1. business and industrial

Working Paper No.38 – Normal Profit
AGL Applied Economic and Policy Research
What is Normal Profit for power generation?
Paul Simshauser and Jude Ariyaratnam
Level 6, 144 Edward Street
Brisbane, QLD 4001
June 2013
Abstract
One of the seemingly complex areas associated with energy-only wholesale electricity
pools is at what point market power abuse is present on the supply-side. It shouldn’t be
this way. If a theoretically robust measure of normal profit exists, identification of
potential market power abuse is straight-forward. Such a definition readily exists and
can be traced back to the ground-breaking work of financial economists in the 1960s.
But using this framework in a post-2008 financial crisis environment requires careful
application. In this article, we explore how the Capital Asset Pricing Model can be
applied in atypical capital market conditions, and when combined with a multi-period
dynamic power project financing model, pragmatic estimates of benchmark wholesale
power prices can be derived. This in turn can guide policymakers as to whether price
spikes or bidding above marginal cost in wholesale markets warrants any investigation at
all.
Keywords: Profit, Project Finance, Electricity Prices.
JEL Codes: D61, L94, L11 and Q40.
1. Introduction
Price spikes in gross pool, energy-only, uniform first-price auction wholesale markets typically
trigger regulatory inquiry. Policy intervention may be warranted if supranormal profits are being
extracted on a sustained basis through generator bidding behaviour in the presence of
demonstrable barriers to entry. But episodes of transient price spikes in energy-only markets
should not represent an ‘automatic’ trigger for inquiry let alone policy intervention, particularly if
underlying prices are otherwise driving merchant generators to a state of financial distress.
Economic theory has long demonstrated that energy-only spot electricity markets can clear
demand reliably, and can provide suitable investment signals for new capacity (Schweppe et al.
1988). But such analysis typically presumes unlimited market price caps, limited political or
regulatory interference, and by deduction, a largely equity capital-funded generation fleet able to
withstand wildly fluctuating business cycles. Unfortunately the real world isn’t this convenient.
Rarely are generators devoid of scheduled debt repayments and so theories of spot energy
markets suffer from the inadequate treatment of how non-trivial sunk capital costs are financed
(Peluchon, 2003; Joskow, 2006; Finon, 2008; Caplan, 2012; Nelson and Simshauser, 2013).
Additionally, wholesale price caps do exist and are enforced – in some instances excessively so –
by regulatory authorities (Besser et al. 2002; Oren, 2003; de Vries, 2003; Wen et al. 2004; Finon
and Pignon, 2008, Joskow 2008a, Simshauser, 2010). Intensely competitive energy-only markets
are known to produce inadequate net revenues to support investment in the optimal least cost
generating portfolio, otherwise known as the ‘missing money’ problem (Neuhoff et al. 2004; de
Vries, 2004; de Vries et al. 2008; Bushnell, 2005; Roques et al. 2005; Cramton and Stoft, 2006;
Joskow, 2008b; Finon, 2008; Simshauser, 2008). In short, given substantial fixed and sunk costs
associated with power generation, and low marginal production costs, persistent generator
bidding at short run marginal cost does not result in a stable equilibrium (Bidwell and Henney,

Paul Simshauser is the Chief Economist at AGL Energy Ltd and Professor of Economics at Griffith University. Jude Ariyaratnam is
a financial analyst at AGL Energy Ltd. The authors are grateful to Rob Prest (Macquarie Capital), James Nelson (PwC) and AGL
Energy Ltd’s Applied Economic and Policy Research Council for reviewing earlier drafts. However, as noted in Appendix IV, any
errors or omissions remain entirely the responsibility of the authors.
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AGL Applied Economic and Policy Research
2004; Simshauser, 2008; Nelson and Simshauser, 2013). Generator bidding must, therefore,
deviate from strict marginal cost at some point. But given an oligopolistic market environment,
at what point might this cross a line and represent a potential abuse of market power that warrants
investigation and possible intervention by policymakers? If a pragmatic measure of Normal
Profit exists, then the combination of historic base load spot prices and futures prices for call
option contracts can provide suitable guidance.
Identifying a theoretically sound measure of Normal Profit is of vital importance to the industry,
policymakers, and in turn, the overall efficiency and welfare of the macro economy. The
allocation of resources within an economy relies quite fundamentally on such constructs, whether
this is through the investment decisions of firms, or by decisions made by policymakers that
influence or directly impact on investment outcomes. But Normal Profit needs to be very
carefully defined.
The concept of Normal Profit is unremarkable in economics but oddly enough is very rarely
identified in practice. This is primarily because profit announcements by firms (and reported by
the media) are dominated by accounting statistics and ratios based on the traditional measure of
Net Profit after Tax. Finance theory is clear – NPAT is nothing more than a residual measure.
When NPAT is determined by traditional accounting axioms, it represents the residual funds
available for distribution to stockholders after all other claimants have been satisfied. NPAT does
not describe the ‘pitch’ of profits generated, that is, Normal or otherwise.
In order to assess the pitch of profits, a suitable benchmark must first be defined. Economic
theory has long told us that this is measured by the opportunity cost of funds employed. By the
1960s, the economics profession had produced profoundly more refined quantitative definitions,
viz. the marginal cost of capital or expected returns of rational investors based on a one factor,
two-parameter model of risk and return. The origins of such developments can be traced back to
Sharpe1 (1964) and Lintner (1965). If profits of the firm meet the marginal cost of capital, a
Normal Profit has been generated. Supranormal profits are achieved when profit exceeds the cost
of capital and conversely, economic losses occur when returns fail to meet expected returns.
For highly capital-intensive industries like power generation, temporal issues associated with
accounting results create further complications. Accounting numbers use arbitrary reporting
periods (e.g. monthly, quarterly, annual) to measure NPAT. While this is both desirable and
necessary for managerial and agency purposes, discrete accounting period reporting is
fundamentally a static analysis, whereas for investment or policymaking purposes, Normal Profit
should be considered in a dynamic context. There are no capital-intensive assets likely to deliver
lifecycle economic returns within a decade, let alone a single accounting period. More commonly
with capital-intensive assets, expected returns occur over multiple decades and in power
generation are subject to (nominally) 5-7 year business cycles, with actual returns oscillating
considerably around the mean outcome. Normal Profit, then, must be considered as a multiperiod dynamic inquiry rather than a static analysis based on a collection of half-hour price spikes
during a short episode of hot weather, for example.
In economics literature, from a benchmark perspective the Internal Rate of Return (IRR) of
investments is the most prominently used theoretical long-run profitability concept, as Salmi and
Virtanen (1997) explain. Finance literature on the other hand has a distinct bias towards net
present value analysis, although as Brealey, Myers and Allen (2011) observe, IRR comes from
respectable ancestry, and for our purposes, can be expected to provide conforming results under
all of the conditions that we envisage in this article.2
1
Prof William Sharpe was awarded the 1990 Nobel Prize in Economic Sciences for his research in this area.
See for example Brealey, Myers and Allen (2011, pp 109-115) for a discussion of the conditions where IRR calculations deviate
from NPV calculations.
2
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AGL Applied Economic and Policy Research
Normal Profit is of central importance in policymaking – if benchmarks are over-estimated
consumer welfare can be adversely affected and resource allocation to other industries may be
scaled-back to inefficient levels. Conversely, underestimation of Normal Profit can lead to policy
settings that benefit consumers in the short run but the associated wealth transfers adversely affect
industry investment, competition and innovation in the long run, and will eventually harm
consumers. Neither outcome is desirable. From a policymaking perspective, as the capital
intensity of an industry increases, the consequence of error (in either direction) compounds.
Capital is scarce and will inevitably find its optimal use.3
The purpose of this article is to set out a theoretically robust and pragmatic approach which
defines ‘Normal Profit’ in power generation which is then transposed into base electricity prices
and call option prices. This requires that we define the cost of debt and the cost of equity capital
for the two most prominent business combinations in merchant energy markets, and to set out a
clear quantitative methodology for quantifying the long run marginal cost of power generation
given prevailing capital and factor market conditions. While our application to power generation
uses Australian data, the framework is equally applicable to other regions with energy-only
market models such as those in Australia, Texas, New Zealand, Singapore, Alberta (Canada) and
Europe amongst others.
This article is structured as follows. Section 2 briefly discusses Normal Profit. Section 3 then
defines the estimated cost of equity. Section 4 outlines a dynamic power project financial model
which produces generalised long run marginal cost estimates for multiple technologies. Section 5
summarises the results and Section 6 applies the results to policymaking. Concluding remarks
follow.
2.
What is Normal Profit?
Normal Profit can be defined as the firm’s total cost of production, including the opportunity cost
of funds employed. The ‘opportunity cost of funds employed’ requires further clarification,
however. The accounting treatment of equity costs is inadequate because it treats such resources
as a ‘residual claim’. In economics, no such assumption is made – equity returns are treated as a
fixed cost, just as the interest and principal repayments on debt are considered fixed costs under
accounting principles. And so a firm’s total cost of production includes all costs, including the
opportunity cost of capital which translates to a normal (i.e. fair) level of profit to equity
investors. It goes without saying that, in practice, the mere treatment of equity resources as a
fixed cost does not of itself produce a profit. Charging equity costs to a profit and loss statement
is a foreign concept in financial accounting. However, the importance of incorporating equity
costs as a charge against revenue has long been accepted in economic theory as a prerequisite to
the survival of the firm as Thompson and Formby (p. 241, 1993) noted:
…Whenever the profitability of a business is consistently below what can generally be
earned in other enterprises of equivalent business risk, stockholders can be expected to
seek greener pastures for their investment funds. Because additional resources and
capital will tend to be withheld from an enterprise if profits fall below normal levels for
sustained periods, it is appropriate to consider this minimum profitability as a cost. It is
a cost in the sense that unless revenues from the firm’s operations are adequate to
provide acceptable rewards to stockholders, the capital funds needed to sustain
operations will dry up and the firm, in time, will wither and die. In other words, in the
long run some minimal amount of profit is a condition of survival…
3
For the electricity industry, the matter is further intensified by the portfolio weightings associated with institutional investors. The
typical institutional investor with an Australian investment mandate has an asset allocation of c.10% of their total Funds Under
Management for ‘infrastructure class’ assets. Electricity then forms only a component part, and needs to compete with other
infrastructure classes such as ports, roads and gas pipelines. Further still, power generation needs to compete with transmission and
distribution infrastructure opportunities for this scarce capital.
