Cash flow model of an oil and gas project

Quick refresher

The model is a chain of formulas: production × price = revenue. From revenue we subtract the payments levied on revenue, operating and capital expenditure, income tax and abandonment costs. All the numbers rest on the assumptions sheet.
The production profile passes through build-up, plateau (steady production at the maximum rate) and decline, and is cut off at the economic limit. The first years of production decide the economics: in the example project more than half of the reserves are produced in the first three of seven years.
The price in the model is the field price (netback): the market price minus transport and the quality discount. Transport is counted once, either in the price or in the costs.
Operating expenditure consists of a fixed part and a variable part. As production declines, the cost per barrel rises. Production is stopped when the year's revenue, after the payments levied on it, no longer covers the costs that stopping would avoid.
Payments on revenue (royalty) do not depend on profit and raise the economic limit. Income tax is calculated year by year, with depreciation of capital expenditure and carry-forward of losses (a loss in one year reduces the tax of later years).
Costs do not fall together with the price, so the result does not change in proportion to the assumptions: in the example project a price 20% lower reduces the total cash flow by 41% and the net present value (NPV) at a rate of 10% by 57%.

Key relationships

\mathrm{NCF}_t = Q_t P_t - O_t - C_t - A_t - T_t

net cash flow of a year: revenue minus operating and capital expenditure, abandonment and payments to the state

Q_t = 365\,u\,q_t

annual volume from the daily flow rate $q_t$ and the uptime factor $u$

o_t = \dfrac{F}{Q_t} + v

operating expenditure per barrel rises as production declines

Q_{\text{lim}} = \dfrac{F}{P\,(1 - r) - v}

economic limit: the annual production at which revenue after royalty equals the costs

Common pitfalls

Multiplying the daily flow rate by 365 without allowing for downtime and for an incomplete first year.
Counting transport twice — in the field price and in operating expenditure — or not at all.
Mixing constant prices and nominal prices in one model: a “flat” nominal oil price with costs in constant prices.
Calculating income tax in a single line, “rate × profit for the project”, without spreading the deductions over the years.
Leaving in the profile the years when production is below the economic limit, and forgetting abandonment.
Typing numbers over formulas: such a model stops responding to changes in the assumptions.

After this lesson you can

describe the rows of the model and the order in which they are calculated, from the production profile to the net cash flow
describe the production profile (build-up, plateau, decline, economic limit) and convert flow rates into annual volumes and revenue
list the stages of capital expenditure and the main factors that decide its size, and distinguish fixed operating costs from variable ones
calculate the economic limit of production and explain how price, costs and payments levied on revenue affect it
describe in general terms how a model calculates payments to the state: on revenue, on profit, under production sharing terms
check a model: that the rows add up, the units, the kind of money, and the response to a change in assumptions

The model as a chain of calculations

In the lesson Project cash flow the project's cash flow is put together in a table: items in the rows, years in the columns. There the numbers were taken ready-made. A working model has almost no ready-made numbers. Every cell is a formula based on a small set of input assumptions. If the price or the start-up year changes, everything is recalculated, from revenue to taxes.

The calculation runs as a chain. The production profile multiplied by the price gives revenue. We subtract from it the payments that depend on revenue, and the operating expenditure. Capital expenditure is subtracted in the year it is paid, but it enters the income tax calculation gradually, through depreciation. At the end of the project's life, the abandonment costs are added as a further cost.

Net cash flow of a year by the rows of the model

\mathrm{NCF}_t = Q_t\,P_t - O_t - C_t - A_t - T_t

where:

$\mathrm{NCF}_t$ net cash flow of year $t$ , US$ million
$Q_t$ sales volume of the year, million bbl
$P_t$ field price, $/bbl
$O_t$ operating expenditure, US$ million
$C_t$ capital expenditure in the year it is paid, US$ million
$A_t$ abandonment costs, US$ million
$T_t$ payments to the state: on revenue and on profit, US$ million

Units: US$ million per year; all rows in the same kind of money (constant prices or nominal) and in one currency

Holds when

the same formula as in the lesson on cash flow, except that revenue is expanded into volume times price and abandonment is separated from capital expenditure
each row is assigned to the year of actual payment; depreciation is not in the formula, because it is needed only to calculate the tax
if there are several products, revenue is summed over the products

Each term is a separate row of the model with its own formula and its own source of data. The value of a model is that the rows are linked. Lower production means lower revenue, royalty, variable costs and tax, but not lower fixed costs.

Rows of the model and their sources

Row: Production profile
Who provides the forecast: reservoir and development engineers: analogues (similar fields), material balance, reservoir simulation model
What determines it: reserves, the number and productivity of wells, the capacity of the facilities

Row: Price
Who provides the forecast: the commercial department, the company's scenarios
What determines it: the market, product quality, the route to the buyer

Row: Capital expenditure
Who provides the forecast: drilling engineers, designers, cost estimators
What determines it: depth and number of wells, the development scheme, infrastructure

Row: Operating expenditure
Who provides the forecast: the operations department
What determines it: staff, energy, repairs, the volume of liquid, transport

Row: Payments to the state
Who provides the forecast: tax specialists
What determines it: legislation and the terms of the contract

Row: Abandonment
Who provides the forecast: designers
What determines it: the number of wells and facilities, reclamation requirements

Row	Who provides the forecast	What determines it
Production profile	reservoir and development engineers: analogues (similar fields), material balance, reservoir simulation model	reserves, the number and productivity of wells, the capacity of the facilities
Price	the commercial department, the company's scenarios	the market, product quality, the route to the buyer
Capital expenditure	drilling engineers, designers, cost estimators	depth and number of wells, the development scheme, infrastructure
Operating expenditure	the operations department	staff, energy, repairs, the volume of liquid, transport
Payments to the state	tax specialists	legislation and the terms of the contract
Abandonment	designers	the number of wells and facilities, reclamation requirements

The model brings the forecasts of different departments into the same units, and this is where the discrepancies between them show up. For example, a production profile may assume 30 wells while the budget pays for 25.

