What is this paper about

1
What is this paper about?

• Use option valuation theory to develop a new
  approach to valuing leases for offshore petroleum
• Theoretical and practical problems not present in
  applying options to financial assets

2
Why is valuation important?

• Firms perform valuations as inputs to their
  bidding process
• Government uses to establish presale reservation
  prices and to study effect of policy changes on
  revenue (underestimates)
• Bidding process involves billions of dollars
• ? important to obtain accurate valuations

3
3 Stages

• Exploration
• seismic and drilling activity
• quantities of hydrocarbon reserves
• costs of bringing them out
• Development
• put equipment in place to extract oil
• platforms, production wells
• converts undeveloped reserves to developed
• Extraction
• Use the installed capacity to take the
  hydrocarbons out of the ground

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Relinquish?
Exploration
Results favorable?
Relinquish?
Extraction
Development
5
DCF Approach

• Specify distributions for
• Exploration costs, quantities of hydrocarbon
  reserves, development costs, hydrocarbon prices,
  and operating costs
• An analyst determines whether it is optimal for
  the firm to explore, develop and extract
• Analyst makes assumptions about timing, and rate
  of extraction
• The time path of cash flows determined
• Involves multivariate Monte Carlo simulations

6
Major Weaknesses of DCF

• The proper timing is not transparent
• Different assessments of future statistical
  distributions by different companies
• Choosing correct set of risk-adjusted discount
  rates is a difficult task
• Very complex and costly
• The assessments of geological and cost
  distributions can wary widely

7
Tract Valuation by the Option Valuation Approach

• Characteristics of the Stages
• Exploration
• Development
• Extraction
• Valuation
• Petroleum Reserve Market Equilibrium
• Valuing Undeveloped Reserves
• Valuing Unexplored Tracts
• Exploration and Development Lags
• Optimal Investment Timing
• Comparative Statics
• Comparison of Option Valuation and Discounted
  Cash Flow Approaches

8
Tract Valuation by the Option Valuation Approach

• Characteristics of the Stages-Exploration
• The exploration stage consists of the option to
  make the exploration expenditures and to receive
  undeveloped reserves. Its very similar to a
  stock option.
• The main difference is the uncertainties ( the
  quantities of hydrocarbons ) in the exploration
  stage.

9
Tract Valuation by the Option Valuation Approach

• Characteristics of the Stages-Exploration
• We can represent the exploration stage as the
  option to spend the exploration cost , and
  receive the expected value of undeveloped
  reserves
• where
• random quantity of recoverable hydrocarbons
  in the tract
• per unit development cost, a function of
  quantity
• current value of a unit of developed
  hydrocarbon reserves
• probability distribution over the quantity
  of hydrocarbons
• current per unit value of
  undeveloped reserves given the current per unit
• value of a developed reserve
  and per unit development cost
• current date
• expiration date

10
Tract Valuation by the Option Valuation Approach

• Characteristics of the Stages-Development
• Once exploration has provided an indication of
  the quantity of hydrocarbons, the leaseholder has
  the option to pay the development costs and
  install the productive capacity.
• Characteristics of the Stages-Extraction
• The leaseholder has the option to extract the
  hydrocarbons after he has exercised the
  development option.

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Tract Valuation by the Option Valuation Approach

• Valuation-Petroleum Reserve Market Equilibrium
• In equilibrium, the expected net payoff from
  holding a developed reserve must compensate the
  owner for opportunity cost of investing in that
  reserve.
• Assume the rate of return to owner follows the
  diffusion process
• where
• the number of units of petroleum in a
  developed reserve
• the value of a unit of developed reserve
• the instantaneous per unit time net
  payoff from holding the reserve
• the required rate of return to the owner
• the instantaneous per unit time standard
  deviation of the rate of return
• an increment to diffusion process

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Tract Valuation by the Option Valuation Approach

• Valuation-Petroleum Reserve Market Equilibrium
• comes from two sources
• The profits from production
• The capital gain on holding the remaining
  petroleum
• Assume a developed reserve follow an exponential
  decline
• Then the net payoff can be written as
• where the net payoff is over a short interval
  . is the after-tax
• Operation profit from selling a unit of petroleum
  

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Tract Valuation by the Option Valuation Approach

• Valuation-Petroleum Reserve Market Equilibrium
• The process for the value of a producing
  developed reserve
• the payout rate of the producing
  developed reserve
• the expected rate of capital gain

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Tract Valuation by the Option Valuation Approach

