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ALFRED
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WORKING PAPER
SLOAN SCHOOL OF MANAGEMENT
ONE FOR YOU, THREE FOR
ME...
...or...
...the
Philip
WP
Design of Optimal Production Sharing Rules
for a Petroleum Exploration Venture
Hampson, John Parsons and Charles
#3034-89
Blitzer
January 1989
revised July 1989
MASSACHUSI
INSTITUTE OF
TECHNOLOGY
MEMORIAL DRIVE
CAMBRIDGE, MASSACHUSETTS
50
02139
OCT
4
1989
ONE FOR YOU, THREE FOR
ME...
...or...
...the
Philip
WP
Design of Optimal Production Sharing Rules
for a Petroleum Exploration Venture
Hampson, John Parsons and Charles
#3034-89
Blitzer
January 1989
revised July 1989
5
OCT
4 1989
HECSVB)
ONE FOR YOU, THREE FOR ME.
.THE DESIGN OF OPTIMAL PRODUCTION SHARING RULES
FOR A PETROLEUM EXPLORATION VENTURE
Philip
Hampson, M.I.T
John Parsons, M.I.T, and
Charles Blitzer, M.I.T. and the World Bank'
revised July 1989
Comments and
Address
all
suggestions are welcome.
correspondence
to:
Professor John E. Parsons
Department of Finance
MIT School of Management
50 Memorial Drive
Cambridge,
02139
MA
'
This research has been supported in part by the Finance, Investment and Contracts Program of
is based on Philip Hampson's Master's Thesis, "The
the M.I.T Center for Energy Policy Research and
Design of Optimal Production Sharing Rules for a Petroleum Exploration Venture," M.I.T, 1988.
research assistance of Raghuram Rajan and Sung-Hwan Shin is greatly appreciated.
The
1
1.
Introduction
In mid-1986 a state
with a U.S.
oil
owned
Company
Oil Resources Authority signed an oil and gas exploration agreement
with the following terms.
exploration and development over a defined territory
that a portion of the oil production
A
second portion of the
Company
oil
In this paper
to provide the
Company
owned by
would be assigned
to
20%
we
is
its
expenses.
to 25,000
and to 50,000
with a financial incentive to pursue an exploration and development program
The
actual contract sharing rule
find that the optimal sharing rule assigns the
Under
is
compared
model developed by Grossman and
Company
a larger share of the small
the optimal sharing rule the
Company's share of a
declining significantly in the size of the discoveries, in contrast with the Company's slightly
increasing share under the actual contract.
Replacing the actual contract with the optimal sharing rule
could increase the expected return on the project by as
a result of
for
analyze this production sharing rule as an agency contract designed
discoveries than does the actual contract.
discovery
contract specified
compensate the Company
against the optimal sharing rule derived using the Principal-Agent
We
The
the Authority.
share as total production rose from
that maximizes the net financial return to the Authority.
Hart (1983).
the exclusive rights to
would be divided between the Company and the Authority, with the
receiving a 25, 22, and
barrels per day.
The Company obtained
much
as
$336
million.
The
increased
NPV
is
improved incentives for the choice of an optimal exploration program on the part of the
Company, and
also a result of ensuring that the
marginally profitable wells.
decreases the project
NPV
Company
enjoys a financial interest in completing
In most cases the failure of the actual contract to provide proper incentives
by between 5 and 12%, although for some marginal projects the extra
incentive costs completely cancel the value of the project.
An
important contribution of
more than
just general
financial contracts: in
this
paper
significantly
demonstration that existing agency models can provide
insights regarding the types of incentives that should
some
cases
it
is
parameters of the contracts themselves.
depend
is its
upon the
be incorporated into
possible to use these models to fine tune the design and the
Several significant caveats must be noted.
specification of the parameters in the
Our
specific results
model with which the optimal
2
sharing rule
is
derived and with which the value of both the actual contract and the optimal sharing rule
are estimated.
A different estimate
of the relationship between the
and the probability of finding a given
Our
closer to the actual contract.
amount of
depend
results
one model we are highlighting one
oil,
also
mind than those
set of incentive
that are at the center of the
been expended creating
In choosing
An
problems and abstracting from another.
a completely different set of objectives
These caveats do not
Grossman and Hart model.
diminish the significance of the results-on the contrary.
effort in recent years has
wells drilled
upon the choice of agency model.
argument could be made that the actual contract was written with
in
number of exploratory
for example, might yield an optimal sharing rule
Although
a myriad of
a significant
agency models
amount of research
in finance,
almost no work
has given attention to the actual use of any single model in order to improve the detailed design of a
specific financial contract.
to
do
this
is
Highlighting the problems and caveats that arise in the course of an attempt
one of the contributions of
The remainder of
this
paper.
the paper proceeds as follows. In section 2
using traditional capital budgeting techniques and
decisions.
In section 3
Agent model and
the sharing rule that
In section 6
2.
we
we
fit
in section
is
the
oil
we
calculate the
we
first
analyze the
exploration project
best exploration and development
exploration contract problem to the Grossman-Hart Principal-
4 we present the derived optimal sharing
implicit in the actual contract,
discuss the results
oil
and we compare
and some problems raised by the
In section 5
rule.
it
we
calculate
with the optimal sharing rule.
Section 7 concludes.
analysis.
The Project
We
begin our study with a brief capital budgeting analysis of the
oil
exploration project.
Authority intends to grant exploration and development rights under contract to the
horizon of 25 years.