CalculatedWhere the revenue of the example project goes over its whole life: out of US$600 million of revenue, after royalty, operating expenditure, income tax, capital expenditure and abandonment, US$210.4 million of net cash flow remains for the owners.

The example project over its whole life: totals by row

Row: Revenue
Total, US$ million: 600.0
Share of revenue: 100%
Per barrel, US$: 50.00

Row: Royalty
Total, US$ million: −60.0
Share of revenue: 10.0%
Per barrel, US$: 5.00

Row: Operating expenditure
Total, US$ million: −102.0
Share of revenue: 17.0%
Per barrel, US$: 8.50

Row: Income tax
Total, US$ million: −55.6
Share of revenue: 9.3%
Per barrel, US$: 4.63

Row: Capital expenditure
Total, US$ million: −160.0
Share of revenue: 26.7%
Per barrel, US$: 13.33

Row: Abandonment
Total, US$ million: −12.0
Share of revenue: 2.0%
Per barrel, US$: 1.00

Row: NCF
Total, US$ million: 210.4
Share of revenue: 35.1%
Per barrel, US$: 17.53

Row	Total, US$ million	Share of revenue	Per barrel, US$
Revenue	600.0	100%	50.00
Royalty	−60.0	10.0%	5.00
Operating expenditure	−102.0	17.0%	8.50
Income tax	−55.6	9.3%	4.63
Capital expenditure	−160.0	26.7%	13.33
Abandonment	−12.0	2.0%	1.00
NCF	210.4	35.1%	17.53

Production over the project is 12 million bbl. The sums are added without discounting, in constant prices. The data in this example are assumed for illustration.

Production profile: build-up, plateau, decline

Revenue starts with production, so the first row of the model is the production profile: the volume of output by year. For most fields it passes through four stages.

Build-up: Production grows with the number of producing wells, so the pace of growth is set by the drilling schedule and the productivity of the first wells. We can speed it up by drilling some of the wells ahead of time, before the facilities are ready. Almost anything can disrupt build-up, from a drilling accident to a reservoir that turns out worse than forecast. A delay in the first years hurts the economics more than anything else.
Plateau: Production is no longer limited by the reservoir but by the capacity of the facilities and the number of wells. The height and duration of the plateau are a design decision.
Decline: The reservoir can no longer sustain the plateau: pressure falls, and the output contains more and more water and gas. An accumulation made up of isolated blocks declines faster than a single accumulation with an active edge-water drive (water at the edge of the reservoir that pushes the oil towards the wells). Several measures slow the decline: infill wells (new wells between the old ones), water or gas injection, pumps and gas lift (lifting oil by injecting gas into the well). Each such measure is appraised as a separate project.
Economic limit: Production is stopped when it no longer pays for the running expenses. This happens earlier than the reservoir is physically depleted.

CalculatedProduction profile of the example project: two years of development, build-up, a two-year plateau and decline. The light bars show an assumed continuation of production, declining by 30% a year, from the example on the economic limit. The dashed line is the limit, 0.15 million bbl a year.

The higher the plateau, the sooner the oil is produced and the more it is worth in today's money (Discounting and present value). The reserves do not grow as a result: the same oil is simply produced earlier. So why is the plateau not made as high as possible? Four circumstances limit it.

The reservoir. In some accumulations, if oil is taken out too fast, water or gas breaks through to the wells and bypasses the oil, and the ultimate oil recovery falls.
Costs. Every additional thousand barrels a day means more wells, separators (vessels that separate oil, gas and water), pumps and larger pipes. Capacity that is fully used for three years out of fifteen has to pay for itself within those three years.
Sales. Oil can usually be sold in any quantity, but gas can be sold only in the amount written into the supply contract and accepted by the pipeline. So gas fields have a lower and longer plateau.
The rules. The state approves the field development plan, and it may have its own requirements for the rate of withdrawal and for oil recovery.

So the plateau is a compromise. We compare options with different plateau heights by net present value (NPV), and we appraise an acceleration of production as a separate investment (Acceleration projects and incremental analysis).

A useful measure of a profile is the annual withdrawal on the plateau as a share of the recoverable reserves (the oil that can be produced). For large fields it is usually a few per cent a year, and for small ones 10% or more. This is a guide, not a standard. We use it to check whether a profile is plausible, not to build one.

Before development begins, we build the profile from analogues (similar fields) and simple calculations. Later we build it from material balance (an account of the oil and the pressure in the reservoir) and a reservoir simulation model (a computer model of the reservoir). In any case, the sum of production over all the years cannot exceed the recoverable reserves, which are the oil in place (Volumetric estimation of hydrocarbons in place) multiplied by the recovery factor. This is the first check of a profile.

Annual volume from the daily flow rate

Q_t = 365\,u\,q_t

where:

$Q_t$ production in year $t$ , bbl per year
$q_t$ average daily flow rate of the field on the days when the facilities operate, bbl/d
$u$ uptime factor: the fraction of calendar time during which the facilities operate, fraction

Units: any consistent set: bbl/d and bbl per year, t/d and t per year, m³/d and m³ per year

Holds when

$q_t$ is the average flow rate over the year; if only the rates at the start and the end of the year are known, an average is taken that allows for the shape of the decline curve
in the year of start-up and the year of shutdown, the actual number of days of operation is used instead of 365
$u$ allows for planned repairs and downtime; it is taken from the operating experience of similar facilities

A handy rule: a flow rate in thousand barrels a day, multiplied by 0.365, gives million barrels a year when the facilities run without downtime.

In other unit systems (1)

Tonnes and barrels

Q\,[\text{bbl}] = \frac{6.2898}{\rho}\;m\,[\text{t}]

$m$ is the mass of the oil in tonnes, $\rho$ is its density in t/m³ at 60 °F (15.6 °C), to which the volume of a barrel is referred (barrels per tonne).