• Valuation-Petroleum Reserve Market Equilibrium
• Comparison of Variables Pricing Models of Stock
  Call Options and Undeveloped Petroleum Reserves

15
Valuing Undeveloped Reserves What is it Why
do we need it?

• Given a tract that has been explored, we find
  X(V, T-t, D)
• Firms need to value reserves to make decisions
• It is done before valuing an unexplored tract

16
Comparison of the valuation with Stock Call
Options

• Current stock price
• Variance of rate of return
• Exercise price
• Time to expiration
• Riskless rate of interest
• Dividend

• Value of developed reserve discounted for
  developed lag
• Variance of rate of change of the value of a
  developed reserve
• Per unit development cost
• Relinquishment requirement
• Riskless rate of interest
• Net production revenue less depletion

17
Finding X(V, T-t, D)

• Invoke standard arbitrage arguments by
  replicating the undeveloped reserves payoff by
  holding a portfolio of developed reserves and
  riskless bonds.
• Holding nonproducing developed reserves -
  feasible but inefficient
• Holding producing developed reserves - works

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Problem

• We use the Black-Scholes price as the price of
  the call option
• The price of the contingent claim should equal
  the cost of a strategy that replicates the
  returns of that claim
• But the option would earn a subnormal
  rate of return not an equilibrium situation
• Excess of writers to buyers drives down call
  price

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The second one works

• The holder of a producing developed reserve earns
  a fair rate of return
• The payout is identical to a proportional
  dividend on a stock
• The PDE for valuing the option on stock can be
  used for valuing an undeveloped reserve

20
Invoking standard arbitrage arguments

• It is difficult to effect the actual arbitrage
• We use an equilibrium analysis given by
  Constantinides 1978
• The equilibrium model of the petroleum reserves
  in brought in through ?

21
Boundary conditions

• X(Vt, T-t, D) Vt D if Ct Ct and CsltCs
  for all sltt
• Ct Vt / D
• Ct Boundary that maximizes solution
• Ct hits Ct from below for the first time
• Ct can be used for any lease since it is
  independent of V and D

22
Ct - a closer look

• Hitting boundary decreases with time
• Option value decreases with time
• No time no option value
• Vt - D is not positive anymore

23
Boundary Conditions

• X(0,T-t,D) 0 for all t
• If there is no value for the developed
  hydrocarbon reserve then there is no value for
  the undeveloped reserve
• X(VT, 0, D) max0, VT D
  if Cs lt Cs for every s lt T
• There are no closed forms for the solution to the
  PDE and Ct
• Use numerical solutions

24
Valuing Unexplored Tracts

• Complications due to the properties of the
  development option and optimal development timing
• Assume that development begins immediately after
  successful exploration collapse the two options
• More later

25
Finding W(V, T-t, S)

• From the development option, we have
• Recall,
• In an exploration option, you pay and get
• Or paying and
  getting
• Value of unexplored tract is

26
The collapsing technique

• With no geological uncertainty, S gt D if
  V/S exceeds hitting boundary then so will V/D
• With geological uncertainty this is not the case
• We get a lower bound to the true option value

27
Exploration and Development lags

• Let t be the length of the lag
• The value of the claim at t to receive a
  developed reserve at tt is
• By beginning development at t, the firm gets this
  claim
• The underlying asset in both these options is the
  claim
• Also, Vt follows a diffusion process
• We replace Vt with Vt

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Optimal Investment Timing

• Begin development or exploration the first time
  that Ct hits Ct from below
• Insights
• Reserves with low investment costs will hit the
  boundary before those with high investment costs
  Herfindahls equilibrium
• Properties with shorter investment lags will be
  explored or developed before those with longer
  lags

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Comparison of OV and DCF approaches

• Reduces the amount of information required
• Estimation of future developed reserve values
• Determination of risk-adjusted discount rates
• Explicit modeling of the extraction stage

30
Data Sources For Results

• Calculate the market value for offshore petroleum
  tracts awarded to industry in federal lease sale
  no. 62 in November 18, 1980
• 21 of the 38 tracks compared (available data)
• Data on the tracts they used is protected by
  privacy laws
• Paper only looks at bonus bidding with a fixed 16
  2/3 royalty on the tracks
• Used for tracts valued at lt 10,812,077
• Company owes 16 2/3 in amount or value of
  production saved, removed or sold

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Who Benefits?