The
development period, and
reverts to the Authority.
exhausted
at this point.
contract horizon
is
broken down into
20 year production period.
a
We
We
assume that
examine the
all
for a time
a 3 year exploration period, a
At the end of
this
horizon the
of the cash flows relevant to
project's value
Company
under a
set of scenarios: the
two year
oil field
this project
The
title
have been
two key variables
3
are
(i)
the
number of
former variable
a matter of
is
every choice of a
number of
project cash flows.
methodology
wildcat wells drilled in exploration, and
choice, the latter
wells drilled
Adelman
similar to that in
in
a
oil
neighboring countries.
from figures derived for
An
(1986).
166% of
equal to a
development
we
calculate a set of
average output of 250 barrels per day (bbl/day) was
This figure
is
similar to average daily
Exploration, development and production costs were scaled up
An
average well depth of 10,800 feet was assumed,
and similar to previous wells
drilled in the host
was derived. Adelman (1986) estimates that
drilling costs,
costs, or $272/barrel/day.
is
The
oil
price
is
assumed to have
to the average of the F.O.B. Persian Gulf prices quoted in the
The wellhead
transportation cost to the point of shipment.
price structure.
All analysis
have an effect on the
is
conducted
Moreover
in constant
in this section
so this factor does not affect our calculations.
5%
price
is
a martingale type structure, in
The expected
March
of
15,
oil
price
is
set equal
1988 issue of the Wall Street
assumed to be $13.00
less
$2.00
a
This can be viewed as a somewhat conservative expected
1988 U.S.
real value of recoverable costs.
given low inflation forecasts.
development
Production costs are assumed to be
equal to the expected future value.
roughly $13.00 per barrel.
total
thus development costs of $1,360,000 per well are assumed.
development cost of $5,443/barrel/day.
which case the current value
Journal,
For
Using U.S. Department of Energy "Indexes and Estimates of Domestic Well Drilling Costs"
costs are roughly
is
The
on the former.
size of discovery,
wells in the host country.
this typical sized well.
a total drilling cost of $819,760 per well
This
the realized size of the discovery.
variable conditioned
and for every realized
similar to average well depths in a neighboring country
country.
(ii)
random
Exploration, development and production cost assumptions were derived using a
assumed for commercially producing
output rates
is
A 10%
dollars.
However, these
we
Due
to tax rules, inflation will
effects are
judged to be small
are considering the project's value pre-tax and
discount rate
is
applied to
all
cash flows received
by both the Authority and by the Company.
In Table
drills
1
we
present a sample set of cash flow figures for the scenario in which the
Company
2 wildcat wells and makes a discovery of size 456 million barrels in total or 50,000 bbl/day.
Since the actual contract
is
written in terms of
oil
production per day, this
is
1
The
the measure used in the remainder of this paper.
4
$1.64 million cash outflow in year
The cash
bbl/day.
enough
The
total
NPV
for the project
under
To determine the optimal exploration and development program
relationship
million cash outflow
wells to bring production
up
to 50,000
inflow of $187.15 million in years 6 through 25 are the receipts from the sale of the
net of the production expenses.
oil
The $136.08
the expenditure on exploration.
1 is
in each of years 4 and 5 are the costs of developing
between the
fit
it
scenario
is
it
is
$891.44 million.
necessary to describe the
programs and the probable value of a discovery.
set of possible exploration
To make our problem tractable and to
this
into the
framework of the agency model
that
we
we
use,
represent the choice of an exploration and development program as a two stage decision problem. First
the project
to
drill.
management decides once and
for
all
on
number of
a level of exploration-the
wildcat wells
Second, given the results of the exploration program, the project management decides
if it
will
develop the property for commercial production. To formalize the probability relationship between the
exploration program and the discovery size
approaches used
in the
= 1...20. Each program
aj, j
be
on the program,
the index
probability of
making a discovery of
the probability of finding any
H(q).
finding
is
A binomial
oil:
G(j)
=
\-(l-6y,
is
is
j,
size
G(j),
oil,
distribution
a discovery of size q
use a method that
exploration geology literature,
exploration programs,
drilled:
we
is
i.e.,
Adelman
represents a fixed
identical with the
where
is
<S
modeled
between exploration and discovery
number of
We
20 possible
(1983).
number of
number of
q given an exploration program
and the probability, given a
called the wildcat probability.
as a
a,
specify
wildcat wells that are to
wells to be drilled.
The
composed of two
parts:
is
find, that
drilled.
size
The
the discovery
is
of size
q,
probability, H(q), that the find
lognormal distribution with parameters
As the next
we approximate
fx
and a, and
is
assumed
step in specifying the probability relationship
the lognormal distribution over discovery size
with an 8 point discrete probability distribution. Each point
is
exactly
one standard deviation apart from
In terms of the logarithm of discovery size, the eight points in question begin
-3.5
standard deviations to the
the
mean
in units
al.
consistent with a
used to relate the number of wildcat wells drilled to the probability of
independent of the number of wells
the next on the log scale.
et
is
left
of the
mean and
of one standard deviation.
progress to 3.5 standard deviations to the right of
This process yields a 20 x 9 matrix which
we
refer to as
5
the 'exploration-discovery matrix.'
discovery was
made
conditional
probability of a discovery of size
The
on action
q,
element
first
the
a^
on
conditional
each row denotes the probability that no
in
element of the matrix,
ji-th
action
p^a,),
Each row of the matrix
aj.
is
denotes the
a probability
distribution across outcomes.
Associated with each discovery
size, q„
we
calculate a 'development NPV,'
7r(q,),
representing the
value of developing the find for commercial production, exclusive of the sunk exploration costs.
will
be some cases
which the exploration program yields a find but the
in
small that the investment necessary for commercial development
element of the capital budgeting problem
development
is
warranted.
undeveloped and we
left
for
is
set
^(q^sO.
is
2.
as a
row
so
this
NPV
would be negative, then we assume the
find
For our set of cost and price assumptions the size of discovery
warranted
Augmenting the matrix
program, D(a,), as well
is
Therefore, a key
determining for which discovery sizes commercial
is
quite small, 59 bbl/day.