6.2898 is the number of barrels in a cubic metre. At $\rho = 0.86$ t/m³ a tonne holds about 7.31 barrels.

Worked exampleThe profile of the example project in numbers

Given (assumed data)

Production in years 3–9: 1.6; 2.4; 2.4; 2.0; 1.6; 1.2; 0.8 million bbl
Oil density: 0.86 t/m³
Uptime factor $u$: 0.95

Solution

Recoverable reserves are the sum of the profile: 12 million bbl, or $12/7.31 = 1.64$ million t.
Withdrawal on the plateau: $2.4/12 = 20$ % of the reserves a year — typical of a small field.
Average flow rate on the plateau per calendar day: $2.4\cdot 10^{6}/365 = 6575$ bbl/d, that is 1045 m³/d, or 899 t/d.
The facilities operate 95% of the time, so their capacity must be at least $6575/0.95 = 6921$ bbl/d.
By the end of the plateau, that is in the first three of the seven years of production, 6.4 million bbl, or 53% of the reserves, have been produced.

Answer: The plateau is 6575 bbl/d (899 t/d), or 20% of the reserves a year; it needs facility capacity of about 6921 bbl/d.

What it means. More than half of the oil is produced in the first three years, and these are the years that lose least value in discounting. So an error in the start-up date or in the pace of the build-up costs the project more than an error of the same size in the production “tail”. Facility capacity is an example of the link between rows: a higher plateau means higher capital expenditure too. The data in this example are assumed for illustration.

Price and revenue

Revenue is the sales volume multiplied by the price, for each product. Besides oil, an oil field yields associated gas (gas that comes out with the oil), and liquid hydrocarbons can be separated from the gas. A gas field yields gas and condensate (a light liquid). If there is little associated gas, gathering and transporting it may not pay. Then the gas is injected back into the reservoir, used for the field's own needs or, where this is still allowed, flared (burned off). It brings no revenue, but it does bring costs. At fields where liquid hydrocarbons and gas are about equal in value, the main product depends on the ratio of prices, so we set a price scenario for both.

Revenue and the field price

R_t = \sum_j Q_{j,t}\,P_{j,t}, \qquad P_{j,t} = P^{\text{mkt}}_{j,t} - d_j - c_j

where:

$R_t$ revenue of year $t$ , US$ million
$Q_{j,t}$ sales volume of product $j$ : production less own use, losses and reinjection, million bbl, billion m³
$P_{j,t}$ field price of the product, $/bbl, $ per thousand m³
$P^{\text{mkt}}_{j,t}$ market price to which the sale is linked: the benchmark crude (a reference grade of oil, such as Brent), the gas price at the delivery point, same
$d_j$ quality discount (for a premium the sign is reversed), same
$c_j$ cost of transport to the market, if it is not included in operating expenditure, same

Units: volume and price in consistent units; the price in the same kind of money as the whole model

Holds when

transport is counted once: either deducted from the price or shown as a line of operating expenditure
the price is a scenario assumption, not a prediction; the model must allow it to be changed in a single cell
in a model in constant prices the price is set in constant prices: an unchanged nominal price means that in real terms it declines (Inflation: nominal and real money)

The field price is called the netback. It shows how much the project receives for a barrel “at the exit from the field”, and it can be compared directly with the cost per barrel.

The price of $50/bbl in the example project is already a field price. It could have come about, for example, like this: a market price of the benchmark crude of $60/bbl, a quality discount of $2/bbl, and transport by pipeline and by sea of $8/bbl. All three numbers are assumed. What matters is that an expensive route to market reduces revenue just as a low price does.

Gas is sold in other units, per thousand cubic metres or per unit of energy, and in other markets, often under long-term contracts. To add up oil and gas production, we convert gas into barrels of oil equivalent by its heat of combustion (the heat it gives when burned): about 6 thousand cubic feet, or roughly 170 m³, per barrel. This is a conversion of energy, not of money. We calculate revenue from gas from the price of gas, and we do not multiply equivalent barrels by the oil price.

Another source of revenue is a fee for services. If the project accepts someone else's production into its pipeline or onto its treatment plant, it receives a tariff (a fee) for every barrel. For the owner of the facilities this is revenue that can prolong their life after their own production has declined. For the user it is operating expenditure in place of capital expenditure of its own.

Capital expenditure: stages and factors

The capital expenditure of an exploration and production project does not arise all at once, but in several stages. Before each stage the company takes a separate decision, with its own appraisal.

Stages of capital expenditure

Stage: Exploration
What is paid for: seismic surveys, exploration wells
Which decision is appraised: whether to drill a well; after a discovery, whether to appraise it

Stage: Appraisal
What is paid for: appraisal wells, tests, extended well test
Which decision is appraised: whether to develop the field, and with which scheme

Stage: Development and drilling
What is paid for: production and injection wells, gathering and treatment of the product, pipelines, power supply
Which decision is appraised: the main investment decision; usually the largest sum

Stage: Further investment during production
What is paid for: infill drilling, pressure maintenance, artificial lift, gas compression
Which decision is appraised: each measure is its own incremental project

Stage: Abandonment
What is paid for: plugging and abandoning wells, dismantling facilities, reclamation
Which decision is appraised: mandatory; its timing depends on the economic limit

Stage	What is paid for	Which decision is appraised
Exploration	seismic surveys, exploration wells	whether to drill a well; after a discovery, whether to appraise it
Appraisal	appraisal wells, tests, extended well test	whether to develop the field, and with which scheme
Development and drilling	production and injection wells, gathering and treatment of the product, pipelines, power supply	the main investment decision; usually the largest sum
Further investment during production	infill drilling, pressure maintenance, artificial lift, gas compression	each measure is its own incremental project
Abandonment	plugging and abandoning wells, dismantling facilities, reclamation	mandatory; its timing depends on the economic limit

The costs of past stages have already been spent by the time of the next decision. They are sunk costs and do not enter its appraisal (Project cash flow).