• Relatively low royalty system used since the OCS
  Lands Act in 1953
• Negative- results in greater risks to the lessee
  from finding a dry hole
• Positive- more rewards (lower contingency
  payments to the government) if a commercial field
  is discovered.
• If a dry hole is found, then the tract is
  unusable and the company loses money
• If a commercial field is discovered
• the company reaps the benefits for the first year
• the next year the government recategorizes the
  tract

32
Calculating royalty on large tracts

• eg. sliding scale royalty
• higher royalty rates for larger reservoirs with
  higher production rates
• Rj bln(Vj/s) (in Millions)
• Rj is percent royalty due in quarter j
• b 13.0
• Vj is the value of production in quarter j

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USGS

• Information obtained by USGS for tracks
• Mean and variance for quantities of recoverable
• oil reserves
• condensate reserves
• gas reserves
• Probability that the tract is dry
• Expected
• exploration cost
• development cost
• USGS estimate of tract value (estimated using DCF
  calculation with the above as input parameters)

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Inputs into Valuation Equation Developed reserve
value

• Compare with current market value
• 12/barrel of oil
• 1/6 cost of a barrel of oil for an mcf of gas
• 2/mcf as benchmark
• 3/mcf from private bakers for latter 1980s
• Unavailable information to authors would be
  available to firms break down the valuation
  based on the quality of the tract based on market
  value
• Hydrocarbon quality
• Cost structure
• Tax regime

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Inputs into Valuation Equation Variance

• Variance of the rate of change in the value of
  developed reserves
• Techniques
• Estimate based on past data on market values of
  developed reserves
• Neg market value data is not publicly available
  regularly enough to estimate the variance
  directly
• Estimate based on Gruy et al. 1982 developed
  reserve prices tend to be 1/3 of crude oil prices
• Therefore, use the variance of the rate of change
  of crude oil prices as a proxy for the variance
  of the rate of change of developed reserve prices

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Inputs into Valuation Equation Variance (cont.)

• Representative period 1974-1980
• Periods of crisis
• Periods of tranquility
• Using monthly data from 1974-1980 ?20.02019 -gt
  ?0.142 To account for increase in perceived
  uncertainty (Jacoby and Paddock1983)
  ?20.0625 -gt ?0.250
• Per Barrel Crude oil Wellhead price ranges
  implicit in standard deviations Year 0 1980 _at_
  36/barrel
• 95 confidence

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Inputs into Valuation Equation Expected Stages
12 Costs

• Expected exploration costs before tax (USGS)
• 10 of the costs are depreciated (not taxable)
• DjAj6QojQgj?
• Qoj recoverable oil reserves on jth tract
• Qgj recoverable gas reserves on jth tractAj
  tract-specific scaling parameter that considers
  water depth and drilling depth ? 2/3
  (Mansvelt Beck and Wiig 1977)
• represent total reserve volume measured in
  terms of cubic feet of gas equivalent (BTU
  conversion factor 1 barrel 6 mcf)

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Inputs into Valuation Equation Expected Stages
12 Costs

• Calculating the track-specific parameters Aj
  using a fitting procedure.
• Step 1 Take second-order Taylor Expansion of Dj
• variances of oil quantities
• variances of gas quantities
• covariance between the above two
• Note bars represent expected values (which cant
  keep)
• Step 2 Arbitrary assumption ?ogi 0.5 ?oj ?oj
• Solve for Aj to get
• Use the track specific means for distributions
  Dj, Qoj, Qgj
• Result Track-specific development cost functions
  to approximate the true developtment cost
  functions (information is protected by USGS)

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Option Valuation Comparisons

• Comparison with USGS Estimates
• Differences should be due primarily to
  differences in the financial valuation techniques
• To increase the fairness of the comparisons, we
  assign a zero to the tracts
• Other analysts might derive different DCF values
  using the same geological and cost data

41
Option Valuation Comparisons

• Comparison with Industry Bids
• The cost and geological data used by the USGS may
  deviate from industry expectations
• Even if the underlying USGS data match industry
  expectations, we still do not observer industry
  valuations directly

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Option Valuation Comparisons

• Result
• Compare between option valuation, USGS and
  industry bid values
• OV option valuation
• USGS USGS DCF valuation
• GB Geometric mean of industry bids
• HG High (winning) industry bid

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Comparative Statics

• Variance
• Given that oil and gas have been found, there is
  little likelihood that exploration and
  development will not occur immediately
• Relinquishment requirement
• Both of them do not have much effect in the data
  set. But they would affect tract value in areas
  subject to higher unit investment cost

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Exploration and Development Timing

• Low-cost tracts should be explored or developed
  immediately
• High-cost tracts should be held from exploration
  or development
• The firm need only calculate C V/D to decide
  whether a tract should be explored or developed
  immediately