=
display of the exploration-discovery matrix for the case of S
given in Table
is
a
column
listing
2
0.4, e*
= 2500 and a = 20%
is
the cost for each size of exploration
associating each size of discovery with
its
development NPV. In Figure
four rows from this matrix are graphed, showing the probability distributions across discovery size as
the
number of
wildcat wells drilled increases.
This matrix contains
all
of the information necessary for calculating the efficient choice of an
exploration program and the expected
program which
6
=
0.4
number of
and e"
=
is
expected
NPV
One
for the project.
development
NPV
less
simply chooses that exploration
exploration costs.
Table 3 presents
alternative parameters describing the probability distributions.
2500, then the
best
first
$7.38 million; the expected
program
NPV
yields the greatest expected
the results for a
if
is
upon development
which commercial development
A
1
If
size of the discovery
not worthwhile.
is
There
NPV
of the exploration program
is
number of
wildcat wells
from development
$156.98 million.
The
is
is
9;
For example,
the cost of this exploration
$164.36 million; and the ex ante
data indicate that the optimal
number
of wildcat wells increases as the location parameters of the lognormal discovery size probability
Here, as elsewhere,
we
ignore any option values
in calculating
our
NPVs. We do
not believe they are significant in our context.
6
The optimal number of
distribution increase.
an increase
rule of
to
fall
in
decreases with
A
These are the project values
best' case.
'first
the absence of any agency problems.
If
both the Authority and the
the optimal exploratory drilling effort and development decisions and
contract with the
Company
to execute that exploratory drilling
if
drilling effort
Company
a fee as
could assess
and development program, then the
full
NPV
first
of the project. The
reimbursment for the exploration and development costs and
Company's commitment
for the opportunity cost of the
would be
that
Company
the Authority could successfully
implemented and the Authority could anticipate earning the
Authority would pay the
rough
3
refer to these solutions as the
best could be
this territory
be that doubling the wildcat probability parameter causes optimal
to
by a factor of one-half.
calculated in
on
the productivity of the drilling effort as expressed by the wildcat parameter S.
thumb seems
We
wildcat wells to be drilled
to this project.
When
these perfect information
conditions are not met, however, the problem of moral hazard in the Company's actual exploration and
development decisions make
made
in this
paper are that
drilling effort,
and
(ii)
it
(i)
is
infeasible to attain these first best results.
the Authority
the Authority
claims that the discovery
is
is
is
unable to monitor the Company's choice of exploratory
unable to verify the size of a discovery whenever the
too small to merit commercial production.
for the Authority to give the
The two key assumptions
Company an
As
a consequence
incentive contract that induces the
Company
it
to
is
Company
necessary
implement
the 'second-best' exploratory drilling program and to complete marginally profitable discoveries.
3.
The Principal-Agent Model
The
principal-agent
model
that
we
use to derive a solution to the optimal incentive contract was
developed by Grossman and Hart (1983).
is
The model
is
composed of two
parts.
The
first
component
the specification of the relationship between the action choice and the project's probable outcome.
The optimal number
falls with an increase in the productivity of the drilling effort
exploratory well with greater probability, reducing the marginal value of
additional exploratory well could be applied with greater
of exploratory wells to be drilled on this territory
because the total benefits of exploration are captured with the
the second and subsequent exploratory wells, and because the
first
same expenditure on an
marginal return to a different territory on which no exploratory well has yet been drilled.
7
For our case
this
is
the probability model just described which relates the choice of an exploration
program and the development NPV.
The second component of
the relevant features of the principal and the agent.
owner of the
program.
project.
In the
The agent
G-H model
is
In
the principal's
function
utility
The
principal
possible to incorporate risk aversion.
We
first
is
risk neutrality,
The agent or
the
Company
is
described by a
functions that are admissable in the
Company
risk aversion,
The
in
utility
G-H
the Authority, the
defined over the space of possible profit
typically
is
modelled as
risk neutral,
although
is
expected profit maximization.
function defined over exploration programs,
In this paper
I.
is
the description of
present the results under the assumption of the
we
restrict ourselves to a subclass
model: U(a,I)= V(I-D(a)), where D(a)
pursuing the exploration program
a.
The Company's
is
utility
a,,
of those
and
utility
the expense incurred
function must exhibit
V"<0.
Authority's problem
is
to choose an incentive contract or sharing rule,
elements that are the payments to be made to the
outcome,
is
and therefore the objective function for our problem
over the Company's compensation,
by the
our case the principal
is
Company, the manager of the exploration and development
the
levels-in our case the development NPV's.
it
G-H model
the
7r„...7r<>.
In
additon
development expenses, but not
interpreted as the
it
is
for
assumed
that
Company
in the
a vector with
event of each possible realized
the Authority reimburses
exploration expenses.
I=I1,...I9>
the
Company
Therefore the payments
I
First,
V
a r choose I(a^»[I 1 (a
such that
such that
l
),..J < (a )]
f
e argmin
S^Jpfo) U(ar I,)] >
V
a k ^a r
sJp.Ca,)
U mjn
2 '[p^)
,
U(a,,I,)]
I,]
and
> sjp,(a k ) U(a k ,I,)].
all
should be
Company's share of the development NPV. The optimal incentive contract
using a pair of programming problems.
for
is
derived
8
i.e.,
for
each exploration program that the Authority might
like
the
Company
to implement,
the
the least cost incentive contract for which
(ii) it is
in the
Company's
interest to
accept the contract as against the best available alternative, and
(iii) it is
in the
Company's
interest to
Authority chooses
(i)
choose the specified exploration program
results presented in the
we have added
paper
action
a^
C^s
and we define
aj
2
Company
the additional constraint that the payment to the
be both non-negative and bounded above by the
implements
For most of the
as against all other exploration programs.