What decides the largest sum, the cost of development and drilling? It is convenient to divide the causes into three groups: what nature gives, what the designer chooses, and what does not depend on the project.

What determines capital expenditure on development

Group: Nature: location
What exactly: land or sea, water depth, distance from roads, pipelines and the market
How it affects the cost: offshore and far from infrastructure the costs are several times higher; a long route to market also means a pipeline or a tariff

Group: Nature: reservoir and fluid
What exactly: depth, pressure and temperature; size of the accumulation and how it is divided into blocks; oil viscosity (thickness), gas fraction, hydrogen sulfide and carbon dioxide
How it affects the cost: depth sets the cost of a well, and the structure of the accumulation sets the number of wells; gas, viscous oil and acid gases (hydrogen sulfide and carbon dioxide) need more complex and more expensive treatment

Group: Project decisions
What exactly: number and type of wells, plateau height, gathering and treatment scheme, buying, leasing or using someone else's facilities for a tariff
How it affects the cost: a horizontal well costs more than a vertical one but replaces several; other parties' capacity replaces capital expenditure with operating expenditure

Group: External conditions
What exactly: prices of steel, equipment and contractors' services; safety and environmental requirements
How it affects the cost: change independently of the project and can move the estimate in either direction

Group	What exactly	How it affects the cost
Nature: location	land or sea, water depth, distance from roads, pipelines and the market	offshore and far from infrastructure the costs are several times higher; a long route to market also means a pipeline or a tariff
Nature: reservoir and fluid	depth, pressure and temperature; size of the accumulation and how it is divided into blocks; oil viscosity (thickness), gas fraction, hydrogen sulfide and carbon dioxide	depth sets the cost of a well, and the structure of the accumulation sets the number of wells; gas, viscous oil and acid gases (hydrogen sulfide and carbon dioxide) need more complex and more expensive treatment
Project decisions	number and type of wells, plateau height, gathering and treatment scheme, buying, leasing or using someone else's facilities for a tariff	a horizontal well costs more than a vertical one but replaces several; other parties' capacity replaces capital expenditure with operating expenditure
External conditions	prices of steel, equipment and contractors' services; safety and environmental requirements	change independently of the project and can move the estimate in either direction

Someone else's facilities have their own service life, which is checked against the life of the project. Standard solutions are cheaper than unique ones.

In the model, capital expenditure is entered in the year it is paid. The estimate is spread over the drilling and construction schedule. A contingency (a reserve sum for unforeseen work) is added, and the earlier the stage of project definition, the larger it is. A shift in the schedule changes both the financing requirement and the NPV, even if the total is the same (Cumulative cash flow and payback period). Abandonment costs go into a separate row at the end of the project's life. They are easy to forget because they are far off, but the obligation arises with the first well.

Operating expenditure and the economic limit

Operating expenditure is everything needed to keep the field running: staff, electricity and fuel, chemicals, maintenance and repair of equipment, well workovers, water treatment and disposal, transport of the product and tariffs for other parties' facilities, equipment rental, insurance, administrative expenses. In the model it is shown for the years of production.

Part of these costs hardly depends on production: staff and maintenance of the facilities are needed as long as the field is running. Another part grows with the volume: energy for lifting and pumping the liquid, chemicals, the transport tariff. A simple model is written exactly that way: a fixed sum per year plus a rate per barrel. In the example project it is US$6 million a year and $5/bbl. A detailed model ties each item to what it really depends on: the number of wells, the volume of liquid produced together with water, and the volume of injection. This is why at a late stage, when the water cut (the share of water in the liquid produced) grows, the cost per barrel of oil rises faster than the simple formula implies.

Operating expenditure per barrel

o_t = \frac{O_t}{Q_t} = \frac{F}{Q_t} + v

where:

$o_t$ operating expenditure per barrel in year $t$ , $/bbl
$O_t$ operating expenditure of the year, US$ million
$Q_t$ production of the year, million bbl
$F$ fixed costs per year, US$ million
$v$ variable costs, $/bbl

Units: US$ million divided by million bbl gives $/bbl

Holds when

costs are divided into a fixed part and a part proportional to production
all sums are in constant prices of one year

While production is on the plateau, the cost per barrel is at its minimum. As production declines, the fixed part is divided by a smaller and smaller volume, and the cost per barrel rises: slowly at first, and very fast at the end. These costs show the price (after the payments levied on revenue) below which it is more profitable for a working field to shut down. If we arrange the fields of a region in ascending order of these costs, we can see what share of production withstands a given price.

Sooner or later the revenue of a given year stops covering the expenses of that year. To continue production beyond that point is to lose money every year. The annual production at which revenue, after the payments levied on it, equals the costs is called the economic limit.

Economic limit of production

Q_{\text{lim}} = \frac{F}{P\,(1 - r) - v}

where:

$Q_{\text{lim}}$ annual production at the economic limit, million bbl per year
$F$ fixed costs of the year that can be avoided by stopping production, US$ million
$P$ field price, $/bbl
$r$ share of revenue taken by the payments levied on revenue (royalty), fraction
$v$ variable costs, $/bbl

Units: US$ million per year divided by $/bbl gives million bbl per year

Holds when

only what depends on the decision to stop is compared: next year's revenue and costs. Past capital expenditure and depreciation do not take part in the comparison
income tax takes a share of positive profit and does not change the sign of the result, so it is not in the formula
abandonment costs lie ahead under either decision; only their timing depends on it (see the advanced section)
the formula holds while the denominator is positive: if the price after royalty is below the variable costs, every barrel loses money

Production continues as long as the annual volume is above $Q_{\text{lim}}$ . Per barrel, the same condition reads like this: the cost per barrel $F/Q + v$ must not exceed the price after the payments levied on revenue, $P(1 - r)$ . The limit is higher when the price is lower, when the fixed costs are larger, and when the payments that do not depend on profit are larger.

