both quantities are instances of departure from the FCM condition that allow the regulator discretionary intervention to introduce incentives that induce the firm to reduce costs.

Departing from FCM by allowing higher revenues in period t as in Equation [3] requires using the future value—value at the end of period t using the rate r_t, of the amount $X_{t - 1}$ established in the previous period, t − 1. Further, accounting for any difference in forecast and out-turn capex requires adding an amount $Y_{t}$ to the Equation [4].

Appendix 1 shows what Equations [3] and [4] result in, respectively,

{\hat{R}}_{t} = r_{t} K_{t - 1} + {\hat{O}}_{t} + {\hat{D}}_{t} + (1 + r_{t}) X_{t - 1}

[5]

K_{t} = K_{t - 1} + I_{t} - {\hat{D}}_{t} + (O_{t} - {\hat{O}}_{t}) + (R_{t} - {\hat{R}}_{t}) + Y_{t}

[6]

Building upon Biggar’s approach (Biggar 2004, 9), we would like to understand how the regulator’s departure from the FCM condition affects the discounted value of the firm’s future profit stream. This relation will help us then move forward with the main question this chapter addresses, which is about the scope and effect of incentives on the cost reduction behavior of the firm. The operator’s profit stream from t to a future certain time T is:

π_{t} = \frac{K_{T}}{\prod_{i = t}^{T} (1 + r_{i})} + \sum_{s = t}^{T} \frac{R_{s} - O_{s} - I_{s}}{\prod_{i = t}^{s} (1 + r_{i})}

[7]

where $K_{T}$ is the amount of the RAB accrued to its investors if the operator ceased to exist at the future time T.

In order to establish how any regulatory intervention on the FCM condition, as stated above, will impact the operator’s bottom line, it will be convenient to state how the operator’s profit stream relates to the amounts by which each BBM equation is altered.

Appendix 1 demonstrates that the operator’s profit stream is

π_{t} = \sum_{s = t}^{T} (\frac{X_{s - 1}}{\prod_{i = t}^{s - 1} (1 + r_{i})} + \frac{Y_{s}}{\prod_{i = t}^{s} (1 + r_{i})}) + K_{t - 1}

[8]

As seen, Equation 8 establishes that the profit stream is the sum of boundary expressions for the RAB at the time limits of the discounted value and the sum of the streams of possible regulatory interventions.

Remember that our approach, following Biggar, is to understand how the regulator can depart from FCM to provide incentives to the regulated operator.

In order to make progress on such endeavor, let us assume that if at period t the regulator decides (or needs) to increase the allowed level of revenue—the X amount in Equation 5, this only depends on opex (actual or forecast) of period t. Likewise, if at period t the regulator decides (or needs) to intervene on the difference between actual and forecast capex—the Y amount in Equation 6, this only depends on capex (actual or forecast) of period t.

In addition, the regulator expects the operator to reduce costs (opex) and keep the level of its investments (capex). Cost reductions can be passed on to users as better prices, and investments are necessary to keep the quality of services (QoS) provided. In general, if $E$ represents any of opex (⁠ $O$ ⁠) or capex (⁠ $I$ ⁠), and $\hat{E}$ represents the corresponding forecast expenditure (opex or capex), we will follow Biggar to assume that at period t, any regulatory intervention amount deviating from FCM only depends on actual $E_{t}$ and forecast ${\hat{E}}_{t}$ expense of period t. Also, a simplifying assumption is that any forecast expenditure ${\hat{E}}_{t + 1}$ (target expenditure) depends exclusively on the most recent actual expenditure, $E_{t}$ ⁠, and not on previous expenditures, that is, ${\hat{E}}_{t + 1} = {\hat{E}}_{t + 1} (E_{t})$ ⁠.

It is then convenient to our objective of investigating how incentives impact the operator’s profit stream to express such relation by means of calculating the derivative of the profit stream at period t with respect to any expense, as represented by $E_{t}$ ⁠. If $Z_{t}$ represents any of the two amounts the regulator would allow as departures from FCM, and $E_{t}$ is its corresponding expense type (for instance, a higher level of revenue to cover unexpected operational expenses), Appendix 2 demonstrates the following result:

\frac{d π_{t}}{d E_{t}}_{} = \frac{1}{(1 + r_{t})} \frac{\partial Z_{t}}{\partial E_{t}} + \frac{1}{(1 + r_{t}) (1 + r_{t + 1})} \frac{\partial Z_{t + 1}}{\partial {\hat{E}}_{t + 1}} \frac{d {\hat{E}}_{t + 1}}{d E_{t}}

[9]

Equation 9 reveals that a change in the expenditure affects profits through its direct effect on the amount $Z_{t}$ that the regulator has decided to depart from FCM, and an indirect effect through the forecast expenditure, ${\hat{E}}_{t + 1}$ ⁠. As shown in the second term of [9], the power of incentive to reduce expenditures also depends on the effect that actual expenditure has on the next-period forecast expenditure and the effect of such next-period forecast expenditure on the present value of profit (either through the revenue equation or the asset-based roll-forward equation).