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AGL Applied Economic and Policy Research
In our experience, a surprising number of policymakers, regulators and microeconomics
professionals (from academia and industry) misinterpret the appropriate quantitative value for the
marginal cost of capital. The reason for this, we suspect, is that the theoretical construct of
‘opportunity cost’ must shift from theory to practice, all the while ensuring that in the process the
result does not violate the basic axioms and constraints of credit metrics and taxation implications
– all of which are important in defining the true marginal efficiency of equity and debt capital.
Producing reliable estimates of a firm’s cost of capital and the level of profit which constitutes
‘normal’ is therefore an exercise best applied using financial economic principles. Turvey (2000,
p.2) also notes that in power generation, the estimation of long run marginal costs requires
engineering and operational research skills and rarely requires accounting skills.
3. What is the marginal cost of capital in atypical economic conditions?
Among the most important variables in determining Normal Profit in capital-intensive industries
like power generation is the cost of capital as Nelson and Simshauser (2013) demonstrate. The
cost of debt capital is directly observable from the capital markets. The cost of equity capital is
not – it is the subject of economic estimation models. The estimated marginal cost of equity
capital is not a single number – for merchant power generators it will be quite different for the
two most prominent business combinations (1) merchant utilities with an investment-grade credit
rating, and (2) project financed merchant utilities.4
The viable level of debt within these two business combinations can be quantified through
detailed power project modelling which we explain in Section 4. These lead to very different
gearing levels with project financing typically ranging from 60-80% and investment-grade
entities exhibiting values closer to 30-40%. The expected cost of equity is different for each
business combination – the marginal efficiency of equity capital for a project finance will
gravitate towards 15-16%, whereas marginal equity costs for an investment grade integrated
merchant utility is typically 11-12%. In other words, the expected IRR of power project post-tax
cash flows will range from 11-16% with the variation explained by the relevant business
combination and consequent level of debt within the capital structure.
3.1
Estimating the cost of equity: Sharpe-Lintner Capital Asset Pricing Model
Since the marginal cost of equity capital must be estimated, a brief discussion of its derivation is
warranted, noting that a truly vast amount of literature on this topic exists from a mechanistic
perspective. What follows is therefore focused on the key elements of its application in ‘atypical
capital market conditions’ – where there is considerably less literature readily available.
With any portfolio of investments, there is always some component of risk that affects all asset
classes, known as ‘systematic’ or market risk. Systematic risks are those variables that affect the
entire economy, albeit some assets are affected by these variables more than others. A good
example of systematic risk is a rise in consumer prices. All things being equal, rising general
inflation is likely to lead to higher interest rates, labour costs or both (amongst other impacts).
Such movements in these economic variables generally adversely affect all firms, although for
power generation, interest rate changes are amplified given the capital-intensive nature of the
sector.
Non-systematic risks on the other hand are those that affect a single or a small group of stocks,
and can therefore be essentially eliminated at minimal cost through diversification at the investor
level. An example of a non-systematic risk for power generation is mild weather, which is
usually associated with adverse commodity sales. Since non-systematic risk can be virtually
eliminated at almost no cost by diversification at the investor level, there is no reward for bearing
We consider that these two business combinations represent the ‘book-ends’ of the feasible business models from a cost of equity
perspective.
4
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AGL Applied Economic and Policy Research
it. However, systematic risk cannot be eliminated through diversification, and thus, stockholders
must be rewarded by suitable (expected) returns for that risk. The cost of equity capital is most
typically approximated through the Capital Asset Pricing Model5 (CAPM), which as noted earlier
can be traced back to Sharpe (1964) and Lintner (1965). The model is defined as follows:
(
)
(1)
Where:
Ke
Rf
Rm
i
= post-tax cost of equity capital
= the risk free rate of return
= the expected market return
= the equity beta for the ith firm, which ex ante can be used as predictive, and
i
=
(
)
(2)
Where:
Ri
Rm
2
m
= the returns from the ith firm
= the returns from the stock market as a whole
= the variance of market returns as a whole
The intercept term (Rf ) is the risk free rate and is a purely theoretical construct. In practice
however, the current yield of long-dated government bonds are used as a proxy. Regulators in the
NEM typically use contemporaneous values for Rf .6 The expected return of the total market
(Rm) is approximated by reference to very long run average returns from the stock market over
and above long dated government rates at the time (i.e. Rm – Rf). Over the last 128 years this
calculation, also known as the Market Risk Premium (MRP), has averaged 6.1% (Brailsford,
Handley and Maheswaran, 2012).
The crucial factor in the CAPM is the equity beta ( i) for the ith firm– which is concerned with the
measure of systematic risk for a company. As equation (2) implies, a firm that has the same
general risk characteristics as the aggregate stock market will return a i equal to 1.0. The
generation business unit of an investment grade merchant utility, for example, would typically
have i in the range of 0.95 to 1.15 as IPART (2013) explains. The higher leverage associated
with project financed merchant power plants will produce markedly higher earnings volatility and
therefore will have i greater than 1.0, typically in the range of 1.5 to 1.8.7 Of course, while i is
mathematically defined based on equation (2), this is an historical calculation and in practice i
and the CAPM must be used to define (expected) future returns.8
3.2
Applying the Sharpe-Linter CAPM in atypical capital market conditions
Throughout most of the last 20 years, the CAPM could be mechanistically applied as outlined in
Section 3.1 to the power generation industry and produce relatively stable and reliable estimates
for
over time. The collapse of Lehman Brothers in September 2008 and the Global Financial
There are other equity cost estimation models such as Fama and French’s (1997) three factor model. However in the Australian
energy sector, the CAPM is most widely used.
6
For example, Rf is often determined in regulatory determinations by reference to the 30-day rolling average yield on 10-Year
Australian Government Bonds.
7
The variable
is based on the work undertaken by the NSW economic regulator, IPART (2013) and PWC (2013). The range for
was found to be 0.95-1.15 and so we have opted to use the midpoint of 1.05 as our set point. Using the gearing levels implied in the
SFG analysis, the Asset Beta
value which appears later in Table 2 for generation can be expressed as
5
) (
⁄[(
[(
) (
)]. This can then be rearranged to produce an equity beta for merchant plant such that
)]
where the term
is the value of equity and D is the value of debt.
8
This is of course a critical shortcoming with the CAPM framework and the estimation of equity costs, but it nonetheless represents
the most widely used equity cost estimation model.
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Crisis that followed has however produced atypical capital market conditions. A ‘mechanistic’
application of the CAPM anytime since October 2008 through to the time of writing in 2013
would produce results that are intuitively erroneous.
Our reference to atypical capital market conditions is not a reference to economic recession. By
atypical, we mean a situation whereby yields on government bonds are especially low – which
implies a general state of ‘loose credit’ – while simultaneously the market for corporate debt is
contracting with rising spreads. Bernanke (1983) shows that the Great Depression and in
particular, the 1930-33 financial crisis in the US exhibited atypical conditions not observed in
other economic recessions. The prime cause was the 1930-33 financial crisis and associated
insolvency of large numbers of banks. We consider the Global Financial Crisis of 2008-09
produced outcomes in capital markets that are directionally consistent with Bernanke’s (1983)
description of 1930-33.
The relevance of atypical capital market conditions to the CAPM is that a mechanistic application
of MRP uses a very long run data set for both variables in the MRP calculation (i.e. Rm – Rf), in
our case 128 years, but simultaneously uses a contemporaneous value for the intercept Rf . This
combination is problematic in atypical capital market conditions. In Figure 1, we demonstrate
this by mechanistically applying the CAPM to produce
estimates for a power generator from
July 1997 through to June 2013 and assume MRP = 6.1% and i = 1.05, which is relevant to a
generation business with an investment-grade credit rating. Notice that by following the
mechanistic application of the model, the value of marginal equity costs
falls once the 2008
financial crisis sets in.
Figure 1:
10-Year Govt Bond Yields vs. Mechanistic CAPM Estimate
Source: RBA, AGL Energy Ltd.