To keep the tables short, the production of the example project stops in year 9, when it is still far from the limit. Now we see what a “tail” of production would give, and where it would have to be cut off.

Worked exampleWhen to shut down a field

Given (assumed data)

Price and royalty: $50/bbl; royalty 10% of revenue
Operating expenditure: US$6 million a year + $5/bbl
Production after year 9: declines by 30% a year: 0.56; 0.39; 0.27; 0.19; 0.13 million bbl in years 10–14

Solution

After royalty and variable costs, each barrel leaves $50\cdot 0.9 - 5 = 40$ dollars.
Economic limit: $6/40 = 0.15$ million bbl a year — about 411 bbl/d, or 56 t/d, for the whole field.
In years 10–13 production is above the limit; revenue less royalty and operating expenditure is 16.4, 9.7, 5.0 and 1.7 million dollars.
In year 14 production, 0.1345 million bbl, is below the limit: $40\cdot 0.1345 - 6 = -0.62$ million dollars. The cost per barrel reaches $49.6 against a price after royalty of $45.
If production continues to the end of year 13, production over the project rises from 12 to 13.4 million bbl, the total cash flow from 210.4 to 236.6 million dollars, and the NPV at 10% from 100.1 to 112.1 million dollars.
Without royalty the limit would be $6/45 = 0.133$ million bbl a year, and at a price of $30/bbl it would be $6/22 = 0.273$ million bbl a year: the last profitable year would be year 12.

Answer: The economic limit is 0.15 million bbl a year; it is profitable to produce until the end of year 13, which adds 12% to production and 12% to NPV.

What it means. The economic limit is not a property of the reservoir. It moves with the price, the costs and the terms of payments. That is why recoverable reserves are also an economic quantity: at a price of $30 the same reservoir yields less oil (Classification of reserves and resources). Royalty is levied on revenue regardless of profit, and it stops production earlier than income tax would. The data in this example are assumed for illustration.

CalculatedOperating expenditure per barrel in the example project and in its assumed “tail”: $7.5 on the plateau, $12.5 in year 9, and in year 14 it exceeds the price after royalty, $45/bbl. This is the economic limit expressed in cost per barrel.

Payments to the state in the model

The terms of subsoil use are different in every country, and often in every contract, and they change over time. But in a cash flow model almost any payment to the state belongs to one of a few types, and each type is calculated in the same way.

Types of payments to the state and their place in the model

Type of payment: On production or revenue: royalty, mineral extraction tax, export duty
What it is calculated on: the volume or value of the production
What matters in the model: start from the first tonne and do not depend on profit; raise the economic limit

Type of payment: On profit: general income tax, special taxes on income from subsoil use
What it is calculated on: revenue minus permitted deductions
What matters in the model: deduction rules are needed: running costs at once, capital costs through depreciation, losses by carrying forward to future years (moving them to later years)

Type of payment: On excess profit
What it is calculated on: profit above a set rate of return or a set ratio of income to costs
What matters in the model: apply only to profitable projects; calculated on a cumulative basis

Type of payment: Production sharing
What it is calculated on: production: part goes to recover the investor's costs, the rest is shared between the state and the investor
What matters in the model: the model calculates shares of production, not a tax; cost recovery in a year is usually capped

Type of payment: One-off and fixed: bonuses, area fees, contributions to an abandonment (sinking) fund, social obligations
What it is calculated on: the terms of the contract
What matters in the model: depend on neither production nor profit; often fall in the early years

Type of payment	What it is calculated on	What matters in the model
On production or revenue: royalty, mineral extraction tax, export duty	the volume or value of the production	start from the first tonne and do not depend on profit; raise the economic limit
On profit: general income tax, special taxes on income from subsoil use	revenue minus permitted deductions	deduction rules are needed: running costs at once, capital costs through depreciation, losses by carrying forward to future years (moving them to later years)
On excess profit	profit above a set rate of return or a set ratio of income to costs	apply only to profitable projects; calculated on a cumulative basis
Production sharing	production: part goes to recover the investor's costs, the rest is shared between the state and the investor	the model calculates shares of production, not a tax; cost recovery in a year is usually capped
One-off and fixed: bonuses, area fees, contributions to an abandonment (sinking) fund, social obligations	the terms of the contract	depend on neither production nor profit; often fall in the early years

The lesson Petroleum fiscal systems and taxation covers how these mechanisms are built and how they have changed in different countries. Take the current rates and rules from the country's legislation and from the contract, not from the examples.

Four general properties of these calculations matter when we build a model. The examples in this lesson use a deliberately simple assumed regime that does not reproduce the legislation of any country.

Order. Payments are calculated in a chain, because some are deducted in calculating others: royalty usually reduces taxable profit. A wrong order is an error in all the years at once.
Memory. Income tax depends on past years: on the balance of costs not yet depreciated and on accumulated losses. So it is calculated year by year, not in a single line “rate × profit for the project”.
Boundaries. The rules decide whether the costs of one project can be deducted from the income of another. A ban on this is called a “ring fence”. If it is allowed, a new project reduces the company's taxes even before its first oil, and this saving is its incremental cash flow.
Kind of money. Taxes are calculated in nominal money; depreciation deductions do not grow with inflation (Inflation: nominal and real money).