Power of Incentives

A regulator introducing the BBM approach, or any other regulatory scheme, can opt for using incentives to steer the operator to maintain or increase the QoS for a service or collection of services. One major regulatory concern is to identify how effective an incentive can be. In other words, the regulator is concerned with the “power of the incentives.” The power of the incentive of a regulatory scheme to achieve a regulatory objective depends on the value of the derivative of the present value of the operator’s profit stream to the change in effort exerted on maintaining or raising such objective.

We first turn our attention to the power of incentives to maintain the QoS. As a function of the QoS provided, the power of incentive to achieve a given level of QoS can then be expressed as

\frac{d π_{t}}{d Q_{t}}_{}

which, recognizing the relationship found between the profit stream and the level of opex at a period t, can also be expressed as $\frac{d π_{t}}{d O_{t}} \frac{d O_{t}}{d Q_{t}} .$ We can simplify the analysis and assume a linear dependency of the operational expense O on the QoS level so that we can assume that $\frac{d O_{t}}{d Q_{t}}$ = 1. In this case, we would focus on $\frac{d π_{t}}{d O_{t}}$ ⁠, which is exactly what Equation 9 calculates.

We now turn to investigate the exact form of the power of incentives to reduce expenditures in a BBM regulatory model. We have assumed that $Z_{t}$ only depends on actual $E_{t}$ and forecast ${\hat{E}}_{t}$ ⁠, so at first sight, we need to state how the deviation $Z_{t}$ from FCM is related to both the forecast expenditure ${\hat{E}}_{t}$ and the actual expenditure $E_{t}$ ⁠. A common choice is to let $Z_{t}$ be the difference between ${\hat{E}}_{t} and$ $E_{t}$ ⁠, that is, $Z_{t} = {\hat{E}}_{t} -$ $E_{t}$ ⁠. This is observed in the regulator’s setting up the revenue equation to account for the deviation of the actual expenditure from its forecast.

Next, let us recall our assumption that the regulator’s forecast expenditure depends somehow on the expenditure of the same kind from the previous period. One interesting case arises when the regulator considers that as long as the time t expenditure does not reach a certain threshold, the forecast expenditure is independent of it; otherwise, the forecast expenditure is based on the difference between the actual period t expenditure and the threshold; this situation is detailed in scenario 1 below. A common approach is that the forecast expenditure is exactly the same as the current expenditure, as in scenario 2 below. Finally, as in scenario 3, let us consider the forecast expenditure’s necessity to account for the error incurred when the actual expenditure, at period t, is compared to the expenditure that had been forecast for the period; this is basically a way to compensate for the discrepancy between actual and forecast values, which may have impacted the profitability of the operator. The rationale for each scenario attends to a particular regulatory objective, which we do not discuss here. The three scenarios are:

Scenario 1: The forecast expenditure ${\hat{E}}_{t + 1}$ is independent of past expenditure $E_{t}$ as long its values do not exceed a threshold $e_{t}^{0}$ ⁠; otherwise, ${\hat{E}}_{t + 1} = E_{t} - e_{t}^{0}$ + $e_{t + 1}^{0}$ ⁠.
Scenario 2: The forecast expenditure ${\hat{E}}_{t + 1}$ is exactly the same as the actual expenditure $E_{t}$ from the previous period.
Scenario 3: To calculate the forecast expenditure, the actual expenditure is additively corrected by a fraction of the forecast error from the previous period (the difference between forecast ${\hat{E}}_{t}$ and actual expenditure $E_{t}$ ⁠).

Using Equation 9, as presented in Appendix 3, Table 1 summarizes the expression for the power of incentive under each of the three scenarios discussed above.

TABLE 1

The Power of Incentives to Reduce Expenditure in Three Scenarios

	${\hat{E}}_{t + 1} (E_{t})$	$\frac{d Π}{d E_{t}}$ ⁠, Power of Incentive
1	$E_{t} - e_{t}^{0}$ + $e_{t + 1}^{0}, if E_{t} \geq e_{t}^{0}$ $e_{t + 1}^{0}, if E_{t} < e_{t}^{0}$	$- \frac{r_{t + 1}}{(1 + r_{t}) (1 + r_{t + 1})} if E_{t} \geq e_{t}^{0}$ $- \frac{1}{1 + r_{t}}, if E_{t} < e_{t}^{0}$
2	$E_{t}$	$- \frac{r_{t + 1}}{(1 + r_{t}) (1 + r_{t + 1})}$
3	$E_{t} + α ({\hat{E}}_{t} - E_{t})$	$- \frac{α + r_{t + 1}}{(1 + r_{t}) (1 + r_{t + 1})}$

It is convenient to factor out the term − $\frac{1}{1 + r_{t}}$ and restate the meaning of the remaining expressions. In what follows, the power of incentive is understood to be a positive number so that the higher the power of incentive, the stronger the designed incentive to reduce current expenditure.

Scenario 1 provides the operator with the strongest incentive as long as the expenditure is kept below an established threshold $e_{t}^{0}$ ⁠, which could be set up tight. Otherwise, the situation is identical to Scenario 2.

Scenario 3 becomes Scenario 2 when $α = 0$ ⁠. When $α = 1$ ⁠, the operator finds itself with the strongest incentives to reduce its expenditures. However, this is a situation whereby the regulator simply estimates the future expenditures using the same value of its own estimate from the previous period, disregarding any information about actual expenditure.

