[N SEARCH OF OPTIMAL CONTRACTS
IN THE CONSTRUCTION BUILDING INDUSTRY
MIT LIBRA4RIES
U7 1
by
3 9080~ 00571707 6
AMAURY LOUIS PROUVOST
Ingenieur des Arts et Manufactures
Ecole Centrale de Paris. France
(1987)
Submitted to the Sloan School of Management
in Partial Fulfillment of
the Requirements of the Degree of
Master of Science in Management
at the
Massachusetts Institute of Technology
January 1989
Copyright Amaury L. Prouvost
All rights reserved
1989
The author hereby grants to MIT permission to reproduce and to
distribute copies of this thesis document in whole or in part.
Signature of Author
Sloan( chool of Management
January 15, 1989
Certified by
/
AN,
John E. Parsons
Assistant Professor, Finance
Thesis Supervisor
Accepted by_
Jeffrey A. Barks
Asiociate Dean, Master's and Bachelor's Program
pAsS- INST. rrc
MAY 1 0 1989
~FA RiF-
-2-
In Search of Optimal Contracts
Industry
In the Construction Building
by
Amaury L. Prouvost
Submitted to the Sloan School of Management
on January 15, 1989 in Partial Fulfillment of
the Requirements of
the Degree of
Master of Science in Management
ABSTRACT
In 1985 the Paris Chamber of Commerce and Industry signed a
contractual agreement with DUMEZ for the construction of a
university near Paris, the Ecole Superieure d'Ingenieurs en
The ESIEE project as realized
Electrotechnique et Electronique.
by DUMEZ was a success, because of an overall well designed
contract
the expertise
and because of
Paris Chamber of
Commerce
of
the
contractor. The
stipulated sum contract
had chosen a
with a number of penalties for cost overruns and delays. Was this
an
Indeed,
optimal choice?
building
construction
when designing
project,
financial
everlasting question of which contract
incentives
to
include in
the
a
type to choose
contract.
The
for a
contract
analysts
answer
face
the
and which
to this
question will be a crucial factor in determining the ultimate
investment value of the project.
It is the author 's contention that the form of the optimal
contract depends on
specific
characteristics of
the project as
well as parameters defining the owner and contractor's behaviors.
An optimal contract will give the contractor a share of the
which solves at best the tradeoff between
project risks,
incentives and their costs. The quality and quantity of design
information have been identified as key factors influencing the
Precisely, a well designed
definition of the best contract.
stipulated sum contract will be optimal when the quantity and
quality of design information is high, whereas a well designed
profit sharing contract will be optimal when this information is
poor or average.
The thesis applies an effort-probability model to quantify
this information parameter and determine the optimal contract for
It then compares this optimal design to the
the ESIEE project.
real contract used by the Paris Chamber of Commerce and brings
out the possible tradeoff between optimal and legal incentives.
Thesis Supervisor: Professor John E. Parsons
Title:
Assistant Professor of Finance
-3-
Acknowledgements
I would like to thank John Parsons who helped me to define
my thesis topic and provided much guidance in dealing with most
challenging issues.
I am also very grateful
to DUMEZ, which
allowed me to use their contracts to illustrate my analysis and
moreover financed my studies at the Sloan School.
-4-
Warning
Although the analysis performed in this thesis is based on
real contracts, which were used by French professionals of the
Construction Building Industry, the reader should be aware of the
two following points:
- Real figures were not available so that the author had to build
a case as conceivable and credible as he could possibly imagine.
A few details of the contracts studied were modified for the
purpose of the illustration.
Therefore. although the theoretical conclusions reached in this
study are believed to be correct, it is all the more possible
that they would not apply to the case studied, had the real
numbers and exact contracts specifications been used.
-5Contents
p 7
Introduction
2
3
1.1
Problem Definition
1.2
Summary of Results
1.3
An Optimal Contract for the ESIEE Project
1.4
Overview of Study and Argumentation
Contracts in the Construction Building Industry
2.1
The ESIEE Project
2.2
The French Legal Framework
2.3
Role of Contracts
2.4
Risks Facing the ESIEE Construction Project
2.5
Contract Types Description
2.6
Contract Types Modelling
2.7
The ESIEE Contract
2.8
An alternative contract for the ESIEE project
p 15
p 54
The Bidding Process
3.1
The Bid Format & Factors
3.2
The Owner's Behavior
3.3
The Contractor's Behavior
3.4
The Level of Competition - Auctions Theory in Perspective
3.5
The Quality and Quantity of Design information
3.6
Related Development Risks - Completion Delays
3.7
Construction Risks - Costs Overruns
3.8
Operations Risks
3.9
Incentives and Effort Level
3.10
The Contract Type
3.11
Submitting a Bid
Influencing the Bidding Process
-6-
4
Optimal contract Determination
p 89
4.1
Possible Scenarios for the ESIEE Project
4.2
Optimal Contract Determination - The Process
4.3
Construction Costs and Revenues are Fixed: An Academic Case
4.4
High Level of Design Information: Evaluation of Contracts
4.5
Average Level of Design Information: Evaluation of Contracts
4.6
Information Level & The Optimal Contract Type
4.7
Contract Parameter Determination
4.8
The Trade-off between Optimal and Legal
4.9
Toward Optimal
Incentives
Incentives Implementation
5
Conclusion
p 134
6
Appendices
p 135
7
6.1
Appendix # 3.6 - Cash Flows in Case of Delays
6.2
Appendix # 3.10 - The Contract Type
6.3
Appendix # 3.11 - Submitting a bid
6.4
Appendix # 4.3 - Optimal Contracts with no uncertainty
6.5
Appendix # 4.4A - Optimal Contracts
6.6
Appendix # 4.4B - Risk Premiums
6.7
Appendix # 4.5 - Optimal Contracts
Bibliography
-
-
Hi Lev of Inf
Av Lev of Inf
p 204
-7-
I Introduction
1.1 Problem Definition:
In 1985
the Paris Chamber of Commerce and
contractual
university
agreement
near
with
Paris,
DUMEZ
The
Ecole
Electrotechnique et Electronique in
for
the
Industry signed a
construction
Superieure
the Cite
of a
d'Ingenieurs en
Descartes in Marne
La Vallee.
This contractual
process,
agreement
which involved
was
the
result
DUMEZ and several
of
of
a bidding
its competitors.
The contract bid was fixed by the "Acte d'Engagement" proposed by
DUMEZ,
which won the bid.
Stipulated
Sum Contract
The Paris Chamber of Commerce chose a
for
this
project,
penalties for cost overruns and delays.
with
a global
lump
sum of
FF
with
Hence,
34,800,000.
clauses fixed the penalties for late
a
number of
works were paid
Liquidated damages
completion
and bonuses for
early completion of the project.
The ESIEE
project
as
realized
by
DUMEZ
was
a success,
because of an overall well designed contract and moreover because
of the expertise of
the contractor.
for a construction building
financial
analysts
contract type
contract.
the
designing a contract
such as the ESIEE project,
everlasting
question
to choose and which incentives
to
The answer to this question will be
in determining the
Indeed
face
project,
When
several
ultimate
major
investment
problems
may
value
arise
of
which
include in the
a crucial factor
of
from
the project.
a contractual
agreement between the owner of the project and the contractor:
-8-
Incentives included
(i)
the contract
in
'force' the contractor to complete the
enough to
may not be
job on schedule and within
budget;
the owner than
Additional incentives may be more costly to
(ii)
the benefits they can be hoped to produce.
incentives and their costs to the owner.
financial
does
only
Not
the
the
determine
contract
benefits of
between the
there is an obvious tradeoff
Thus
Why is it so?
that the
payoffs
contractor will receive from completing the project, but moreover
it
risks
allocates
contractor
the
between
But at which price?
budget completion of the project.
will
and within
and ensure on time
give incentives to the contractor
The risk
has to bear.
the risks he
indeed price
owner.
contractor allows to
Shifting some risks from the owner onto the
averse contractor
the
and
the owner risk
Because the contractor is usually risk averse and
neutral, "it would be best to allocate all risks to the owner, in
the
bear
contractor to
be
payment
retains no
agent
an
requires
none of the risk
independent of
agent
considerations.
incentives
of
abscence
the outcome.
incentive to
the
considerations."
Hazard - 1987).
right
(John
balance
or
Parsons -
thAt gA
Thus
the agent costly
problem then becomes one ot tinding the
determines
that the agent's
But. in
perform well.
incentive implies giving
For the agent Qr
the
giving the
risk.
The
financial contract which
tradeoff
between
thp
tWA
Financial Contracting & Moral
-9-
optimal contract?
an
Commerce,
of
so,
And if
schedule and budget?
it
push
him to
be
will
Commerce
what
Indeed,
the owner?
incentives to
choose the right
work within
be
contract
incentives
of
cost
risks.
optimal
to the
the contract
if
this case
in
Only
maximize
and
of these
cost
the
is
minimized only
properly allocates various types of
will the ESIEE
create the necessary
Does
which is necessary to complete the
level of effort,
Chamber
to
the contractor
incentives to
Paris Chamber of
as designed by the
Is The ESIEE contract,
the project
investment value.
1.2 Summary of Results:
Three main types of contracts are used
building industry:
the Cost plus Fee Contract (CFC), the Profit
Sharing Contract (PSC)
its unique
Contract (MCFC)
or Maximum Cost plus Fee
and the Stipulated Sum Contract
has
the construction
in
(SSC).
characteristics with
Each of these contracts
respect to
allocations of
Previous work
development related risks and construction risks.
demonstrated that: (i) the Cost plus Fee Contract does not create
sufficient incentives,
from completion
Sum
often
Contract
creates enough
usually suffer
the project will
and cost overruns.
delays
misallocates
owner will have
so that
the Stipulated
(ii)
incentives to the
contractor, but
risks between the two parties,
to pay a
very high price for
so
that the
these incentives.
-10-
plus Fee
the Profit Sharing Contract and the Maximum Cost
(iii)
risks and
allocating
in
contracts
Contract are usually better
creating incentives.
on
depends
contract
really
specific
characteristics of
parameters defining the owner and
design
the type
information,
the owner and
factors concerning
the
for
competition
the level of
end-use,
project with
of
will
considered,
be the
the quality and quantity of
costs,
construction
variability of
behaviors. Among
contractor's
be
as
as certain
well
as
project,
the project to
characteristics of
such
circumstances,
various
the
the optimal
that the form of
It is the author's contention
project. Important
contractor
the
to its
respect
will
be risk
preferences, attitudes toward bearing some risk, the contractor's
with
experience
reputation,
the
projects,
similar
share
the
of
contractor's
in
project
attention
to
contractor's
the
franchises, the maximization function of the owner.
This thesis demonstrates that under
circumstances which are
seldom,
optimal contract
anymore and the Stipulated
better contract.
is not an
the Profit Sharing Contract
not likely to be
Sum
Contract
is a
We summarize below the mere conclusions of the
thesis:
I-
The
revenues are
optimal:
fixed,
then
the final choice
other considerations.
costs and
are that if construction
first findings
either
of
type
of
contracts
contract should then
could be
be based on
-11-
if construction
The second and mere findings are that,
11-
costs and revenues are uncertain, then a well designed Stipulated
Sun
Contract
design
designed Profit
well
a
whereas
high,
is
information
and quality of
the quantity
will be optimal when
Sharing contract will be optimal when this information is poor or
contract type
not mean that the
does
this
However,
average.
which is not optimal, does not allow the owner to get substantial
from
profits
contract
will
contract
of
bring
the
higher
second
profits
than
a
contract of the optimal type could reveal
itself
designed
best
the
Thus
type.
best
that the optimal
it means
Rather,
the project.
poorly designed
less profitable
than a well designed contract of the second best type.
Thus, the third findings are that the optimal contract
I1Ishould
contract,
but
itself.
A
determination
also
precise
of
by
definition
a precise
definition
contract's
the choice
by
not only
determined
be
of
the
parameters,
of
of
contract
so
as
the type of
the contract
means
to
the
design
incentives at best.
1.3 An Optimal Contract for the ESIEE Project:
The thesis determines these optimal contract designs
situation encompassed for
the
ESIEE
project,
and
study to a similar project for which the quantity and
design
information would
be
different.
in the
extends the
quality of
-12-
the level of design information
In the case of our project,
is very high, which means that the Stipulated Sum Contract is the
optimal
contract type.
Thus the Paris Chamber of
actually chosen the optimal
We
contract type.
have modelled the contracts so
Contract is
defined
by
Commerce has
a
profit
that
sharing
the Profit Sharing
factor
p,
and the
liquidated damages factor 8
Stipulated Sum Contract
by a
and a
liquidated damages sum.
Our study shows that for this particular
example, the best Stipulated Sum Contract is defined by 0 = 0.70,
and that the profits to the
owner are FF
2,131,692; whereas the
best Maximum Cost Plus Fee contract is defined by
p=
that the profits to the
1,790,143.
The Stipulated
profit surplus of FF
341,549, which
owner are FF
Sum Contract is better by a
represents 19%
more profits.
The real ESlEE contract,
though of the optimal
to profits to the owner of FF 1,198,490.
lower
than
contract,
the profits
or 44%
thus not the best
importance of
contract:
gained
with
which are FF 2,131,692.
FF (933,202)
0.24, and
well
as we shall see,
the
best
stipulated sum
The real ESIEE
contract.
specifying
These profits are much
The difference is as high as
less profits.
designed
type, leads
This
clealry
the incentives
the ESIEE contract
contract is
shows the
included
in the
penalizes delays
too much and does not reward enough early completion.
If we modify our case,
in order to
get a
but with an average level of design information,
Sharing Contract becomes optimal.
similar project,
then the Profit
Our study shows that the best
Profit Sharing Contract is then defined by p
0.14 and that the
-13-
profits to the owner are FF
The best Stipulated Sum
1,427,605.
Contract is also defined by 0 = 0.14 and the profits to the owner
are
FF
The Profit Sharing Contract is better
1,012.991.
profit surplus of
414,614
FF
which
represents
by a
about 40% more
profits.
The previous
case
type depends on the
The
higher
clearly shows that
quality and quantity
the level
of
design
the optimal contract
of design information.
information,
probability that the Stipulated Sum Contract will
contract.
the
higher the
be the optimal
We demonstrate that the quantity and quality of design
information modifies
the risk structure
in such a way
that the
optimal contract type changes according to this information.
1.4 Overview of Study and argumentation:
The study is limited to situations, which are most likely to
happen.
certain
First,
parameters
are
fixed
order
in
to
recognize unique characteristics: (i) the owner is supposed to be
risk neutral;
(iii)
the
(ii)
the contractor is supposed to be risk averse;
level of
competition is
supposed to be
fixed; (iv)
contractor's experience and attention to reputation are
well;
(v) the owner goal function is to maximize the profit from
the project.
variables:
Second,
(i)
situations
construction
contractor; (iii)
are defined by
the quantity and quality of
which determine the probabilities of
of
fixed as
costs;
(ii)
delays
the following
design information,
and the variability
the level of effort chosen by the
the revenues from the project.