Income tax calculation in the example project, US$ million

Year: Year 3
Revenue: 80.0
Royalty and costs: 22.0
Depreciation: 32.0
Income tax: 5.2

Year: Year 4
Revenue: 120.0
Royalty and costs: 30.0
Depreciation: 32.0
Income tax: 11.6

Year: Year 5
Revenue: 120.0
Royalty and costs: 30.0
Depreciation: 32.0
Income tax: 11.6

Year: Year 6
Revenue: 100.0
Royalty and costs: 26.0
Depreciation: 32.0
Income tax: 8.4

Year: Year 7
Revenue: 80.0
Royalty and costs: 22.0
Depreciation: 32.0
Income tax: 5.2

Year: Year 8
Revenue: 60.0
Royalty and costs: 18.0
Depreciation: 0.0
Income tax: 8.4

Year: Year 9
Revenue: 40.0
Royalty and costs: 14.0
Depreciation: 0.0
Income tax: 5.2

Year: Total
Revenue: 600.0
Royalty and costs: 162.0
Depreciation: 160.0
Income tax: 55.6

Year	Revenue	Royalty and costs	Depreciation	Income tax
Year 3	80.0	22.0	32.0	5.2
Year 4	120.0	30.0	32.0	11.6
Year 5	120.0	30.0	32.0	11.6
Year 6	100.0	26.0	32.0	8.4
Year 7	80.0	22.0	32.0	5.2
Year 8	60.0	18.0	0.0	8.4
Year 9	40.0	14.0	0.0	5.2
Total	600.0	162.0	160.0	55.6

“Royalty and costs” is royalty plus the operating expenditure of the year. Tax = 20% × (revenue − royalty and costs − depreciation). The sum of depreciation equals the capital expenditure, US$160 million, and this is one of the checks of the model. The data in this example are assumed for illustration.

In year 8 revenue is lower than in year 7, but the tax is higher, because depreciation has ended. This is how the model “remembers” past years. Another feature shows up when the price is changed.

The example project at different oil prices

Price: $30/bbl
NCF over the project, US$ million: 37.6
NPV₁₀, US$ million: −13.7
IRR, %: 6.7
Government take, %: 56

Price: $40/bbl
NCF over the project, US$ million: 124.0
NPV₁₀, US$ million: 43.3
IRR, %: 19.2
Government take, %: 40

Price: $50/bbl
NCF over the project, US$ million: 210.4
NPV₁₀, US$ million: 100.1
IRR, %: 29.6
Government take, %: 35

Price: $60/bbl
NCF over the project, US$ million: 296.8
NPV₁₀, US$ million: 157.0
IRR, %: 38.7
Government take, %: 33

Price: $70/bbl
NCF over the project, US$ million: 383.2
NPV₁₀, US$ million: 213.9
IRR, %: 47.1
Government take, %: 32

Price	NCF over the project, US$ million	NPV₁₀, US$ million	IRR, %	Government take, %
$30/bbl	37.6	−13.7	6.7	56
$40/bbl	124.0	43.3	19.2	40
$50/bbl	210.4	100.1	29.6	35
$60/bbl	296.8	157.0	38.7	33
$70/bbl	383.2	213.9	47.1	32

Government take is the sum of payments to the state divided by the project's cash flow before these payments (revenue minus all costs), without discounting. NPV₁₀ is net present value at a rate of 10%, IRR is the internal rate of return (Net present value (NPV), Internal rate of return (IRR)). The data in this example are assumed for illustration.

The poorer the project, the larger the share of its cash flow that the state takes: 56% at a price of $30 against 32% at $70. The reason is royalty: it is paid on revenue even when there is almost no profit. A regime in which such payments dominate is called regressive (the state takes a larger share from poorer projects). Income tax at a constant rate takes the same share of profit. Excess profit taxes make a regime progressive: the government take rises together with the profitability of the project.

Assembling the model, timing of payments and checks

Order of assembly

1
Assumptions sheet
All the input numbers in one place, with units, the kind of money (constant prices of which year, or nominal) and the date for which they hold.
2
Production and sales
The profile by year, conversion of units, deduction of own use and losses.
3
Prices and revenue
The field price for each product; revenue is the product of volume and price.
4
Capital expenditure and abandonment
The estimate by year of payment, with a contingency; abandonment after the last year of production.
5
Operating expenditure
A fixed part and parts tied to production, the number of wells and the volume of liquid.
6
Payments to the state
First the payments levied on revenue, then depreciation, carry-forward of losses and income tax, year by year.
7
Cash flow and indicators
NCF by year, cumulative flow, NPV, IRR, payback period (Cumulative cash flow and payback period, Net present value (NPV), Internal rate of return (IRR)).
8
Checks
That the rows add up, the units, and the response to a change in assumptions (see the list below).

We choose the period, the moment of the flow within the year and the time origin as described in the lesson Project cash flow: usually a calendar year and mid-year. Assembling the rows raises a few more questions about timing.

Year of start-up. If production begins in October, a quarter of the annual volume falls in the first year, not all of it. The same applies to the year of shutdown.
Payment delays. Revenue arrives a few weeks after shipment, taxes are paid in advance or after the end of the period, and contractors are paid by stages of work. An annual model usually neglects this. A monthly model, which is needed for the financing plan, takes it into account.
One convention for all rows. If revenue is assigned to the middle of the year, then so are costs and taxes. A large payment at the start of the year, such as a bonus, is shown separately.
Date of the assumptions. Last year's estimate and this year's price are money of different years. Before assembly we bring them to one year (Inflation: nominal and real money).

We check a finished model before we look at its indicators.

The sum of production over the years equals the recoverable reserves adopted in the project.
The sum of depreciation equals the capital expenditure. Losses carried forward are used by the end of the project, or are shown explicitly as unused.
The project's NCF equals revenue minus all costs and payments, both by rows and by columns.
At a zero price only costs remain in the model; when the price changes by 10%, revenue changes by exactly 10%.
In the last years of production, revenue after the payments levied on it covers operating expenditure, so the profile does not go beyond the economic limit.
Every row has its units and kind of money labelled; no number is typed over a formula.