In this instance, falling government bond yields gives the appearance that Ke is also falling. But
in a financial crisis, this is an erroneous conclusion as Bernanke (1983, p266) noted in the context
of the 1929-33 US episode:
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…the idea that the low yields on Treasury [bonds]… during this time signalled a general
state of “easy money” is mistaken; money was easy for a few safe borrowers, but difficult
for everyone else. An indicator of the strength of lender preferences for safe liquid assets
(and hence of the difficulty of risky borrowers in obtaining funds) is the yield differential
between Baa corporate bonds and Treasury bonds…
In Figure 2, we present historical credit spreads between Australian Government Bonds and BBB
rated corporate bonds from January 2000 through to June 2013, along with Bernanke’s (1983) US
Baa corporate bond spread data from the Great Depression which runs from July 1929 to March
1933. We contrast these data with the mechanistically determined average values for Ke as
derived in Figure 1. The Figure 2 results are important with respect to the application of the
CAPM. First, note the shape of the US Baa corporate spread data trace from the Great
Depression – Bernanke (1983) explains that the sharp rise in spreads coincided with an
accelerating rate of bank failures. The 1929-33 data has been aligned to the Australian BBB bond
spread data by matching the peak of the bank failures as reported by Bernanke (1983) with the
collapse of Lehman Brothers in September 2008. As an aside, the correlation coefficient between
the two data sets is 0.88. Note that just as 10 year government bond yields fall sharply in 2008,
BBB corporate spreads rise sharply and coincide with the collapse of Lehman Brothers in
September 2008. In these circumstances, institutional investors adopted a “risk off” approach,
meaning that investment funds shift from risky corporate bonds and equities towards low risk
Treasury bonds or Australian Government bonds – hence the falling value of 10-year
Government bonds and rising BBB spreads.
Figure 2:
Australian BBB Corporate Bond Spreads vs. Mechanistic Rm
Source: Bernanke (1983), RBA, AGL Energy Ltd.
As an economic model reliant on assumptions and data inputs to produce estimates of , when
applied mechanistically, the CAPM tells us that equity investors would accept lower risk
premiums in the middle of a financial crisis – as Figure 2 highlights. So when government bonds
are trading at record lows,
is apparently valued at historic lows. As Gray (2013b)
demonstrates, such an approach erroneously suggests that the value of
is the lowest at any
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point in the last 40 years. From a practical perspective, it is difficult to imagine the conditions
where corporate debt investors require substantially higher premiums while simultaneously,
corporate equity investors accept the lowest risk premium on record. Indeed, Gray (2013b)
explains that whether judged by Dividend Growth Models, the practice of independent experts,
advice from investment banks currently raising capital or other indicator variables from finance
literature9, none point toward values for
at multi-decade lows. On the contrary, the weight of
evidence is that
is currently slightly above the long run average.
None of this means the CAPM is broken – only that its application requires judgement in atypical
capital market conditions. Some regulatory authorities in Australia have nonetheless persisted
with applying it mechanistically.10 For our purposes, we maintain the historic MRP of 6.1% and
opt to use a 10-year average of Rf over the period immediately prior to the collapse of Lehman
Brothers in 2008. We also test this against an expanded value of MRP provided by conventional
dividend growth models (i.e. from 6.1% to a range of 7.4-8.3%)11 to ensure that our long run
average approach remains reasonable for marginal equity raisings. This approach is similar to
that adopted by the independent regulator in New South Wales (IPART, 2013).
4. Generalised long run marginal cost of generation plant – PF Model
The model we use to produce a theoretically sound profit benchmark and generalised long run
marginal cost estimates for generating plant is a dynamic, multi-period model with all outputs
expressed in nominal dollars and post-tax discounted cash flows focusing on and solving for the
expected
whilst simultaneously meeting binding debt sizing parameters. The model, known as
the PF Model, is a variation to the coal-fired power plant PF Model in Simshauser (2009) and the
combined cycle gas turbine PF Model in Simshauser and Nelson (2012), and Nelson and
Simshauser (2013). Whereas those models were focused on a single technology project
financing, our PF Model solves for multiple technologies, business combinations and revenue
possibilities, and simultaneously solves for convergent price, debt-sizing, and equity returns .
To begin with, since all outputs are expressed in nominal dollars, costs are increased annually by
a forecast general inflation rate estimate (CPI) with prices escalating at a discount to our assumed
CPI. Inflation rates for revenue streams
and cost streams
in period (year) j are calculated
in the model as follows:
[
(
)] , and
[
(
)]
(4)
In this instance,
is the adjustment factor of 1.0 for costs and
relates to revenues and is set at
0.75. The discounted value for
is intended to reflect single factor learning rates that
characterise generating technologies over time.12
4.1
PF Model for base, semi-base and intermittent power plant
Energy output from each power plant (i) is a key variable in driving revenue streams, unit fuel
costs and variable Operations & Maintenance costs. Energy output is calculated by reference to
installed capacity , capacity utilisation rate
and run time t, which in the PF Model is
8760hrs for each period j. Auxillary losses
arising from on-site electrical loads (such as air
compressors, lighting, induced and forced draft fans and so on) need to be deducted.
9
See for example Petkova and Zhang (2005) who examine the MRP in relation to default premiums, term premiums and treasury bills
and dividend yields.
10
The exceptions to this are the NSW independent regulator, IPART and the Australian Energy Market Commission. See IPART
(2013) and AEMC (2012) for details.
11
See Gray (2013b) for a summary of dividend growth model results.
12
See Frontier Economics (2013) at pp31-35 for a useful explanation of learning curves as they relate to power generation
technologies.
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(
)
(5)
There are two options for convergent electricity prices in the PF Model. The first option is to
exogenously set unique forecast prices for each period j (e.g. from a dynamic partial equilibrium
model of the relevant power system), while the second option, which is our default option and
used throughout this article is a calculated price in year one which escalates electricity price
at
the rate of
from equation (4). Additionally, ancillary services revenues have been set at
0.25% of electricity sales.13 Thus revenue in each period j is defined as follows:
(
)
(6)
To determine the short run marginal cost of the ith plant in the jth period, the thermal efficiency for
each generation technology needs to be defined. The constant term ‘3600’14 is divided by the
thermal efficiency variable to convert the result from per cent to kJ/kWh, which is then multiplied
by the commodity cost of raw fuel . Variable Operations & Maintenance costs is also added
to provide a pre-carbon short run marginal cost. To the extent that the plant has non-zero CO2
emissions and faces an emissions trading regime, the CO2 intensity of output for the ith plant
needs to be computed along with the relevant CO2 price,
. In order to define a value for plant
carbon intensity , the relevant combustion emissions factor ̇ and fugitive CO2 emissions from
the fuel source ̂ are multiplied by the plant heat rate. Marginal running costs in the jth period is
then calculated by the product of short run marginal production costs by generation output and
escalated at the rate of .
(
{[(
⁄ )
(
)
(
)]
|
( ̇
̂)
⁄ )
}
(7)
Fixed Operations & Maintenance costs of the plant are measured in $/MW/year of installed
capacity
and are multiplied by plant capacity and escalated.
(8)
Earnings Before Interest Tax Depreciation and Amortisation (EBITDA), a frequently used
accounting-based measure, in the jth period can be defined as follows:
(
)
(9)
Unless plant is acquired, capital costs associated with development involve a multi-period
construction program. Capital costs are therefore defined as follows:
∑
(
)
(10)
Ongoing capital spending for each period j is determined as the inflated annual assumed capital
works program.
(11)
13
14
This factor is based on average ancillary services revenues as a percentage of overall energy market revenues.
The derivation of the constant term 3600 is: 1 Watt = 1 Joule per second and hence 1 Watt Hour = 3600 Joules.
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Plant capital costs give rise to tax depreciation ( ) such that if the current period was greater
than the plant life under taxation law (L), then the value is 0. In addition, also gives rise to tax
depreciation such that:
( )
(
)
(12)
From here, taxation payable ( ) at the corporate taxation rate ( ) is applied to
Interest on Loans defined later in (16), less . To the extent ( ) results in non-positive
outcome, tax losses ( ) are carried forward and offset against future periods.
(
)
(
)
less
(13)
Our debt financing model computes the interest and principal repayments on different debt
facilities depending on the type and tenor of each tranche. For example, we model project
financings with two facilities; (1) nominally a 5-year bullet, requiring interest-only payments
after which it is refinanced with two consecutive 10-year amortising facilities. The first
refinancing is set in a semi-permanent structure with a nominal repayment term of 20 years, while
the second is fully amortised over the 10 year tenor. The second facility (2) commences with a
tenor of 12 years as an amortising facility, again set within a semi-permanent structure with a
nominal repayment term of 27 years. This second tranche is refinanced in year 13 and
extinguished over a further 15 year period. Consequently, all debt is extinguished by year 27.
The decision tree for the two tranches of debt was the same, so for the Debt Tranche where = 1
or 2, the calculation is as follows:
{
(14)
refers to the total amount of debt used in the project. The split (S) of the debt between each
facility refers to the manner in which the debt is apportioned to each debt tranche. We assume
35% of the debt was assigned to Tranche 1 and the remainder to Tranche 2 in a manner consistent
with Simshauser (2009). Principal
refers to the amount of principal repayment for tranche T
in period j and is calculated as an annuity:
(
[
(
(
))
| {
)
(15)
]
In (15),
is the fixed (reference) interest rate and
is the credit spread or margin relevant to
the issued Debt Tranche. The relevant interest payment in the jth period ( ) is calculated as the
product of the (fixed) interest rate on the loan by the amount of loan outstanding:
(
)
(16)
Total Debt outstanding , total Interest and total Principle for the ith plant is calculated as
the sum of the above components for the two debt tranches in time j. For clarity, Loan Drawings
are equal to
in year 1 as part of the initial financing and are otherwise 0.
In equation (14) one of the key calculations is the initial derivation of . This is determined by
the product of the gearing level and the acquisition/development cost. The gearing level in turn is
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AGL Applied Economic and Policy Research
formed by applying a cash flow constraint based on credit metrics applied by capital markets. In
this instance, the variable in our PF Model relates specifically to the business combination and
the credible capital structure achievable. The two relevant combinations are Vertically Integrated
(VI) merchant utilities and stand-alone Project Financed Merchant (PF) businesses.