-14-
the study determines under which circumstances a well
Then,
designed Profit Sharing Contract will be optimal, and under which
optimality
Here.
optimal.
designed
a well
circumstances
Stipulated Sum
be
should
understood
This
profits for the owner.
maximization of
contract will be
as
the
be achieved
will
when incentives allocate risks at best and at the least cost.
describe
the role of
contracts in the construction building industry with
an emphasis
The
on
next
of
part
the ESIEE project.
process
outcome.
and
the
will
the thesis
third
The
various
part
parameters
the bidding
evaluates
can
which
influence its
In the fourth part we define the optimal
the ESIEE project in both scenarios of high and
and quality of
design
then
to
compared
concluding remarks.
the
information.
real
These
contract.
The
contract for
average quantity
optimal designs are
fifth
part gives
-15-
2 Contracts in the Construction Building Industry:
2.1 The ESIEE Project:
The analysis is based on the study of
was used
by
French
a description
of
the
contract that
the construction building
in
a project which was realized
industry for
give
Professionals of
a real
contract
We shall
France.
in
on
later
this study
(section 2.7 - The ESIEE Contract).
of a university
The project was the construction in 1985-86
near
l'Ecole Superieure d'Ingenieurs en Electrotechnique
Paris.
et Electronique (ESIEE).
the "Cite Descartes -
of
d'Ouvrage"
the
The exact location of the School is in
La
Marne
was
project
The owner or "Maitre
Vallee".
the
Chamber
of
Commerce and
Industry of Paris and the contractor or "Entrepreneur" was DUMEZ.
a French Construction Building Company whose
annual turnover was
The Architect or "Maitre
about 17 billion French francs in 1987.
d'Oeuvre" was BEFS INGENIERIE. an Engineering Consulting firm.
The object of the contract was the construction of the group
of buildings
forming
the
ESIEE
on
the
Cite
Descartes site.
Contractual agreement was formed of various pieces which
described in section 2.7.
be completed was included
Particulieres"
technical
(CCTP).
specifications
will be
The exact description of the works to
in the "Cahier
This
of
contractual
des Clauses Techniques
piece
each works part and
contains
all
gives precise
plans for these parts.
Works are
divided in 29
parts,
each of which is precisely
defined. The 29 parts are the following:
-16-
Part
#3:
#1:
Main work:
Gymnasium
Outside
structures;
carpentries,
partitions:
part
carpentries
part
part #11:
floors;
part #2: Metallic constructions: part
part
#4:
glaziery;
#7:
Plaster
Watertightness;
part
#6:
partitions;
part #5:
Industrialized
part
#8:
Inside
#9: Metal-works; part
#10: Tiled floors, flags
Thin floors; part #12:
Hangings ceilings; part
#13:
Speci al doors;
#15:
Heati ng and air-conditioning; part #16: Plumbing; part #17:
Electrifyin g;
Security;
#22:
part #14: Mural paintings and coatings; part
#18:
part
part #20:
Cook ing
cooling
#24:
Decorative installations
accoustic c eilings;
areas,
urb an
regulated
the
Particulieres"
same
(CCAP),
currents;
Decorative
and
metal
equipments;
#23:
part
works;
part
part
Scenic
#25:
Site preparation; part #28: Green
part
#29:
"Cahier
des
Reception.
Clauses
which is described
All parts are
Administratives
later.
that the am ount of design information available
We shall come
#19:
#26: Decorative
According to
the previou s description and the reading of the CCAP,
is very hig h.
part
part #21: Elevators; part
installations;
part #27:
furniture;
by
amperage
Fire protection;
and
part
equipments;
Low
back on this
we can see
for this project
very important issue
later on in the course of the analysis.
We can now describe the project with respect to construction
and
financ ing aspects.
are
concerned,
most
expected construction
Ist,
1985.
Thus,
1st.
1987.
The
As far as
important points
period
was 24
nstruction characteristics
are
the
following: The
months, beginning July the
construction was to be completed by July the
Land purchase cost
was FF
6,500,000 and Base
-17-
Construction Costs,
31,000,000:
as
submitted
these costs do
profit and effort,
rate was 10%
in
not
the
include
which were part
DUMEZ
bid,
contractor's overhead,
of the bid.
The Design fee
of construction costs, or FF 3,100,000.
costs were thus 40.600.000.
were FF
Total base
It should be understood
that these
costs were estimated costs, as of the beginning of year 1985.
we shall see
later,
these
costs
and
delays
were
As
subject to
variations.
Let us
The
now describe
Paris Chamber
7.600,000.
amount of
of
be
eight
Commerce
and
Industry's
The chamber had contracted
FF
33,000,000,
reimbursable in 20
now
the financing aspects of
with
an
installments,
Loan 1.
beginning
of
12% and
These loans will
The funds will
July 1,
were FF
borrow a total
rate
years, beginning July 1987.
referred to as
funds
loans to
interest
the project:
be received in
1985. The reimbursement
annuity will be FF 5,086,292 for 20 years.
For
details
on
the
project
construction
and
financing
characteristics, please see exhibits # 2.1-1 & 2.1-2.
A chamber of Commerce statute is particular.
Commerce is sometimes considered
considered
goal
in
operations
as
this
of
a public
project
one.
is
the project.
to
as a
The Chamber of
private entity, sometimes
However, the Chamber of Commerce
maximize
This will
the
be
profits
taken as
from the
the basic
assumption for the rest of the study.
The Paris Chamber of Commerce
it
could hope
cash flows
to
had estimated the
receive from operating
would come from students
cash flows
the university. These
tuitions for
a small part,
-18-
Exhibit 2.1-1
Project Characteristics - Construction
----------------------------------------------24
Expected Construction Period (months)
0
Delay (Months)
Land Purchase Cost
Base Construction Costs (do not include
Contractor's overhead, profit and effort)
Design Fee rate
Design Fees
6,500,000
31,000,000
Total Base costs
Present Value @15% of funds invested
40,600,000
37,306,708
10.0%
3,100,000
Project Characteristics - Financing
----------------------------------------------40,600,000
Total Base costs
7,600,000
Chamber of Commerce's funds
33,000,000
Amount borrowed under Loan 1
Loans interest rate (effective)
Funds received in 8 installments
January 1st - year 1
April Ist - year I
July 1st - year I
October Ist - year I
January Ist - year 2
April Ist - year 2
July Ist - year 2
October Ist - year 2
Additional Loan (if necessary)
January Ist - year 3
Reimbursement in 20 years
beginning December 31st - year 3
Amount of annuity
12.0%
7,333,333
3,666,667
3,666,667
3,666,667
3,666,667
3,666,667
3,666,667
3,666,667
0
5,086,292
Amortization Schedule for loan
-----------------------------------------------30,286,808
Total Present Value of funds borrowed
Value at the beginning of year 3
37,991,772
of funds borrowed (January Ist)
w
0
0
Amortization Schedule for loan
Year
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
Loan Balance
Start of Period
0
19,857.754
37,991,772
37,464,493
36,873,940
36,212,520
35,471,731
34,642,046
33,712,800
32,672,044
31,506,397
30,200,872
28,738,685
27,101,035
25,266,867
23,212,599
20,911,819
18,334,945
15,448,846
12,216,415
8,596,093
4,541,332
Interest expense
for period
0
12.0%
Payment
(3,467,351)
(18,333,333)
(14,666,667)
4,559,013
5,086,292
4,495,739
5,086,292
5,086,292
5,086,292
5,086,292
5,086,292
5,086,292
5,086,292
5,086,292
5,086,292
5,086,292
5,086,292
5,086,292
5,086,292
5,086,292
5,086,292
5,086,292
5,086,292
5,086,292
5,086,292
(1,524,421)
4,424,873
4,345,502
4,256,608
4,157,046
4,045,536
3.920,645
3,780,768
3,624,105
3,448,642
3,252,124
3,032,024
2,785,512
2,509,418
2,200,193
1,853,862
1,465,970
1,031,531
544,960
0
0
Principal
Reduction
(19,857,754)
(18,134,018)
527,279
590,553
661,419
740,790
829,684
929,247
1,040,756
1,165,647
1,305,525
1,462,187
1,637,650
1,834,168
2,054,268
2,300,780
2,576.874
2,886,099
3,232,431
3,620,322
4,054,761
4,541,332
Loan Balance
End of period
19,857,754
37,991,772
37,464,493
36,873,940
36,212,520
35,471,731
34,642,046
33,712,800
32,672,044
31,506,397
30,200,872
28,738,685
27,101,035
25,266,867
23,212,599
20,911,819
18,334,945
15,448,846
12,216,415
8,596,093
4,541,332
0
H-
-20-
and from research projects for the main part.
cash inflows are shown in
exhibit
#
2.1-3.
The details of the
For the purpose of
estimating profits from the project, a standard Net Present Value
Analysis has been used,
rate representing
Commerce,
using a capitalization rate of
the cost of capital for the
when including all
Paris
risks considerations.
15%, this
Chamber of
Construction
costs are considered as incurred in the project.
25
NPV = E
(Cash Inflows
j=0
According
Cash Outflows)
1.15
j
exhibit #
to the analysis performed in
total Present Value of
the base
-
Operating Income
case assumptions.
the project is
completed
Under the base
case,
FF
FF 38,707,522 under
The base case assumptions
exactly
within
schedule
are that
and budget.
taking construction costs, sales proceeds,
taxes and tax shields into
for the project of
is
2.1-3, a
account,
2,208,933.
we get a
Net Present Value
The ESIEE project
is thus a
valuable investment for the Paris Chamber of Commerce.
Before
industry,
analyzing
contracts
the
construction building
we give a rapid overview of the French Legal Framework
for construction contracts.
useful
in
This description will
reveal
for the analysis of contracts in the French context.
itself
-21-
Exhibit 2.1-3
Project Characteristics - Operations
Gross Income per year
Operating Expenses
Pretax Income
18,000,000
(10,000,000)
8,000,000
Capitalization rate
Tax rate
Capital Gains rate
Depreciation
15.0%
28.0%
28.0%
18 years SL
Net Present Value Components
PV of Operating Income
Plus: PV of Operations Gains/Losses
38,707,522
0
PV of Net Operating Income
38,707,522
Plus: PV of Construction Costs
Plus: PV Sales Proceeds
Plus: PV of Taxes
Net Present Value
(34,893,006)
1,518,882
(3,124,465)
2,208,933
w0
0
0
W
W
W
Cash Flow Projections
Complete on Time - Real Construction Costs = Estimated Costs.
-------------------------------------------------------------------------------------------------4
3
2
I
0
Year
Gross Operating income
Less: Operating Expenses
Operations Loss/Gain
Net Operating Income
0
0
Plus: Sales Proceeds
Land Purchase
Design fees
Base Const. Costs
(6,500,000)
(3,100,000)
Before Tax Cash Flow
(9,600,000)
Less: Interest Expenses
Less: Depreciation
Taxable Income
Less: Taxes 028%
After Tax Cash Flow
18,000,000
(10,000,000)
0
8,000,000
18,000,000
(10,000,000)
0
8,000,000
H-
(16,333,333)
(14,666,667)
0
(16,333,333)
(14,666,667)
8,000,000
8,000,000
(4,559,013)
(2,255,556)
(4,495,739)
(2,255,556)
1,185,432
1,248,705
0
0
0
0
(9,600,000)
(16,333,333)
(14,666,667)
0
I
2
19,857,754
15,751,088
(331,921)
7,668,079
(349,637)
7,650,363
Loan Cash Flows
Year
Funds received
Interest Payments
Loan's principal reduction
Total cash flows
19,857,754
15,751,088
3
(4,559,013)
(527,279)
(5,086,292)
4
(4,495,739)
(590,553)
(5,086,292)
C-,-
(A)
r~-)
W
0
W
W
W
4P
lp
Cash Flow Projections
Complete on Time
Year
Gross Operating Income
Less: Operating Expenses
Operations Loss/Gain
Net Operating Income
5
6
7
8
9
18,000,000
(10,000,000)
18,000,000
(10,000,000)
18,000,000
(10,000,000)
18,000,000
(10,000,000)
18,000,000
(10,000,000)
8,000,000
8,000,000
8,000,000
8,000,000
8,000,000
8,000,000
8,000,000
8,000,000
8,000,000
8,000,000
Plus: Sales Proceeds
Land Purchase
Design fees
Base Const. Costs
Before Tax Cash Flow
~J.
C-'(J.)