9
total
I^)].
[Pi(a,)
development NPV, O^I^Tr,.
We
We
say that
1^)
define the incentive cost of implementing
as C(aj)-D(aj).
Second,
choose a
argmax 2
e
9
[Pi( a j)
n]
-
C( aj)-
a
i
i.e.,
find the exploration
program
that yields to the Authority the greatest
payments that must be made to the Company to induce the choice of
the triple [a
,C
,1
]
as follows: a
contract that implements a
,
,
this
[Pi( a
)
n]
We now
-
C(a
),
I
=
C =2
SB
net of the
I(a
the incentive
),
'[p,(a
i«l
Define
)
n]
D(a
-
FB
)
-
FB
or equivalently the incentive cost for the project.
apply this model to derive the optimal sharing rule with which to finance the
exploration project and in the next section
4.
NPV
exploration program.
the second best exploration program;
or equivalently, the optimal sharing rule; and,
SB
2 ._
development
we
oil
discuss the results.
The Optimal Incentive Contract
In Table 4 the optimal sharing rule
An
analysis of the
Of
course
payment.
payments made
when no
is
displayed for the parameter values e"
= 2500 and
help us to understand the incentive problem for this
made under
the optimal sharing rule the
Company
payment
payment equal
in these events.
to the full
6
=
0.4.
oil project.
receives a zero
Discoveries of size 10 or 50 bbl/day should not be developed and therefore the
also receives a zero
receives a
discovery
will
is
Company
For discovery sizes 239 and 1,143 bbl/day the Company
development NPV: our
ceiling constraint
on the payment
is
binding
9
for these two events.
For discovery
sizes ranging
from 5,467 bbl/day to 597,720 bbl/day the Company
receives payments that are approximately invariant at $30 million.
make
optimal to
a
comparable payment
payment would have exceeded the
NPV
is
falling
from 100%
in
for discoveries of size
is
is
to pay the
this characteristic,
The
a fixed 'bonus'
while the
Company
is
is
at
low discovery
sizes
is
is
agency contract
Our
sharing rule has
made.
Therefore
it
is
the incentive payment.
First,
the Authority
optimal for the Authority to bear
on the development
NPV
all
is
of
provides an
Second, the probability matrix relating exploration levels to outcomes
has been specified so that conditional
given size
size
efficient
we have bounded
the risk except where making the Company's income contingent
incentive for greater exploration.
The
a consequence of two earlier assumptions.
risk averse.
the development
size.
whenever a commercial discovery
except for the fact that
optimality of a fixed 'bonus'
risk neutral
The Company's share of
a clear rationale for this shape of the optimal sharing rule.
Company
would have been
239 and 1,143 bbl/day to 30.6% for a discovery
of 5,467 bbl/day and to 0.3% for the largest discovery
There
it
the cases of discovery sizes 239 and 1,143 bbl/day, but the
development NPV.
full
Unconstrained
upon making
independent of the exploration
a find, the probability of
effort.
making
a discovery of a
Therefore, the absolute size of the discovery
provides the Authority with no "information" about the Company's choice of an exploration program,
and consequently there are no incentive benefits to be derived from making the Company's income
contingent on the absolute size of the discovery.
Instead,
it
is
optimal to give the
bonus-approximately $29.97 million-whenever a commercial discovery of any
In Table 5 the optimal sharing rules are displayed for a
the exploration-discovery matrix.
The
first
two columns
full set
list
Company
4
The
in the
list
these parameters.
is
shown
is
made and
in
in
The number of
the third column.
insurance contracts.
made
to the
the event of each of the eight possible discovery
relationship between these two assumptions and the special shape of the optimal sharing rule
in
made."
the payments net of development costs that are to be
event that no discovery
(1979) as a rationale for deductibles
is
a fixed
of alternative parameters defining
exploratory wells to be drilled in the second best exploration program
The remaining nine columns
size
Company
was pointed out
in
Holmstrom
10
sizes.
Since the absolute size of the eight discoveries are different for each set of probability
Table 6 summarizes the
parameters, the columns are indexed only by the ordinal size of the discovery.
project results under the second best sharing for the
number of wildcat
full set
of scenarios, including the second best
wells to be drilled, the cost of the exploration
expected payment made to the
Company under
program incurred by the Company, the
the optimal sharing rule, and the expected profit to the
Authority under both the optimal sharing rule and under the assumptions of the
scenario in which
d =
1
2500 and 6 =
million for the Authority, or roughly
illustration
of
how
first best.
For the
0.4 the optimal sharing rule achieves an expected profit of $136.81
87%
of the
first
best expected level.
Figure 3 provides a graphical
incentive costs vary with median discovery size and wildcat probability.
As median
discovery size and wildcat probabilities increase, the incentive cost measured as a fraction of the
best profit decreases.
size of
The
500 bbl/day with
median discovery
increasing,
incentive cost
is
from $3.37 million
to $164.25 million.
keeping the median discovery size constant
5.
An Agency
We now
first
best expected profits for a
4%
at
median discovery
best profits for a
absolute value, however, the incentive cost
in
As we change
is
the wildcat probability from 0.2 to 0.6,
500 bbl/day, the incentive cost
15%--from $3.37 million
of
first
is
falling
from
32%
of
first
to $2.33 million.