Scenarios 2 and 3 reveal the ability of the regulator to achieve higher incentive power without solely relying on the rate of return. To achieve a higher target power in Scenario 2, the regulator would have to allow a higher rate of return. In fact, without any other regulatory tool, the power of incentive is only proportional to the rate of return for small values, which is the typical case, severely limiting the regulator’s ability. On the other hand, if the regulator desires to achieve a given power of incentive $p^{*}$ ⁠, it can decide to use a relatively high value of $α$ ⁠, for which the range of values is [0, 1] and fine-tune it with an additional change in the rate of return, if necessary. In fact, for small values of $r_{t + 1},$ $p^{*} \approx α .$

Optimal Time of Investment

The standard analysis of an unregulated profit-maximizing monopolist, when applied to both replacement investment in response to rising maintenance costs and to the investment required to cater for growing demand, indicates that the monopolist will undertake both types of investment later than is optimal in terms of social welfare. This section will build on this result by comparing

Cost Based versus Price Based

Borrman and Brunekreeft (2020) formally establish the result. They derive a mathematical analysis of the extent of the timing difference in terms of some key parameters relating to the growth rate of maintenance with the age of the network assets in the case of replacement investment and the growth of demand in the case of capacity increasing investment.

In their article, the authors propose that the firm faces a regulated price p₁^R, before the investment is made and a regulated price p₂^R, after investment. Then the firm maximizes the regulated discounted profit, V^R(.), to find the optimal investment time T^R:

m a x V^{R} (T) = \int_{0}^{T} ({p_{1}}^{R} - c) Q_{1}^{R} (t) e^{- r t} d t + \int_{T}^{\infty} ({p_{2}}^{R} - c) Q_{2}^{R} (t) e^{- r t} d t - I e^{- r t} [7]

The market quantities Q₁ and Q₂ are then determined by the market-clearing prices, p₁ and p₂, while profits of the regulated firm are determined by the regulated prices, p₁^R and p₂^R.

They assume that right before demands reach maximum capacity, that is, Q₁ = K_max, regulated price is such that p₁^R< p₁, and for the post-investment period p₂^R = p₂ at Q₂ = Q₁ (p₂).

The quantities from the binding capacity condition at the end of period 1 and the demand function for the post-investment period are as follows:

Q_{1}^{R} = K_{m a x} and Q_{2}^{R} (t) = \frac{(a - p_{2}^{R}) e^{g t}}{b}

[8]

The latter follows from the assumption that demand is linear and grows over time at rate g, or

P (Q, t) = a - b e^{- g t} Q

Borrman and Brunekreeft (2020) go on to use the latter two expressions [8] in [7] and find the optimality condition for the investment time T^R:

\frac{(p_{2}^{R} - c) (a - p_{2}^{R})}{b} e^{g T^{R}} - (p_{1}^{R} - c) K_{m a x} = r I

[9]

Their interpretation of cost-based regulation and price-based regulation puts the two approaches on extreme opposites in the sense that the two differ by assuming that in cost-based-regulation prices are allowed to change from the ante-investment time to the post-investment time. In contrast, in price-based regulation, regulated prices do not change on the time range of our interest.

By modelling the effect of regulation, Borrman and Brunekreeft (2020) demonstrate that “cost-based” regulation—where investment results in higher regulated prices—incentivized earlier investment than “price-based” regulation—where regulated prices are independent of the timing (and level) of investment. These results are intuitively correct.

Intuitively, the extent to which investment increases the regulated prices in the case of “cost-based” investment is a key factor determining the extent to which investment is accelerated relative to the case of “price-based” regulation.

The model suggests that if investment increased regulated prices sufficiently, it would be possible to achieve the socially optimal timing for replacement investment (or indeed to accelerate the timing even further, which would be inefficient). Still, acceleration to this extent is not possible in the case of capacity increasing investment.

Modelling the Impact of Regulatory Price Decision on the Optimal Time of Investment

With the full regulatory toolbox still to be completed, we would like to undertake a preliminary analysis of some aspects of either regulatory decisions already made or proposed regulatory measurements most likely to be approved shortly. The latter is in a very advanced state and, barring determinations on some minor points, can be already counted as part of the regulatory framework.

The situation studied in this section is that of the regulatory scheme already in place and the regulator using prices, not only revenues, as regulatory instruments. This will be the situation in New Zealand as the first regulatory period only allows the regulator to constrain the revenue, but later periods might see the determination of prices. How such determination affects the optimal time at which investment must be done is the subject of our analysis.

Our analysis follows that of Borrman and Brunekreeft (2020, 5), which involves formulating how the profitability of an entity regulated under the BBM approach depends on (i.e., as a function of) its replacement and capacity expansion investment decisions and then examining what decisions would maximize that profitability expression. The profitability analysis is complemented by formulating an expression for how social welfare depends on (i.e., as a function of) the same investment decisions. The difference between the decisions that would maximize profitability and those that would maximize social welfare is then determined.

Thus the key focus of the analysis is a comparison of the level of replacement and capacity expansion investment that would maximize the regulated entity’s profitability under a BBM regulatory approach versus the levels of such investments that would be socially optimal. Therefore, the analysis provides an indication of the risk of regulatory outcomes deviating from the social welfare-maximizing outcome. It thus provides regulatory policymakers and the regulators who implement that policy with information that may help reduce the deviation of regulatory outcomes from the socially welfare-maximizing outcome. While unresolvable uncertainties and practicalities make elimination of the deviation unachievable, the analysis may be helpful in limiting the deviation.