Less: Interest Expenses
Less: Depreciation
Taxable Income
Less: Taxes @28%
After Tax Cash Flow
(4,424,873)
(2,255,556)
1,319,572
(369,480)
7,630,520
(4,345,502)
(2,255,556)
1,398,942
(391,704)
(4,256,608)
(2,255,556)
(4,157,046)
(2,255,556)
1,487,837
1,587,399
7,608,296
7,583,406
(416,594)
(444,472)
7,555,528
(4,045,536)
(2,255,556)
1,698,908
(475,694)
7,524,306
Loan Cash Flows
Year
Funds received
Interest Payments
Principal reduction
Total cash flows
5
(4,424,873)
(661,419)
(5,086,292)
6
(4,345,502)
(740,790)
(5,086,292)
7
(4,256,608)
(829,684)
(5,086,292)
8
9
(4,157,046)
(4,045,536)
(929,247)
(5,086,292)
(1,040,756)
(5,086,292)
I-.
w
0
W
0
0
0
0
0
a
Cash Flow Projections
Complete on Time
Year
Gross Operating Income
Less: Operating Expenses
Operations Loss/Gain
Net Operating Income
10
11
12
13
14
18,000,000
(10,000,000)
18,000,000
(10,000,000)
18,000,000
(10,000,000)
18,000,000
(10,0000,000)
18,000,000
(10,000,000)
8,000,000
8,000,000
8,000,000
8,0000000
8,000,000
8,000,000
8,000,000
8,000,000
8,000,000
8,000,000
(3,920,645)
(2,255,556)
1,823,799
(510,664)
(3,780,768)
(2,255,556)
1,963,677
(549,830)
(3,624,105)
(2,255,556)
2,120,340
(593,695)
(3,448,642)
(2,255,556)
2,295,802
(642,825)
(3,252,124)
(2,255,556)
2,492,320
(697,850)
7,489,336
7,450,170
7,406,305
7,357,175
7,302,150
10
11
12
13
14
Plus: Sales Proceeds
Land Purchase
Design fees
Base Const. Costs
Before Tax Cash Flow
Less: Interest Expenses
Less: Depreciation
Taxable Income
Less: Taxes 028%
After Tax Cash Flow
Loan Cash Flows
Year
Funds received
Interest Payments
Principal reduction
Total cash flows
(3,920,645)
(1,165,647)
(5,086,292)
(3,780,768)
(1,305,525)
(5,086,292)
(3,624,105)
(1,462,187)
(5,086,292)
(3,448,642)
(1,637,650)
(5,086,292)
(3,252,124)
(1,834,168)
(5,086,292)
w
W
W
W
0
W
0
W
V
Cash Flow Projections
Complete on Time
Year
Gross Operating Income
Less: Operating Expenses
Operations Loss/Gain
Net Operating Income
15
16
17
18
19
18,000, 000
(10,000,000)
18,000,000
(10,000,000)
18,000,000
(10,000,000)
18,000,000
(10,000,000)
(10,000,000)
8,000,000
8,000,000
8,000,000
8,000,000
8,000,000
8,000,000
8,000,000
8,000,000
8,000,000
8,000,00
(3,032,024)
(2,255,556)
2,712,420
(759,478)
(2,785,512)
(2,255,556)
2,958,933
(828,501)
(2,509,418)
(2,200,193)
(2,255,556)
(2,255,556)
3,544,251
(992,390)
(1,853,862)
(2,255,556)
3,890,583
(1,089,363)
7,240,522
7,171,499
7,094,193
7,007,610
6,910,637
16
17
18
19
(2,785,512)
(2,300,780)
(5,086,292)
(2,509,418)
(2,576,874)
(5,086,292)
(2,886,099)
(5,086,292)
18,000,000
Plus: Sales Proceeds
Land Purchase
Design fees
Base Const. Costs
Before Tax Cash Flow
Less: Interest Expenses
Less: Depreciation
Taxable Income
Less: Taxes @28%
After Tax Cash Flow
3,235,026
(905,807)
Loan Cash Flows
Year
Funds received
Interest Payments
Principal reduction
Total cash flows
15
(3,032,024)
(2,054,268)
(5,086,292)
(2,200,193)
(1,853,862)
(3,232,431)
(5,086,292)
H-
I-
Cash Flow Projections
Complete on Time
Year
Gross Operating Income
Less: Operating Expenses
Operations Loss/Gain
Net Operating Income
20
21
22
23
24
18,000,000
(10,000,000)
18,000,000
(10,000,000)
18,000,000
(10,000,000)
18,000,000
(10,000,000)
18,000,000
(10,000,000)
8,000,000
8,000,000
8,000,000
8,000,000
8,000,000
8,000,000
8,000000
8000,00
8,000,000
8,000,000
(1,465,970)
(2,255,556)
4,278,475
(1,197,973)
(1,031,531)
(544,960)
6,968,469
(1,951,171)
7,455,040
(2,087,411)
8,000,000
(2,240,000)
8,000, 000
(2,240,000)
6,802,027
6,048,829
5,912,589
5,760,000
5,760,000
22
23
24
Plus: Sales Proceeds
Land Purchase
Design fees
Base Const. Costs
Before Tax Cash Flow
Less: Interest Expenses
Less: Depreciation
Taxable Income
Less: Taxes 028%
After Tax Cash Flow
0
Loan Cash Flows
Year
20
Funds received
Interest Payments
Principal reduction
Total cash flows
-----
(1,465,970)
(3,620,322)
(5,086,292)
21
(1,031,531)
(4,054,761)
(5,086,292)
(544,960)
(4,541,332)
(5,086,292)
0
0
0
0
--------------------------------------------------------------------------------------
w
a
0
0
0
Cash Flow Projections
Complete on Time
Year
Gross Operating Income
Less: Operating Expenses
Operations Loss/Gain
Net Operating Income
25
18,000,000
(10,000,000)
8,000,000
Plus: Sales Proceeds
Land Purchase
Design fees
Base Const. Costs
50,000,000
Before Tax Cash Flow
58,000,000
~a.
Ct
(\J
Less: Interest Expenses
Less: Depreciation
Taxable Income
Less: Taxes 028%
After Tax Cash Flow
LAJ
58,000,000
(16,240,000)
41,760,000
Loan Cash Flows
Year
Funds received
Interest Payments
Principal reduction
Total cash flows
25
0
0
-28-
2.2 The French Legal Framework:
This section can be usefully skipped by the reader who is at
all familiar with the French legal settings.
For any
industry,
market
firms'
transaction
attention
technical aspects.
in
the
usually
However,
construction building
focuses
obligations
on
financial and
and rights
which are
purely administrative or legal should not be neglected.
Indeed,
a market
transaction will
be defined
by both the
market text or contract and regulations which are not included in
the contract.
both
The contract
the contractor
market transaction.
defines rights
and the owner that
are
"decrets"
particular
to the
and are
imperative.
regulations applying to
They are defined by various
and "circulaires", as well as by the "Code des Marches
Publics".
Jurisprudence
resolving legal disputes.
to consider
in
have a direct
also
the context of
impact
on
an
important
the ESIEE project,
the incentives,
this implies that
on,
plays
role
in
These public regulations are important
Commerce can legally include in
later
obligations of
In the French context, regulations which are
external to the contract text are public
the industry,
and
that
the contract.
the
As
because they
Chamber of
we shall see
an optimal contract design
may be
difficult to achieve.
The
between
French
Public
Transactions.
legal framework makes an
Market
The
Transactions
distinction
regulations,
is
essential distinction
important
firms
Market
Private
and
In
rights,
the
French
competent
settings,
because
law-courts,
and applicable jurisprudence differ deeply for these
-29-
two different categories
of
market
transactions.
Criteria for
classifying market transactions in these two categories have been
progressively
determined
transaction will
criteria.
be
by
French
considered
otherwise it will
jurisprudence:
as public,
A
market
if it satisfies two
be considered as
private.
The two
criteria are the following:
-
The project,
object of the transaction, must be a public
work in the legal sense.
Construction works are public
are considered as a public good.
if they
Or in other words, if they are
executed for the sake of the community at large.
- A 'public person' must be the signatory for the contract.
According to the previous classification, we can now specify
the
sets
of
contractual
pieces
pieces
contractual pieces
and
for
texts
these
which
two
for a Public
will
market
be
considered as
transactions.
transaction are
the following:
The "Cahier des Clauses Administratives Generales"
defines
administrative
contractor
The
rights
("Entrepreneur")
"Cahier
des
defines technical
d'Engagement"
Clauses
and
The
obligations
(CCAG), which
of
both
the
and the owner ("Maitre d'Ouvrage"),
Techniques
specifications
or bid offer by
for
generales"
the
(CCTG), which
industry,
the contractor,
the
the "Acte
"Cahier des
Clauses Administratives Particulieres" (CCAP) and the "Cahier des
Clauses Techniques
Particulieres"
paricular contractual
Thus,
the
particular
(CCTP),
dispositions
construction
contract
and general clauses,
for
will
which
the
be
the priority
determine the
contract involved.
defined
of
variable in the limits of the current legislation.
which
by
both
can be
-30-
The
contractual
pieces
for
a
private
transaction
regulated by the general principle of contractual
are
liberty, which
means the abscence of any compulsory form for the conclusion of a
contract.
A verbal
agreement can
cases.
However,
official
administrative
contractants
even
are
and technical norms.
has been developed
AFNOR".
Like
sufficent
recommended
type projects the previous CCAG and CCTG
norm
be
can be
to
contracts,
the
refer
to
For public works
used, whereas a
for Building type projects,
for public
in most
the "Norme
priority
of various
contractual pieces should be given particular attention.
For the project under consideration, Public regulations will
apply.
because
statute
in
this setting.
Commerce has
design.
the Chamber of
to
comply
Commerce benefits from
This means also that
with
regulations
We now examine the major roles
then turn to major risks facing
the Chamber of
concerning contracts
contracts
the ESIEE
a public
perform, and
construction project,
and that a right contract has to mitigate.
2.3 Role of Contracts:
As noted in the previous section,
role
with
respect to
obligations of
many
the parties
financial agreements.
to the implications of
issues,
first
the
great
administrative
involved,
rights and
technical specifications,
A major part of this study will be devoted
the financial agreements
construction building contract.
are
contracts play a critical
included in any
Among reasons for
flexibility
owners
and
this choice,
contractors
do
-31-
actually
second,
final
have
the
in
specifying
dramatic
impact
these
financial
agreements
these agreements can
investment value of the construction
and
have on the
project. Other issues
will be referred to principally to address this central question.
With respect to financial agreements,
major functions (Ronald Pastore -
Construction Contracts and the
Investment Value of Commercial Real
they
determine the
completing
payoffs
the project.
the
contracts perform two
Estate
Developments): First.
contractor
Second,
they
will
allocate
receive from
the different
types of risks between the contractor and the owner.
Allocation
of
the
various
types
of
risks
between
the
contractor and the owner is an essential property of construction
contracts.
because it
determines the
incentives the contractor
will have, to complete the job on schedule and within budget. The
interaction between payoffs to
the contractor
and allocation of
various types of risks will determine the investment value of the
project,
which
contract'
will allocate the right risks to the contractor at the
we
are
looking
to
maximize.
The
'optimal
minimum costs to the owner.
The
trade-off
between
specifying
the
payoffs
to
the
contractor to yield the best set of incentives and the allocation
of risks is known as the Moral Hazard
problem.
Let us give two
examples of this trade-off to illustrate our argument.
For that
purpose, we consider the Paris Chamber of Commerce opportunity to
invest and get a substantial
return
on
its
investment
if the
project is completed on time.
The problem is to know whether the
contractor has the incentives
to
complete the
job on schedule.
-32-
If the payoff to the contractor does not depend on the completion
date,
it is very likely that the contractor will not produce his
maximum effort to
costly to
finish works
him.
contractor to
Thus,
on time,
the owner will
complete job on time.
because this effort is
give
incentives
To give the
incentive,
the contract can make "the payment to
contingent
on
uncertain,
the contractor's payment is
the
project's
outcome.
agent
therefore bears a portion of
(John
Parsons
-
contractor will
avoid
losses.
Financial
a higher
the
risk
&
of
effort
well.
The
the project."
Moral
Hazard). The
level
in
order to
However, these incentives are costly to the owner,
for this reason that they imply a sharing of the
between
outcome is
uncertain as
Contracting
now choose
contractor an
the contractor
Since
the
to the
the owner and
the
contractor
and
the
contractor is risk averse (The contractor being
worsens the case).
of his profits.
Indeed the owner will
The share the owner
project's risks
fact
that the
risk averse only
have to give up
has to give up
a part
depends on
the contract chosen, as we shall see in the next section.
The second example of Moral Hazard Theory comes out
consider quality problems.
The
tradeoff
here
quality and the cost of construction works.
a Cost plus
incentive
Fee contract,
to
reduce
expenditures.
owner,
which
who
would prefer
strictly
contract will
limits
quality
of
between the
If the owner chooses
the agent will not have
the
However,
is
when we
works
the negative
by
reducing
this may turn to be very costly
to
choose a
construction
to the
Stipulated Sum contract,
costs.
In
effect,
give a strong incentive to the contractor
this
to limit
-33-
expenditures.
from the project?
higher return
get a
of works in order to
not to reduce quality
Even a strong quality supervision might not be
enough to solve the problem.
to give
incentive
However, does the contractor retain any
Thus, once more the owner will have
the right incentives
to the contractor,
and this turns
out to be a share of the project's profits and risks.
outcome of the project depends on
the
payment to the
him
the incentive
contractor contingent on
to
perform
examples mean that the profit
adequate contract
shows that this
the quality
to
is not
the
task
of
Since the
works, making
this outcome gives
optimally.
Do these
sharing contract will be
solve moral
hazard
always the case.
issues?
the only
This thesis
However, this section
suggests that a good contract should include the features
Profit
Sharing
incentives to
contract,
which
the contractor.
to
allow
An optimal
the same cost and quality incentives,
create
of the
the
right
contract will
create
but at a least cost to the
owner.
This
section has shown
the
critical
role
risks
play in
determining the final investment value of a construction project.
We now have to be a bit more specific
about the kinds
the owner and the contractor will have to cope with,
which
of
analysis
project.
will
be
based on
and examine
risks.
The risk
the examples provided by
the ESIEE
the two parties should
bear
these
of risks,
-34-
2.4 Risks facing the ESIEE Construction Project:
In order to design an appropriate contract, the owner has to
assess
the risks
magnitude,
as
facing
well
the
project,
as which
their
party has more
types
and their
expertise to bear
these risks, and finally the incentives necessary to handle these
risks properly.
Usually, a construction project faces the following types of
risks:
The construction risks, the general development risks and
the operations
risks.
All these risks are
considered from the
perspective of their financial implications.
Construction risks are borne because of the uncertainties of
the
construction
process.
construction process is
Because
subject to
common are the possibilties for:
which can force the
design
costs,
uncertainties. Most
expensive techniques
engineering
sudies,
difficulties,
like
(iv)
rising
problems
other
labor
due
current
and
to
but
materials
bad weather conditions, strikes or even accidents.
In the
case of the ESIEE project,
with different probabilities.
known,
the
(i) unforeseen site conditions,
(iii)
preliminary
unpredictable
several
complexity,
design changes due to poor initial quality
information,
unsufficient
its
contractor to use more
and/or materials, (ii)
of
of
although
drainage
such
risks are incurred
Site conditions
problems
are
are
not
pretty well
impossible.
Engineering problems would merely depend on the experience of the
contractor.
structures,
Engineering
problems could arise
like the Gymnasium,
main buildings.
Other
for the metallic
or the glass structures
possibilities for causes
in the
of engineering
-35-
problems is the
great complexity of electrical
research laboratories.
electrical,
The ESIEE is a specialized university in
electrotechnical
and
electronic
electrical installations for research
art installations.
installations in
studies;
purposes are
hence
state of the
Other construction risks, like the possibilty
of bad weather or strikes, should not be underestimated.
General
development
financial feasibility.
construction
risks,
risks
They
but
affect
are
are
not be
very
the
different
the
are
overall
consequences of
in
nature. Most
possibilities that
completed on schedule,
will not be respected and that the
specified quality.
project's
usually
important general development risks
the project will
the
that the budget
buildings will not
be of the
These risks dampen the profitability
of the
project from the costs point of view.
For the ESIEE project,
delays are a big source of concerns.
because, as we shall see later on, each semester of delay reduces
the project's expected NPV by FF 1,893,647.
With a one-semester
delay, the project's expected NPV falls from FF 2,208,933 down to
FF 315,287.
