Quick refresher
- External uncertainty cannot be reduced by studies. It can only be described, partly passed to others (hedging, contracts, stabilisation clauses, the structure of financing), and allowed for in the decision. A stabilisation clause is a term that protects the investor from harmful changes of the rules after the money is spent.
- In the short term, the demand for oil and its supply react weakly to the price, so a small supply disruption raises the price by tens of per cent. We measure the changeability, called the volatility, as the standard deviation of the logarithmic returns. We turn it into a yearly figure by multiplying by the square root of the number of periods in a year.
- A forward curve is the set of delivery prices for future dates, at which a deal can be made today. Contango (future prices above the spot price, which is the price for immediate delivery) is limited by the cost of storage and of money. Backwardation (future prices below the spot price) is not limited by anything: in a shortage, the spot price can be much higher than future prices.
- A price model is also an assumption. With the same yearly volatility of 25%, the probability of a negative NPV of the example project is 23% with a random-walk price and 2% with mean reversion.
- External variables are linked: contractors charge more when oil is expensive, the tenge strengthens when oil is expensive, and the state raises taxes when prices are high. Some links reduce the risk, and others cut off the gain. We set them in scenarios and in simulation explicitly.
- Debt raises both the return and the risk for shareholders, and the lender looks at the coverage of the debt in each year. Flexibility, which is the possibility to wait, to expand or to stop a project, is worth money, and the more so the higher the uncertainty.
yearly volatility from the returns over a period (years): for months,
the upper limit of the forward price: spot plus interest and storage
variance of the logarithm of the price after years with mean reversion; at it is
the return on equity at a ratio of debt to equity
debt coverage: the cash flow available for debt service divided by the interest and repayment of the year
- Taking one price scenario for a forecast and building the decision as if the price were known.
- Setting costs, the exchange rate and taxes independently of the price: in the “worst” scenario impossible combinations appear, and the real links are lost.
- Taking the forward price for a forecast of the future price, and mixing nominal futures with a model in constant prices.
- Putting the whole regulatory risk into a premium on the rate: it “punishes” distant flows with no link to concrete events.
- Judging a project with debt by the IRR of the project: shareholders care about the cash flow after debt service and the margin against the covenants.
After this lesson you can
- name the sources of external uncertainty of a project and explain how they differ from technical uncertainty
- explain why the oil price is so changeable, calculate volatility from a series of prices, and read a forward curve, contango and backwardation
- compare the price models, the random walk and mean reversion, and build a simulation of the NPV of a project from them
- estimate how costs that follow the price, the tenge exchange rate and changes in taxes act on a project, taking their link with the price into account
- calculate how debt raises the risk for shareholders (the IRR of equity, which is the return on the shareholders' own money, and the debt service coverage ratio), and estimate the value of flexibility with a simple real option (the right, but not the duty, to act later)
Uncertainty that a well cannot reduce
We reduce the uncertainty of the subsurface (volumes, flow rates, recovery) with data: appraisal wells, studies, experience of development (Geological and technical uncertainty of a project). External uncertainty is different by nature. No study will make the oil price in five years more exact, and a government's decision on a tax does not depend on the quality of the reservoir model. We can only describe it, by a range, a distribution or scenarios. We can pass part of it to others for a fee, and we can allow for it in the decision.
- Source
- Product market
- What is known inexactly
- the prices of oil, gas and oil products; the price differences between grades and delivery points
- How it is managed
- hedging, gas contracts, flexibility of the project
- Source
- Costs
- What is known inexactly
- the prices of services, equipment, materials and labour
- How it is managed
- fixed-price contracts, the timing of purchases
- Source
- Currency and inflation
- What is known inexactly
- the exchange rate of the tenge to the dollar, the growth of prices
- How it is managed
- matching the currencies of revenue, costs and debt; indexation
- Source
- Financing
- What is known inexactly
- interest rates, access to credit, the terms of lenders
- How it is managed
- the structure of the debt, a fixed rate, a margin against the covenants (the conditions set by the lender)
- Source
- The state
- What is known inexactly
- taxes, duties, regulation, the terms of the contract
- How it is managed
- stabilisation clauses, arbitration, diversification across countries
- Source
- Partners
- What is known inexactly
- the decisions, money and interests of the other participants
- How it is managed
- a joint operating agreement, the right to vote
| Source | What is known inexactly | How it is managed |
|---|---|---|
| Product market | the prices of oil, gas and oil products; the price differences between grades and delivery points | hedging, gas contracts, flexibility of the project |
| Costs | the prices of services, equipment, materials and labour | fixed-price contracts, the timing of purchases |
| Currency and inflation | the exchange rate of the tenge to the dollar, the growth of prices | matching the currencies of revenue, costs and debt; indexation |
| Financing | interest rates, access to credit, the terms of lenders | the structure of the debt, a fixed rate, a margin against the covenants (the conditions set by the lender) |
| The state | taxes, duties, regulation, the terms of the contract | stabilisation clauses, arbitration, diversification across countries |
| Partners | the decisions, money and interests of the other participants | a joint operating agreement, the right to vote |
Hedging, insurance, contracts and project finance are covered in the lesson on the transfer of risk.
External risks have three common features. They are common to all the projects of a company: a fall of the oil price hits all the fields at once, so diversification across areas does not protect against it (diversification of a company). They are linked with each other: contractors charge more when oil is expensive, the tenge strengthens when oil is expensive, and taxes grow together with the price. They do not disappear with time: technical uncertainty turns into knowledge by the end of development, while the price and the taxes stay unknown until the last year.
Oil and gas prices: where the swings come from
Oil is a world commodity: its price is made by the demand and supply of the whole world, and its changes reach almost any field at once. The demand for oil is derived: what we need is not oil itself but petrol, diesel, aviation fuel and raw material for chemicals. In a crisis, when fewer goods are carried and fewer people fly, demand falls within a few months. Efficient engines, electric cars and gas instead of oil change it slowly, over years. Supply depends on the decisions of the producing countries. These include the agreements of OPEC+ (the Organization of the Petroleum Exporting Countries and the countries that joined its decisions, among them Kazakhstan). Supply also depends on investments of past years, accidents, wars and sanctions.