(
)
(
(
)
)
|
(
)
(
|
∑
)
)(
[(
)
(17)
]
{
The variables
and
are exogenously determined by credit rating agencies. Values for
are exogenously determined by project banks and depend on technology (i.e. thermal vs.
renewable) and the extent of energy market exposure, that is whether a Power Purchase
Agreement exists or not. For clarity,
is ‘Funds From Operations’ while
and
are the Debt Service Cover Ratio and Loan Life Cover Ratios.
At this point, all of the necessary conditions exist to produce estimates of the long run marginal
cost of power generation technologies, and a suitable benchmark for what constitutes Normal
Profit. As noted at the outset of this article, in economics literature IRR is the widely used
theoretical long-run profitability concept. The relevant equation to solve for the price
which
produces a normal profit given
whilst simultaneously meeting the binding constraints of
and
or
given the relevant business combination is as follows:
∑
[
] (
)
( )
∑
(
)
( )
The primary objective is to expand every term which contains
Interest and Tax terms is as follows:
∑
[(
( )
)
)
∑
(
(
)
)
((
(
)
(
)
] (
(19)
)
)(
)
We then solve for
term is on the left hand side of the equation:
(
)
(
∑
(
(
)
)
( )
( )]
∑
∑
[ (
)
(
)
(
)
(
)(
( )
(
))
(20)
such that:
∑
∑
)
.
∑
∑
. Expansion of the EBITDA,
( )
We then rearrange the terms such that only the
Let
(18)
)
( )
((
)
(
)
(
∑
)(
(
(
)
))
(
)(
)
)
( )
)
( )
( )
(
)
(21)
( )
4.2
PF Model for peaking power plant
Certain adjustments to the PF Model are required to accommodate long run marginal cost
estimates for peaking plant. For base, semi-base and intermittent plant, the normal estimation
procedure is to identify the relevant convergent electricity price
that is sufficient to produce an
IRR equal to . The value for
is found by solving equation (21), and one of the most
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AGL Applied Economic and Policy Research
sensitive variables is energy output , which is in turn driven by the value for
. In general,
values for
are comparatively predictable in that base load plant have high capacity factors
and intermittent plant, over time, exhibit output factors within a comparatively tight range given
long-run average weather conditions. Peaking plant on the other hand exhibits fluctuating values
for
due to the natural volatility inherent in short-run weather patterns and temporal shocks to
the demand-supply balance.
This has two primary implications. First, defining a single electricity price
for peaking plant is
̅̅̅̅̅
virtually meaningless in the absence of an expected fixed or ‘sticky’
. Second, attempting to
define a value for
is likely to render such a project unbankable due to the uncertainty over
values for
in application (i.e. by project bank credit committees). Consequently, peaking
plant requires a distinct revenue model in its own right. In our opinion, the appropriate way to
express generalised long run marginal cost estimates for peaking plant is to define the ‘carrying
cost’ of plant capacity, ̅ . This requires only small modifications to the calculation of revenues
in our PF Model. The result produced is a single capacity price
which essentially reflects the
equilibrium price of a sold call-option contract at the commonly traded NEM strike price for such
instruments of $300/MWh. Equations (5) and (6) require reconfiguring as follows:
, and
(
)
(22)
Here, the value of energy output is set to zero, which means marginal running costs will
also be zero. In practice will have a non-zero value and so
would also be non-zero, and
under most conditions will exceed marginal running costs . This differential between
and
, while somewhat contentious to model, will be limited in each sub-period of j by the call
option strike price, and for our purposes we assume it to be zero. Putting the typically trivial
value of this to one side, revenue
for the ith peaking plant is hence the product of installed
capacity , the price of that capacity
(which is expressed in $/MWh), being the number of
hours in a year as noted earlier in equation (5), and the revenue escalation factor. The value for
, which will also exactly equals ̅ , is a vitally important one as it also defines the ‘missing
money’15 in an energy-only market under conditions of intense competition and perfect plant
divisibility and availability as Section 6 later demonstrates. It also represents a useful benchmark
in helping to establish potential presence of market power abuse and barriers to entry.
5. Model Results – Generalised Long Run Marginal Cost of Power Generation
Our PF Model results rely quite crucially on the engineering estimates of capital and maintenance
costs of plant. These key variables along with fuel market costs are set out in Table 1. Note that
the parameters have been derived from Worley Parsons (2012), ACIL Tasman (2012) and
Frontier Economics (2013) who produce these estimates for the independent market operator
(AEMO) and for New South Wales’ independent economic regulator (IPART).
The term ‘missing money’ was first discussed by Cramton and Stoft (2006), and later Joskow (2006), and describes a situation
whereby market price caps (set low to constrain market power) adversely affect average clearing prices thus resulting in inadequate
returns to investors in generation plant. Steed and Laybutt (2011) identify c.$6 billion in ‘missing money’ in the NEM from 20002010 even with a market price cap of $10,000/MWh.
15
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Table 1: Engineering & Cost Parameters
Model Variable
Unit
i=
Black Coal Black Coal Brown Coal
CCGT
Wind
OCGT
QLD
NSW
VIC
VIC
SA
QLD
NSW
Plant Capacity
MW
k
1000
1000
1000
400
400
400
400
Capacity Factor
%
CF
90.0
90.0
90.0
85.0
85.0
85.0
85.0
Auxillary Load
%
Aux
6.0
6.0
7.0
3.0
3.0
3.0
3.0
Thermal Efficiency
%
ζ
39.0
39.0
28.0
50.0
50.0
50.0
50.0
Raw Fuel
$/GJ
F
1.00
1.42
0.40
5.00
7.00
8.00
8.50
Variable O&M
$/MWh
v
1.28
1.28
0.10
4.08
4.08
4.08
4.08
Fixed O&M
$/MW
f
52,768
52,768
36,700 10,188 10,188 10,188 10,188
Combustion Emissions kg CO2 /GJ ġ
90.2
90.2
92.0
50.6
50.6
50.6
50.6
Fugituive Emissions
kg CO2 /GJ ĝ
8.7
8.7
8.7
18.6
18.6
18.6
18.6
Carbon Price
$/t
CP
7.50
7.50
7.50
7.50
7.50
7.50
7.50
Capital Cost
$/kW
X
2,500
2,500
3,000
1,200
1,200
1,200
1,200
Capital Works
$ '000
x
5,000
5,000
5,000
2,000
2,000
2,000
2,000
Useful Life
Years
L
40
40
40
30
30
30
30
Sources: Worley Parsons (2012), ACIL Tasman (2012), Frontier Economics (2013)
CCGT
CCGT
CCGT
NEM
200
37.5
1.0
n/a
n/a
12.23
40,750
7.50
2,000
1,000
25
NEM
450
n/a
1.0
35.0
8.00
10.19
4,075
50.1
5.7
7.50
783
1,000
30
In addition to these parameters, we also require financial and economic parameters, which are
presented in Table 2.
Table 2: Financial Economic Parameters
Model Variable
Unit
Inflation
%
CPI
Risk Free Rate
%
Rf
Market Risk Premium (Rf-Rm)
%
MRP
2.5
5.8
6.1
Generation Asset Beta
#
βa
0.73
Equity Beta Factor VI
#
βVI
1.05
Equity Beta Factor IPP
#
βIPP
1.58
Tax Rate
%
τc
30.0
Effective Tax Rate
%
τe
21.3
5Yr Interest Rate Swap
%
RT
3.6
12Yr Interest Rate Swap
%
RT
4.5
PF Credit Spread (5 Yr)
bps
CT
250
PF Credit Spread (12 Yr)
bps
CT
300
BBB Credit Spread (5 Yr)
bps
CT
180
BBB Credit Spread (12 Yr)
bps
CT
225
BBB Credit (FFO/I)
times
δVI
4.0/5.0
BBB Credit (FFO/D)
times
ωVI
0.2
DSCR & LLCR
times
δIPP
1.8-2.2
Sources: PWC (2013), Gray (2013a, 2013b), Simshauser and Nelson (2013).
In Figure 3 we present the stylised cost of capital for merchant generation. Debt costs are largely
based on 7-12 year bond pricing for varying credit quality. Note the range for project finance
runs from about 50-67.5% (and by chance the results are currently equivalent to bond pricing +/15 basis points). We consider the cost of equity to be largely sticky at our long run calculated
value for
for any credit quality below BBB and do not contemplate credit ratings beyond Adue to inherent industry risk, otherwise
varies according to our Asset Beta. This is based on
judgement, and a lack of practical evidence to the contrary. Note that the Weighted Average Cost
of Capital is notionally minimised at a BBB credit rating.
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Figure 3:
Stylised cost of capital for merchant generation
Combining the parameters in Tables 1 and 2 with equations (3) – (22) in our PF model produces
generalised long run marginal cost estimates for multiple plant types in total dollars and on a unit
cost basis – the latter being more useful for any subsequent comparative analysis. In Figure 4, we
present the model results on a unit cost basis under the financing conditions historically activated
by merchant power producers using project finance to either develop or acquire a power project
for each technology i.