With a two-semester delay, this NPV becomes negative
with a FF (1,578,360)
not
value.
worth undertaking
In this last case, the project is
anymore,
should be avoided in all cases.
present
values
occur,
because
periods at least as long as
of financing through
costs.
higher
so
that
a
two-semester delay
These dramatic reductions in net
delays
wipe
these delays and
interest
out
revenues for
increase the costs
expenses
and opportunity
-36-
The fact
that
not
the project would
completed within
be
budget can be the direct consequence of construction risks, which
become general development risks,
if
they are
principal and not only by the contractor.
might occur as well,
supported by the
Other budget overruns
like the overcosts in designing the program
or organizing the research department.
Quality is also an important concern for the
First,
the buildings must meet very high security
ESIEE project:
standards. If
this is not the case, additional costs would be incurred in order
to meet these standards.
the
amount
of
maintenance.
money
Third,
Second, quality of works will determine
needed
in
future
years
for
high quality standards are needed
buildings
for the
maximum efficiency from
research departments in order to get the
this department.
This
consideration leads us
to
the
third
type
of risks
namely the operations risks.
These are the
risks that come from the uncertainty of revenues.
The higher the
facing the project,
uncertainty of revenues,
project.
In the case of the ESIEE project, these risks are very
because revenues are highly uncertain. Revenues for
substantial,
the
university
depend on many
attract good researchers,
groups,
the
factors,
such as its ability to
its ability to form efficient research
its ability to find profitable projects,
industry
revenues,
the higher the operations risks for the
the
community,
standard
Because of uncertainty in
and so on.
deviation
its links with
of
NPV
for
the
project
-37-
attributed to
2,000,000
this
uncertainty is
depending on the delay.
between FF
1,800,000 and FF
The operations risks will be
usually borne by the owner.
Whereas it is clear
that the contractor has
to bear the construction
operations
risks,
risks,
a good
uncertainties in the
are due to general
and the owner more
question
is
should
construction process and
manage the
some of these
development managerial aspects.
an example to illustrate our argument.
of
who
to bear the
In fact, some of these risks are due
general development risks.
to
more expertise
operations could be caused
Let us give
A delay in the beginning
by different
reasons.
The first
reason could be an unsufficient contractor's managerial effort to
coordinate the advancement of works.
The second reason could be
the owner's inability to organize research programs on
both cases the result would be
for
the
first
operating
expenses as well.
is
risks will
have
year
However,
very different.
to
the same:
reductions in revenues
probably
It is thus likely that
be
In
higher
interest
in each case the origin of the risk
general development
shared between both parties.
design of contract incentives,
we have
and
time.
in order to reduce
Thus the
all the risks
just described, becomes a critical task for the owner.
Many forms of contract are used in the construction building
industry,
all
of
them
having
strengths
and
weaknesses with
respect to the allocation of risks and the design of incentives.
-38-
2.5 Contract Types Description:
This section describes the various forms
in
the construction
clauses
of
the
building
CCAPs,
industry.
which
help
incentives to the contractor.
of
contracts used
We first describe the
to
create
non
financial
We then turn to financial clauses
included in these contracts.
Whatever
Stipulated
the
form
Sum or
implement
non
contractor
to
similar to
all
altogether.
of
the
Maximum Cost
financial
do
Job.
a better
forms
works
plus
of
is
performed
which
so
As far as quality issues
the
-
These
contracts
Cost
-
Fee
incentives,
CCAP includes several clauses.
the
contract
plus
CCAP tries to
will
an
that
we
discuss them
are concerned.
independent
implement the modifications that
works,
security
isolation.
Second,
the origin,
the
construction.
contractor,
final
of
engineering firm.
respect and
recommended
people,
case
acoustic
use
of
specifications
supervision firm
on
for
an
isolation,
of
thermic
up to control
materials
adverse
and
works
agrees
for
plans
needed for
outcome
for
designed
to the architect
approval.
the
by the
The technical missions are solidity
contractor must be submitted
contractor
been
a supervision process is set
the
the ESIEE
all resulting costs would be at his expense.
building
performed
have
quality and the
In
the
incentives are pretty
French law makes it compulsory for the contractor to
of
push
First, a technical supervision of
by
technical supervision firm.
Fee.
during
Fourth,
Third,
by
the
and the technical
additional
construction.
contractual
the
guarantees
tests are
Fifth,
on
the
works
-39-
(10
watertightness
incentives
merely
try to
because
quality issues,
financial incentives
incentives
aimed
plus
year
solve the
hazard
moral
an
cost
works and financial
and
overruns
Fee and Profit
Sharing
contracts
delays.
whereas
overruns is the Stipulated
When choosing the stipulated sum contract for the
Paris
problem for
As
best contracts to enhance quality of works are
contract to limit cost
the
financial
obvious trade-off between
enhance quality of
limiting
Non
guarantee).
there is
to
at
discussed before.
Cost
(2
installations
high-tech
and adequate performance of
year guarantee)
Chamber
of
Commerce
incentives to ensure the quality
has
to
contract gives little financial incentives
Sum contract.
ESIEE project,
design
of works,
the best
non financial
because this type of
to
the contractor as
far as quality issues are concerned.
Contracts
are
therefore
mainly
distinguished
in
their
Three main types of contract are used in the
financial clauses.
industry: the Cost plus Fee Contract, the Stipulated Sum Contract
and
plus
the Maximum Cost
designate
as
the Profit
Fee Contract
Sharing Contract).
the contractor
Contract reimburses
(which
fee
to
cover the
contractor.
overhead
The Cost plus Fee
for all direct
costs incurred for completing the project and
expenses
and
shall also
we
and indirect
pays an additional
the
profits
of the
The Stipulated Sum Contract fixes the total payment
made to the contractor for completion of the works as a lump sum.
Thus this
contractor.
form
of
contract places construction
In this
direct costs overruns,
case,
a
risks onto the
the contractor bears all
complete
opposite
risks for
situation from the
-40-
Cost plus Fee Contract in
of
view,
Stipulated
that respect.
Sum
Contracts
project's construction costs within
From the owner's point
perfectly
budget.
maintain
the
However, the owner
has to pay for these strong incentives; the contractor will price
the construction risks he has to bear and include a corresponding
risk
premium
expertise
in
than
his
Because
the owner to
risk premium may be
themselves,
bid.
the
contractor
cope with construction
no more costly
to the owner
has more
risks, the
than the risks
depending on the situations.
Cost plus Fee Contracts and Stipulated Sum Contracts usually
include
clauses dealing with
the
possibilty
clauses will introduce penalties for late
for
early completion of the project.
of
delays.
completion and bonuses
These
clauses are called
Liquidated Damages clauses and require the contractor
owner
for
losses
incurred
because
of
Such
late
to pay the
completion.
The
liquidated damages fees are fixed in advance and agreed upon when
the
contract
is signed.
They are a means of
shifting general
development risks from the owner to the contractor.
the contractor will accordingly
risk premium in his bid
they allow to
share the
damages
increase
also
completion.
implement
Contracts,
price these risks and
for accepting the project.
general
the
development
likelihood
Liquidated damages clauses
for Stipulated
As a result,
of
include a
But because
risks, liquidated
early
are
Sum Contracts than
or
usually
for Cost
on
time
easier to
plus Fee
because "Cost plus Fee Contracts are merely used when
specifications for the project, and overall schedule as a result.
are not all well defined when the works begin."
(Ronald Pastore
-
-41-
liquidated
give
damages,
which only include
incentives to the
little
very
of Commercial
Value
Thus Cost plus Fee Contracts,
Real Estate).
weak
Investment
Contracts and the
Construction
Previous
contractor to finish the job on time and within budget.
works on Construction contracts have clearly shown the weaknesses
By using a Cost plus Fee Contract, the
of this type of contract.
owner will certainly forego a substantial part of the profits.
The
third
of
type
be better called a Cost
Sharing Contract.
we are
which
Under this contract,
reimbursed for d irect and indirect
agent is
Plus,
cost.
maximum
those
is known as the Maximum Cost plus Fee Contract and may
studying,
the
among
contract,
both
share
parties
than
completing the project for less
Thus
parties.
to a
savings
from
the
the maximum cost.
the
In the
losses are also
case when costs are higher than the maximum cost,
shared between the
costs up
Maximum
plus Fee
Cost
contract is equivalent to a Pro fit Sharing Contract, in which the
would be
figure
Revenue
Contract allocates a
when
contractor,
account.
of
share
all revenues
the
that both parties will have to wait
figure
is
losses
or
profits
and costs have
Revenues are usually not
When the Revenues
The Profit Sharing
fixe d in advance.
to know their
fixed in advance,
taken into
been
known before a
to the
long time so
final profit.
at the expected
value for instance, it is possible for the contractor to know his
as
soon as the job has been
final
profit
case,
the Profit Sharing
completed.
Contract is exactly equivalent
In this
to the
-42-
Maximum
Cost plus Fee Contract.
will designate either
In the
two contract
following analysis, we
type by either
name, unless
specified.
As said earlier,
Contract and
the
this thesis focuses on
Profit
Sharing
the Stipulated Sum
Contract.
In
the following
section. we give a mathematical formulation of these contracts.
2.6 Contract Types Modelling:
The
previous
section
has
introduced
the
necessary
terminology to define the contracts under study.
Let
us
now
modelling is
kept
results will
be
model
the
very
easy
three
simple
on
to interpret,
types
of
purpose,
contract.
This
so that numerical
so as to get
more general
hints to design optimal contracts in the industry.
(i) The Cost plus Fee Contract is modelled as follows:
P = C + F
P is the payment to the contractor,
C is the Total construction cost (direct and indirect costs,
not including contractor's overhead expenses and profits)
F is
the fee received
by the contractor to
cover overhead
expenses and profits.
(ii)
The Maximum Cost plus Fee (Profit Sharing) Contract is
modelled as follows:
P = p NPV(c,dr) - F
P is the payment to the contractor,
-43-
NPV(c,d,r) is the Project Net Present Value for construction
cost scenario c, delay scenario d and revenue scenario r,
p is the profit sharing factor (0 < p < I),
F is the franchise fee retained by the owner.
(iii)
The Stipulated Sum Contract is modelled as follows:
P = S - LD
LD = d*O*A
P is the payment to the owner,
S is the Stipulated Sum,
LD are the liquidated damages,
d is the delay in semesters.
0 is the liquidated damages factor (0 > 0),
A is a lump sum.
It
is
also
interesting
to
note
the
differences between these different types of
following points will be demonstrated in
similarities
contract.
the fourth
and
All the
part of the
thesis.
First the three types
of
contract
differ
greatly
in the
allocations of the three major types of risks:
(i) As far as construction risks are concerned, the Cost plus fee
contract does
not give
any of
these risks
to
the contractor,
whereas the Stipulated Sum contract allocates all of them
to the
contractor and the Profit Sharing contract only a share of them.
(ii)
General develoment risks are not borne by the contractor in
the case of the Cost plus Fee contract and are shared between the
contractor and the owner in all other cases.
-44-
Operating risks are always fully borne by the owner but in
(iii)
which allocates a share
the case of the Profit Sharing contract,
of these risks to
Sharing
contract and the Profit
Maximum
The
the contractor.
Cost
in that
only
differ
Contract
plus Fee
respect.
Second,
the
contracts
are
similar
in
the
following
circumstances:
(i) When revenues are certain, the Maximum Cost plus Fee contract
(better called the Cost Sharing contract)
contract
lead
to
the same
payoffs to
and the Profit Sharing
the contractor
and the
owner.
(ii)
When revenues and construction costs are certain, the Profit
Sharing contract,
the
Maximum Cost
plus
Fee contract
and the
Stipulated Sum contract are similar.
(iii)
When there
(revenues,
is
no
construction
uncertainty
at
and
costs
all
the
for
the project
completion
date
are
certain), all contracts are similar.
All
closely
parameters
studied
in
previously
parts
introduced
3
and
4
of
will
of
course be
this
thesis.
For
clarification purposes, however, we rapidly give a description of
scenarios and ranges for parameters.
Contracts are studied for
two
different
levels
of design
information, a high level and an average level.
Total
base case.
construction costs are
equal to FF 34,100,000
in the
Three costs scenarios are considered in the study for
each level of design information.
-45-
Four
completion
considered,
scenarios are
a two-semester
delay scenario, a one-semester delay scenario, on-time completion
and one-semester ahead of schedule completion.
A
number
of
revenues
scenarios
also
taken
into
11 different revenue scenarios have been studied.
consideration.
The Franchise fee F retained
either positive or negative.
fee,
are
by
the owner can
in
fact be
In the case of a negative franchise
the owner is actually giving up
an additional fee
to make
the project attractive enough for the contractor.
The Liquidated damages factor 0 varies between 0
0 <
Lump
1),
although this should
sum A is
equal to
between expected
the next.
FF
not be necessarily
1,893,647.
net present values
and 1 (0 <
the case. The
This is the difference
from one
delay scenario to
Liquidated damages LD are thus calculated as in table
2.6.
table 2.6
Delay
LD
2 *
I semester
I * 0 * A
On time
After this modelling has been
contract,
*
A
0
-1 semester
real
0
2 semesters
-
0 * A
exposed,
we can describe the
which was chosen for the ESIEE
project.
As we
shall see, this contract is of the Stipulated Sum Contract type.
-46-
2.7 The ESIEE Contract:
The
CCAP
contract
submitted to
for the ESIEE project was
determined
several
consideration. The
contractors
contract bid was then fixed by
for
the "Acte
by the
d'Engagement" proposed
by DUMEZ, which won the bid.
The
Paris
Stipulated Sum
Chamber
contract
of
for
penalties
for cost
overruns
paid with
a global
lump sum.
Commerce
this
and
project,
and delays.
Industry
with
chose
a
a
number of
Hence, Works will be
Prices submitted in the
bid are
supposed to take all direct and Indirect costs necessary
for the
execution
Clauses
of
works,
Techniques
in
conformity with the CCTP
Particulieres"),
("Cahier des
specifications
and plans.
even if the charges are not specified explicitly.
The global
prices
various
types of
works.
Unit prices
works and
and the
subjections depending on
As
a consequence,
reclamation
will
be
determined by unit
corresponding
global
price
the definition
the Chamber of
for any omission
of
quantities
take
prices for
of these
all execution
of corresponding works.
Commerce
will
not admit any
quantity or price,
or for any
misinterpretation of remitted documents.
More precisely,
unit prices and completion delays penalties
are set according to the following clauses:
Unit Prices:
Sub jections to
be
taken into
account:
-47-
Unit Prices for the contract are determined when
general
and
particular
conditions,
contractual
organization.
on
the
subjections,
terms,
resulting
building
The CCAP draws contractors'
following
taking all
yard
local
"Cahier
point
energy supply,
Particularly
of the "Cite
des Charges"
with
natural
and
various
important
Descartes",
works
to
site
servitudes from
are
the
specific
However, the most crucial
conditions
at only -1m (minus
respect to
which are included in the
de 1'EPAMARNE.
respect
estimated to be
and
points:
regulation.
regulations
site
particular attention
Site conditions should be closely studied with
access facilities,
from
is
one meter)
the
water level,
under the ground
level.