The main reason why the price swings so much is that demand and supply react weakly in the short term. In other words, the price elasticity is low (consumption changes little when the price changes). The cars, aircraft and factories are already bought, and the wells are already drilled. To change equipment and habits, or to bring in new fields, takes years. So, while consumers and producers have not had time to adapt, even a small shortage or surplus of oil moves the price by tens of per cent. With time the reaction grows, and the price comes back. The mechanism and the calculation of the jump in price when supply is disrupted are covered in the lesson on the history of the oil industry. For the assessment of a project, the consequence matters: a high price itself creates forces that lower it, and a low price does too. The model of mean reversion of the price (the section below) is based on this.
Grades and delivery points. Oil is sold at the prices of benchmark grades (the standard oils that other prices are quoted against), such as Brent, WTI (West Texas Intermediate) and Dubai, with a premium or a discount. The difference, the differential, depends on quality (light low-sulfur oil is dearer, because it gives more light products), on the distance to the buyer and on what the market lacks now. It also changes. According to the National Bank's estimate, in September 2026 the Kazakhstan blend CPC Blend was sold at a premium of US$2–4 to Dated Brent (the price of physical North Sea oil for loading in the next few weeks), although it usually sells at a discount (MunaiHub weekly review, September 2026). The price at the field, the netback, is found by subtracting transport and the discount (price and revenue).
Gas. There is no single world price of gas: in Europe, Asia and North America it can differ several times over. The reason is transport. Gas goes by pipeline, or it is liquefied and carried by tankers, and per unit of energy this costs much more than carrying oil. In ordinary conditions, gas with the same energy takes about a thousand times more volume. The price risk of a gas project is largely set by the contract. If the gas price is tied to oil or to oil products, the project gets the volatility of oil. If it is tied to the exchange price of gas, it gets the volatility of its regional market. A take-or-pay condition, under which the buyer pays for an agreed share of the volume even if it did not take it, protects the seller from a fall of demand. A long contract with a fixed formula reduces the price risk, but leaves the risk that the formula will turn out unfavourable.
In Kazakhstan the price of gas for many producers is not set by the market. The state, through the national operator, the national gas company QazaqGaz, has a pre-emptive right: it can buy first the raw and commercial gas that subsoil users sell. The price covers the costs of production, processing and transport plus a profit margin of no more than 10%. For the gas of new areas under contracts after 1 January 2023, the price is set by a formula tied to the export price and to the domestic price caps. There are exceptions, for example the gas of gas and gas-condensate fields (the Law “On Gas and Gas Supply”, Article 15). The Ministry of Energy sets the wholesale price caps of commercial gas on the domestic market (the same law, Articles 6 and 20). The rules of the Ministry of Energy are on the pages of the “Legislation” section of MunaiHub. A regulated price reduces the price risk but replaces it with a regulatory one: the state can change the formula.
Volatility and the forward curve
We measure the changeability of the price by the volatility: the standard deviation (the usual measure of spread) of the logarithmic returns over a chosen period. A logarithmic return is the logarithm of the ratio of two successive prices; for small changes it is simply the percentage change. We take logarithms because the price changes in per cent, not in dollars: a rise from 50 to 60 and a rise from 100 to 120 US$/bbl are the same relative change. Volatilities over different periods are brought to a year.
- yearly volatility, fraction per year
- sample standard deviation of the returns over the period , fraction per period
- length of the period: a month is of a year, a trading day is about , years
- price at the end of the period , US$/bbl
Units: fractions (in the text, per cent)
- the returns of adjacent periods are independent; then their variances add up, and the standard deviation grows as the square root of time
- if the price has mean reversion, over long periods the spread grows more slowly than the root (see the section on price models)
A volatility of 30% a year means that over a year the price will change, with a probability of about two thirds, by no more than about 30% in one direction or the other, provided that the price has a log-normal distribution.
- Prices at the end of the month, 13 months
- 68.0, 71.5, 69.0, 74.5, 79.0, 76.5, 70.0, 65.5, 67.0, 62.5, 66.0, 70.5, 73.0 US$/bbl (assumed)
- Returns for a month: , and so on, 12 values in all.
- Their mean is 0.0059, and the sample standard deviation is .
- The yearly volatility: , about 20.9%.
- In a year the price will, with a probability of about 68%, be between and US$/bbl. The correction keeps the expected price equal to the present one.
What it means. Twelve observations give a rough estimate: another year of the same market can easily give 15 or 35%. That is why we calculate volatility from long series, from daily prices over years, and check that it has not changed. Monthly prices must be taken at the end of the month: monthly averages smooth the swings and understate volatility. The data in this example are assumed for illustration.
- Year
- 2008
- Average, US$/bbl
- 96.94
- Lowest and highest
- 33.73–143.95
- Volatility
- 50%
- Year
- 2014
- Average, US$/bbl
- 99.02
- Lowest and highest
- 55.27–115.19
- Volatility
- 18%
- Year
- 2015
- Average, US$/bbl
- 52.32
- Lowest and highest
- 35.26–66.33
- Volatility
- 41%
- Year
- 2020
- Average, US$/bbl
- 41.96
- Lowest and highest
- 9.12–70.25
- Volatility
- 115%
- Year
- 2022
- Average, US$/bbl
- 100.93
- Lowest and highest
- 76.02–133.18
- Volatility
- 47%
- Year
- 2024
- Average, US$/bbl
- 80.52
- Lowest and highest
- 70.31–93.12
- Volatility
- 27%
- Year
- 2025
- Average, US$/bbl
- 69.14
- Lowest and highest
- 59.93–83.48
- Volatility
- 31%
- Year
- 2026, to 14 October
- Average, US$/bbl
- 94.85
- Lowest and highest
- 61.08–138.21
- Volatility
- 70%
| Year | Average, US$/bbl | Lowest and highest | Volatility |
|---|---|---|---|
| 2008 | 96.94 | 33.73–143.95 | 50% |
| 2014 | 99.02 | 55.27–115.19 | 18% |
| 2015 | 52.32 | 35.26–66.33 | 41% |
| 2020 | 41.96 | 9.12–70.25 | 115% |
| 2022 | 100.93 | 76.02–133.18 | 47% |
| 2024 | 80.52 | 70.31–93.12 | 27% |
| 2025 | 69.14 | 59.93–83.48 | 31% |
| 2026, to 14 October | 94.85 | 61.08–138.21 | 70% |
MunaiHub calculation from the daily Brent spot prices of the US Energy Information Administration (EIA), read on 17 October 2026. The average is over working days, and the volatility is the standard deviation of the daily logarithmic returns multiplied by . The data refer to the years named and do not describe the current market.