Analysis of the Actual Contract
turn our attention to an analysis of the incentives
negotiated between the
distinct clauses
Company and
embedded
in
the actual contract
There are a large number of provisions and
the Authority.
of the contract which specify the obligations of each party and the payments that
be made under various circumstances.
contract and construct from
It
the contract
is
necessary
first
40%
this implicit
of the discovered crude
that the
sharing rule
oil
will
to dissect the various provisions of the
them the share of the project value
each possible outcome. After constructing
Under
of
Measured
size of 25,000 bbl/day.
best expected profits to
32%
a wildcat probability of 0.2 and decreases to
first
we
Company would
analyze
its
receive under
incentive properties.
production-hereafter referred to as
'cost
The formula divides the
'cost
petroleum'-is assigned for the recovery of costs according to a formula.
11
petroleum' on a pro rata basis between the Authority and the
party has outstanding in
Development
The Company
recovery pool.
the cost
costs are paid by the
Company and
The
according to the total that each
pays
all
exploration expenses.
5
these are factored into the pool according to a
depreciation rate determined by the national tax law.
Company's portion of the pool.
Company
Production costs are also included
in
the
Authority's portion of the cost recovery pool consists in a $13
million seismic and exploration data fee.
The remaining 60% of crude
oil
production plus any cost
petroleum not used for cost recovery-hereafter referred to as 'shared petroleum'-is divided between
the Authority and
Company
according to a step function formula.
'shared petroleum'
when
production
lies
total
between 25,000 and 50,000
The Company must
size:
also
bbl/day,
lies
between
20% when
and
The Company
and 25,000 bbl/day,
total
production
is
shares in
22% when
total
25%
of
production
greater than 50,000 bbl/day.
pay a number of bonuses to the Authority that are dependent on discovery
$1 million for every 25,000 bbl/day. These bonuses are considered
the conditions of the contract.
In addition, the
non -recoverable payments under
Company must pay
a $40,000 per year advanced
education scholarship to the nationals of the host country during the exploration period increasing to
$160,000 per year
host country
if
a
commercial discovery
computed
at
30%
shields
due
less
remaining
declining balance.
to leverage.
No
34%
this
flows to the
5
The Company
66% on
recoverable expenses.
subject to income taxes in the
as total
revenues
of development expenditures are
classified
provisional
66%
is
income defined
are eligible for immediate recovery.
loss carryforwards are permitted.
The Authority does not
however, the host country more than
From
made.
an effective rate of
under the sharing agreement
as depreciable, the
is
likely
No
The
allowance
depreciation schedule
is
made
is
for interest tax
allow interest tax shields within this contract structure;
does allow for such deductions as a general
rule.
information we have constructed an accounting system with which to calculate the cash
Company and
to the Authority
Therefore the Company's share of the
oil
produced
under various scenarios for exploration programs and
will
be contingent upon
its
expenses incurred
in exploration.
To be consistent
with our earlier assumption that the Authority cannot observe the Company's exploration effort it is necessary to assume that what is
unobservable is the number of quality' or Valuable' exploratory wells drilled. The Company can always drill another exploratory well, but only
carefully planned
and properly executed wells contribute
significantly to the probability of disovering
oil.
12
With
discovery sizes.
contract.
In Table 7
this
we
accounting system
we can
calculate the sharing rule that
NPV
for the project, the
under the actual contract, and the portion of the development
Figure 4
A
we graph
NPV
payments made
that these
calculated in the earlier section
displayed in Figure 4 should be
is
implicit in the actual contract with the optimal sharing rule
interesting.
The
compared
values for the actual contract displayed in Table 7
to the graphs displayed in Figure 2.
the optimal sharing rule and the actual contract
a generally fixed
is
fit
Company
Company.
drilling effort
Company
a
While the optimal
size.
development NPV, the actual
and then declines very
slightly.
the actual contract to our agency model and derive the exploration program that the
company would choose.
the
a sharply declining share of the project's
a share that initially increases
The graphs
contrast between
nominal payment for a discovery, the actual contract gives the
Company
sharing rule gives the
The
4.
While the optimal sharing rule gives the
striking.
nominal payment for a discovery that varies significantly with the discovery
We now
Company
payments represent. In
should be compared to the values for the optimal sharing rule displayed in Table
contract gives the
to the
these percentages as a function of discovery size.
comparison of the sharing rule
Company
implicit in the
and assumptions on the number of wildcat
a set of different discovery sizes
list
wells drilled and the associated development
is
These
It is
then possible to calculate the expected return to both the Authority and
results are displayed in Table 8.
and the Authority's expected
the case of the optimal sharing rule.
One
should compare the Company's chosen
profits displayed in Table
The ex ante expected
8 to those displayed
profits to the Authority
contract are significantly lower than they are under the optimal sharing rule.
in
Table
6,
under the actual
For example, for the
scenario where
d =
contract, while
under the optimal sharing rule the project yielded the Authority between $10 and $17
million profit.
For the scenario where
1
500 regardless of the wildcat probability the project
d =
1
2500 and 6
=
is
worthless under the actual
0.4 the actual contract yields the Authority
$7.76 million less in expected profit than does the optimal sharing rule, a loss of
project value.
5.7% of the
For larger values of the median discovery size and the wildcat parameters the dollar
total
loss
13
and the portion of project value
in value
million
lost
from the actual contract increases signficantly--up to $330
and 8.5%.
The
actual contract
compares poorly
in the actual contract are expensive.
to the optimal sharing rule primarily because incentives given
But given that a find
correlated with the size of the discovery.
discovery
is
Therefore
payment
In the actual contract the
is
to the
made
Company
highly
is
the absolute size of the
an exogenous random variable unrelated to the Company's choice of an exploration program.
randomness
this
to choose an
payment
in the
to the
Company does
not add to the Company's incentive
expanded exploration program. Moreover, the average payment
increased to compensate for the additional risk that the
sharing rule the
Company
discovery of any size
receives nothing
made.
is
when no
Company
discovery
is
Since the event of a discovery
is
is
to the
Company must be
forced to bear.