All subjections from contractual pieces should be taken into
account,
resulting
prescriptions
incidences.
and dispositions,
In
particular,
as well
any
within or any contradiciton between contractual
lack
as financial
of precision
pieces should be
solved before the signature of the "Acte d'Engagement".
Building
yard
installations
should
services to complete their job in normal
works organization
works
by
co
and
should
allow the
subcontractors
not
impinge
conditions.
simultaneous
when
public
Futhermore
execution of
necessary.
Security
regulations on the buiding yard should be closely respected.
Unit Prices also take weather conditions into account
20
days of bad weather.
up to
No modification of quantity or price of
works is admitted after the contract has been signed.
Nature of unit prices:
-48-
Unit Prices are revisable according to market indexes.
prices registered in the contract are prices fixed for
Mo.
when the contract is signed.
Unit
the month
The formula used to modify the
prices is the following:
P = Po (0.15 + 0.85 Z)
where P is the revised price,
is variable according to Z
Ic,
lo',
Po is the initial price and Z
a 1/lo +
b l'/lo' + c I"/lo" + ...
Io" are price indexes for the month Mo: 1, 1',
price indexes for the current month;
whose sum is
equal to
a,
b,
c
1 and reflecting the
I" are
are coefficients
various amounts and
types of works involved in the project.
Completion Schedule and Delays:
The total execution period is set
to 24
months according to the
following schedule:
- Beginning of works: June the Ist, 1985.
-
Operations
necessary for reception of
works:
May
the 15th,
1987.
- Beginning of moving in and buidings installation: June the 1st,
1987.
Completion dates are determined according to the contractual
completion
parts,
schedule;
These
and are considered as independent
Additional deadlines are set
crucial
dates are set up
for
an
adequate
for all
contractual deadlines.
up for particular tasks,
advancement
deadlines are also contractual ones.
29 works
of
works;
which are
these
tasks
Deadlines are posponed only
in the case of bad weather for more than 20 days, or acts of god,
-49-
or strikes if they are not limited to
is admitted
provided,
because of
the contractor.
the lack or imperfection
since the project allows
the
No delay
of information
contractor
to
get all
necessary information on schedule.
Liquidated damages for Completion delays are the following:
- from the first to the 6th day: FF 500 ,
-
from the 7th to the 15th day:
FF 1,000
plus 1/10,000 of
the market price,
-
from the 16th day:
FF 1,500
plus 1/3000 of the contract
price.
All previous penalties are applicable to:
-
all tasks that are on the critical path.
-
all other tasks,
from the day following the 'late start'
day for the job, these jobs being then on the critical path.
These penalties will be automatically granted to
the owner.
as soon as a delay has been recorded for a particular task.
The previous
contract
description fits very well
modelling of a Stipulated Sum Contract.
with our
Would it be possible to
consider a Maximum Cost plus Fee contract for
the ESIEE project?
2.8 An Alternative Contract for the ESIEE Project:
Another contract form for the ESIEE project
the Maximum Cost plus Fee Contract.
a
Maximum
Cost
plus
Fee
would have been
In this section, we describe
contract,
which
was
used
for the
realization of public works for the French Government in overseas
-50-
territories.
The project, realized in French Polynesia, involved
the construction
of
works similar
to
roads
and
bridges. The
contract was signed between the French Government and DUMEZ.
General Contract terms:
and
conditions
for the
construction took
the
type
Because of
project,
due
place and the level
the various constraints
to
of
the
where the
information provided,
was a "Rfgie
of contract chosen
site
d'Intrst Commun" or
Maximum Cost plus Fee Contract.
Principles for the contract were the following:
(i)
Costs
(headquarters
to
the
general
contractor
costs,
that
are
overhead
unverifiable
expenditures),
contractor's profit and costs for which it is preferable
leeway
to
the contractor
(local
director
the
to give
salary, exceptional
bonuses,...), are paid with a lump sum.
All these costs will
now be considered as
the Fee,
F , to
the contractor.
(ii)
Real costs necessary for the construction and which are
verifiable
will
be
paid
by
the owner.
These
costs will be
referred to as RC.
(iii)
In
contractor,
contract.
the
maximum
efficiency
This bonus/penalty is equal to 25%
real
Itemization",
(iv)
get
an incentive bonus/penalty has been
between the
explained
order to
Elf.
cost
of
works
The process
and
their
from the
included in the
of the difference
"Final Estimative
to estimate the Elf
figure is
later on in this section.
The contract
also
includes penalties
for delays and
bonuses for work completed ahead of schedule, namely:
-51-
-
1/3000 of the contract price penalty for any day of delay,
-
1/6000 of the contract price bonus for any day of advance.
(v)
Finally, the contractor supports all costs that are not
necessary for the normal
),
completion
of
works (bad workmanship,
except for acts of god (wars,...).
Real Costs Accounting:
A: Personnel expenses or wages.
B: Purchases of materials and consumables.
C: Rental expenses
Initial and Final Estimative Itemization Accounting:
For the purpose of
the Elo and
Elf
accounting,
each Unit
Price is redetermined according to the following rules:
- wages: for the expatriated personnel, real wages plus 120%
of the real wages in
order to
take the general
expenses of the
contractor into account; for the local personnel, real wages plus
65% of the real wages.
- materials: Prices accounted for are prices of materials on
the site plus 35% for general expenses.
- machines rental: real
prices.
The difference between the
Elf account and the
Elo account
comes from the costs of additional works,
which were not planned
when the contract
unexpected costs. This
was signed,
and
from
difference is as follows.
Other expenses to take into account in the Elf:
-
estimative expenses for
initially unplanned construction
works, according to the previous rules.
-52-
-
unexpected or exceptional expenses resulting from acts of
which the contractor
such as strikes for
god,
unresponsible.
is recognized as
Unit prices are computed according to determined
compensations.
Z Accounting:
in the RC &
are
the
Elf are included in the Z account.
following:
machine-tools,
and
Costs that are not included in the Fee, F, or
Transportation
costs
Among such costs
of
materials
and
taxes and customs costs for all expenses, bonuses
penalties for construction
advances
and
delays, inflation
effects, interests on overdue payments, and so on.
Payments for completed works:
The
final amount
paid
to the contractor is
the following
sum.
Final
Payments = P = Fr + 3/4 RC + 1/4 Elf + Z
Fr is the readjusted fee.
Final Fees to the contractor:
According to the final payments to the contractor, the final
fees are:
Final Fees = Final Payments
Ff = Fr + 1/4 (Elf
-
RC - Z
RC)
Minimum Fees to the contractor:
In the case
value in
when 1/4
the computation of
value of (Fr - 0.2 Fo).
are Fm
signed.
=
0.2 Fo.
(Elf -
RC) is negative, its absolute
the final fees
is
limited
to the
Thus the minimum fees for the contractor
Fo is the fee agreed upon when the contract is
-53-
Computation of the Readjusted Fee:
The
readjusted
fee
Fr
is
computed
with
the
following
formula.
Fr = 0.2 Fo + 0.65 (D/Do) Fo + 0.15 (Elf/Elo) Fo
with Do
the contractual time
limit,
D the time limit with
continuation clauses and bad weather days.
The contract
Maximum
Cost
as
plus
factor p would be
described
above,
Fee contract,
equal to
for which
0.25,
from the project are fixed.
can
be
modelled
by a
the profit sharing
and considering that revenues
These expected revenues would be Elf
for the purpose of the payment to the contractor.
This
part
of
the
thesis
has
introduced,
described and
discussed
the contracts,
which can be considered for
project.
The next
of
process,
value
of
that is
part
to say,
the project from
the
thesis
examines
how the contractor will
his point of
which fits the type of the contract.
view and
the ESIEE
the bidding
estimate the
submit a bid
-54-
3 The Bidding Process:
3.1 The Bid Format & Factors Inflencing the Bidding Process:
Depending on the contract type chosen by the
bids submitted by the contractors,
owner's proposal,
who have chosen to answer the
several forms.
will take
Principal, the
Typically
the bid
will be:
-
a
-
wage rates,
lump
for
sum for the Stipulated
overhead
Sum Contract,
machine rentals rates,
and profits in
the
materials costs and a fee
case
of
the
Cost
plus Fee
Contract,
-
a
maximum cost
factor
and
a
for the project,
franchise
fee
for
possibly
the
a
Maximum
profit sharing
Cost
plus Fee
Contract.
Which contractor the owner will decide to choose, depends on
the goals function of the owner.
the contractor,
who
considerations
like
Usually, the owner will choose
submitted the lowest
earlier
proposed
bid.
However, other
completion
dates,
or
conformity to quality specifications, as well as the contractor's
reputation,
can
be
essential
factors
in
the
final decision
process.
There are
numerous
different
factors
influencing
process and the bid value for a particular
of
this
ESIEE
part of the thesis
project.
following issues:
We
shall
is
give
project.
to study these
particular
the bidding
The purpose
factors for the
attention
to
the
-55-
-
The owner's behavior will influence the choice
bid.
the
of the winning
Among issues of interest are the minimum value attached to
project,
toward risk -
the owner's attitude
how the owner
will price risk and what are his/her risk preferences
-,
and the
goal function of the owner.
-
The contractors'
the owner.
behavior will influence the bid submitted to
Once more
the contractor's attitude toward
the most relevant question
determine
the
optimal
in that respect.
risk
allocation
risk is
This attitude will
and
the
various risk
premiums attached to these risks.
- The level of competition will determine the bidding strategy of
the
contractors.
The
type
of
relationship between the bid and
auction
the
also
determines
contractor's
the
valuation of
the project.
-
The contractor's experience with similar projects will
of the factors to determine the relationship between the
the
contractor's
ability to finish the job on
time
be one
bid and
and within
budget.
-
The quality and quantity of design information is the focus of
this thesis and will affect the bids in several manners.
affect the various types of risks facing the
It will
ESIEE project. More
specifically, it will modify the uncertainties the contractor and
the owner have
to
cope
with
for the duration
of the project.
Thus it will modify the risk structure of the project
the risks
Precisely,
premiums
(i)
the
contractor
will
include
and change
in
his bid.
Variations in Construction risks will affect the
possibilty for costs overruns, and the attached risk premium as a
-56-
result;
the
(ii)
Variations in General development risks will affect
possibility for completion
delays,
and
the
attached risk
premium as a result.
-
Revenues may also play a role
in the determination of the bid.
This will depend on the contract form.
Variations in Operations
risks
lower
will
affect
the possibility for
revenues received
from the project, and the attached risk premium as a result.
-
Incentives
effort
included
level
by
the
in
the contract will enforce
contractor,
who
will
a certain
price
its
bid
accordingly.
-
Of course, the type of contract chosen will be a primary factor
influencing
the
bid.
The
contract
type
will
determine the
mechanism for submitting a bid.
The bidding process will
now be analyzed along
parameters briefly presented in
this
the various
introductory section.
3.2 The Owner's Behavior:
The
owner's
winning bid in
behavior
several ways.
will
influence
the
In this section,
choice
of the
we shall expose
which factors are important with respect to the owner's behavior,
and illustrate our argument in the case
of the
specifying the main characteristics of the
ESIEE project by
Chamber's of Commerce
behavior.
The owner will choose the winning bid according
or utility function.
into account.
The goal function can
to his goal
take many variables
Among most important variables is the
bid value.
-57-
which will
project.
determine the expected
net
present
value
If the completion schedule is respected,
present value of
from the
then the net
the project is simply the difference between the
expected revenues and the value of the bid.
Other
date,
variables are
on which the
contract,
can
be
typically
contractor
commits
a decision
soon
the ESIEE project,
is
project be finished on time,
if the
three months
Incentives
will
completion
take
care
date
of
is
the
wants the
In the case of
or one semester ahead
that the
of schedule.
ahead of
schedule
Thus, the Chamber
of Commerce will not choose the bid according
the
signing the
owner
as possible.
would be worthless to the Chamber of Commerce.
instead
by
essentially concerned
The project being completed only
date;
The completion
itself
factor,
project to be operational as
the owner
essential.
to
the completion
imposed
schedule
in
the CCAP.
issue.
Quality standard is another important factor; the Chamber of
Commerce is concerned about the quality of works, should it be of
construction works or of high-tech
installations
contractor,
for
laboratories.
the Chamber of Commerce
the reputation
this
research
installations like electrical
lowest
of
the lowest
bid contractor,
quality works is
demonstrated.
When
will pay
bidder.
only if
Thus,
choosing
the
much attention to
The Chamber will choose
his
reputation
the goal
for high
function of the
Chamber of Commerce should take the quality factor
into account.
This
bids
will
be
done
by
eliminating
the
lowest
if
contractors who submitted them do not have a good reputation.
the
-58-
In determining the
owner,
utility
function
of
the
we should also know the owner's attitude
the Chamber of Commerce risk
As a sound financial
lover:
lover,
investor,
the Chamber is certainly not risk
is risk neutral or risk averse,
If
He
is
risk
toward risk. Is
risk neutral or risk averse.
this hypothesis is thus not kept.
answer.
principal or
Whether the principal
is not such an easy
question to
he weighs gains
neutral,
and losses
equally when evaluating the project.
On the contrary, when he is
risk
to
averse,
he gives more
weight
losses
than
to gains,
preferring to have a sure small retu rn on the project rather than
a high
but more
Commerce is risk
risky return.
neutral,
assume that the
We
and that it wants simply
expected profits from the project.
Chamber of
to maximize
We are aware that this should
not be necessarily the case.
The last
point to
consider
function for the owner has to
owner
would be
That is to say,
project.
value
accept for
the owner could
greater than
formulating
do with the minimum
If none of the bids
equal or
refuse to
willing to
before
a utility
valuation the
undertaking the project.
put a reservation price
allows
this
undertake the project.
him to get
a net present
reservation price,
The
Chamber
on the
of
he would
Commerce is
supposed not to
put any
ESIEE project.
The reservation price is simply set according to
particular
reservation
price
for the
the positive net present value rule of the CAPM.
Hence,
the utility function of the Chamber
be modelled as follows:
If CR > 7,
Up (NPV,CR) = NPV
of Commerce can
-59-
Up (NPV,CR) = 0
if CR <= 7,
Up is the utility function of the principal,
NPV is the expected net present value of the project,
CR is the contractor's reputation and should be superior to 7 (on
a 0
for the Chamber of Commerce considering
level scale)
to 10
the contractor's bid for the project.