In calm years the volatility of Brent is about 20–30% a year, and in crises it is two to four times more. The figures of the table show something else too: in one year the price can fall several-fold (2008, 2020), or more than double (2026). A project designed for a “flat” price will go through several such years during its life.
The forward curve. Besides the price “today”, the spot price, the market gives delivery prices for future dates. They come from futures (standard contracts traded on an exchange) and from forward contracts (private agreements to deliver later at a price fixed now). The set of these prices by delivery date is called the forward curve. If the future prices are higher than the spot price, the curve is called contango, and if they are lower, backwardation.
- Date
- 17 April 2020 (contango)
- 1st month
- 18.27
- 2nd
- 25.03
- 3rd
- 29.42
- 4th
- 31.20
- Date
- 8 March 2022 (backwardation)
- 1st month
- 123.70
- 2nd
- 119.65
- 3rd
- 115.21
- 4th
- 110.83
| Date | 1st month | 2nd | 3rd | 4th |
|---|---|---|---|---|
| 17 April 2020 (contango) | 18.27 | 25.03 | 29.42 | 31.20 |
| 8 March 2022 (backwardation) | 123.70 | 119.65 | 115.21 | 110.83 |
Settlement prices of contracts 1–4 of the New York Mercantile Exchange, from EIA data. On 20 April 2020 the nearest (May) contract closed at minus US$37.63/bbl: during the pandemic demand fell, and the storage at the delivery point was filling up, so the holders of contracts paid money not to have to take the oil. The data refer to the dates named.
- forward price for delivery in years, US$/bbl
- spot price today, US$/bbl
- interest rate per year: the cost of the money put into the oil, fraction per year
- cost of storing a barrel until the delivery date, US$/bbl
- time to delivery, years
Units: any currency, nominal money
- there is free storage and money at the rate ; otherwise the limit shifts
- there is no lower limit: storage does not help someone who needs the oil now
If the forward price is above the spot price plus the cost of carry (the cost of storage and of the money tied up in the oil), it pays to buy oil, store it and sell it by the forward, with no price risk. Such deals raise the spot price and lower the forward price until the gain disappears. So contango is never larger than the cost of storage and of money.
- Spot
- $80/bbl
- Rate
- 5% a year
- Storage
- $0.6/bbl a month, for 6 months
- Six-month forward
- $88/bbl
- Oil bought today and sold in 6 months costs US$/bbl.
- The forward price of 88 is higher: to buy, store and sell by the forward brings US$/bbl with no price risk.
- Such deals go on until the spot price rises or the forward price falls enough that the gain disappears.
What it means. The upper limit of contango is set by storage and by the cost of money. When the storage is almost full, storage becomes dearer, and contango becomes steeper, as in the spring of 2020. The curve has no lower limit: in a shortage, the holders of oil will not sell it cheaply for a future delivery. The data in this example are assumed for illustration.
Backwardation can be very steep. According to EIA data, on 9 October 2026 the spot price of Brent was US$130.03/bbl, and the December Brent futures on the ICE exchange (Intercontinental Exchange) cost about US$104 that evening (MunaiHub weekly review). The market was paying a quarter more for oil now than for oil in two months.
Price models and simulation of NPV
To go from one price scenario to a distribution of NPV, we need a model of how the price can change from year to year. There are two simple models. In the random walk, each year the price gets a random push, and the push stays forever: the uncertainty grows without limit. In mean reversion, the deviation of the price from its long-term level partly disappears each year, because a high price causes more production and savings, and a low price causes less investment.
- deviation of the logarithm of the price from the level in year ; , —
- the share of the deviation that remains after a year: 1 is a random walk, less than 1 is mean reversion, —
- yearly volatility, the standard deviation of the yearly push, fraction per year
- independent standard normal random numbers, —
- the expected price of each year, US$/bbl
- variance of ; at it equals , —
Units: prices in constant dollars of the base year
- the correction keeps the expected price of each year equal to : the models change the spread, not the average level
- the logarithm of the price is normally distributed, and the price is log-normal and in the model cannot become negative
- and are constant; in reality volatility changes, and the long-term level of the price is unknown and changes too
With mean reversion, the variance does not grow without end but tends to a limit . A deviation fades by half in years at (the derivations are in the advanced section).
Chart: the horizontal axis shows years from 0 to 10, and the vertical axis shows the price from 0 to 120 dollars per barrel. Both bands start at the point 50. The band of the random walk widens without limit: after 8 years from 16 to 96, after 10 years from 13 to 101. The band of mean reversion reaches, within 2–3 years, a width from 32 to 71 and does not widen further. The horizontal dotted line is the expected price, 50.
- Project
- from the library's examples (Net present value (NPV)); NPV at 10% and a constant price of $50/bbl is 100.1 million dollars
- Price in years 2–9
- random; the expected price of each year is $50/bbl; the yearly volatility is 25% (assumed)
- Models
- random walk () and mean reversion (; a deviation fades by half in 1.36 years)
- Trials
- 10,000; the same random numbers for both models
- The first trial: , , … For year 2 both models give and a price of US$/bbl.