In the optimal
made, and a fixed bonus when
a
informative of the extent of the
exploration program, the bonus serves to increase the Company's incentive to expand the exploration
program. However, since the bonus
risk
born by the Company
There
is
is
is
invariant with respect to the size of the discovery, the additional
minimal.
a second source for the superiority of the optimal sharing rule.
optimal sharing rule
we made
sure that the
Company would
which commercial production was a negative
would receive
positive.
payment
if
This guaranteed that the
development
example,
a positive
if
NPV
the
was
positive.
Company
a discovery
The
Company will complete fewer
was commercialized
sure that the
Company
which the development
NPV was
also
for
made
incentive to develop
actual contract does not have a
if
the discovery size
if
all
discoveries for which the
is
is
when
For
comparable structure.
greater than 975 bbl/day.
Company
The
the discovery size were greater than 59 bbl/day.
profitable wells
from a given exploration program
incentive
we
has drilled 2 wildcat wells, then under the actual contract the
decision would be to develop the well
A comparable
receive a zero payment for discoveries for
decision and
Company had an
has an incentive to develop a well
6
NPV
In our design of the
only
efficient
Since the
faced with the actual contract, the Company's return
also less ex ante.
6
problem was documented by Wolfson (1985) for certain types of
oil
and gas limited partnerships
in
the U.S.
14
We
have postponed a variety of issues raised in the course of deriving our solution, and
we now
turn our attention to an analysis of these issues.
6.
Discussion
It is
common
practice in the corporate finance literature to
chooses the firm's projects as
if
the firm were neutral towards ideosyncratic
corresponds correctly with the decision rule that would result
that
is
assume that the management of
if
This assumption
risk.
the corporation exists in an environment
approximately well described by diversified shareholders and perfect capital markets.
management of the corporation or the agent
is
a firm
If the
neutral towards the project's ideosyncratic risk, then, as
has been established by Harris and Raviv (1979), the efficient incentive contract takes
on
The
and development
principal, in this case the Authority, should simply sell the rights to exploration
Company,
to the agent, the
and allow the Company to bear
for a fixed fee
contract negotiated in the case under study does not
fit
this description.
all
We
of the
a trivial form.
The
risks.
believe that in
actual
many
cases
these modelling assumptions and the incentive contract that they predict do not correspond very closely
with the real context at hand.
In this paper
risks at
hand
we have assumed
in the project
because
the equilibrium decision rule for the
of
risk neutrality
is,
we
that the
we
Company
management of
believe, a strong
one
that
private information about the projects in which
may
projects, then
we
(1982).
A
neutral and
who
If,
it
the firm would
that
we have
fit
makes sense only
more
to the ideosyncratic
relevant to our case
this description.
in a
model of
The assumption
relatively perfect
however, the management of each firm possesses
is
if it
investing
were averse
similar suggestion yielding the
The environment
some degree, averse
and private information about
its
own
believe the consequent imperfections in the financial markets
lead the firm to rationally behave as
particular project.
to
think that in another environment
information and frictionless financial markets.
management of these
is,
in
to the ideosyncratic risk associated with each
same conclusions has been made by Holmstrom
mind could even incorporate
hold diversified portfolios.
individual investors
who
are risk
Rather than focus on modeling the environment that might
15
generate
this risk aversion,
interesting
problem
we chose
in this
paper to take
that arises in this environment:
how
it
as a primitive
to design
and
and focused instead on the
calibrate an optimal sharing rule
between the Authority and the Company.
The second
issue regarding the specification of utlity functions concerns the risk neutrality or risk
We
aversion of the principal.
assumption
is
made
in the theoretical literature primarily
interesting results and the
principal's risk neutrality.
risk aversion.
have modeled the problem as
problem and
G-H model
However, the
There are many arguments
as risk averse or risk neutral.
solution are
its
However,
that can
as
if
the principal were risk neutral.
because
risk
much more
aversion
is
This
not necessary for
transparent in the case of the
can easily be adapted to the case of the principal's
be made for modeling the principal
Holmstrom (1982) points
in
any given case
out, the principal's aversion to the
ideosyncratic risk of the project does not immediately follow from the capital market imperfections
mentioned
earlier as
an explanation for the agent's
risk aversion.
Instead of assessing here the merits of a position for or against modeling the principal as averse
to the ideosyncratic risk,
we merely
note the important consequences that a change
in this
assumption
has for the design of the optimal sharing rule and the comparison of the actual contract with
Table 9
we
Company. The payments
Company
size so that
the
development
NPV
to 0.2%.
same
report the optimal sharing rule for the case that the Authority exhibits the
aversion as the
is still
to the
Company
This remains in sharp contrast with the sharing rule that
particular values
we
that
parameterization of the
risk.
The Company's share of
declining significantly as the discovery size increases,
derived
utility
for
far
the
In
risk
increase very moderately with the discovery
shares a portion of this exogenous
expected returns to the Authority remain
it.
above those
in
is
the
moving from 100% down
implicit in the actual contract.
the actual contract.
Of
The
course the
optimal sharing rule depended significantly upon the
functions for both the Authority and for the
Company.
the optimal sharing rule under the assumption of two different functional forms for the
We
calculated
utility
function-
-logarithmic and exponential--and also for different parameters determining the degree of risk aversion.
While the exact values
for the
payment
to the
Company do
change, the general structure of the optimal
16
sharing rule remains as
Company
we have
described
In particular, under
it.