The Chamber of Commerce will choose the bid which verifies:
(1) Up(NPVCR) > 0
(2) Up(NPV,CR) =
MAX (Up(NPViCRi))
i
The
previous
Chamber of
rule
Commerce.
allows to choose
We
now have
the best
to study
bid for the
the process under
which the bids are prepared by the contractors.
3.3 The Contractor's Behavior:
As a corporation
averse.
expenses.
a
risk
considered
coverage,
contractor
will
be
considered risk
He will prefer a project with a sure and small return to
a project with
expenses
the
high
averse,
the form
in
various
In
but
of
risky
return.
because
costs of materials, insurance
wages,
cover
contractor is
has significant operating
he
and
finance charges
order to
The
non
administrative overhead
compressible
expenses, the
contractor will be willing to accept a contract which
a small profit above these costs,
to incur losses.
gives only
but allows the corporation not
-60-
The contractor's behavior will thus be modelled by a utility
function,
which reflects
the risk
aversion
of
the contractor.
This utility function should be a rising and concave
function of
the profit gained from the project.
Risk
preference is another issue to
modelling
of
the
contractor's
be
behavior.
contractor will prefer to bear those risks,
more expertise and which can be
he can choose.
risks
reduced by the
will be
course of action he could choose.
risk
by
specifying
structure
structure
will
the
be
less
range of actions
determined
However,
revenues risks,
influenced by whatever
a different utility function
contractor
in which the contractor
or
This risk preference could be
faces.
faces
Basically
by the contract type.
aversion factor could be higher for the
contracts.
the
For instance, he will prefer to bear construction
these latter risks
reflected
Obviously,
for which he has the
rather than general development risks
because
considered for the
revenues
for each
the
risk
The risk
Profit Sharing Contract,
risks
unlike
in other
for simplicity purposes, the risk aversion
factor will be kept constant along various risk
structures.
The
final result of the study will not be changed by this hypothesis,
as we shall discuss later.
A possible form for utility functions when the agent is risk
averse is:
Uc
Uc = a (I -
expl-b*Y)
is the contractor utility,
a is a scaling constant
used to define
with respect to y,
b is the risk aversion factor,
the interval
Uc =
(0,1)
-61-
Y is the profit generated by the payoffs.
This
it
rising with Y and concave;
is
function
has the basic
properties to model risk aversion.
Because
in
competition
intense
of
construction building
the
profit margins are usually small.
industry,
utility value I
construction
margin
to a profit
costs.
equal to
utility value 0
The
We shall
5%
affect the
of total base
is affected
to zero
The average profit margin of a typical very competitive
profits.
firm is 4 to 5 per cent.
the case of
In
costs
FF
are
the ESIEE project,
34,100,000.
With
this
base construction
total
figure
Cost
and
the
principles exposed above, the parameters a and b are equal to:
a = 1.016492229
b = 2.41714 10E-6
assume
We will
accepting
that the
the contractor for
minimum utility to
This utility level corresponds to
the project is 0.4.
when all risk premiums
a profit figure of FF 206,884,
are equal
These profits are only 0.6% of total base construction
to zero.
costs, thus a very small figure.
Risk premiums are zero when the
project suffers from no uncertainty, or when the contractor bears
no
risk.
these cases,
In
the profit
Y
is
certain
and the
contractor's utility is simply of the above form.
Ucmin = 0.4
Ymin
When
Random
the contractor
variable
defined over
-Y,
= FF 206,884
bears some
risks,
whose probability
a range of
possible
the profits Y
become a
distribution, P('Y), is
outcomes Yi.
We assume that
-62-
only a finite number
of outcomes Yi,
contractor, are possible.
levels of
This is the case, when a finite number
of profits for the project is possible.
exclusive outcomes,
profits for the
the
contractor's
Over a range of mutually
expected
utility
can be
defined as:
Uc(Yi) * P(Yi)
E
E(Uc)
i
The risk
averse
contractor
will
choose the
course of action,
which produces outcomes Yi with the higher expected utility.
According to
the previous
analysis,
one
question is the range of actions the contractor
conducting the project.
very interesting
can
choose when
Obviously, the contractor has the option
to decide whether it is in his interest to spend a high
effort for the project.
The
contractor
can
indeed
level of
prefer to
spend very little effort on a particular project, or any level of
effort according to what he thinks is optimal.
Contractor's effort, here, means the amount of time, energy,
skills
and money spent on
ensure
that
schedule.
a
particular
the project will
Of
course,
to each
be
completed on
level of
certain cost and a certain return to the
the effort level,
return.
the higher the cost,
effort
in
order to
time and within
corresponds a
contractor.
The higher
but also the
higher the
We assume the cost function is strictly rising with the
effort level, that is to say:
dCE > 0
dE
or
project,
CE(Ei+i) > CE(Ei)
-63-
when effort level is rising with i.
CE is the cost of effort, E is the effort level.
On
the
the contrary,
necessarily rising with
show
study will
the effort
that the
return is not
even if this will be
level,
the case in most cases.
For the purpose of
the ESTEE project,
model of contractor's effort.
six different effort levels
delays.
adopt a discrete
The contractor can choose between
El,
E2,
etc, to E6. To each effort
level correspond different outcomes for the
to completion
we
project with respect
This will be specified
later.
each effort level corresponds different costs to
Also, to
the contractor,
as follows:
Table 3.3
Effort Level
Cost of Effort
El
FF
0
E2
FF
50,000
E3
FF
150,000
E4
FF
250,000
E5
FF
410,000
E6
FF 1,200,000
The contractor will choose the effort level, which maximizes
his utility function, as follows:
MAX
Ej
E Uc(Yi/Ej) * P(Yi/Ej)
i
The behavior of the contractor is now modelled.
We can turn
on
the bidding
to the analysis
process.
of
competition and its
impact
-64-
3.4
The
Level
of
Competition
Auctions
-
Theory
in
perspective:
It is essential to know what kind of auction the
use to
choose
the winning bid.
The owner has
among simplest auctions he can use,
the English auction,
auction:
(ii)
also
bid auction.
the oral,
(i)
open ascending-bid
descending-bid
first-price sealed bid auction;
several options;
are the following types:
called
the Dutch or
owner will
auction:
(iii)
the
and (iv) the second-price sealed
With the first price sealed bid
auction, potential
contractors submit sealed bids and the highest
the contract for the price he bid.
bidder is awarded
Under the second-price sealed
bid auction, bidders submit sealed bids having been told that the
highest bidder wins the contract
but pays
a price equal
not to
his own bid but to the second highest bid.
The
purpose
of
this
thesis
Suffice to say that the four
result for the owner under
is
not
to
study auctions.
previous auctions lead
a certain number
the bidders are risk neutral,
(ii)
to the same
of assumptions:
the independent-private-values
assumption applies, (iii)
the bidders are symmetric, (iv)
is
alone.
a function
of
bids
verified,
since
contractors
assumption
seems
to
be
The
are
verified,
valuation depends on private
first
risk
because
specifications
known
by
the
any
one
second
bidder's
and is thus
On the other hand,
value for the project
contractors,
is not
The
costs and productivity
and site conditions,
payment
assumption
averse.
independent from any oher bidder's valuation.
there exists a true common
(i)
resulting from
but this true value
because
it
suffers
from
is not
many
-65-
uncertainties.
verified.
Thus
the
second
hypothesis
is
not
The third assumption holds if there is
difference in cost structures or
comparative advantage for some
bidders are drawing their valuations
distribution F.
no systematic
other variable,
bidders;
if
in other
from
the
stricity
there is no
words, If all
same probability
This assumption is supposed to hold.
The fourth
assumption holds for the Stipulated Sum Contract, but not for the
Cost
plus
Fee Contract or the Maximum Cost
plus
Fee Contract.
Actually,
for these latter types of contract the payoff that the
owner will
finally receive depends on the ex-post actions
of the
bidder and their impact on the net present value of the project.
So,
where are we?
Obviously all types of auctions will not
give the same result for the
owner and the optimal
be a
It will
very complicated one.
reservation
prices,
subsidizing
making some information public,
include such
certain
auction will
features like
classes
and so on.
of
bidders.
It is not at all the
scope of this thesis to determine the optimal auction in the case
of
construction
building
contracts.
simple second-price sealed
to interpret.
Yet,
bid auction,
in the case of
English auction will lead to
advantage of
the
If the
owner
results are very simple
risk averse contractors, the
better results for
second-price
chooses a
sealed
bid
the owner.
auction
The
over other
simple auctions is that the contractors submit their valuation of
the project as
a bid for
the
contract.
Submitting
valuation
is
contrary,
the bidders will submit bids which will
number
of
indeed
bidders in
the
optimal
the case
of
bidding
strategy.
the exact
On
the
depend on the
the first-price
sealed bid
-66-
auction.
If n
is the number of
uniformily distributed,
to (n-1/n)*Vi.
to
if
valuations are
then contractors will submit
where Vi are the valuations
We can see that
tend
bidders and if
the number
to
bids equal
the contractors.
of bidders rises,
then the bids
the valuation figures.
Thus we will
assume that the level of
competition
ESIEE project is sufficiently high to ensure that
for the
bidders almost
submit a bid equal to their valuations under a first-price sealed
bid auction.
This means that contractors will
order to get an
expected utility
acceptable utility value Ucmin =
various
kinds of
result.
In
assumption:
auctions
summary,
value Uc equal
0.40.
will
we
contractors will
submit
not
make
The
vary
the
submit
to the minimum
outcomes under the
significantly
following
bids
a bid in
equal
as a
symplifying
to
their own
valuation and will be paid according to their own bid.
The
quantity
following
and
sections
quality
of
will
design
analyze
the
information
impact
on
of the
the bidder's
valuation for the project, the heart of the problem at hand.
3.5 The Quality and Quantity of Design Information:
The level of information for the ESIEE project is very high:
The quality and
quantity
plans and specifications
precise,
so
that
of
design
provided
there is
by
needed.
the
is excellent;
architects
very little uncertainty
materials to use for the various works,
be
information
Engineering problems
are very
about what
what amount of work will
have been also
specified and
-67-
solved
before
interest
the
is the
natural ground
project
begins.
water level at
level.
One
issue
only minus one
This means that
of particular
meter below the
very efficient drainage
techniques should be used for the project.
Also all contractual,
financial, or regulations subjections have been clearly specified
and are available to the contractor for him to preparing his bid.
Because
of
this
contractor will be
for the
project
very
high
level
able to forecast
with
introduced because
great
of
information,
the costs and
accuracy.
Little
of these informational
the
the schedule
uncertainty is
problems.
This means
that, globally, all risk premiums, which are due to informational
problems
will
greatly reduced
be
in
the
case
of
the ESIEE
project.
First,
the
expenditures
for
contractor
can
project:
the
precisely
materials
costs,
forecast
the
wages costs,
machines rental costs, financial and insurance expenses, overhead
and design expenses.
Thus the total cost for the project will be
forecasted with great certainty,
will
be
very
little.
accordingly be set
The
to a low
so that the
construction
value by the
construction risks
risk
premium
will
bidders, when valuing
the project.
Second,
the schedule for
great certainty;
time necessary to
problem.
Thus,
the project can be
designed with
the contractors can assess the right amounts of
solve engineering problems
like
the probability for delays will
the drainage
be smaller and
-68-
the
general development risks will
contractors
will submit bids
be minimized.
with low
As a result,
general development risk
premiums.
This
high
parameters of
However,
level of
the project as
we can
available
level.
information will
also
defined in the
imagine
that
for the ESIEE project
Under
this
new
be
be
scenario,
reflected in the
next two sections.
the
level
of information
much
lower
than
parameters
the true
specifying
the
project will introduce more uncertainties in order to reflect the
higher probabilities for delays or cost overruns.
In fact, this
could happen, for instance, if the Chamber of Commerce ran out of
time to precisely define the specifications before the beginnings
of works,
or if the full extent of the drainage problem
was not
known.
3.6 Related Development Risks - Completion Delays:
Completion delays
owner,
are a
major
source
of
concern
to the
because they affect the project's final investment value.
By postponing first day of operations, completion delays wipe out
revenues
losses
received from the project for the
show
up
in
a
diminished
present
delay
period. These
value
of operating
revenues for the project.
Four completion delay scenarios are considered for the ESIEE
project.
On time completion, one and two semester delays and one
semester
ahead of schedule completion
been
evaluated.
are the cases
Each semester of delay drives
which have
the net present
-69-
value of
the project down
happens merely
because
each
of revenues.
4.000.000
by
an
amount of FF
semester
of
1,893,647. This
delay
wipes
Research projects cannot
be undertaken
and academic programs cannot begin as long as the works
been finished.
project,
out FF
have not
We get the following net present values
for the
when considering only the variability due to completion
delays:
Table 3.6
Length of delay
Project Net Present Value
Incremental Value
2
FF
I
FF
315,287
FF
1.893,647
0
FF
2.208.933
FF
1,893,646
-1
FF
4,102,580
FF
1,893.647
(semesters)
(1,578,560)
This table shows the dramatic effect of completion delays
profitability
of
the ESIEE project.
Exact cash flows
on the
for the
project under various scenarios can be consulted in the exhibits.
Note that each day of delay corresponds to a loss of FF 10.520 in
revenues,
and each week to a loss of FF 73,642. The owner should
find the right incentives to motivate the contractor,
makes his best to avoid these delays.
so that he
These incentives
an appropriate liquidated damages clause,
will be
will expose the
which
contractor to a share of the FF 73,642 weekly loss.
Depending
contractor
will
spend
on the
incentives included in
will choose a different course
a
different
level
of
of
effort
the contract, the
action, namely he
on
the
project.
-70-
the next question to
Therefore,
answer is how
the contractor's
effort level affects the outcomes for the project, that is to say
the completion date.
The completion date of the
factors:
and,
first,
second,
project.
for the
high
on
project will depend on
as just said,
the level
two main
on the contractor's effort level
of
information
available
for the
For the ESIEE project, we consider two different cases
level of information
level
of
information.
available:
For
each
an average level and a
level
of
information
considered, the possibility for completion delays is described by
a Delay
Probability matrix.
* 4 probability matrix, P,
This 6
specifies a distribution of the random variable -completion delay
and
corresponding random
variable
'NPV,
for
each
of the six
contractor's effort levels.
Information level
'Length of delay (semesters)
2
1
0
-1
NPVi
NPV2
NPV3
NPV4
El
Pi,1
P1,2
P1,3
P1,4
E2
P2,1
P2,2
P2,3
P2,4
E3
P3,1
P3,2
P3,3
P3,4
E4
P4,1
P4,2
P4,3
P4,4
E5
P5,1
P5,2
P5,3
P5,4
E6
P6,1
P6,2
P6,3
P6,4
-Project net present value
Contractor Effort Ei
Please see the exhibit #
3.6-1 for the matrices corresponding to
the two cases of information level.