We use the model by Borrman and Brunekreeft (2020) to afford analytical indications of the relationship between the timing of investment decisions and the firm’s profitability, as well as the effect of capacity expansion investment decisions on social welfare. We illustrate how their model works by considering how it can be used to provide insights into the implications of the New Zealand regulatory framework.

In order for such a model to be mathematically tractable, a set of simplifying assumptions is adopted in this article. These assumptions reflect, to the extent possible, the key features of the New Zealand UFB FTTH network.

Firstly, the number of end-users is held constant. Consistent with this assumption, the “last mile” fiber connections from the aggregation cabinets to individual premises are assumed to be in place. While there will be a need for maintenance, in particular, repair to damage caused by roadworks and related construction activities, this expenditure is not the focus of attention in the modelling. Specifically, the need for this expenditure and the level of it is not a function of end-user busy hour traffic, which is the focus of attention.

For the purposes of the modelling considered in this article, the exact details of the source of the throughput constraint are not examined in detail. The key assumption is that increasing throughput capacity requires expenditure. The expenditure could be categorized into investment and increases in operating expenditure, but for the purpose of the current analysis, there is no need to make such a distinction. The increased expenditure required to provide and support an increase in throughput capacity can be treated as an investment, with any increase in ongoing operating expenditure being captured as a present value amount.

In summary, for the purpose of the analysis in this article, the focus of attention is on the components that determine busy hour throughput. The decision variable controlled by the regulated entity is the scale of investment in those components.

The second major simplifying assumption is that the end-user demand for busy hour throughput grows at a constant rate. This is adopted as an assumption because it reflects the current situation in regard to busy hour throughput. This assumption could be replaced by a more general form of growth in a future analysis, albeit at the cost of complicating the solution of the equations.

We analyze the BBM regulatory framework by, first, using Borrman and Brunekreeft’s (2020, 4) approach and then assuming that post-investment regulated price is defined as responding to investment in capacity expansion by allowing a mark-up over the ante-investment regulated price that depends on the size of investment I, the capacity constraint K_max, the WACC or weighted average cost of capital W, and a term that reflects a possible regulator’s inclusion of an additional margin to the cost of capital as follows.^⁴:

p_{2}^{R} = p_{1}^{R} + \frac{I \cdot (W + μ)}{K_{m a x}}

[10]

Using the preceding relation Equation [9] is now:

\frac{(p_{2}^{R} - c) (a - p_{2}^{R})}{b} e^{g T^{R}} - (p_{2}^{R} - \frac{I \cdot (W + μ)}{K_{m a x}} - c) K_{m a x} = r I

Which can be solved for T^R, defining a function of the post-investment price $p_{2}^{R}$ ⁠:

T^{R} = l n ({[\frac{b ((r - W - μ) I + (p_{2}^{R} - c) K_{m a x})}{(p_{2}^{R} - c) (a - p_{2}^{R})}]}^{\frac{1}{g}})

We want to investigate how the optimal investment time T^R is affected by decisions on the value of the post-investment price; in other words, we calculate $\frac{\partial T^{R}}{\partial p_{2}^{R}}$ ⁠.

By renaming $b (r - W - μ) I + (p_{2}^{R} - c) K_{m a x})$ as $f (p_{2}^{R})$ and $(p_{2}^{R} - c) (a - p_{2}^{R})$ as $h (p_{2}^{R})$ the partial derivative $\frac{\partial T^{R}}{\partial p_{2}^{R}}$ is:

\frac{\partial T^{R}}{\partial p_{2}^{R}} = \frac{\partial l n ({[\frac{f (p_{2}^{R})}{h (p_{2}^{R})}]}^{\frac{1}{g}})}{\partial p_{2}^{R}} = \frac{1}{g} \frac{h (p_{2}^{R})}{f (p_{2}^{R})} [\frac{f^{'} (p_{2}^{R}) h (p_{2}^{R}) - f (p_{2}^{R}) h^{'} (p_{2}^{R})}{{(h (p_{2}^{R}))}^{2}}]

Which simplifies to

\frac{\partial T^{R}}{\partial p_{2}^{R}} = \frac{1}{g} [\frac{f^{'} (p_{2}^{R})}{f (p_{2}^{R})} - \frac{h^{'} (p_{2}^{R})}{h (p_{2}^{R})}]

Now, returning to the full expressions for f and h,

\frac{\partial T^{R}}{\partial p_{2}^{R}} = \frac{1}{g} \frac{K_{m a x}}{b ((r - W - μ) I + (p_{2}^{R} - c) K_{m a x})} + \frac{1}{g} \frac{2 p_{2}^{R} + c - a}{(p_{2}^{R} - c) (a - p_{2}^{R})}

[11]

From the equation above, we observe that $p_{2}^{R}$ is constrained to be in the interval (c, a), that is, c < $p_{2}^{R}$ < a. The critical point here is the middle point between c and a.

When $p_{2}^{R}$ is exactly that point, the second term in [11] vanishes. T^R displays an increasing trend with a small increase in $p_{2}^{R}$ ⁠, that is, as $p_{2}^{R}$ moves away from c, approaching a if $p_{2}^{R}$ is larger than the middle point between c and a. The latter suggests an incentive for the firm to delay investment if it knows the regulated price is set larger than the middle value between c and a.