- Year 3. Walk: , , price . Reversion: , , price US$/bbl.
- The prices of years 3–9 in this trial: with the walk 36.5, 19.9, 14.2, 17.8, 17.7, 17.2, 19.5; with reversion 41.3, 24.6, 23.5, 40.3, 44.2, 45.6, 54.4 US$/bbl. The project model gives an NPV of −73.6 and 14.6 million dollars.
- Over all the trials, the walk: the mean NPV is 99.3, the standard deviation is 137.4 million dollars; P90 is −41, P50 is 72, P10 is 273 million dollars; NPV is negative in 22.7% of the trials.
- Mean reversion: the mean is 99.9, the standard deviation is 60.4; P90 is 28, P50 is 94, P10 is 180 million dollars; NPV is negative in 2.3% of the trials.
- A check: the average price of year 9 over the trials is 49.7 and 49.8 US$/bbl. The models change the spread of the price, not its average level.
What it means. The mean NPV is almost equal to the NPV at a constant price: the income of the project is almost proportional to the price, and the expected price is the same. The difference is smaller than the random error of the simulation itself: the standard error of the mean (the typical error of a mean found from a sample) with 10,000 trials is 1.4 and 0.6 million dollars. The one non-linearity of the model is the income tax: it does not refund the loss of a low year but only carries it forward to later years (non-linearity). So with a random walk, when the price can stay low for years, the expected NPV is slightly below the NPV at a constant price. With mean reversion such years are rare, and the difference is hardly visible. The main difference is in the spread. With the walk, the bad years add up, and the price can stay low for years. With mean reversion the deviations fade. The statistics of prices do not tell clearly which model is closer to the truth. Distant futures swing less than near ones, which points to a partial reversion. So the choice of a price model is an assumption of the same kind as the volatility, and we show it together with the result. How simulation works in general is covered in the lesson on scenarios. The data in this example are assumed for illustration.
Two falling curves: the horizontal axis shows NPV from minus 100 to 400 million dollars, and the vertical axis shows probability from 0 to 100 per cent. The mean-reversion curve is steep: it passes through 98 per cent at zero NPV, through 90 per cent at 28, through 50 per cent at 94 and through 10 per cent at 180 million. The random-walk curve is gentle: 77 per cent at zero NPV, 90 per cent at minus 41, 50 per cent at 72 and 10 per cent at 273 million.
Costs, the tenge exchange rate and inflation
Costs follow the price. When oil gets dearer, companies drill and build more, drilling rigs, vessels and crews are busy, and contractors raise their rates. After a year or two new equipment comes to the market, and the rates fall. When oil gets cheaper, services get cheaper after it, with a delay. This link partly reduces the price risk, and we need to set it explicitly in scenarios (consistent scenarios).
- Project
- from the library's examples, NPV at 10%
- Link
- capital and operating expenditure change by 0.4% when the price changes by 1% (assumed)
- Prices
- $35/bbl and $65/bbl, 30% below and above the base
- At $35/bbl with the costs unchanged, NPV = 14.83 million dollars. If the costs have become cheaper by %, NPV = 36.32 million dollars.
- At $65/bbl: 185.44 million dollars with the costs unchanged, and 163.94 if the costs have risen by 12%.
- The swing of NPV between the two prices: without the link, and million dollars with the link.
- The break-even price by NPV: $32.4/bbl with the costs unchanged, and $26.5/bbl with the costs that follow the price.
What it means. The link works in both directions: when oil is expensive, contractors take part of the gain. It is incomplete and delayed: the costs under contracts already signed and equipment already bought do not depend on the price. So in the first years after a fall of the price, the project is protected less than the calculation shows. The size of the link is assumed; we estimate it from the history of the prices of services in the region. The data in this example are assumed for illustration.
The tenge exchange rate. Oil is sold for dollars, but a large part of the costs (wages, local services, electricity) and the taxes are paid in tenge. A weaker tenge reduces these costs in dollars and improves the dollar flow of an exporter. A stronger tenge makes it worse. With time, local prices rise after the weakening of the currency, and part of the gain disappears (inflation and currency). For a company that sells on the domestic market for tenge but owes in dollars, the picture is the opposite: a weaker tenge increases its debt in tenge (currency risk).
- Dates
- 4 February 2009 → 6 February 2009
- Official rate, ₸ per US dollar
- 122.32 → 149.97
- The dollar rose
- by 22.6%
- Brent, US$/bbl
- 43.68
- Dates
- 11 February 2014 → 13 February 2014
- Official rate, ₸ per US dollar
- 155.56 → 184.50
- The dollar rose
- by 18.6%
- Brent, US$/bbl
- 109.21
- Dates
- 20 August 2015 → 21 August 2015
- Official rate, ₸ per US dollar
- 188.38 → 255.26
- The dollar rose
- by 35.5%
- Brent, US$/bbl
- 45.63
| Dates | Official rate, ₸ per US dollar | The dollar rose | Brent, US$/bbl |
|---|---|---|---|
| 4 February 2009 → 6 February 2009 | 122.32 → 149.97 | by 22.6% | 43.68 |
| 11 February 2014 → 13 February 2014 | 155.56 → 184.50 | by 18.6% | 109.21 |
| 20 August 2015 → 21 August 2015 | 188.38 → 255.26 | by 35.5% | 45.63 |
The official rates of the National Bank of Kazakhstan on the dates stated; the price of Brent is the spot price, from EIA data, on the first date. On 20 August 2015 the government and the National Bank announced a move to a freely floating exchange rate and to inflation targeting.