Figure 4:
PF Model generalised long run marginal cost estimates – Project Financing
At the bottom of each bar in Figure 4 the “per cent” result relates to the gearing level achievable
under energy market equilibrium conditions. So for example, the Black Coal Queensland (QLD)
plant has 65 per cent debt within the capital structure. The bars are comprised of the individual
cost elements of the plant, starting with Unit Fuel Costs , Unit Carbon Costs (
) through
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AGL Applied Economic and Policy Research
to the Unit Cost of Equity, all of which is expressed in dollars per Megawatt Hour ($/MWh). At
the top of each bar is the PF Model’s calculated unit price
in which the IRR of the project
exactly equals the cost of equity
while simultaneously meeting all binding credit metrics
specified in equation (17) using the Table 2 parameters. To be clear,
is also the generalised
long run marginal cost or entry cost for each individual technology. Note also that these unit
costs also represent market equilibrium or the ‘centre of gravity’ for base load futures contract
prices over the long run given an optimal stock and mix of plant. The unit cost of an Open Cycle
Peaking (OCGT) plant is expressed as the ‘carrying cost of capacity’ or ̅ for reasons identified
in Section 4.2.
Our alternate business combination results are presented in Figure 5 and arise from producing
generalised estimates for plant that have been financed ‘on-balance sheet’ by an entity with an
investment-grade credit rating. The structural changes to unit costs in this instance are limited to
capital and taxation, and this is primarily due to binding constraints in equation (17). For ease of
comparison, we have included the headline Project Finance results from Figure 4 as the black
diamond markers in Figure 5. What this analysis illustrates is that there is no marked benefit in
either structure, with the exception of wind plant.16 Note however that wind farms are assumed to
be backed by an investment-grade Power Purchase Agreement, and thus use different credit
metrics (i.e. a DSCR equal to 1.35x which enables substantially higher gearing) and a constant
value for
(i.e. equivalent to the horizontal section of the
curve in Figure 3).
Figure 5:
PF Model generalised long run marginal cost estimates – Balance Sheet Financing
From this one would conclude that all wind turbines should be project financed rather than
financed on-balance sheet. However, our PF Model has one significant limitation in this regard –
it does not model portfolios of plant at the enterprise level. In practice, credit rating agencies
treat half of the PPA’s present value as ‘synthetic debt’ on the balance sheet of the counterparty
who writes the instrument. This in turn has a real opportunity cost to vertically integrated firms –
since their level of total corporate debt must be modified downwards accordingly, and so the
apparent gains from writing PPAs over balance sheet financings are partially illusory.
16
Although as Nelson and Simshauser (2013) argue, greenfield merchant power project financings are not currently plausible.
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6. Application to policymaking
Understanding Normal Profit and the long run marginal cost of production is clearly important for
investment decision-making. In our experience, firms in the energy industry use a framework
that is consistent with that presented in Sections 3 and 4 and extend the revenue lines with power
system simulation modelling and so it is not necessary to elaborate further. However, the
investment decisions of firms in fixed power assets in the energy industry are influenced quite
fundamentally by policy settings – again in our opinion, more so than many other industries given
the role of electricity in the economy and the political economy of electricity tariffs. As such,
understanding Normal Profit is important as it will frequently form a pivot point in policy
formulation and regulatory settings. Industry and consumer groups, and in some instances
politicians themselves, have sought to change NEM market policies, rules and regulations based
on perceived levels of supranormal profits gained or economic losses incurred in both the
wholesale and retail markets.
6.1
Wholesale market benchmark
Severe price spikes in gross pool, energy-only, uniform first-price auction wholesale markets
typically form a trigger for regulatory inquiry. For policymakers, intervention may be warranted
if supranormal profits are being extracted on a sustained basis through generator bidding
behaviour in the presence of demonstrable barriers to entry. But episodes of transient price spikes
in wholesale markets should not represent an ‘automatic’ trigger for inquiry let alone policy
intervention given the nature of energy-only markets. The reason for this is quite simple. There
is no stable equilibrium in energy-only markets given a market price cap and a reliability
constraint due to the substantial fixed and sunk costs associated with power generation. This can
be demonstrated theoretically and through power system simulation modelling.
Proposition I: In an intensely competitive energy-only market with a uniform first-price
auction clearing mechanism and perfect plant divisibility and availability, aggregate
revenues for the optimal plant mix and for any number of optimal plant technologies will
fall short by at least the carrying cost of peaking plant capacity, ̅ .
Let the ith plant have marginal running costs of
and total fixed and sunk costs (including the
opportunity cost of capital) of ̅ . Let price in period be set on the basis of a uniform, first price
clearing auction such that the short run marginal cost of the marginal plant
sets price. The
intercept between plant n and n+1 occurs when:
̅
̅
(23)
Rearranging this becomes:
̅
̅
(
)
(24)
Under any optimal plant mix for any number of optimal plant technologies, aggregate revenues
will always fall short by at least ̅ . We provide a mathematical proof for Proposition I in
Appendix II and present a static partial equilibrium analysis in Figure 6 and applied results in
Table 3 using our modelling outcomes from Section 5. This helps to explains the importance of
our approach to modelling peaking plant and in particular, the use of equation (22) which solves
for ̅ . The concept that power system revenues will fall short by fixed capacity costs ̅ when
clearing prices are set to marginal cost has long been understood by energy economists and can
be traced back to Electrcitie de France’s then Chief Economist Marcel Boiteux, and his groundbreaking article on peak load pricing in electricity wholesale markets (Boiteux, 1949). The
framework developed by Central Electricity Generating Board of England & Wales’ Chief
Economist, Tom Berrie, provides an especially useful static partial equilibrium model of a power
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AGL Applied Economic and Policy Research
system which demonstrates this – although note that we have added a third (Price Duration) chart
to Berrie’s (1967) two-chart framework using our Section 5 results from Figure 4.
Figure 6:
Static Partial Equilibrium Model (ex-carbon): Victorian Region FY13
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Figure 6.1 illustrates the Marginal Running Cost Curves of the three generating technologies for
base (brown coal), semi-base (CCGT) and peaking (OCGT) duties. The y-axis intercept for each
technology represents the fixed and sunk costs ( ̅ ), and the slope of the curves represents
marginal running costs ( ). The x-axis measures plant capacity factor
from equation (5).
Note intercepts and identify the point at which the most efficient plant switches to the next
technology, given the rich blend of fixed and variable costs in line with equation (24).
Figure 6.2 illustrates a Load Duration Curve. This is a representation of the 17,520 half-hourly
electricity load points in a year but ranked in descending order rather than as a time-series, with
the y-axis measuring electricity load (MW) and the x-axis measuring ‘time exceeded’.17 Figure
6.3 is the corresponding Price Duration Curve, that is, the spot price set in each half-hour period
in Figure 6.2 under the conditions of a gross pool, energy-only, uniform first-price auction
clearing mechanism, with the y-axis measuring price and the x-axis also measuring ‘time
exceeded’.
The Figure 6 static partial equilibrium model assumes firms are free to install perfectly divisible
plant capacity with perfect plant availability (and hence no requirement for a reserve plant
margin) in any combination that satisfies differentiable equilibrium conditions. The model also
assumes a perfect transmission system and hence no constraints on the economic order of plant
dispatch. Table 3 sets out all energy production and cost results and notes that the system average
spot price of $55.43/MWh (i.e. the average of results in Figure 6.3) falls short of system average
cost of $66.04/MWh by the amount equivalent to ̅ – that is, $10.60/MWh (per Figure 4).
Table 3: Static Partial Equilibrium Results given Perfect Plant & Transmission System Availability
Plant Type
Capacity
Production Fixed Costs
(MW)
(GWh)
($m)
Brown Coal
4,853
38,167
1,957
CCGT
1,544
9,067
267
OCGT
3,191
1,968
290
Total
9,588
49,202
2,514
Average Spot Price
Diff (Avg Unit Cost less Avg Spot Price)
Running Costs
($m)
200
363
172
735
Total Costs
($m)
2,157
630
462
3,249
Avg Unit Cost
($/MWh)
56.52
69.50
234.61
66.04
55.43
10.60
CF j i
(%)
90
67
7
59
Once the assumptions of perfect plant divisibility and availability are relaxed, Average Unit Cost
can be expected to rise, and Average Spot Price can be expected to fall, as discrete power plant
blocks are added (i.e. lumpy plant entry) and requisite excess capacity (i.e. additional OCGT
plant) is purposefully added to ensure power system reliability constraints are met.
Simultaneously, a Value of Lost Load or Market Price Cap is introduced (i.e. the spot price that
applies during shortages) and in the NEM is $13,100/MWh. This offsets some, but not all,
additional costs and only if the optimal number of blackouts occurs annually within the reliability
constraint as Simshauser (2008) demonstrates.
6.2
Discussion
The key issue arising from the quantitative plant-specific results in Section 5 and the aggregate
industry result from Section 6.1 is that even with the perfectly optimal plant mix and a zero
reserve margin, no plant has any prospect of earning Normal Profits when conditions reflect
intense competition. From a policymaking perspective, the question that follows is does this
actually matter? After all, traditional welfare economics commences with the presumption that
economic efficiency is maximised when prices are set at marginal cost. However, the model of
perfect competition also assumes constant or decreasing returns to scale and that clearing prices
result in Normal Profits to efficient firms.
17
In this instance, live FY13 half-hourly load data from the Victorian region has been used.
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In industries with increasing returns to scale, where fixed and sunk costs are non-trivial, and
where marginal costs are very low (or zero in the case of renewable energy18), clearly a problem
exists as Figure 6 and Table 3 demonstrate. Varian (1996) notes that under such conditions,
persistent uniform pricing at industry short run marginal cost is not economically viable. In a
terminal industry, this may not warrant further consideration. But the electricity industry is not
terminal as evidenced by the level of plant availability in the NEM. While it is true that
electricity demand has contracted marginally over the past 3-4 years, longer run projections
exhibit mild but nonetheless positive growth. Furthermore, existing plant is aging and will one
day need replacement, and new plant will be required to meet renewable policy objectives.