In contrast, as $p_{2}^{R}$ moves towards c, the second term in [11] negatively increases, while the first term positively grows. The two effects render the situation ambiguous, at least from a first-order approach; we need to further look into the relative sizes of the two terms in [9] as a function of changes in $p_{2}^{R} .$

We also want to investigate how the optimal investment time T^R is related to m, the correction in the cost of capital that the regulator allows to account for any underestimation.

We assume that the rate of return is comparable to the WACC, $r = W,$ and the regulated price p₂^R, after investment, is such that $c \leq p_{2}^{R} \leq a .$

From $T^{R} = \frac{1}{g} l n ({[\frac{b ((r - W - μ) I + (p_{2}^{R} - c) K_{m a x})}{(p_{2}^{R} - c) (a - p_{2}^{R})}]}^{})$

if $T^{R}$ is to be non-negative, then, renaming $p_{2}^{R} - c$ as $m_{c}$ and $a - p_{2}^{R}$ as $m_{a}$ the following condition must be met:

\frac{- b μ I + b m_{c} K_{m a x}}{m_{c} m_{a}} \geq 1

From which it follows that:

μ \leq \frac{m_{c} (b K_{m a x} - m_{a})}{b I} \equiv μ_{1}

Notice that we’ve renamed the upper bound of $μ$ as $μ_{1}$ ⁠.

Since $μ$ must be non-negative, finding the value of $T^{R}$ when $μ = 0,$ we obtain:

T^{R} = \frac{1}{g} l n (\frac{b K_{m a x}}{m_{a}})

which means that either $b K_{m a x} \geq a - p_{2}^{R}$ ⁠. Figure 2 shows the relation between $T^{R}$ and $μ$ graphically.

FIGURE 2

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The effect of a regulator’s added margin to the cost of capital on the optimal time of investment.

For the reasons discussed earlier in this article, the change to BBM regulation in New Zealand may potentially reduce the incentive for the network operators to delay investment compared to the case of TSLRIC regulation. Furthermore, they will still face an incentive to economize on investment—that being an intended incentive under BBM regulation.

However, specific features of the New Zealand implementation of BBM regulation could be particularly relevant regarding the timing of investment.

Firstly, the precedent is that the regulator will implement some form of quality regulation. This quality specification may include a form of obligation to expand throughput capacity to accommodate the rapid growth in demand for throughput, which is a conspicuous feature of traffic on current IP networks, specifically video traffic. However, it is yet to be decided what form of quality regulation will be applied. This is likely to be intensively debated in submissions of the regulator’s proposed implementation of BBM regulation.

Secondly, implementing BBM regulation of the electricity lines, gas pipelines, and international airports regulation in New Zealand has included an “uplift” in the cost of capital estimates used. This uplift is the addition of a margin above the central estimate of the WACC. The rationale for this margin is that it considers the asymmetry whereby underestimation of the WACC would be more detrimental to end-users—as a result of depressing investment—than overestimation.

One effect of the uplift is that the increase in regulated prices due to investment (given the BBM regulation is “cost-based”) is likely to be greater than the cost of investment on a probabilistic basis.

This effect of the uplift should (on a probabilistic basis) accelerate the timing of investment.

The overall effect on the timing of investment will reflect the combination of the form of quality regulation obligation to accommodate growth in the demand for capacity and the size of the uplift.

As noted in the previous section, the use of cost-based BBM regulation could, in principle, overcome the delay in investment (compared to the socially optimal timing) resulting from “price-based” BBM regulation. As also noted that acceleration could, in principle, be excessive regarding replacement investment.

The actual outcome in New Zealand will depend on the decisions of the regulator regarding the form of quality regulation and the size of the uplift applied.

Conclusion

Applying the BBM approach to regulating LFCs in New Zealand deserves analysis and assessment, to the extent possible, of the incentives introduced on the regulated provider’s ability for cost reduction and quality-of-service goal-reaching.

Two representative aspects of the fundamental issue, the power of incentive to reduce expenditure and the optimal timing of investment, were analyzed within the current regulatory framework for the telecommunications sector in the country. In particular, the problems studied correspond to the regulatory approach known as the PQ-path by which Chorus, the country’s largest telecommunications provider and owner of the largest fiber facilities, will be regulated from January 1, 2022.

This article examined, under commonly accepted regulatory decisions about the implementation of BBM, the power of the incentive structure revealed by the revenue equation and the asset-based roll-forward condition, the central pillars of the BBM. It also investigated the relationship between the proposed regulatory approach, in particular, the way revenue is capped and its impact on the time of investment. This is a problem of the greatest regulatory concern because, in sectors where investment is expected for the continuous maintenance of the infrastructure, delays in investment decisions may be detrimental to the quality of the service provided.

Both sections “BBM in New Zealand” and “Optimal Time of Investment”, using separate modelist approaches, shed light on respective courses of action for the regulator who oversees the use of the BBM approach. The concluding statements can be assessed within the respective analytical frameworks presented in each section. In fact, in section “BBM in New Zealand”, an argument is made that price-based regulation is better for efficiency incentives. On the other hand, in section “Optimal Time of Investment”, the article argues that cost-based regulation is better for investment.