Worked exampleThe model at work: a price 20% lower

Given (assumed data)

Project: from the library's examples; one assumption changes
Field price: $40/bbl instead of $50
Discount rate: 10% (real)

Solution

Year 4: revenue $2.4\cdot 40 = 96$ million dollars, royalty 9.6 million dollars; operating expenditure (18) and depreciation (32) are unchanged.
Income tax: $0.2\cdot(96 - 9.6 - 18 - 32) = 7.28$ million dollars; the NCF of the year is 61.12 million dollars instead of 78.4.
Over the whole project, revenue is 480 million dollars (20% less), and NCF is 124.0 instead of 210.4 million dollars: 41% less.
NPV at 10% is 43.3 instead of 100.1 million dollars (57% less); the internal rate of return is 19.2% instead of 29.6%.
By trial and error we find the price at which NPV at 10% is zero: $32.4/bbl.

Answer: A price 20% lower reduces the project's NCF by 41% and its NPV at 10% by 57%; the project withstands a price down to $32.4/bbl.

What it means. The result does not change in proportion to the price, because costs do not fall together with revenue. The whole loss of revenue, except for the share borne by royalty and tax, falls on the owners' cash flow. The price at which NPV becomes zero is a handy measure of the safety margin. We compare it with the prices in the company's scenarios (Sensitivity analysis and scenarios). The data in this example are assumed for illustration.

Terms and symbols

Production profile: Production by year: build-up, plateau, and decline to the economic limit.
Production plateau: The period of highest production, limited by the capacity of the facilities and the number of wells.
Field price (netback): The market price minus the cost of transport to the market and the quality discount.
Fixed and variable costs: Fixed costs are the part of operating expenditure that does not depend on production. Variable costs are the part that is proportional to it.
Economic limit: The annual production below which revenue, after the payments levied on it, does not cover the costs that stopping would avoid.
Depreciation for tax: The spreading of capital expenditure over the years in calculating income tax. It is not part of the cash flow itself.
Government take: The ratio of the sum of payments to the state to the project's cash flow before these payments.

Common mistakes and misconceptions

Wrong

“The production profile is the developers' business; the economics just accepts it.”

In fact

The profile, the costs and the economics are linked. The height of the plateau decides the number of wells and the capacity of the facilities, and the end of the profile, the economic limit, depends on price and costs. The profile and the costs are agreed in one model.

Wrong

“Transport is already included in the field price, but just in case let us add it to operating expenditure as well.”

In fact

That is a double count: the cash flow is understated by the cost of transporting each barrel. Transport is counted once, and the model says where.

Wrong

“Income tax is the rate multiplied by the project's profit over its whole life.”

In fact

Tax is calculated by year. Depreciation deductions and carried-forward losses do not arrive when the costs are spent. How the tax is spread over time affects NPV, and unused deductions change its total too.

Wrong

“Production should continue as long as the wells give oil.”

In fact

Production continues as long as the revenue of the year, after the payments levied on it, covers the costs that stopping would avoid. Years below the economic limit reduce the cash flow.

Wrong

“The price has fallen by 20%, so the project has become 20% worse.”

In fact

Costs do not fall together with the price. In the example project a price 20% lower reduces the project's NCF by 41% and NPV at 10% by 57%.

In depth: advanced detail

Buy or lease: costs move from one row to another

A large facility can be leased rather than bought, or we can use someone else's facility for a tariff. Examples are a treatment plant, a floating production system (a ship or platform that produces and processes oil at sea) and a compressor station (a plant that raises the pressure of gas). Then capital expenditure falls and operating expenditure rises. In total, leasing is usually more expensive than buying, because the owner of the facility must also make a profit. But the payments shift to years when the project already has revenue.

Worked exampleLeasing an oil treatment plant

Given (assumed data)

Purchase: US$60 million out of the capital expenditure of year 2 (as in the example project)
Lease: US$12 million a year over the seven years of production, US$84 million in all
Tax: lease payments are deducted from profit in the year they are paid; discount rate 10%

Solution

Capital expenditure: $160 - 60 = 100$ million dollars; depreciation is 20 million dollars a year instead of 32.
Operating expenditure in each year of production is higher by US$12 million; over the project it is 186 instead of 102 million dollars.
Maximum cash outlay: 80 instead of 140 million dollars (the minimum of the cumulative flow is −80 instead of −140); payback period 3.9 instead of 4.4 years.
NCF over the project: 191.2 instead of 210.4 million dollars. Leasing costs $84 - 60 = 24$ million dollars more than buying, of which 4.8 million is returned by the lower income tax.
NPV at 10%: 103.9 against 100.1 million dollars; the internal rate of return is 39.1% against 29.6%.
Seven payments of US$12 million for a facility worth US$60 million mean that the owner of the facility earns about 9.2% a year.

Answer: Leasing reduces the maximum cash outlay from 140 to 80 million dollars and raises IRR from 29.6 to 39.1%, but reduces the project's NCF by 19.2 million dollars; NPV at 10% hardly changes.

What it means. Leasing is in essence a loan: the project pays the owner of the facility about 9.2% a year. This rate is close to the 10% discount rate, so NPV hardly changes. A small gain comes from a lease rate slightly below 10% and from a larger tax deduction: all US$84 million of lease payments are deducted from profit, not US$60 million of depreciation. But the indicators that have investment in the denominator (IRR, payback period, profit-to-investment ratio) improve noticeably, even though the project as a whole earns less. So be careful when you compare, by these indicators, projects with different ownership schemes for the facilities. The lease payment is also a fixed cost. If it can be dropped together with the shutdown of production, the economic limit rises from 0.15 to 0.45 million bbl a year. The data in this example are assumed for illustration.

Abandonment: timing, deferral and taxes

In the main section we found the economic limit without allowing for the time value of money (a sum received or paid sooner is worth more than the same sum later). But stopping production brings abandonment closer, and it pays to defer a large payment. Deferring a payment $A$ by a year at a rate $i$ saves $A\,i/(1+i)$ in the money of the year in which it was due. So it is worth continuing production as long as its annual loss is smaller than this sum.