The devaluations (sharp falls of the tenge) of 2009 and 2015 came after a collapse of the oil price. On 3 July 2008 Brent cost US$143.95/bbl, in August 2014 it averaged about 100, and on the days of the devaluations it was 44–46. February 2014 shows that the rate does not depend on oil alone: Brent then cost $109/bbl. The link with oil works in the other direction too: in 2026, when oil got dearer, the tenge strengthened, from 505.53 tenge per dollar on 2 January to 452.12 on 17 October, by 12% (the official rates of the National Bank). The republican budget for 2026 was calculated at a price of $60/bbl and a rate of 540 tenge per dollar, and the draft budget for 2027 at $70/bbl and 480 tenge (the forecast for the budget of 2026–2028; MunaiHub weekly review, September 2026).
- Operating costs
- $15/bbl at a rate of 505.53 ₸ per US dollar (2 January 2026); 60% of them are paid in tenge (assumed)
- Rates
- 452.12 ₸ per US dollar (17 October 2026) and, for comparison, 600 ₸ per US dollar (assumed)
- Assumption
- the tenge costs have not changed in tenge
- The tenge part: dollars, or ₸ a barrel.
- At 452.12 ₸ per dollar: dollars; the costs are US$/bbl, which is 7.1% more.
- At 600 ₸ per dollar: dollars; the costs are US$/bbl, which is 9.5% less.
What it means. In the same months the average spot price of Brent rose from $66.6/bbl in January 2026 to $127.0/bbl in the first half of October (EIA). The revenue per barrel almost doubled, while the costs rose by 7.1%. For an exporter the link “expensive oil, strong tenge” is a partial natural protection. In good times it takes away a little of the gain, and in bad times, when oil gets cheaper and the tenge weaker, it softens the blow. The tenge prices themselves change over a year, so in a model the exchange rate and inflation are set together. The share of the tenge costs is assumed.
Inflation. Expected inflation by itself hardly affects the real NPV, if the flow and the rate are consistent. The risk comes from unexpected inflation and from its unevenness. The tax deductions for depreciation are not indexed, long contracts with a fixed price lose their real value, and the oil price does not have to rise together with local prices (where inflation is not neutral).
Taxes and rules: the risk of changing conditions
The investor knows, before the investment decision, the taxes and duties, the requirements for safety, environmental protection and gas flaring, and the rules for purchases from local suppliers and for deliveries to the domestic market. It puts them into the cash flow like any other costs. What creates uncertainty is something else: the conditions may change when the money is already invested and one cannot leave the project without loss.
Why do conditions change? Before investing, the investor can choose another country. After that, the platform and the pipeline cannot be taken away, and the bargaining power passes to the state. Conditions that suited both sides at a price of $50/bbl seem to the state too soft at $100. This is called the “obsolescing bargain”: the deal goes out of date. So taxes are most often raised when oil is expensive. A windfall tax is introduced (it takes a share of the extra income that high prices bring), and rates and duties are raised. Tax breaks are given when oil is cheap and there is not enough investment. A budget deficit can raise taxes with no link to the price.
- Taxes and duties: rates, bases, scales, deductions; new windfall taxes.
- The product market: export duties and bans, compulsory deliveries to the domestic market, regulation of the prices of gas and oil products.
- Technical requirements: new standards of safety or environmental protection, applied retroactively to facilities that already operate; a ban or a limit on gas flaring (associated gas).
- Contract and law: revision of the terms, limits on selling interests, and in the extreme case the termination of the contract or nationalisation.
A stabilisation clause is a condition of a contract or a law that protects the investor from changes that make its position worse. Freezing clauses apply the law as of the date of the contract to the project. Economic equilibrium clauses let the changes apply, but the state must restore the investor's economic position, by compensation or by changing other terms. A clause does not make the risk zero. It usually does not extend to safety and to the protection of nature and health, and its enforcement may need a long international arbitration (a case heard by independent arbitrators).
In Kazakhstan the Subsoil Code protects signed contracts from changes of legislation that worsen the results of the subsoil user. This does not apply to national security, defence, environmental safety, health care, taxation, customs regulation and the protection of competition (Article 36). So the tax terms of most contracts change together with the Tax Code. A stable tax regime is kept by production sharing agreements concluded before 1 January 2009 that passed the compulsory tax examination, and by contracts approved by the President, for the taxes whose stability is directly stated in them (Article 755 of the Tax Code; in more detail). An example of a change already adopted: from 2027 the rate of the mineral extraction tax (MET) on oil will be taken from a matrix “annual production × world price”, and the oil of the payers of this tax is released from the rent tax on export (how the regime is changing).
- Project
- from the library's examples; royalty 10%, income tax 20%
- Event
- with a probability of 0.3, from year 5 the royalty becomes 15% (assumed)
- Rate
- 10%
- If the rise happens, the NPV of the project is 90.59 million dollars instead of 100.13. The loss is million dollars.
- Expected NPV: million dollars.
- The same NPV without the event would be given by a rate of 10.35%, a premium of 0.35 percentage points.
- For comparison, a premium of 5 percentage points “for country risk”: NPV at 15% is 64.38 million dollars, which is 35.75 million less.
What it means. A premium of 5 points would mean that the investor expects events more than ten times heavier than this, or counts the same thing twice. Besides, a premium hits the distant flows regardless of when and what may change (the premium and time). It is more reliable to list the events that really can happen, to estimate their probabilities and consequences, to put them into the flow or into a decision tree (Decision trees and the value of information), and to name in the conclusion what is left. The probability and the size of the change are assumed.
Changes of taxes are most often linked with the price: a windfall tax is introduced when oil is expensive. Then the regulatory risk cuts off exactly the good outcomes, and in a calculation with one price it is not seen at all.
- Trials
- the same 10,000 as in the example with the price models
- Tax
- from project year 5, half of the excess of the price over $60/bbl on each barrel; it reduces the base of the income tax (assumed)
- At a constant price of $50/bbl the tax is not paid: NPV stays at 100.1 million dollars.
- Random walk: the mean NPV million dollars; the high outcome P10 ; the low outcome P90, −41 and −41, does not change.
- Mean reversion: the mean NPV ; P10 million dollars.