When we consider these results together, a dichotomy is revealed. Perhaps the limitations of the models (being stylized and not dealing with uncertainty yet) may lead to this situation. This dichotomic situation,^⁵ which under the current limitations, is hard to escape, poses the question of whether this is a “middle of the road’ situation for the regulator to choose. The highly stylized approach chosen for analysis with no risk and no asymmetric information may limit the interpretation of results afforded by the B&B model. However, the results were found to provide a baseline for the novelty scenario that telecommunications regulators in New Zealand are facing with the introduction of the BBM approach to the regulation of the FTTH network. Together with the other half of the article, such baseline observations are useful in their own right and for the next step in analyzing the New Zealand approach to regulating a fiber platform.

List of Acronyms and Abbreviations

ADSL–Asymmetric Digital Subscriber Line

BBM–Building Blocks Model

CFH–Crown Fiber Holdings

DFAS–Direct Access Fiber Access

FCM–Financial Capital Maintenance

FFLAS–Fiber Fixed-Line Access Services

FTTH–Fiber-to-the-home

ICABS–Intra Candidate Area Backhaul

ID–Information Disclosure (determination)

IM–Input Methodologies

LFC–Local Fiber Company

OECD–Organization for Economic Cooperation and Development

PON–Passive Optical Network

PPP–Public–Private Partnership

PQ–Price-Quality (path)

P2P–Point-to-Point

RAB–Regulatory Asset Base

RBI–Rural Broadband Initiative

TSLRIC–Total Service Long Run Incremental Cost

UFB–Ultra-Fast Broadband

VDSL–Very high-speed Digital Subscriber Line

WACC–Weighted Average Cost of Capital

APPENDIX 1

The operator’s profit stream, as in Biggar (2004):

{\hat{R}}_{t} = r_{t} K_{t - 1} + {\hat{O}}_{t} + {\hat{D}}_{t} + (1 + r_{t}) X_{t - 1}

[5]

K_{t} = K_{t - 1} + I_{t} - {\hat{D}}_{t} + (O_{t} - {\hat{O}}_{t}) + (R_{t} - {\hat{R}}_{t}) + Y_{t}

[6]

Assuming actual and forecast revenue are the same, that is, $R_{t} = {\hat{R}}_{t}$ ⁠, from [5]:

{\hat{O}}_{t} + {\hat{D}}_{t} = {\hat{R}}_{t} - r_{t} K_{t - 1} - (1 + r_{t}) X_{t - 1}

Then, using [6], and replacing ${\hat{O}}_{t} + {\hat{D}}_{t}$ in it:

K_{t} = K_{t - 1} + I_{t} + O_{t} - (R_{t} - r_{t} K_{t - 1} - (1 + r_{t}) X_{t - 1}) + Y_{t}

or

K_{t} = (1 + r_{t}) K_{t - 1} - (R_{t} - I_{t} - O_{t}) + (1 + r_{t}) X_{t - 1} + Y_{t}

Rearranging terms, the above equation becomes:

R_{t} - I_{t} - O_{t} = (1 + r_{t}) K_{t - 1} - K_{t} + (1 + r_{t}) X_{t - 1} + Y_{t} (*)

On the other hand, from Equation 7, the operator’s profit stream from period t to period T is:

π_{t} = \frac{K_{T}}{a (t, T)} + \sum_{s = t}^{T} \frac{R_{s} - O_{s} - I_{s}}{a (t, s)}

where $a (t, s) = \prod_{i = t}^{s} (1 + r_{i})$ ⁠; the profit stream can be rewritten as,

π_{t} = \sum_{s = t}^{T - 1} \frac{R_{s} - O_{s} - I_{s}}{a (t, s)} + \frac{R_{T} - O_{T} - I_{T}}{a (t, T)} + \frac{K_{T}}{a (t, T)}

and using (*) for $K_{T}$ ⁠, it becomes:

π_{t} = \sum_{s = t}^{T - 1} \frac{R_{s} - O_{s} - I_{s}}{a (t, s)} + \frac{R_{T} - O_{T} - I_{T}}{a (t, T)} + \frac{(1 + r_{T}) K_{T - 1} - (R_{T} - O_{T} - I_{T}) + (1 + r_{T}) X_{T - 1} + Y_{T}}{a (t, T)}

Further, using (*) for $R_{s} - O_{s} - I_{s}$ on the expression above,

π_{t} = \sum_{s = t}^{T - 1} \frac{(1 + r_{s}) K_{s - 1} - K_{s} + (1 + r_{s}) X_{s - 1} + Y_{s}}{a (t, s)} + \frac{K_{T - 1}}{a (t, T - 1)} + \frac{(1 + r_{T}) X_{T - 1} + Y_{T}}{a (t, T)}

π_{t} = \sum_{s = t}^{T - 1} (\frac{(1 + r_{s}) X_{s - 1} + Y_{s}}{a (t, s)}) + \frac{(1 + r_{T}) X_{T - 1} + Y_{T}}{a (t, T)} + \sum_{s = t}^{T - 1} (\frac{(1 + r_{s}) K_{s - 1} - K_{s}}{a (t, s)}) + \frac{K_{T - 1}}{a (t, T - 1)}