Accordingly, policymakers cannot ignore how fixed and sunk costs are treated by policy changes.
It is not the role of policymakers to deliver profits to power companies. Nor however is it their
role to set policies that constrain the ability of firms to earn Normal Profit over the business cycle.
How does this translate into practice? Section 6.3 provides a useful applied example but in
summary, spot price outcomes in an intensely competitive energy-only market with a reliability
constraint cannot be considered a pragmatic benchmark for which to devise policy settings.
Generators persistently bidding at marginal running costs will result in prices that clear below
system average cost as Figure 6 and Table 3 demonstrate. Simshauser (2008) demonstrated that
when the assumptions of perfect plant divisibility and availability are relaxed, there is not a stable
equilibrium that will calibrate supply to demand in a manner consistent with stated reliability
standards in the long run (absent extremely high market price caps). Further, as Bidwell and
Henney (2004, p22) explain, even with high wholesale market price caps, a stable financial
equilibrium could only be reached if the physical power system is operating ‘near the edge of
collapse’. At some point generator bidding must deviate from short run marginal cost or
blackout-induced Market Price Cap events must increase in frequency. Benchmarks for
policymaking must therefore turn to plant and fleet-wide generalised long run marginal cost
estimates, respectively.
6.3
Application to wholesale markets
Mountain (2013) concludes that the imposition of carbon pricing from 2012 improved the
profitability of all generators, with wholesale prices more than doubling and gains extracted after
power generators exercised market power in the NEM. The analysis compared spot prices over a
nine month period before and after the carbon policy change – nine months being the limit of data
available at the time. This type of analysis can be reproduced – Table 4 draws on the relevant
spot market data from the independent market operator, using Victorian region data as an
example.19
Table 4: Victorian average spot prices Period-on-Period Change (FY12 vs. FY13)
Month
Jul
Aug
Sep
Oct
Nov
Dec
Jan
Feb
Mar
Avg
FY13 Spot
Incl. CO2
($/MWh)
73.46
55.76
53.48
51.27
77.18
52.18
54.27
53.59
52.31
58.17
CO2 Price Average Carbon FY13 Adj. FY12 Spot Spot Price
Intensity Excl. CO2 Pre- CO2 Difference
($/t)
(CO2 /MWh) ($/MWh) ($/MWh) ($/MWh)
23.00
1.166
46.65
29.49
17.16
23.00
1.182
28.57
29.95
-1.38
23.00
1.213
25.58
26.98
-1.40
23.00
1.225
23.09
23.61
-0.52
23.00
1.244
48.57
26.58
21.99
23.00
1.258
23.25
22.18
1.07
23.00
1.237
25.81
24.03
1.78
23.00
1.187
26.29
25.85
0.44
23.00
1.221
24.24
23.70
0.54
23.00
1.215
30.23
25.82
4.41
Source: AEMO.
18
While many renewable energy technologies have zero or negligible fuel costs, Biomass plant is a notable exception.
Mountain (2013) analyses production-weighted spot prices for all generation plant types. Here, we focus on the time-weighted spot
price in Victoria and compare these with our estimates of brown coal plant costs. Mountain’s (2013) FY13 production-weighted price
is $58/MWh and FY12 is $26/MWh – which is consistent with the result in Table 4 (results in columns 1 and 5).
19
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The time-weighted average spot price for the first nine months of FY13 in Table 4 is
$58.17/MWh and the Carbon Adjusted FY13 spot price (column 5) averages $30.23/MWh. This
adjusted price has been derived by stripping the estimated carbon impact (i.e. CO2 price x
Average Carbon Intensity) from FY13 spot prices, such that $58.17 – ($23/t x 1.215t) =
$30.23MWh.20 The final column compares the adjusted FY13 spot price with the FY12 spot
price, which results in a difference of $4.41/MWh. This differential is identified as a gain to the
profitability of generators since wholesale price rises exceeded carbon costs.21 Mountain (2013)
concluded that such an outcome is not consistent with a competitive market, while the Energy
Users Association of Australia added that the regulator should be granted greater scrutiny over
generator bidding.22
There are many reasons why a regulator might be granted greater scrutiny over generator bidding
– but our Table 4 analysis does not comprise one of them as it over-simplifies a very complex set
of spot market outcomes. It ignores the role and effects of (1) short run weather on aggregate
demand, (2) generator outages on aggregate supply, and (3) volumetric losses of individual plants
– all of which are known to be non-trivial. Above all though is the suitability of the initial
benchmark.
Using this analysis in Table 4 is, in our opinion, wrong in economics for the reasons outlined in
Section 6.2. Using a Period-on-Period unit price benchmark that is demonstrably below system
average cost, or worse still, equal to system short run marginal cost in an industry with substantial
fixed and sunk costs runs a high risk of producing a Type II error as Figure 6 and Table 3
demonstrate. Table 3 noted that the perfectly optimal plant mix for Victoria would produce
aggregate annual costs (including Normal Profit) of $3,249 million. The FY12 spot price from
Table 4 was $25.82 and annual output from Table 3 was 49,202GWh meaning that total spot
revenues earned by plant was $1,270 million. As a result during the ‘base year’ of the analysis,
generators incurred economic losses (compared to spot prices) of at least $1,900 million.23
Regardless, a nine month period is too short to draw meaningful conclusions on the levels of
industry competition and profits of a fleet of capital-intensive power stations with useful lives
spanning several decades.
The Table 4 analysis lacks a pragmatic and theoretically robust Normal Profit benchmark. The
application of Sections 3 and 4 along with the parameters from Section 5 can however provide
suitable insights. We have re-run the PF Model under conditions of a zero carbon price for the
relevant base plant in Victoria. We also analyse the financial viability of highly efficient new
entrants in the PF Model whereby the unit price
is set as an input equivalent to the FY12 value
in Table 3 rather than that derived by equation (21). Figure 7 illustrates these results.
This assumes the carbon price was passed-through at the industry’s average carbon intensity for the reasons explained Nelson, Orton
and Kelley (2012). One implication of this is that all brown coal generators are incurring losses on carbon costs because their CO 2
intensities of 1.28t – 1.55t/MWh are above the average intensity of 1.215t/MWh.
21
See in particular Mountain (2013, p.24).
22
See in particular the EUAA Media Statement “Power generation prices need closer monitoring” – released 27 June 2013. Available
at www.euaa.com.au.
23
In reality, hedge contracts struck at higher values in preceding periods would have reduced these loses materially. On the other
hand, the Victorian region is currently oversupplied and as such economic losses would have been greater than implied given the
additional capital stock deployed.
20
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AGL Applied Economic and Policy Research
Figure 7:
Comparison of generalised long run marginal costs with Table 4 FY12 spot prices
The horizontal line in Figure 7 represents the FY12 actual spot price of $25.82/MWh. This is
then compared with brown coal and CCGT plant entrants under the two business combinations,
project finance (PF) and a vertically integrated entity (VI) using BBB credit-rated debt. The first
two bars show the brown coal result for PF and VI, while the second two bars show the
equivalent results for a CCGT plant. The final two bars illustrate the financial out-workings that
coal plant (i.e. the lowest cost entrant excluding CO2) would face if exposed to a convergent
electricity price of $25.82/MWh.
From inspection of the final two bars in Figure 7 it is evident that the Brown Coal PF plant is
completely bankrupt and unable to pay its interest expense, let alone the principal. There are no
equity returns whatsoever. The Brown Coal VI plant, due to its substantially lower gearing level,
is theoretically able to withstand such a price and, assuming its BBB credit rating is held constant,
retains its financial stability. In reality the credit rating will have been stripped (meaning debt
covenants will have been breached requiring remedy), no taxation will be paid (due to the plant
making sizable taxation losses) and the running cash yield would equate to 1.8% compared to
10.0% when the plant is earning a Normal Profit.
Our quantitative results in Figure 7 make it clear that quasi-rents (partial contributions to fixed
costs) commence when prices exceed $28-$35/MWh. But at any price below $53/MWh, brown
coal generators are incurring ‘economic losses’. For a CCGT plant with gas supplied at $5/GJ,
short run marginal costs are not recovered until prices exceed $40/MWh, let alone fixed cost
recovery. Our generalised cost estimates paint a radically different picture to that expressed in
Table 4 in which competition is thought to be inadequate with generators extracting windfall
gains.
How should a policymaker react to such conflicting information? Real world events that
occurred in the period immediately preceding the carbon tax provide the appropriate guidance.
The two largest brown coal plants in Victoria, Loy Yang24 and Hazelwood25 were both recipients
24
AGL Energy acquired 100% of the 2200MW Loy Yang power station and coal mine in June 2012. The implied enterprise value
was $3.1 billion or $1410/kW. AGL Energy raised $1.5 billion from the debt and equity capital markets of which $1.2 billion was
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AGL Applied Economic and Policy Research
of emergency recapitalisations in June 2012 – of $1.2 billion and $650 million respectively.
Absent this, in our professional opinion (and noting that the first author is the former Chairman of
Loy Yang during FY09-FY10), both plants would have experienced financial collapse. Structural
adjustment assistance packages were issued to brown coal plant by the Commonwealth
Government in an attempt to moderate the most acute effects of the carbon price
implementation.26 Yet in spite of this, ex post emergency recapitalisations were still necessary.