- If the tax is introduced with a probability of 0.3, the expected NPV with the walk is million dollars.
What it means. The wider the spread of the price, the more the investor loses from the taxes that switch on at a high price. They work like an option on a price rise (the right to the gain from a rise) that has been sold to the state. So progressive taxes and stabilisation clauses are valued on the distribution of the price, not on one scenario (a good tax system). The data in this example are assumed for illustration.
Financial risk: debt, covenants, partners
A project can be financed with the shareholders' money or with debt. Debt is cheaper than equity (the shareholders' own money; see the cost of capital), but interest and repayment are paid on a schedule at any oil price. So debt is financial leverage: it raises the return of the shareholders when the project earns more than the rate on the loan, and it lowers the return when the project earns less.
- the return on equity for a year, fraction
- the return on all the investment: the profit before interest divided by all the capital, fraction
- the ratio of debt to equity, —
- the rate on the debt, fraction
Units: fractions; before income tax (with tax, both parts are multiplied by )
- the return on the investment does not depend on how it is financed
- the rate on the debt is constant
At each dollar of debt brings the shareholders the difference, and at it takes the difference away. The spread of ROE is times the spread of ROA: debt raises the risk for the shareholders even if the project itself does not change.
The lender looks at something else: whether there will be enough money for the payments of each year. The main measure is the debt service coverage ratio (DSCR). It is the cash flow available for debt service (CFADS), which is the revenue minus operating costs and taxes, divided by the interest and repayment of the year. The loan agreement contains covenants: obligations of the borrower, for example to keep the DSCR not below 1.2–1.4. The level is set in the agreement, and it depends on the lender and the project. If a covenant is broken, the bank may forbid dividends, demand early repayment, or demand extra collateral (assets pledged to the bank).
- the flow of the year that is available for debt service: revenue minus operating costs, payments on revenue and taxes; the capital expenditure on building the project, paid by the loan and by the shareholders' money, is not subtracted, US$ million
- interest and repayment of the principal in year , US$ million
Units: dimensionless
- we calculate it for each year (often for each half-year) and watch the lowest value, not the average.
DSCR = 1 means that the flow just covers the payments. Below 1, there is nothing to pay with without the shareholders' money.
- Project
- from the library's examples at a constant price of $35, $50 and $60/bbl
- Loan
- 90 million dollars in the middle of year 2 (it covers the investment of that year), 8% a year, 5 equal payments in years 3–7 (assumed)
- Simplification
- the income tax is calculated with no deduction of interest (a deduction would improve the flow of the shareholders a little)
- The payment: million dollars a year.
- At $50/bbl the flow of the shareholders is: −50; 0; in year 3, and so on. The IRR of the project is 29.6%, and the IRR of the equity is 44.2%.
- At $35 and $60/bbl, the IRR of the project is 13.3 and 38.7%, and of the equity 17.9 and 57.8%. The swing is percentage points for the project and points for the shareholders.
- At $35/bbl in year 3, the flow available for debt service is 35.52 million dollars. The shareholders pay for the completion of the development (20 million dollars), so their flow is million dollars: they have to pay in 7.02 million dollars.
- The lowest DSCR is at $50/bbl and at 35. A covenant of 1.3 is broken at a price below $30.1/bbl. The break-even price of the project by NPV at 10% is $32.4/bbl.
What it means. While the project earns more than 8%, debt is good for the shareholders. When it earns less, debt hurts them (the curves on the chart cross near the rate of the loan). The lender is better protected: at a price from $30.1 to $31.7/bbl it gets its payments with the agreed margin, while the return of the shareholders is already below 10%. For the shareholders, debt adds one more risk, a liquidity risk (the risk of lacking cash when it is needed): extra payments in bad years and the threat of breaking a covenant. So the margin of the DSCR at a low price is checked in advance. The data in this example are assumed for illustration.
Two rising lines: the horizontal axis shows the oil price from 30 to 65 dollars per barrel, and the vertical axis shows IRR from 0 to 70 per cent. The line of the project rises from 7 per cent at 30 dollars to 43 at 65. The line of the equity is steeper: from 5 per cent at 30 dollars to 64 at 65. The lines cross near a price of 31 dollars, where both equal 8 per cent, the rate of the loan, shown by the horizontal dotted line. The vertical line marks the price 30.1.
- The interest rate. With a floating-rate loan, the payments grow together with the market rates: a rise of the rate by 3 percentage points on a debt of 90 million dollars costs 2.7 million dollars a year extra. A fixed rate moves this risk to the lender for a fee.
- Refinancing. If the loan is shorter than the project, it will have to be replaced by a new one, maybe in a year of low prices, when banks are cautious and charge more.
- The currency of the debt. A dollar loan with dollar revenue is a natural protection. With revenue in tenge, a weaker tenge increases the debt in tenge.
- Leasing. Leased plants are also a form of debt: the payments go into operating costs and bring the economic limit closer at a low price (to buy or to lease).
Partners. Fields are more often developed together, and each participant has its own cost of capital, tax position, attitude to risk and price forecast. A small partner needs quick money, a large one needs reserves for years, and a state company must also meet its plans for production and purchases. The same figures give them different NPVs. Disagreements delay decisions. A participant who has not paid its share of the costs on the operator's request (a cash call) puts the whole project at risk. A joint operating agreement sets in advance how the participants vote, who pays for the one who refuses, and how they leave the project (working interest and partnership).