π_{t} = \sum_{s = t}^{T} (\frac{(1 + r_{s}) X_{s - 1} + Y_{s}}{a (t, s)}) + \sum_{s = t}^{T - 1} (\frac{(1 + r_{s}) K_{s - 1} - K_{s}}{a (t, s)}) + \frac{K_{T - 1}}{a (t, T - 1)} (* *)

Because the sum $\sum_{s = t}^{T - 1} (\frac{(1 + r_{s}) K_{s - 1} - K_{s}}{a (t, s)}) + \frac{K_{T - 1}}{a (t, T - 1)}$ can be rewritten as:

\begin{matrix} K_{t - 1} - \frac{K_{t}}{a (t, t)} + \frac{(1 + r_{t + 1}) K_{t}}{a (t, t + 1)} - \frac{K_{t + 1}}{a (t, t + 1)} + \frac{(1 + r_{t + 2}) K_{t + 1}}{a (t, t + 2)} \\ - \frac{K_{t + 2}}{a (t, t + 2)} + . . . + \frac{(1 + r_{T - 1}) K_{T - 2}}{a (t, T - 1)} - \frac{K_{T - 1}}{a (t, T - 1)} + \frac{K_{T - 1}}{a (t, T - 1)} \end{matrix}

which becomes $K_{t - 1}$ ⁠, because for any s (= t, …, T-1), $\frac{K_{s}}{a (t, s)} = \frac{(1 + r_{s + 1}) K_{s}}{a (t, s + 1)}$ ⁠.

Hence, the profit stream is

π_{t} = \sum_{s = t}^{T} (\frac{X_{s - 1}}{a (t, s - 1)} + \frac{Y_{s}}{a (t, s)}) + K_{t - 1} .

APPENDIX 2

Calculating the power of incentives:

Let us recall that $E$ represents any of opex (⁠ $O$ ⁠) or capex (⁠ $I$ ⁠), and $\hat{E}$ represents the corresponding forecast expenditure (opex or capex). Following Biggar’s, at any period t, any regulatory intervention amount deviating from FCM only depends on actual $E_{t}$ and forecast ${\hat{E}}_{t}$ expense. In addition, the forecast expenditure ${\hat{E}}_{t + 1}$ is a function of only the most recent actual expenditure, ${\hat{E}}_{t + 1} = {\hat{E}}_{t + 1} (E_{t})$ ⁠. Besides, the regulatory deviation from FCM at period t on the revenue equation, X_t, is a function only of period t’s actual and forecast opex, $X_{t} = X_{t} (O_{t}, {\hat{O}}_{t})$ ⁠. The same is true for the regulatory deviation from FCM on the roll-forward equation, $Y_{t}$ ⁠, in relation to actual and forecast capex. Starting with the profit stream equation:

π_{t} = \sum_{s = t}^{T} (\frac{X_{s - 1}}{a (t, s - 1)} + \frac{Y_{s}}{a (t, s)}) + K_{t - 1}

it is observed that when E_t is used to represent opex, then $\frac{\partial Y_{s}}{\partial E_{t}} = 0$ for all s. So the equation becomes

π_{t} = \sum_{s = t}^{T} \frac{X_{s - 1}}{a (t, s - 1)} + K_{t - 1}

To calculate $\frac{d π_{t}}{d E_{t}}$ ⁠, it suffices to deal with the first three terms of the sum because $\frac{d X_{s}}{d E_{t}} = 0$ for all $s > t + 2 .$

When $s = t$ ⁠, $\frac{d X_{t - 1}}{d E_{t}} = \frac{d X_{t - 1} (E_{t - 1}, {\hat{E}}_{t - 1})}{d E_{t}} = 0$

When $s = t + 1$ ⁠, $\frac{d X_{t}}{d E_{t}} = \frac{d X_{t} (E_{t}, {\hat{E}}_{t})}{d E_{t}} = \frac{\partial X_{t}}{\partial E_{t}} + \frac{\partial X_{t}}{\partial {\hat{E}}_{t}} \cdot \frac{\partial {\hat{E}}_{t}}{\partial E_{t}}$ ⁠; since forecast expenditure does not depend on the actual expenditure, then $\frac{\partial {\hat{E}}_{t}}{\partial E_{t}} = 0$ ⁠, and $\frac{d X_{t}}{d E_{t}} = \frac{\partial X_{t}}{\partial E_{t}}$

Finally, when

$s = t + 2$ ⁠, $\frac{d X_{t + 1}}{d E_{t}} = \frac{d X_{t + 1} (E_{t + 1}, {\hat{E}}_{t + 1})}{d E_{t}} = \frac{\partial X_{t + 1}}{\partial E_{t + 1}} \cdot \frac{\partial E_{t + 1}}{\partial E_{t}} + \frac{\partial X_{t + 1}}{\partial {\hat{E}}_{t + 1}} \cdot \frac{\partial {\hat{E}}_{t + 1}}{\partial E_{t}}$ = $\frac{\partial X_{t + 1}}{\partial {\hat{E}}_{t + 1}} \cdot \frac{\partial {\hat{E}}_{t + 1}}{\partial E_{t}}$ because actual future expenditures do not depend on actual current expenditures.