-71-
Exhibit 3.6-1
Construction Completion Delay Scenarios and Expected Profits
Average Level of Information
Delay - Effort Probabilty Matrix
Length of Delay (semesters)
Project Net Present Value
2
1
0
NPV1
NPV2
NPV3
-I
NPV4
Contractor Effort Ei
El
E2
E3
E4
E5
E6
0.810
0.640
0.300
0.184
0.024
0.002
0.171
0.270
0.533
0.305
0.192
0.079
0.016
0.080
0.133
0.376
0.563
0.609
0.003
0.010
0.034
0.135
0.221
0.310
High Level of Information
Delay - Effort Probabilty Matrix
Length of Delay (semesters)
Project Net Present Value
2
1
NPV1
NPV2
0
NPV3
-1
NPV4
Contractor Effort Ei
El
E2
E3
E4
E5
E6
0.950
0.201
0.026
0.009
0.000
0.000
0.048
0.772
0.760
0.124
0.006
0.001
0.002
0.026
0.202
0.769
0.739
0.069
0.000
0.001
0.012
0.098
0.255
0.930
-72-
This probability matrix has very interesting properties that
we recall now:
@ Any element Pi,j gives the probability of
completion
delay j,
given the effort level i: Pi,j = P (NPVj/Ei)
For instance,
when the effort level
the project will be finished
time is 0.511
(0.376
+
is E4,
on schedule or
the probability that
ahead of completion
0.135) in the average information level
case and 0.867 in the high information level case.
a For any effort level I,
possible
outcomes for
the four NPVs
the project.
completely describe the
They constitute a complete
system of events. Thus, we have:
6
for any i
K
Pi,j = I
j=j
* The matrix assumes that any additional contractor effort lowers
the expected delay and therefore increases the project's expected
net present value:
for any i
and
< E('d/Ei)
E('d/Ei+1)
E('NPV/Ei+1) > E(NPV/Ei)
Expected net present values are calculated as follows:
4
E('NPV/Ei) =
E
NPVj * Pij
J=1
These
expected
from the project.
net present values
represent the
gross profits
The owner has to substract the payment made to
the contractor for his overhead
expenses and profits
net profits from
Gross
the project.
Profits are
to get the
presented in
-73-
exhibit #
3.6-2 for the average level of information case and in
exhibit # 3.6-3 for the high level of information case.
In these
exhibits, we see that the higher the effort level,
the higher the
gross
the
expected
information,
level of
gross
profits.
Also,
the higher the
effort.
profits
the
gross expected profits
For instance,
are
FF
higher
for
1,190,151
effort
for
the
level
of
for a given
level 4, expected
average
level
of
information and FF 2,125,613 for the high level of information.
for any i
E('NPV/Ei&HI) > E('NPV/Ei&AI)
HI represents the high level of information,
Al represents the average level of information.
In the exhibits # 3.6-2 and # 3.6-3, the net expected profits are
the
profits that
the owner
would
contractor exactly for the amount
contract
would
be
an
get,
he
enforceable
contract would tie compensation
that the contractor takes.
if
he
could
spends
on
the
contract.
This
directly to the
pay the
job.
The
enforcing
observed action
To ensure that the contractor chooses
the level of effort which gives the highest return, namely effort
level ES
E6
in average information level scenario
and effort level
in high information level scenario, the forcing contract pays
FF 410,000
and
FF
1,200,000
to the contractor
for
each case
respectively,
if he puts effort level E5
and E6 respectively in
the project,
and pays nothing otherwise.
This forcing contract
would
ensure
a net profit
respectively for the
forcing
contract
contractor's
effort
average
is
not
cannot
of
FF
and
1,762,954
high
possible,
be
observed
and
information
however,
directly.
FF 2,768,131
levels.
because
A
the
Note that
-74Exhibit 3.6-2
Construction Completion Delay Scenarios and Expected Profits
Project Net Present Value
Length of delay
(semesters)
2
(1,578,360)
I
315,287
2,208,933
4,102,580
0
-1
Contractor Effort Ei
El
Average Level of
0
50,000
150,000
250,000
410,000
1,200,000
=
=
=
(1,176,907)
(707,282)
127,816
1,190, 151
2,172,954
2,638,791
=
=
=
Net Expected Profits
E(NPV/EI)
E(NPV/E2)
E(NPV/E3)
E(NPV/E4)
E(NPV/E5)
E(NPV/E6)
-
Effort Level
El
E2
E3
E4
E5
E6
50,000
100,000
100,000
160,000
790,000
Information
Gross Expected Profits
E(NPV/EI)
E(NPV/E2)
E(NPV/E3)
E(NPV/E4)
E(NPV/E5)
E(NPV/E6)
1,893,647
1,893,646
1,893,647
Incremental Value
=
=
=
=
=
=
E2
E3
E4
E5
E6
Incremental Value
El
E2
E3
E4
E5
E6
Differences in G.E. Profits
469,624
835,098
1,062,336
982,803
465,837
Differences in N.E. Profits
(1,176,907)
(757,282)
(22,184)
940,151
1,762,954
1,438,791
Variance of Profits
7.7834E+11
1.6796E+ 12
2.0052E+12
3.1791E+12
1.8239E+12
1.2388E+ 12
419,624
735,098
962,336
822,803
(324,163)
Standard Deviation
882,236
1,296,007
1,416,062
1,783,003
1,350,528
1,113,025
-75-
Exhibit 3.6-3
Construction Completion Delay Scenarios and Expected Profits
Project Net Present Value
Length of delay
(1,578,360)
315,287
2,208,933
4,102,580
2
1
(semesters)
0
-1
=
E4
=
1,893,647
1,893,646
1,893,647
Incremental Value
Contractor Effort Ei
El
E2
E3
Incremental Value
0
50,000
150,000
250, 000
410,000
1,200,000
E5
E6
50,000
100,000
100,000
160,000
790,000
High Level of Information
Differences in G.E. Profits
Gross Expected Profits
E(NPV/EI)
E(NPV/E2)
E(NPV/E3)
E(NPV/E4)
E(NPV/E5)
E(NPV/E6)
=
(1,479,890)
=
(12,314)
694,016
2,125,613
2,680,451
3,968,131
=
=
=
=
Differences in N.E. Profits
Net Expected Profits
E(NPV/E1)
E(NPV/E2)
E(NPV/E3)
E(NPV/E4)
E(NPV/E5)
E(NPV/E6)
-
Effort Level
El
E2
E3
E4
E5
E6
El
E2
E3
E4
E5
E6
1,467,576
706,330
1,431,596
554,838
1,287,680
(1,479,890)
(62,314)
544,016
1,875,613
2,270,451
2,768,131
Variance of Profits
1.9111E+11
7.2102E+11
8.4627E+11
9. 1822E+11
7. 1359E+11
2.4369E+11
1,417,576
606,330
1,331,596
394,838
497,680
Standard Deviation
437,166
849,129
919,930
958,238
844,743
493,654
-76-
Effort level
E6
in
undertaking
is
so
expensive,
that
it
the average information level
is
not worthwile
scenario, because
the incremental profits gained by
spending effort E6
effort ES
than the incremental cost E6 -
are less,
FF 465,837,
instead of
E5, FF 790,000.
a The matrix allows
to compute
the variance of the
net present
value for the project for each effort level scenario:
4
V('NPV/Ei) =
E
2
Pij * (NPVj - E('NPV/Ei))
J=1
and the standard variation of profits:
w(~NPV/Ei) =
SQR [V('NPV/Ei)J
SQR is the square root operator.
The standard
deviation is a
good measure of the
profits gained from the project.
variability in
The higher the variability, the
higher the related development risks of the project, and the less
the contractor is willing to sign
level
of
level,
risk exposure.
for this project,
for a given
In order to compensate a
higher risk
the contractor will ask a greater risk premium, if he has
to cope with these risks.
For a given effort level, the variability of the project's NPV is
greater,
the lower the level of
information
available
for the
project.
for any i
v(-NPV/Ei&AI) > a(~NPV/Ei&HI)
For instance, for effort level 5, the standard deviation of gross
profits is FF 1,350,528 for the average level of information, and
only FF 844,743
for the high level of
information.
Indeed, the
-77-
more
provided
information
the
precise
and
accurate
effort spent
the less likelihood of delays for a given
project,
for the
by the contractor and the less variability in the gross profits.
Another remarkable characteristic is the fact that variability in
profits is not linear in the effort level.
more
falling with
with
increases
the
level
effort
variability first
the job,
spent on
effort
Instead of regularly
up
level
to
E4,
and then
This should not be the case, but this means that for
decreases.
spending
the ESIEE project,
spending a high level of
none
effort
or E6) ensures with little
(E5
effort
or E2) or
at all (El
uncertainty a very undesirable or desirable outcome respectively.
If
an
is put on the project,
average effort
outcome
might
construction
if
result
is
a smooth
unexpected
no
then
problem
arises
and
other case, the
but in any
process;
a very good
outcome may be very bad as well.
a The contractor's exposure to related
contract
incentives
determine the
If too little exposure is created by the
certainly choose
will
contract clauses the contractor
profits.
to
will be a primary factor
chosen level of effort.
too little effort
development risks through
on the project
to spend
of the owner's
at the expense
On the other hand , if too much exposure is introduced,
have
the owner will
to
pay a
price
disproportionate
for the
corresponding incentives.
Related
development
risks
are
introducing risk premiums in the bids.
to
these
risks
ensures
on
time
the
first
source
for
But contractor's exposure
completion
of
the project.
-78-
Construction risks,
in
studied
the
section
next
are
also a
crucial element to be considered by the contractor when preparing
his bid.
3.7 Construction Risks - Costs Overruns:
development risks, but
This study is not limited to related
instead assesses the impact of construction risks on contractors'
bids
as
well.
important
risks are likely
Construction
role,
when the contractor
prepares
uncertainty in construction costs will
a secure return
risk,
the
to the
will
play a very
his bid, because
lower the expectations for
In order to alleviate this
contractor.
contractor
to
submit
a
higher
bid
including a
However, this risk premium might be
corresponding risk premium.
less costly to the owner than the loss in profits he would get if
the
contractor
would
not
be
kind of
has for this
the more expertise the contractor
Indeed,
construction risks.
to
exposed
projects, the smaller the risk premium will be.
Two construction risks level scenarios are evaluated for the
project,
ESIEE
Obviously,
information.
will be
qualities
corresponding to
higher
of
in
the
the
two
different
construction costs
the variability of
case
information
of
only
available.
levels of
average
The
quantities and
variations
construction costs are as follows in table 3.7:
Table 3.7
Average level of information
Variations in Construction Costs
Probability
of
-79-
FF
1,000,000
0.25
FF
0
0.50
FF (1,000,000)
0.25
High level of information
Variations in Construction Costs
Probability
FF
250,000
0.25
FF
0
0.50
FF
(250,000)
0.25
We shall adopt the following notations for the previous table:
Level of information
Variations in Construction Costs
Probability
9CC
Qi
0
Q2
SCC
Q3
-
The expected value of construction costs is unchanged and remains
equal to
FF 34,100,000.
equal to FF 5.000
FF
3.125
The variance of
10E11 for an average level of information, and
10E10
for
a
high
level
corresponding standard deviations are FF
respectively.
contractor's
construction costs is
of
information.
707,107
The
and FF 176,777
Obviously, such possible variations can affect the
profits,
if he does not
include construction risk
premiums in his bid.
Another interesting question
is to know
whether variations
in construction costs are dependent on the level of
on
the
job.
Contractor's
construction costs,
the
contractor.
and this
In
this
efficiency
is a
study,
can
effort spent
greatly
influence
variable which characterizes
we
shall
assume
that
the
-80-
with
contractor's expertise and experience
so that variability in construction costs does not depend
fixed,
on
projects is
similar
the
should
Efficiency
efficiency.
contractor's
be
distinguished from effort, because for a given level of expertise
and
the
efficiency,
levels of
can spend different
contractor
effort.
First,
it can be argued that the more effort the contractor
spends on the lob,
construction costs.
firm
construction
to
materials,
However,
in base
likelihood for an increase
the less
This would be explained by the fact that the
spends
ensure
some
wages
that
to
time
remain
find
stable,
in this study we make the assumption
cheapest
the
and
so on.
this is not
that
Variations in construction costs are likely to happen
the case.
for reasons and contingencies which globally do not depend on the
costs
constructions
Typically,
effort.
contractor's
would
increase because of unexpected engineering problems or strikes or
increases in
materials,
the costs of
Construction
influence.
has little
the contractor
which are events on which
costs will
depend on the contractor's efficiency,
but efficiency is not the
In summary,
this study considers only
same variable as effort.
costs
constructi on
in
variations
the
are
which
results
of
exogenous events from the contractor's point of view.
With
the
completion
that
not
longer,
delays
counter
should
necessarily,
can be
considered as independent
intuit ive?
not
construction
assumption,
previous
If
construction
the
construction
costs
be
because a longer construction time
costs
and
events. Is
period is
higher?
Not
might mean less
-81-
put on
effort
the job -
work periods,
non
engineering time,
meaning less
the end being
It may well happen that construction
tied to the project itself.
costs are higher despite the fact that the
ahead of schedule,
-,
are thus directly
construction costs
in
Variations
and so on
with total costs at
costs spent per unit of time,
the same.
fewer machines, less
fewer employees,
or the contrary.
project was completed
This assumption will allow
us to compute the utility functions of the contractor to find the
optimal course of action from his point of view.
The last
source
of
uncertainty
expected during operations
comes
of the project.
from
the revenues
This uncertainty is
discussed in the following section.
3.8 Operations Risks:
Operations risks designate the risks incurred because of the
variability
delays.
of
revenues,
which
is
not
caused
by completion
Revenues might vary in the ESIEE project, because of the
Such reasons include
many reasons exposed ealier in this study.
the more or less ability to find and conduct
good and profitable
research programs, the variable quality of the academic programs,
and so on.
If the owner were risk averse, operations risks would be one
of the primary concerns
to
the owner.
If revenues
are highly
variable, the owner might incur losses from a project expected to
give
a
positive
net
present
supposed to be risk neutral,
value.
However,
the
owner is
in which case he will not price the
-82-
risk borne from the
thing
variability of
which matters for him is
revenues.
the
Finally, the only
expected
profits
from the
project, whatever their variability can be.
This is not the case
of the risk averse
he be exposed to the variability of
revenues, the contractor will
price this risk with a very substabtial risk
several
reasons to
this conclusion.
not be able to affect
variability
does
premium.
There are
First, the contractor will
the variability of
not depend
contractor. Should
on the
revenues, because this
construction process. This
variability depends only on factors on which he has no influence,
and which will be mainly determined after the construction period
is over.