How to allow for external uncertainty in a decision
- Method
- One price scenario
- What it gives
- simplicity, comparability of the company's projects
- The pitfall
- hides the spread; a “flat” nominal price is a fall in real terms
- Method
- Sensitivity and the break-even price
- What it gives
- the margin of safety against the price, the exchange rate and the tax (break-even values)
- The pitfall
- no probabilities and no links between the variables
- Method
- Consistent scenarios
- What it gives
- pictures of the future: the price together with costs, the exchange rate and taxes
- The pitfall
- no probabilities; extreme combinations are unlikely
- Method
- Simulation with price paths
- What it gives
- the distribution of NPV, the probability of a loss
- The pitfall
- the result depends on the price model and the volatility
- Method
- Decision tree and real options
- What it gives
- the value of flexibility: to wait, to expand, to stop
- The pitfall
- needs probabilities and decision rules
- Method
- Transfer of risk
- What it gives
- a hedge, contracts, stabilisation, insurance
- The pitfall
- it costs money and does not cover everything (the transfer of risk)
| Method | What it gives | The pitfall |
|---|---|---|
| One price scenario | simplicity, comparability of the company's projects | hides the spread; a “flat” nominal price is a fall in real terms |
| Sensitivity and the break-even price | the margin of safety against the price, the exchange rate and the tax (break-even values) | no probabilities and no links between the variables |
| Consistent scenarios | pictures of the future: the price together with costs, the exchange rate and taxes | no probabilities; extreme combinations are unlikely |
| Simulation with price paths | the distribution of NPV, the probability of a loss | the result depends on the price model and the volatility |
| Decision tree and real options | the value of flexibility: to wait, to expand, to stop | needs probabilities and decision rules |
| Transfer of risk | a hedge, contracts, stabilisation, insurance | it costs money and does not cover everything (the transfer of risk) |
An NPV calculation with one scenario silently assumes that decisions are taken at once and forever. In reality a company can put off development until the price becomes clearer, start with a first phase and expand it if it goes well, or stop a field earlier at a low price. The right, but not the duty, to take a decision later, when more is known, is called a real option. Its value grows with uncertainty: the wider the spread of the price, the more is gained by the one who can avoid putting money into a bad outcome (Decision trees and the value of information).
- the value of the project today if the decision is put off by a year, US$ million
- the NPV of development a year later, with a high and a low price forecast, at the date of the decision, US$ million
- probability of the high forecast, fraction
- discount rate, fraction per year
Units: US$ million today
- in a year the uncertainty is resolved, and the decision is taken at the price then known
- the right to wait exists: the contract and the regulation do not oblige us to start now; waiting does not reduce the reserves and does not give the market to competitors
It is worth building now only if . The difference is the value of flexibility.
- A small field
- the NPV of development at the date of the decision is million dollars: 3 million bbl of discounted production after tax, $20 of costs and taxes per barrel, and 85 million dollars of investment (assumed)
- Price
- the long-term forecast today is $50/bbl; in a year it will become clear whether it is 60 or 40, with equal chances
- Rate
- 10%
- Build now: million dollars.
- Wait: at 60 dollars , so we build; at 40 dollars , so we do not build. The value of waiting today: million dollars.
- The value of flexibility: million dollars. It is better to build at once only if the forecast is above $56.7/bbl.
- If in a year the forecast turns out 70 or 30 dollars: the value of waiting is million dollars, and the limit is $65.0/bbl.
What it means. The value of waiting does not come from hoping for a rise of the price (the expected price has not changed). It comes from the right not to put money into a bad outcome. The wider the spread, the more valuable this right, and the higher the price at which it is worth building at once. But the right must exist. In Kazakhstan the contract obliges the subsoil user to carry out the work programme and the deadlines approved in the project documents (obligations of the subsoil user, deadlines in the documents), and waiting may cost fines or the area itself. In the same way we value the possibilities to expand a project or to stop it earlier. The data in this example are assumed for illustration.
Terms and symbols
- Volatility
- The standard deviation of the logarithmic returns of the price, brought to a year.
- Price elasticity of demand
- The relative change of consumption divided by the relative change of the price. For oil in the short term it is small.
- Spot, forward, futures
- The price of immediate delivery, the contract price of a future delivery, and the same price in a standard exchange contract.
- Contango and backwardation
- Contango is a forward curve that rises as the delivery date moves later. Backwardation is a forward curve that falls.
- Differential
- The premium or discount of the price of a grade or a delivery point to the benchmark.
- Random walk and mean reversion
- Price models. In a random walk the pushes stay forever. With mean reversion the deviation from the long-term level gradually fades.
- Stabilisation clause
- A condition of a contract or a law that protects the investor from changes of the rules that make its position worse.
- Financial leverage
- The use of debt. It raises both the average return and the spread of the return on equity.
- DSCR and covenant
- The DSCR is the flow available for debt service divided by the payments of the year. A covenant is the borrower's obligation to keep it not below an agreed level.
- Real option
- The right, but not the duty, to change a project later (to wait, to expand, to stop) when more is known.
Common mistakes and misconceptions
“Let us take the price from futures: it is the market's forecast.”
A futures price is a price at which a deal can be made today. It contains the cost of storage and of money, the benefit of having the oil in hand, and a payment for risk. A futures contract can fix the price of part of the production. But it is not a forecast of the price for years, and for a model in constant prices it still has to be converted.
“A volatility of 30% a year means that in 10 years the price can deviate by 300%.”
The spread grows as the root of time, not in proportion: with a random walk it is % in logarithms, and with mean reversion it stops growing after a few years.
“In the worst scenario the price is 30 dollars, the costs are 20% higher, the tenge is stronger, taxes are higher.”
Such a combination is almost impossible: when oil is cheap, services get cheaper, the tenge gets weaker, and the state is more likely to introduce tax breaks. We build a scenario as a consistent picture, and we set the links between the variables explicitly.
“We will allow for the risk of changing taxes with a premium of 5 percentage points on the rate.”
A premium is linked neither with the probability, nor with the time, nor with the size of the change, and it hits the distant flows. In the example of the lesson an explicit event was worth a premium of only 0.35 percentage points. It is more reliable to list the possible changes, to estimate them and to put them into the flow.
“The IRR of the project is 13%, more than the loan rate of 8%, so nothing threatens the shareholders.”
The shareholders get the flow after the payments on the loan. In a bad year they have to pay in, and if a covenant is broken, the bank may forbid dividends or demand early repayment. We check the flow of the shareholders and the margin of the DSCR at a low price.