Putting these expressions back into $\frac{d π_{t}}{d E_{t}}$ and accounting for the discount terms $a (t, s - 1)$ ⁠,

\frac{d π_{t}}{d E_{t}}_{} = \frac{1}{a (t, t)} \frac{\partial X_{t}}{\partial E_{t}} + \frac{1}{a (t, t + 1)} \frac{\partial X_{t + 1}}{\partial {\hat{E}}_{t + 1}} \frac{d {\hat{E}}_{t + 1}}{d E_{t}}

The equation above is essentially the same as Equation [9].

APPENDIX 3

Power of incentives in three scenarios.

A common feature of the three scenarios is to present is our assumption that the regulator’s intervention at period t on the revenue equation depends on the current as well as the forecast opex, that is, $X_{t} (E_{t}, {\hat{E}}_{t}) = {\hat{E}}_{t} - E_{t}$ ⁠,

Scenario 1:

{\hat{E}}_{t + 1} (E_{t}) = \{\begin{array}{c} E_{t} - e_{t}^{0} + e_{t + 1}^{0} if E_{t} \geq e_{t}^{0} \\ e_{t + 1}^{0} if E_{t} < e_{t}^{0} \end{array}

Differentiating ${\hat{E}}_{t + 1}$ on $E_{t}$ ⁠, we obtain

\frac{d {\hat{E}}_{t + 1}}{d E_{t}} = \{\begin{array}{c} 1 if E_{t} \geq e_{t}^{0} \\ 0 if E_{t} < e_{t}^{0} \end{array}

which implies that $\frac{\partial X_{t}}{\partial E_{t}} = - 1$ and $\frac{\partial X_{t + 1}}{\partial {\hat{E}}_{t + 1}} = 1$ ⁠, so the power of incentive to reduce opex is

\frac{d π_{t}}{d E_{t}}_{} = - \frac{1}{a (t, t)} + \frac{1}{a (t, t + 1)} = - \frac{r_{t + 1}}{(1 + r_{t}) (1 + r_{t + 1})}, if E_{t} \geq e_{0}^{t}

\frac{d π_{t}}{d E_{t}}_{} = - \frac{1}{a (t, t)} = - \frac{1}{(1 + r_{t})}, if E_{t} < e_{0}^{t}

Scenario 2:

{\hat{E}}_{t + 1} (E_{t}) = E_{t}

\frac{d π_{t}}{d E_{t}}_{} = - \frac{r_{t + 1}}{(1 + r_{t}) (1 + r_{t + 1})}

Scenario 3:

{\hat{E}}_{t + 1} (E_{t}) = E_{t} + α ({\hat{E}}_{t} - E_{t})

\frac{d π_{t}}{d E_{t}}_{} = - \frac{α + r_{t + 1}}{(1 + r_{t}) (1 + r_{t + 1})}

FOOTNOTES

1.

According to Commerce Commission (2021), “Point-to-point FFLAS include single, multilayer or layer 1 backhaul services. For example, the direct fiber access service (DFAS) carries traffic from large single-site customers such as schools, hospitals, or mobile towers or fixed wireless access sites, to a central office.”

2.

ICABS or Intra Candidate Area Backhaul is a backhaul service that “transports traffic from the mobile cell site or fixed wireless access site back to the point of interconnection where the access seeker will connect to its network.”

3.

The quantities for the 3 years of PQP1 are −$85 M for year 1, +$15.6 M for year 2, and +$76.9 M for year 3.

4.

The purpose of including is to recognize that an underestimate would be more detrimental than an overestimate.

5.

This issue was raised by one of the reviewers of this article, bridging a gap brought about by the way this article previously focused on the two separate models presented.

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Author notes

Author’s Note: I would like to acknowledge discussions and work done on a previous version of this article with Mr. Pat Duignan, whose sharp insights inspired a great deal of work.

This work is licensed under Creative Commons Attribution CC-BY-NC-ND

2022

The Pennsylvania State University

This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Power of Incentives and Optimal Time of Investment in a Building-Blocks Approach to Regulation of an Open-Access FTTH Network

ABSTRACT

Background

The UFB Network

New Regulatory Framework in New Zealand

BBM in New Zealand

BBM in New Zealand: The IMs

Components of the BBM

A Model to Estimate the Power of an Incentive Under BBM

Power of Incentives

Optimal Time of Investment

Cost Based versus Price Based

Modelling the Impact of Regulatory Price Decision on the Optimal Time of Investment

Conclusion

List of Acronyms and Abbreviations

APPENDIX 1

APPENDIX 2

APPENDIX 3

FOOTNOTES

BIBLIOGRAPHY

Author notes

Citing articles via

Email alerts

Power of Incentives and Optimal Time of Investment in a Building-Blocks Approach to Regulation of an Open-Access FTTH Network

ABSTRACT

Background

The UFB Network

New Regulatory Framework in New Zealand

BBM in New Zealand

BBM in New Zealand: The IMs

Components of the BBM

A Model to Estimate the Power of an Incentive Under BBM

Power of Incentives

Optimal Time of Investment

Cost Based versus Price Based

Modelling the Impact of Regulatory Price Decision on the Optimal Time of Investment

Conclusion

List of Acronyms and Abbreviations

APPENDIX 1

APPENDIX 2

APPENDIX 3

FOOTNOTES

BIBLIOGRAPHY

Author notes

Citing articles via

Email alerts

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