Loy Yang for example incurred an equity write-off of c.$400 million or 40+% of the postacquisition equity value of $950 million – and this was after accounting for structural adjustment
assistance. The third largest brown coal plant in Victoria, Yallourn also incurred write-downs of
$245 million.27 These write-offs at the three largest brown coal plants occurred because of a legal
obligation Company Directors have to ensure that asset values are reported as fair and reasonable
under Sections 295-29728 of Australia’s Corporations Act 2001 (Cth).
Our observation is that these outcomes were not a surprise to the industry. Table 4 noted that
spot electricity prices in the pre-carbon environment were $25.82/MWh. They had in fact
averaged about $27 throughout FY11 and FY12, and as a result, many plants were in the early
stages of financial distress. That the incumbent plants lasted almost two years without defaulting
on project debt was due to commodity hedge contracts signed in prior years under considerably
more favourable market circumstances. However, as these hedge contracts progressively matured
and were replaced with lower value hedge contracts, emergency recapitalisations became
essential.
Using the Table 4 FY12 spot price result of $25.82 as an efficient benchmark and concluding
subsequent changes represented evidence of inadequate competition and windfall gains, while
those prices were simultaneously driving generators to a state of financial collapse, is not
credible. Figure 7 demonstrates that our Table 4 analysis uses the wrong benchmark over the
wrong timeframe and as a consequence, draws the wrong conclusion.
During FY13, the carbon price could be said to have been transmitted at a pass-through rate of
116% of the average industry CO2 intensity29 - but only after holding all other variables strictly
constant. That is, given a carbon price of $23/t, and emissions intensity of 1.215t/MWh, one
might expect an increase of ($23/t x 1.215t =) $27.94/MWh whereas FY13 spot prices increased
by $32.35/MWh to $58.17/MWh. So under these conditions, generator losses could be said to be
lower than in FY12 provided their output levels are held constant (although data from the
independent market operator reveals a substantial contraction in brown coal production, from
39,856 GWh to 34,112 GWh).30 Figure 8 illustrates the comparative impact with the PF Model
run using a $23/t carbon price.
used to recapitalise the project’s existing debt tranches. There is little doubt that when those debt tranches matured, refinancing would
have only been partially successful and additional equity injections would have been required.
25
The parent entity of Hazelwood power station, GDF Suez, injected $650m of ‘rescue capital’ into its project debt structure using an
intercompany loan during the last week of June 2012. Hazelwood had been unable to secure bank funding. For further details, see the
Australian Financial Review at http://www.afr.com/p/national/rescue_for_power_station_xk639CP4CyQuJIp9ndewYP
26
See Mountain (2013) for details of the structural adjustment assistance.
27
See CLP Group Financial Results (27 February 2012) for details. Available at https://www.clpgroup.com/.
28
Sections 296 and 297 in particular require the application of Australian Accounting Standard AASB136 – Impairment of Assets.
Failure to account for a fair and reasonable carrying value of fixed assets exposes Company Directors to penalties under the
Corporations Act 2001 (Cth), which include monetary fines and jail terms.
29
While the CO2 average intensity of the Victorian region is 1.215t/MWh, the fleet average CO2 intensity of the brown coal fleet is
closer to 1.37t/MWh as Simshauser and Doan (2009) demonstrate. Accordingly, the fleet pass-through rate could be thought of as
103% rather than 116%, again holding all other variables strictly constant.
30
The apparent price premium of $4.41/MWh, when applied to the nine-month FY13 energy output of 34,112 GWh results in an
apparent ‘windfall gain’ of $150 million. However, the loss of output from FY12 to FY13 (of 39,856 GWh less 34,112 GWh) at the
so-called break-even pass-through price of ($58.17 less $4.41/MWh) results in an even greater offsetting loss of $309 million. This
result further undermines the Table 4 analysis.
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Figure 8:
Generalised long run marginal costs vs. Table 4 FY13 carbon-inclusive spot prices
In this instance, the Normal Profit benchmarks change substantially, with brown coal plant rising
to $85-88/MWh, and CCGT plant at $72-$74/MWh. In a post-carbon price analysis, once again,
there is no evidence that windfall profits are being extracted. The final two bars in Figure 8 focus
on CCGT plant as they represent the optimal plant for base duties given a price on carbon. The
CCGT PF plant in Figure 8 is in manifest breach of its financing covenants – unable to repay its
full interest cost let alone principal repayment. The CCGT VI is however able to financially
withstand the lower price as was its Brown Coal VI counterpart in Figure 7 – although again the
firm would be stripped of its investment grade credit rating and would be in breach of debt
covenants. The running cash yield of the plant is just 0.2% compared to 11.2% when the plant is
producing Normal Profits.
One potential criticism of the analysis thus far is that the examination of market power occurs ex
post. However, analysing the price of call option contracts from the futures market provides ex
ante guidance. In particular, if market power abuse is present then we would expect to see
sustained increases in the price of $300 call option contracts across the three-year forward curve
at levels above our unit estimate for ̅ . But as with our analysis of base prices, year-ahead
futures prices for $300 call options in Victoria during 2013 were $4.35/MWh – less than half of
our unit value for ̅ of $10.47/MWh. Once again, there is little evidence of windfall gains.
6.4
Retail Markets
A pragmatic approach to the measurement of Normal Profit in power generation also has an
important relevance to retail electricity markets since the cost of power generation forms an
important part of the overall headline retail tariff. An example to illustrate the application of our
constructs to policymaking involved the determination of an ‘electricity price cap’ for rival
retailers in New South Wales. In determining the generalised long run marginal cost of power
generation, considerable effort was expended by the independent regulator on arriving at suitable
engineering plant and fuel cost estimates, along with credible evidence on the cost of capital from
the capital markets. However, once the data had been collated, two incompatible variables were
(inadvertently) fused in determining the relevant cost of capital, viz. the use of an investmentPage 23
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AGL Applied Economic and Policy Research
grade credit rating and associated credit margins from the corporate bond market, and the use of
gearing levels more suited to a project finance.
Table 5 presents an analysis of our global database of project financings which covers 1953
transactions, 3,772 tranches of debt commencing from the first power project financing in 1981
through to the time of writing in mid-2013, across 89 countries. Of these, only 7.6% of
transactions had a parent company guarantee and only a portion of these parent companies would
have investment grade credit ratings.31 The implication here is that project financings will not
involve credit-rated debt, and so project debt margins will, ceteris paribus, be higher than that
associated with investment-grade bond issuance. This was the result of misinterpreting the
capital structure constraints facing the business combinations.
Table 5: Analysis of project finance deal metrics (real 2013 AUD)
Period
Issuance
(A$m)
Global - 89 Countries
1981-2006
555,703
2007-2013
490,103
Total
1,045,806
Australia
1994-2006
2007-2013
Total
8,913
16,513
25,426
Deals
(#)
Tranches
(#)
Tenor Avg Spread
(Yrs)
(bps)
784
1,169
1,953
1,441
2,331
3,772
10.4
12.1
10.9
133
262
187
32
28
60
49
44
93
10
6
8
113
287
244
The impact of such a decision in policy formulation can be readily quantified through analysing
its impact on the Weighted Average Cost of Capital, which we define in Appendix III. In this
instance, the capital structure was assumed to comprise 50% debt at a spread of 260bps. The
spread for a BBB corporate bond was appropriate at that time based on observed data, but the
gearing level was not. As Figure 5 demonstrated earlier, a black coal plant in NSW could only
sustain gearing levels of about 32% and retain an investment-grade credit rating. The PF Model
is able to compute the generalised long run marginal cost after relaxing the credit rating
constraint, and impute an estimate given a 50% gearing level – the results of which are illustrated
in Figure 9. Note that the differential between the two scenarios equates to $4.29/MWh, and in a
market with total consumer load of 20,100 GWh pa, had a c.$88 million consequence. To be sure,
once the issue was highlighted to the NSW regulator, the framework was suitably modified at the
next pricing reset.
31
Our database shows all transactions listed in Reuters from 1981 through to June 2013. However, our data on guarantors only covers
1080 transactions. Of these 1080 transactions, 70 or 6.48% involved a guarantor – and it was not clear that those guarantors
necessarily had a credit rating in any event.
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Figure 9:
Generalised long run marginal cost – with and without credit rating constraints
7. Concluding Remarks
Policymakers and regulators governing competitive power markets, particularly those based on a
gross pool, energy-only market designs as exists in Australia, Texas, New Zealand, Singapore,
Alberta (Canada) and Europe amongst others, face an interesting dilemma. Our Proposition I and
associated static partial equilibrium model in Section 6 demonstrates that under conditions of
intense competition, perfect plant availability and divisibility with no transmission constraints,
energy-only markets result in clearing prices which are not economically viable in the long run.
When these simplifying assumptions are relaxed, things get worse, not better. One option,
operating a power system on ‘the edge of collapse’ as Bidwell and Henney (2004, p22) explain, is
not politically viable. This means that bidding must, by definition, deviate from strict (short run)
marginal cost at some stage. The judgement of the regulator is to determine whether deviations
represent a sustained departure in the presence of barriers to entry and are a potential abuse of
market power, or whether it merely represents quasi rents and a partial inter-temporal
contribution towards substantial fixed and sunk costs. All too often, regulatory inquiry is static
and ignores the essential time dimension. Policymakers in Australia and the regulator in Alberta
(respectively) clearly understand this balance:
Without affording electricity generators the opportunity to submit dispatch bids or rebids
above marginal cost, new capacity would fail to enter the market and the market would
become vulnerable to periods of inadequate supply. Wholesale market price volatility
and the ability of electricity generators to- from time to time- offer electricity into the
market at prices above marginal cost (sometimes even as high as the market price cap) is
entirely consistent with the design of the NEM… (AEMC, 2013, p. 65)
…wholesale price volatility and price polarity (periods of low prices interspersed with
shorter periods of high prices) are an expected outcome in an electricity market such as
Alberta’s and consistent with effective competition. In fact, these price signals promote
innovation and economic efficiency… (MSA, 2012, p.1).