In depth: advanced detail
Where the formulas come from: the root of time, the correction and the half-life
The root of time. The logarithm of the price over a year is the sum of independent returns over periods . The variances of independent terms add up: , so . For the same reason, over years with a random walk .
The correction . If is normally distributed with a mean of 0 and a variance , the mean of is , not 1: the high values of the exponential outweigh the low ones. If we multiply by , we get a multiplier with a mean of 1, so the expected price stays . The median of the price is then , which is below the expected price, and the more so the larger the spread. In the example of the lesson, the median price of year 9 with a random walk is , about $39/bbl.
The variance with mean reversion. From with independent we get , . This is a geometric progression: . As the variance tends to : at and it tends to .
The half-life. Without new pushes, the deviation after years is . Half is left when , that is . At this is years. In the continuous form of the same model (the Ornstein–Uhlenbeck process) the speed of reversion is , and .
Why a forward can be below the spot price: the benefit of having the oil
Whoever holds oil in storage has something that the holder of a forward does not have: the possibility to sell or process it today, to keep a plant running, and to fulfil a contract when supply is disrupted. This benefit is called the convenience yield . With it, the forward price is written as , where is the cost of storage as a share of the price per year, and the rates are continuous. In ordinary times is small, and the curve is in a small contango. In a shortage is large, and the forward goes below the spot price. This is backwardation, and it is the steeper the sharper the shortage.
For a producer, a steep backwardation is a signal that the high price is temporary: the market is ready to pay much more for oil now than for oil in a few months. Investment decisions for years ahead are not taken at such a price.
Connections to other topics
- Geological and technical uncertainty of a project — the uncertainty of the subsurface, the wells and the facilities, which data reduce.
- Sensitivity analysis and scenarios — sensitivity, break-even values, scenarios and simulation of NPV.
- Petroleum fiscal systems and taxation — how oil taxes are built, their progressivity, and the changes of the regime of Kazakhstan.
- The state and the subsoil: ownership of resources — the stability of conditions in the Subsoil Code and why the risk of conditions reduces the rent.
- Risk reduction and diversification — hedging, insurance, contracts, project finance and partnership.
- Decision trees and the value of information — decisions in time and the value of information, the basis of real options.
- Inflation: nominal and real money — inflation, currency and matching the flow with the rate.
- Choosing the discount rate — the cost of capital, debt, and why a premium on the rate is a crude way to allow for risk.
- Valuation methods: book value and market value — how the price scenario and the risks enter the valuation of fields and companies.
Check yourself
- 1
The daily volatility of the oil price is 2%. What is roughly the yearly volatility, if there are 252 trading days in a year?
- A.about 504%
- B.about 2%
- C.about 32%
- D.about 24%
Show the answer
Correct answer: C. about 32%
%: with independent returns, the standard deviation grows as the root of the number of periods. The answer 504% is a multiplication by 252 instead of the root, and 24% is a multiplication by 12 (as for monthly data).
- 2
Oil futures: for the nearest month 72, in 3 months 69, in 6 months 66 US$/bbl. What is such a curve called, and what does it say?
- A.Contango: the storage is full
- B.Backwardation: oil is needed more now than later
- C.Nothing can be said from the curve
- D.Contango: the market expects the price to rise
Show the answer
Correct answer: B. Backwardation: oil is needed more now than later
The prices fall as the delivery date moves later: this is backwardation. It means that more is paid for oil now than for oil later: the benefit of having it is above the cost of storage and of money. It is not a forecast of a fall of the price, but a price at which a deal can be made today.
- 3
Why, at the same yearly volatility, does a random walk of the price give a much larger spread of the NPV of a project than mean reversion?
Show the answer
With a walk, each yearly push stays forever, and failures add up. The price can stay low or high for years, and the variance of the logarithm of the price grows in proportion to time. With mean reversion, the deviations fade, and the variance stops growing after a few years. NPV depends on the prices of all the production years, so with the walk its spread is much wider. In the example of the lesson the standard deviation is more than twice as large, and the probability of a loss is ten times larger.
- 4
The cash flow available for debt service in the worst year is 39 million dollars; the interest and repayment of this year are 30 million dollars. The covenant requires a DSCR not below 1.4. Is it met?
- A.No: DSCR = 0.77
- B.Yes: DSCR = 1.3
- C.Yes: the flow is larger than the payments
- D.No: DSCR = 1.3, which is less than 1.4
Show the answer
Correct answer: D. No: DSCR = 1.3, which is less than 1.4
: the covenant is broken, although the payments are covered. The lender may forbid dividends or demand measures. We must check the margin of the DSCR at a low price in advance.
- 5
A company with a contract for oil production in Kazakhstan, concluded in 2020, fears a rise of taxes. Does the stability of conditions under the Subsoil Code protect it?
Show the answer
As a rule, no. The Code protects signed contracts from changes of legislation that make their position worse, but not in the field of taxation and a few other fields (Article 36). The tax terms of most contracts change together with the Tax Code. A stable tax regime is kept by production sharing agreements concluded before 2009 that passed the tax examination, and by contracts approved by the President. For contracts on complex projects, some norms of the Tax Code are applied in the version of the date of signing the contract (Article 756). Such a company must assess the risk of a change of taxes itself, with scenarios and probabilities.
- 6
A project with an NPV of +4 million dollars can be started now, or in a year when it will be clear whether the price is high or low. In the bad outcome it will not be started. Why can waiting be worth more than 4 million dollars, even if the expected price does not change?
Show the answer
By waiting, the company puts money only into the good outcome and avoids the loss in the bad one. The value of waiting is the average of the positive NPV of the good outcome and the zero of the bad one, brought back by a year. With a wide spread of the price, it is larger than the NPV of the immediate decision averaged over the outcomes. This is a real option. It exists only if the contract and the regulation allow us to wait, and waiting does not cost the reserves or the area.
Updated: 19 October 2026