NPV when
receive a large fraction of the development
the absolute dollar value of the payment to the
decreasing share of the development NPV.
all
insights
(i) it is
the discovery
Company may be
These two
cases
small,
is
increasing,
important that the
it
and
(ii)
while
always a sharply
is
about the structure of the sharing rule
follow directly from the structure of the exploration-discovery technology and from the moral hazard
for the completion decision.
Were we
to
change
significantly the structure
of the exploration-discovery matrix, the structure of
the optimal sharing rule could be drastically changed.
For example,
if
increased exploration increased
the relative probability of larger discoveries in particular, then the optimal sharing rule could
be one
in
which the Company received a sharply increasing share of the development NPV~see Grossman and
Hart (1983, Propositions
7-9).
There are
incentives for an optimal exploration
an optimal completion decision.
some
also
program
cases in which the most efficient structure of
in direct conflict
is
with the incentives necessary to ensure
In this case the structure of the optimal sharing rule would be highly
contingent upon the relative significance of the two effects.
We
point out the sensitivity of the optimal sharing rule to the specification of the environment not
to diminish confidence in the results, but rather to point out the
the one in this paper.
In doing so, the assumptions
importance of using a model such as
made about
the environment are brought out in
sharp relief and the reasons for a given structure of the sharing rule are
are
more open
to analysis.
If
we
Without the application of the
virtually impossible to identify so precisely the
model used and
it
would have been impossible
G-H
we must
when agency problems
is
superior to
revise our original
Principal-Agent model
it
model of
would have been
important incentive effects implicit in the probability
to
make
a compelling argument for a different structure
of the sharing rule than the one written into the original contract.
conclusion that
transparent and
are not convinced that the derived optimal sharing rule
the actual contract, then the analysis argues that to be consistent
the exploration project.
made more
These points
highlight the general
are central, the financial contract written between two parties
must be carefully tailored to the particular characteristics of the
real assets.
In our opinion, the subject
17
of agency theory in the
field
of corporate finance
is
precisely the exploration of the relationship
between
the characteristics of the real assets and the structure of the financial contracts.
Another important assumption
our use of the
implicit in
G-H model
is
we
that
are concerned with
an essentially one shot decision problem on the part of the Company. In one respect
this
reasonable,
is
since an oil exploration venture does have the peculiar characteristic of a relatively short period of
exploration during which most of the uncertainty
is
made whether or not
operating wells can in
resolved.
At the end of the exploration
to develop the territory for commercial production.
some
the exploration decision
is
is
cases be properly viewed as cash cows.
not a one shot problem.
program as involving a Bayesian updating process
drilled provide information
in
problem
program and not
as
we have done
problem, but
we
some important
respects, though,
which the
from the
results
first
exploratory wells
about whether additional wells should be drilled or whether the exploration
drilled
a simple ex ante choice variable as in
obviously sacrifices
we
think the results that
interesting research
After this point the
For example, one could view the exploration
program should be abandoned. The number of exploratory wells
stochastic
In
a decision
problem would be
is
then the result of a dynamic
our model.
some accuracy and some
Simplifying the decision
interesting
components of the
obtain are interesting and justify this compromise.
An
Company's choice of exploration program
as a
to analyze the
dynamic agency problem and to consider the actual contract as an attempt to provide the optimal
incentives for this type of a problem.
One
final
caveat should be mentioned.
known ex ante and constant over
the
life
In our analysis
of the contract.
we have
The
uncertain requires us to modify several aspects of our analysis.
the exact terms in which the contract
that each party will receive: hence,
the
Company
will
is
written.
when
change even though
its
have solved for the optimal sharing rule
should be
made
to the
Company
in the
the
oil
The
recognition that the future
First,
we must be more
if it
were
oil price
is
careful about
actual contract specifies shares in quantity of oil
price changes, the absolute value of the
share of the
in
treated the oil price as
oil
produced does
not.
On
payments
the other hand,
to
we
terms of the absolute value of the dollar payments that
event of different discovery
sizes.
When
the
oil
price changes
18
these payments should remain fixed; they will represent changing fractions of the development
The question then
be written.
arises,
given that
The Company's choice of an
a given size,
is
modified slightly
incentive purposes.
exist
exploration program affects the probability of a discovery of
when
the principal
We
is
parties.
risk averse, since
However,
upon the
in the face
is
not done for
of an uncertain
results are virtually identical to those presented for the case of a fixed oil price.
other reasons
why one would
write the contract in terms of shares of
may be some other
this is
oil
and identifying
this
oil,
it
oil price
There may
but from the standpoint
Of
not the preferred form.
structure of the Principal-Agent problem in which
contract in terms of shares of
price level.
the risk implicit in the variable price
sharing of the price risk
this
have solved for the optimal sharing rule
of incentives for exploration in a model such as ours
7.
Therefore the incentive payment to the
the size of the discovery and should not depend
needs to be shared between the two
and the
are variable, in which terms should the optimal contract
and not the present value of that discovery.
Company should be determined by
This
oil prices
NPV
course, there
would make sense
to write the
case would be an interesting research task.
Conclusion
We
we have
have analyzed a
valued in the
classical capital
classical
budgeting case in the form of an
We
territory
and the
then analyzed the same contract using
a
model, quantifying the incentives given to the manager of the exploration and
development program, and valuing the project again
optimal incentive contract and contrasted
possible to significantly improve
Agent model.
exploration project and
manner the contract written between the owner of the
manager of the exploration and development program.