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Two important inputs to the judgement required of policymakers and regulators were presented in
Sections 3 and 4 – the cost of equity and the long run marginal cost of generation plant, which
culminate in a theoretically robust measure of Normal Profit as a suitable ‘benchmark’ for which
to gauge activity over the business cycle.
We found that when using the CAPM in atypical capital market conditions, a mechanistic
approach will produce intuitively erroneous results. Longer-run average values were found to
provide for more credible outcomes but should nonetheless be tested against best-estimates for
marginal capital raisings to ensure they are reasonable. There is a wealth of investment banking
experience available to policymakers and regulators to draw upon if in doubt. It is also important
to ensure that the capital structure of the reference ‘business combination’ is tractable – if the
credit spreads on debt are based on an investment grade company, the gearing level selected must
also reflect the credit constraints of such a credit rating.
Our PF Model focused on two business combinations and found that there was little difference in
the ultimate long run marginal cost estimate, although the differences in the thresholds for
bankruptcy were marked. This analysis was then applied in an ex post analysis of base energy
prices against pragmatic estimates for the long run marginal cost of base plant, and an ex ante
analysis of call option prices against the carrying cost of peaking plant, using Victoria as a case in
point.
Prima facie it may be tempting to argue that our Normal Profit benchmark is overstated because
it ignores the fact that the actual plant mix is different from optimality, or that existing plant is
aged/depreciated or holds special resource endowments (such as long-dated fuel contracts at
below market rates). On the other hand, existing plant owners may argue that our benchmark
understates the real costs of existing businesses which were developed or acquired at higher cost
(i.e. when turbine prices were higher in real terms) or fail to account for the industrial/labour
market constraints.
Neither set of arguments holds in the long run. If profit benchmarks are raised to inefficient levels
and new entrants do not enter and compete away the available supranormal profit over the
business cycle, then material barriers to entry may exist and policy intervention may be warranted
where market power is being exercised. On the other hand, if profit benchmarks are set to
suboptimal levels, neither incumbents nor entrants will find it profitable in the long run which has
implications for reliability and an inevitable (and typically unwelcome) price correction of
significance over time. Ultimately, a pragmatic Normal Profit benchmark must be forward
looking, not only with respect to the cost of capital, but of what capital needs to be deployed to
meet incremental demand or replace retiring plant.
8. References
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Appendix I: CAPM and Gamma – accounting for investor level taxation effects
The CAPM outlined in equation (1) defines the cost of equity capital
on a post-tax basis under
a classical taxation system, that is, after corporate taxes and before investor-level taxes. With
dividend imputation credits available to investors in Australia, the expected
can be reduced to
take into account the tax paid on behalf of stockholders.32 Monkhouse (1993) and Officer (1994)
adjusted the Capital Asset Pricing Model to capture the effect of dividend imputation credits in
assessing the effective post-tax cost of equity capital. The Officer (1994) adjustment to the
CAPM model is as follows:
[
(
)
]
(
[(
)
) (
)]
(A1)
Where:
i
= the effective corporate taxation rate
= gamma, the utilization rate of imputation credits
The corporate taxation rate in Australia at the time of writing was 30%. However, the use of
the full value of in equation (A1) runs a high risk of an erroneous result for capital-intensive
assets such as power stations due to their particularly large tax depreciation base. That is, it may
overstate
and induce Type I investment errors by firms, or may result in an overly generous
profit benchmark for policymaking and regulation. The better view is to use the effective rate of
Taxation , and this can be readily estimated by dynamic financial models of power station
assets. Our PF Model finds values of 21.3% for coal plant and 22.8% for CCGT plant.
In order to apply the imputation credit adjustment , a reasonable assessment of the mix and
number of ‘Australian Taxpaying’ shareholders is required, because dividend imputation credits
can only be utilized by Australian taxpaying entities. Considerable debate exists as to the value
of . For example, Hathaway and Officer (2004) found the market places a positive value on
franking credits for Australian firms. Using ATO data and company Franking Account Balances,
they found that from 1988-2002, about $265 billion had been paid in company taxes while
Franking Account Balances totalled $77 billion. Accordingly, 71% of theoretical franking credits
had been accessed and 50% of distributed credits had been redeemed by taxpayers, thus
concluding = 0.5. Cannavan, Finn and Gray (2004, p.193) on the other hand found that while
the value of franking credits was initially valued at about 50% for high-yielding firms, following
the introduction of “the 45-day rule” in 199733, they found the value effects of imputation credits
to be negligible, implying a zero value. Gray (2013a) also reviewed a series of Independent
Expert valuation reports for publicly listed companies and found no evidence of Gamma being
used by practitioners over the past five years. In our analysis, we therefore explicitly assume =
0 and ignore equation (A1) and continue our analysis using equation (1). However, should
taxation law be changed at some point in the future such that Gamma once again becomes valued,
it would be appropriate to use equation (A1) in the Australian context.
32
The dividend imputation system was introduced in Australia in 1987 to avoid the double taxation of equity returns. Prior to
imputation, individual investors receiving the dividend stream were taxed twice; once as company profits and once more as dividends
(i.e. as income in the hands of the individual investor). Following its introduction, credit was given to shareholders for the tax levied
on their dividends at the company level. As a result, corporate tax may be considered a mixture of company and personal tax
(Monkhouse, 1993).
33
The 45 day rule effectively meant that the trade of franking credits by foreign investors could only occur if scrip was held for 45
days around the date of dividend entitlement.
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Appendix II: Mathematical Proof of Missing Money in Energy-Only Markets
“Under any optimal plant mix for any number of optimal plant technologies, aggregate revenues
will always fall short by at least ̅ ”
Proof by mathematical induction:
̅
̅
(
)
(
)
̅)
(
̅
̅
(
̅
̅
)
̅
̅
̅
̅
̅
(
)
(
(
̅
)
̅
(
̅
̅
̅
)
(
)
̅
̅
)
̅
̅
̅
(
)
∑(
)
̅
∑(
)
̅
∑(
)
̅
̅
̅
̅
̅
(
̅
)
̅
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̅
(
̅)
Working Paper No.38 – Normal Profit
AGL Applied Economic and Policy Research
Appendix III: Levelised Cost of Electricity Model
There are two methods for producing generalised long run marginal cost estimates for a given
generation plant technology, fully dynamic multi-period power project finance models and
Levelised Cost of Electricity models. With dynamic power project finance models, a vastly
greater number of inputs are used by comparison to Levelised Cost models, which in turn
generates a more accurate result, and typically, a lower result. However with considerably more
computations involved, the risk of error is also heightened. Dynamic power project finance
models discount post-tax future cash flows to the expected cost of equity
as outlined in
equation (1). Levelised Cost of Electricity models (see below) on the other hand discount pretax, pre-financing cost and production streams to the expected WACC as outlined in equation
(A2).
In some modelling exercises, pre-tax and pre-financing cash flows are discounted at Weighted
Average Cost of Capital to produce estimates of the long run marginal cost of power generation.
In this instance, equation (3) needs to be rearranged to produce a pre-tax estimate of , the cost
of debt needs to be introduced, and both the cost of equity and debt need to be weighted
according to their intended deployment, as follows:
{( )
(
)
–
(
)
)}
(
{( )
)}
(A2)
Where
Ei
Di
Vi
= is the value of equity of the ith firm
= is the value of debt of the ith firm
= Ei + Di
The estimation process for RT and CT is comparatively straight forward. For a project finance, the
primary variables required are debt tenors, the corresponding interest rate swap rate and the credit
spread offered by relevant project bank syndicate – all of which is invariably issued in local
currency in Australia. For bond issues the primary variables are the tenor, the [bank bill rate], the
credit spread, and any adjustment to account for exchange rate swaps for bonds issued in foreign
currency.
Levelised Cost Models involve a dramatically reduced number of variables, using pre-tax and
pre-financing capital and operating cash flows, discounted by the output of the plant using the
pre-tax WACC outlined in equation (4). The general form can be expressed as follows:
∑
[(
) ((
)
( )
)]⁄∑
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[(
)(
)
( )
]
(A3)
Working Paper No.38 – Normal Profit
AGL Applied Economic and Policy Research
Appendix IV: Declaration of the Authors
The authors of this working paper were employed by AGL Energy Ltd at the time of writing.
While the working paper represents the views of the authors, the research was completed as part
of AGL’s public policy development. This is influenced by AGL’s core business activities which
include developing, owning, and operating electricity generation; developing and producing coalseam gas; and retailing electricity and gas to more than 3.5 million customers in Australia.
Earlier drafts of the paper were reviewed by the AGL Applied Economic and Policy Research
Council and comments made by Council members were gratefully received by the authors. The
role of the Council is not to endorse working papers but provide constructive review. In this
context, all opinions, statements, errors and omissions are those of the authors and should not in
any way be attributed to the Council and its members. Members of the Council are Elizabeth
Nosworthy, Prof. Christine Smith, Prof. Stephen Gray, Dr. Judith McNeill, Keith Orchison, Tony
Brinker and Carlo Botto.
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