Worked exampleA loss-making year that pays

Given (assumed data)

Abandonment: US$12 million immediately after the last year of production
Year 14 of the “tail” from the economic limit example: revenue after royalty does not cover the costs: −0.62 million dollars
Discount rate: 10%

Solution

Deferring abandonment by a year saves $12\cdot 0.1/1.1 = 1.09$ million dollars — more than the loss of year 14 (0.62 million dollars).
NPV with production until the end of year 13 is 112.12 million dollars, until the end of year 14 it is 112.26 million dollars: continuing pays, although the total cash flow without discounting falls from 236.6 to 236.0 million dollars.
In year 15 the loss would already be 2.24 million dollars — more than the gain from deferral; NPV falls to 111.96 million dollars.

Answer: Allowing for the value of money, it pays to stop the field a year later than the simple economic limit — after year 14.

What it means. The effect is small, but it shows that the decision to stop is also an investment decision: we compare two cash flows, not the revenue and costs of a single year. In practice the condition of the wells and facilities, the term of the contract and the regulator's requirements limit this, and the abandonment estimate changes over time. The data in this example are assumed for illustration.

In the example project, abandonment costs do not reduce the tax, because by that time the project has no income from which they could be deducted. Current regimes resolve this question in different ways. Some allow the loss of the last years to be set against taxes paid earlier. Others require money to be set aside in advance, during the years of production, in an abandonment (sinking) fund, and these contributions are deducted from profit. In the model, both the sum of the tax and the year in which the money actually leaves the project depend on this. The lesson on the internal rate of return shows how money set aside in advance for abandonment affects the profitability of a project.

Connections to other topics

Project cash flow — the items of cash flow, the incremental principle, the period and the moment of the flow.
Cumulative cash flow and payback period — what the cumulative flow shows: the financing requirement and the payback period.
Net present value (NPV) — the main indicator, calculated from the finished flow.
Internal rate of return (IRR) — the project's rate of return and the effect of late abandonment costs.
Inflation: nominal and real money — constant prices and nominal money in the model, escalation of prices and costs.
Volumetric estimation of hydrocarbons in place — the oil in place, which limits the production profile.
What a reservoir simulation model is and why it is needed — where the production profile for the development options comes from.
Petroleum fiscal systems and taxation — how royalty, income taxes and production sharing are built.
Sensitivity analysis and scenarios — systematic testing of the model against changes in assumptions.
Unit costs per barrel — cost per barrel as an indicator of a project.

Check yourself

1
A field gives 30 thousand bbl/d on the plateau and runs without downtime. What volume goes into the annual model?
1. A.10.95 million bbl
2. B.30 million bbl
3. C.8.2 million bbl
4. D.1.095 million bbl
Show the answer
Correct answer: A. 10.95 million bbl
30 thousand bbl/d over 365 days is 10,950 thousand bbl, that is, $30 \cdot 0.365 = 10.95$ million bbl a year. The answer “30 million” confuses the daily volume with the annual one. The answer 1.095 million is ten times too small, from a slip when moving from thousands to millions. With an uptime factor of 0.95 the model would get 10.4 million bbl.
2
The field price is $60/bbl, royalty is 15% of revenue, variable costs are $8/bbl and fixed costs US$12 million a year. Find the economic limit and say how it will change at a price of $40/bbl.
Show the answer
After royalty and variable costs each barrel leaves $60\cdot 0.85 - 8 = 43$ dollars, so the limit is $12/43 \approx 0.28$ million bbl a year (about 760 bbl/d). At a price of $40: $40\cdot 0.85 - 8 = 26$ dollars, and the limit is $12/26 \approx 0.46$ million bbl a year. Production will have to be stopped earlier, and part of the oil that is profitable to produce at $60 will stay in the reservoir.
3
Which payment to the state raises the economic limit of production?
1. A.Both equally
2. B.Royalty on revenue
3. C.Income tax
4. D.Neither: the limit depends only on the reservoir
Show the answer
Correct answer: B. Royalty on revenue
Royalty is levied on every barrel sold regardless of profit, so it reduces what is left to cover costs, and production becomes unprofitable at a larger volume. Income tax takes a share of positive profit: a year that is profitable before tax remains profitable after it.
4
In the model the field price has already been reduced by transport ($6/bbl), and operating expenditure includes a “transport” row with the same $6/bbl. What will happen to the indicators of a project producing 12 million bbl?
1. A.Nothing: the sums cancel each other
2. B.Only the tax will change
3. C.The cash flow is overstated by US$72 million
4. D.The cash flow before tax is understated by US$72 million
Show the answer
Correct answer: D. The cash flow before tax is understated by US$72 million
Transport is counted twice: once it reduced revenue, and the second time it increased costs. Over the project this is $6\cdot 12 = 72$ million dollars before tax. Royalty and income tax will “absorb” part of the error, but NPV will still be noticeably understated. Transport is shown once, and the model says where it is counted.
5
Why can income tax not be calculated as the rate multiplied by the project's profit over its whole life?
Show the answer
Because tax is paid by year, and the deductions do not arrive when the costs are spent: capital expenditure is deducted through depreciation in the years after start-up, and losses are carried forward. The years in which the tax is paid affect NPV. In addition, some deductions may remain unused, for example abandonment costs when there is no income any more. Then the tax over the project is more than the rate multiplied by the total profit.
6
The oil price in the model has been reduced by 20%, and the project's total cash flow has fallen by 41%. Is there an error in the model?
Show the answer
Most likely not. Revenue fell by 20%, but the costs stayed the same, so what remains, the cash flow, fell by more. Royalty and income tax took part of the loss, but not all of it. The closer a project is to break-even, the more strongly its indicators respond to the price. In the lesson's example NPV at 10% fell by 57%.

Updated: 2 October 2026