Principal-Agent
oil
this
of these incentives.
with the actual one.
upon the design of the
In the course of showing this
application of the model.
in light
we have
Our
results
original contract using
We
solved for an
demonstrate that
it
is
an existing Principal-
highlighted several difficulties in the practical
19
References
Adelman,
M.A
Adelman, M.A,
1986
J.C.
The
Competitive Floor to World Oil Prices," Energy Journal 7:9-35.
,
Houghton, G. Kaufman and M.B. Zimmerman.
Uncertain Future Cambridge,
,
Grossman,
S.J.,
and O.D. Hart.
1983
MA:
1983
Energy Resources
in
an
Ballinger Publ. Co.
"An Analysis of the Principal-Agent Problem," Econometrica
,
51:7-45.
Harris, M.,
and
A
Raviv.
1979
"Optimal Incentive Contracts with Imperfect Information," Journal
of Economic Theory 20:231-259.
,
Holmstrom, B.
Holmstrom, B.
1979
"Moral Hazard and Observability," Bell Journal of Economics 10:74-91.
1982
Teams," Bell Journal of Economics
,
"Moral Hazard
in
,
13:324-340.
Wolfson, M.A 1985 "Empirical Evidence of Incentive Problems and Their Mitigation in Oil and Gas
Tax Shelter Programs," in J.W. Pratt and R.J. Zeckhauser, eds., Principals and Agents: The
Structure of Business Boston: Harvard Business School Press, pp. 101-125.
,
Table
When
1
Sample Project Cash Flows
2 Wildcat Wells are Drilled and a Discovery of 50,000 bbl/day
is
Made
Table 2
Extract from the Exploration Effort
0.4, e"
(6
Discovery Size,
50
239
q,.
1,143
Discovery NPV,
»,,
=
--
Discovery Size Probability Matr
2500,
a = 20%)
(bbl/day)
5,467
26,141 125.000 597,720
($ millions)
Exploration
:n
No. of Wildcat
467
2,233
10,676
Wells Drilled
.6000
.0005
.0086
.0544
.1365
.1365
.0544
.0086
.0005
.1296
.0011
.0186
.1184
.2971
.2971
.1184
.0186
.0011
.0168
.0013
.0210
.1337
.3356
.3356
.1337
.0210
.0013
.0022
.0013
.0214
.1357
.3406
.3406
.1357
.0214
.0013
Cost
Table 4
The Optimal Sharing Rule
Payment
to the
Company
--$ millions,
--as a
S =
0.4,
U(a.I)
eM -
2500,
%
O =
= log(M+l-D(a))
\
I,
Share, IJn,
Table 5
'fable 6
Second Best Results
Median
Second Best
Exploration
Discovery Size
Exploration Effort
Cost
No. Wildcat Wells
($ millions')
e*
fbbl/davl
Wildcat Probability, S
Expected Payment
to the
Company
($ millions')
=
Expected Return
to the Authority
($ millions')
.02
500
4
3.28
5.01
7.03
1,000
4.92
9.26
27.44
2,500
6
9
7.38
19.12
124.69
5,000
12
9.84
36.93
356.03
10,000
14
11.48
54.52
989.81
25,000
17
13.94
98.23
3,757.80
Wildcat Probability, 6
500
1,000
2,500
5,000
10,000
25,000
2.46
=
.04
Table 7
The Sharing Rule
Implicit in the Actual Contract
Discovery Size, q
1,000
2,000
3,000 10,000
25,000
50,000
Development
NPV
75,000 100,000
tt
18
36
54
179
447
893
1,340
1,786
I,
0.05
2.41
4.62
19.90
52.93
99.32
142.16
184.96
Share, I/r,
0.28
6.75
8.62
11.14
11.85
11.12
10.61
10.36
I,
1.68
4.47
7.04
23.34
56.90
101.96
144.55
187.37
I/tt,
9.41
12.51
13.14
13.07
12.74
11.42
10.79
10.49
2 Wildcat Wells
Payment
to the
Company
--$ millions,
--as a
%
10 Wildcat Wells
Payment
to the
Company
--$ millions,
-as a
S
=*
at cM =
2500,
%
a -
;
Share,
Table
Table 9
The Optimal Sharing Rule
Payment
Company
to the
--$ millions,
-as a
S =
0.4.
U(a,l)
eM =
2500.
%
Share,
a = 20%
= log(30+l-D(a))
Principal's Utility Function:
log(30+T-l)
I,
IJir,
with a Risk Averse Principal
Figure 1. Discovery Size Probability Distributions Conditional on the Number of
Exploratory Wells Drilled.
probability
i
i
r
26,141 125,000 597,720
Discovery Size
solid line: 1 exploratory well
dashed line: 4 exploratory wells
alternating dots and dashes: 8 exploratory wells
2
Figure 2.
Parameter.
Optimal
Sharing Rules
Share of
Development NPV
solid line: S =
dashed line: S = 0.4
dotted line: 6 = 0.6
.
for
3
Values
of
the
Wildcat
Probability
4
Figure
3.
Incentive Cost under the Optimal Sharing Rule
[C(a,)-D(a,)]
S '[p^ajjr^a,)
/
]
.
Percent
of First Best
Profits
i
500
1,000
i
i
2,500
5,000
i
10,000
r
25,000
Median Discovery Size
solid line:
dashed line:
dotted line:
= 0.2
6
S
=
.
5-0.6
Figure 4.
Sharing Rules Implicit in the Actual Contract calculated for
Alternative Numbers of Exploratory Wells Drilled.
Share of
Development NPV
1.0
0.8
0.6
0.5
0.4
0.3
0.2
0.1
2000
3,000
10,000
25,000
50,000
75,000 100,000
Discovery Size
solid line: 2 exploratory wells
dashed line: 10 exploratory wells
3
Date Due
JAR
9"**
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3
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I
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