Second, the fact that the owner is risk neutral and the
contractor
is risk averse creates a selection
is
to
likely
accept
undertake if
projects,
which the
a Maximum Cost
plus
Fee Contract,
exposed to revenues risks.
risks will
Sharing Contract
contractor,
contractor would not
he had to make the decision.
With a Cost plus Fee Contract,
operations
problem. The owner
be
a Stipulated Sum Contract or
the
contractor
will not be
In these cases, the risk premium for
zero.
gives a share of
On
the other hand,
the operations
a Profit
risks
through the share of profits/losses he will
to the
receive.
This is not the case with other types of contracts, even with the
Maximum Cost plus Fee Contract
in which revenues are
fixed from
the contractor's point of view.
The variability in revenues is described by the NPV
probability matrix.
For
each
Please see this matrix in
delay scenario,
the matrix gives the
- delay
exhibit # 3.8-1.
distribution of
-83-
Exhibit 3.8-1
Construction completion delay scenarios
and Variability of Project Net Present Value
NPV - Delay Probability Matrix
Delta ( Actual NPV )
Delay
Expected NPV
2
(1,578,360)
1
315,287
0
2,208,933
-1
4,102,580
Probabilities
0.0122
0.0279
0.0655
0.1210
0.1747
0.1974
0.1747
0.1210
0.0655
0.0279
0.0122
Standard Deviation
(5,126,609) (4,613,948) (4,613,948)
(4,026,567) (3,623,910) (3,623,910)
(3,019,925) (2,717,933) (2,717,933)
(2,013,284) (1,811,955) (1,811,955)
(892,487)
(803,238)
(803,238)
0
0
0
803,238
892,487
803,238
1,811,955
2,013,284
1,811,955
3,019,925
2,717,933
2,717,933
4,026,567
3,623,910
3,623,910
4,613,948
5,126,609
4,613,948
(5,126,609)
(4,026,567)
(3,019,925)
(2,013,284)
(892,487)
0
892.487
2,013,284
3,019,925
4,026,567
5,126,609
1,800,000
1,800,000
2,000,000
0
2,208,933
4,102,580
2,000,000
Actual NPV
Delay
Expected NPV
2
(1,578,360)
1
315,287
-1
Probabilities
0.0122
0.0279
0.0655
0.1210
0.1747
0.1974
0.1747
0.1210
0.0655
0.0279
0.0122
(4,298,661) (2,405,015) (1,024,029)
(3,308,623) (1,414,977)
76,013
(509,000) 1,082,655
(2,402,646)
(1,496,668)
396,978
2,089,296
(487,951) 1,405,695
3,210,093
315,287
2,208,933
4,102,580
(1,578,360)
3,012,171
4,995,067
(685,873) 1,118,525
4,020,888
6,115,864
434,924
2,127,242
3,033,220
4,926,866
7,122,505
1,441,565
5,832,843
8,129,147
3,939,197
2,448,207
4,929,235
6,822,881
9,229,189
3,548,249
(6,704,969)
(5,604,927)
(4,598,285)
(3,591,644)
(2,470,847)
-84-
variations
of
variations of
likelihood
revenues
NPVs.
of
the
from
the
project
A probability
variations.
important characteristics of
and
the
resulting
distribution
describes the
following
properties are
The
the matrix:
(i) The variability in revenues does not change the expected NPVs
for
the
project.
Depending
on
the
completion
delays,
two
semester, one semester, on time, minus one semester, the expected
NPVs are still FF
(1,578,360);
FF 315,287;
FF 2,208,933 and FF
4,102,580 respectively.
(ii)
The scope of the variabilty depends on the completion delay
scenario.
have
On time completion
a standard
semester
deviation
ahead of
and one semester
of
schedule
FF
1,800,000
completion
delay scenarios
in
and two
scenarios have a standard deviation of FF 2,000,000
revenues. One
semester delay
in revenues.
We can note, first, that the standard deviation is quite large in
all cases,
reflecting
the overall risk
of
the project; second
that the standard deviation is larger in the case of very late or
very
early completion
these cases,
defection
of
The main explanation is
that in
new uncertainties are introduced, like the possible
some
cancellation of some
completion,
dates.
of
the
researchers,
planned projects
professors,
in the case of
or
the
very late
and like the difficulties to begin research projects
earlier in the case of early completion.
-85-
With this revenue variability,
the project can lead to losses as
large as FF (6,704,969) in the case of a two semester delay (with
a probability
of
9,229,189
the
in
about
1.2%),
case
of
or
early
to
gains
completion
as
large
(with
as FF
the
same
probability).
(iii)
The variability in revenues is supposed to
from the other kinds of variabilities.
likely to be verified
This assumption, which is
in the real world,
easily the optimal course
of
action
be independent
for
will allow
the
us to find
contractor
as a
function of the contract chosen.
The following notations will be adopted for the
NPV
Delay
-
probability matrix:
NPV
-
Delay Probability Matrix
Actual NPVs
Delay
2
1
0
-1
NPVI,4
Probabilities
Ri.1j
NPV1,i
NPVI,2
NPV1,3
R2,j
NPV2,1
NPV2,2
NPV2,3
R3,j
NPV3,1
R4, j
R5,J
R6,j
R7, j
R8, J
R9, j
RIO, j
R11,j
NPV1O,4
NPVI1,1
NPV11,2
NPV11,3
NPVI1,4
-86-
I E (1..41
stands for the delay scenario.
All types
of risk studied have
now been
now necessary to assess how incentives
described.
included
It is
in the contract
will affect the contractor's course of action.
3.9 Incentives and Effort Level:
As seen in section 3.3,
the contractor chooses the level of
effort, which maximizes his utility function, as follows:
E
Max Uc(./Ei) = Max
Uc(./El)
is total utility of
P(Yi/Ej) * Uc(Yi/Ej)
the project to the
contractor when
he spends an effort level EJ:
Yi
is the profit to the contractor:
contract
point,
Yi
will
be
defined differently.
[
Remark: At this
it is only important to note that the set of Yi defines a
complete system of events over
words we have:
if
k#I
the probability space.
Incentives will take the form of
which will
effort
Incentives,
lower the profits Yi,
be
J
financial contract designs
and the resulting utility, when
level chosen by the contractor
however will
In other
then YkOYl = 0
U Yi = 0 = (all possible events)
and
the
depending on the form of the
costly
to the
is
not high enough.
owner, because the
-87profits
Yi
to
incentives,
the
when
contractor
the
will
contractor
be
higher
chooses
the
than
right
without
level of
effort.
The
contract
included,
type
will
define
precisely
the incentives
and therefore determine the optimal action
choice for
the contractor.
Sections
3.10
and
3.11
present
explaining how the optimal action
technical considerations
choice for
the contractor has
been determined practically on Lotus 123 for each of the contract
type studied.
These
sections
have
thus
been
transferred to
appendices # 3.10 and # 3.11 for their main part.
The interested
reader can refer to these appendices.
3.10 The Contract Type:
This
profits
section will
attributed
contract studied.
determine,
to the
Then,
for the
ESIEE
contractor for the
we
project, the
various types of
explain the process
by
which the
contractor chooses the optimal course of action for each of these
contracts.
Please refer to appendix # 3.10 if you are interested
in these technical considerations for implementation purposes.
3.11 Submitting a Bid:
Assuming the contractor
has
chosen
an
optimal
course of
action for a particular project, the next step for him will be to
evaluate
the minimum bid.
Because
of
competition and reasons
-88-
given in the section 3.4,
the contractor will submit a bid which
is equal to his valuation of the project.
bid for the contractor
utility value,
is
thus
which is 0.4.
set by
The minimum acceptable
the
minimum acceptable
Please refer to appendix # 3.11 if
you are interested in technical considerations for implementation
purposes.
-89-
4 Optimal Contract Determination:
4.1 Possible Scenarios for the ESIEE projects
In this
Determination of the optimal
the ESIEE project.
first choose
the
contract for
we shall determine the optimal
part,
right
type
of
contract means
second define
and
contract,
precisely the parameters of the contract.
for the ESIEE project
The optimal contract
possible scenarios
two
different scenarios:
for
information
each
available
quantity of design
a high quality and
project
and
an
of
level
average
such
As we shall see, the optimal contract is different
information.
for
the
We basically consider
for the project.
the
depend on
will
scenario,
suggesting that
plays a critical
role
in
the
level
the design
of information
an optimal
of
contract in the construction building industry.
are
Scenarios
defined
by
delay
costs variabilities and
construction
probability
revenue
matrices,
variabilities for
both levels of information as exposed in part 3 of the thesis.
4.2 Optimal Contract Determination - The Process:
Definition
best contract
contract.
the
of an optimal contract
type
However,
optimal contract
and properly
means both
designing incentives
the process involved for the
will
choosing the
not treat these
two
for this
definition of
steps
in this
-90-
order,
but
rather
sequence.
of
they
First,
contract.
will
be
in
the
opposite
the best design will be defined for each type
This
will
lead
parameters which give the
to
the
determination
highest possible profits
for each type of contract.
of
the
to the owner
These parameters will define one best
designed contract
for
contracts will be
compared to find
profits
addressed
each
among these best
type
of
contract.
Second, these
the one which
designed contracts.
gives highest
The class of the
winning contract will be the optimal contract type.
Let us take an example to
practice.
In the
illustrate how this will
rest of this
section.
we shall
work in
look for the
best designed stipulated sum contract in
the case
level of design information.
probability matrix, the
The delay
of an average
variability of construction costs and of revenues
in
part
3.
Exhibit #4.2-1
shows that the best stipulated
for average quality and quantity of
is defined by 0 equal to
0.14.
profit to
FF
As
are defined as
the owner
of
a reminder,
sum contract
design information available
This contract gives an expected
1,012,991.
we recall the definition of
the stipulated
sum contract:
P
=
S
The contract as written
damages lump
sum A,
stipulated sum S.
FF
1,893,647;
delay.
-
0*d*A
above is defined
the liquidated
damages
by the liquidated
factor
0
and the
The liquidated damages sum A has been fixed to
which is
the loss of NPV due to
a
one semester
-91-
The
owner fixes a
liquidated
contractor proposes a stipulated
Once the bid has been received,
damages
factor
sum S for a bid
the owner
0,
as
and the
an answer.
computes his expected
profits from the project as follows:
E(NPV/Ejo) - E(P/Ejo)
= (E NPVd/Ejo * Pd,jo) - S + 0*(E d*Pd,jo)*A
d
Ejo
is
d
the effort
level chosen
by
the
contractor
given the
specifications of the contract.
E('NPV/Ejo)
is the
expected
Net
Present
Value
of
the ESIEE
project, knowing that the contractor chooses effort level Ejo.
E(P/Ejo)
effort
is the expected payment to the
level Ejo and
the
delay
contractor, knowing his
probabilities
Pd,jo
for this
effort level.
Thus
the
liquidated
process
damages
is
the
factor
corresponding effort level,
0
following:
equal
the liquidated
computations
Please
look
exhibit presents the profits to
liquidated damages factor 0.
at which the effort level
For our case,
0.82.
start
zero,
bid and profits to
we progressively rise
again.
to
We
compute
#
exhibit
the owner as
a
the
the owner. Then,
damages factor
at
with
and do the
4.2-1.
a function
This
of the
In this process, we look for points
Ejo chosen by the
this happens at points
contractor changes.
0 equal to
0.13, 0.14 and
At these points the effort level rises from El
to E4, E4
to E5 and ES to E6 respectively.
At these points, the incentives
included
Just
in
the
contract
are
contractor to spend additional effort
enough
on the
to
convince
project.
the
This has
w
w
0
1P
4P
40
0
0
40
Stipulated Sum Contracts
Average Level of Information
1.2
1,012,991
1
0.8
0.6
0.4
-N
-
U.
-
0
0
0:
-0.2
H-
0
-
-0.4
I"
.
N
-0.6
-N
-0.8
-1
C3
-1.2
-1.4
III
-
-
-1.6
-1.8
0
0.2
0.6
0.4
Liquidated Damages Factor 0
0 Owner's Profit
0.8
1
I.
-93-
First it raises the cost of the contractor's effort
two effects:
and
the proposed
bid as
expected profits from the project.
each other,
Second, it raises the
a consequence.
and which of
the
These two effects are fihting
two
is
more
determined by the cost of additional effort.
we can see that,
contractor
are
factor 0 rises.
important
On exhibit # 4.2-1,
for a given level of effort, the profits to the
actually
falling
This happens,
when
the
because a
liquidated damages
higher
risks given to the contractor and a higher risk
in the bid as
his effort,
will be
a consequence.
0
means more
premium included
The contractor does
not increase
because this would mean a lower expected utility for
the same bid,
or the necessity to increase
same utility.
his bid to
gain the
As long as incentives are not enough to
make the
contractor change his effort level,
of profits to the owner.
a rise in 0 means a decrease
All these points will be
discussed in
more detail in the following sections.
The
process
described
above
is
used
to
determine
the best
stipulated sum contracts and profit sharing contracts for average
and high levels of information available.
4.3
Construction Costs and Revenues are
fixed: An Academic
Case:
In
this
section,
construction
assumption,
costs
and
we
consider
revenues
we get the striking
contract type.
the unrealistic
are
certain.
result that there is
case that
Under
this
no better
All contract types can be designed so as to lead
-94-
to the same expected profits to the owner.
This result makes it
interesting to study this unrealistic case,
because
understand
the fundamental similarities
it helps to
and differences between
contracts.
Why are all contracts equivalent under the constuction costs
and revenues certainties assumption?
The main reasons are first
that, under this assumption, the construction and operations risk
premiums are zero and
the
maximum
cost
second,
plus
fee
that the stipulated sum contract,
contract
and
the
profit sharing
contract allocate the general development risks in the
Thus,
the premiums for these risks
will be the same
same way.
under each
contract.
Results for both scenarios are presented
to #4.3-4
first
and appendices #
the scenario
Under this scenario,
equal
to
0.14
1,509,740.
sharing
of
4.3-1
in exhibits #4.3-1
to # 4.3-26.
average level of
information available.
the optimal contract is
and gives the owner a
total
defined by
net
For both the stipulated sum contract
contract (strictly
Let us consider
profit
0 or p
of FF
and the profit
equivalent to the maximum
cost plus
fee contract in this simplified case) give the same utility, 0.4,
and
payoffs,
FF 253,214,
to the contractor.
chosen by the contractor is ES
premium is FF 46,330.
=
FF
(359,000)
sharing
contract.
contract
-
The effort level
in both cases, and the total risk
The bids submitted by the contractor are F
a negative
and S =
franchise fee -
FF 668.250
,
for
the profit
for the stipulated sum
A precise evaluation of both contracts is presented in
exhibits #4.3-2 and #4.3-3.
-95When there is
no
information problem for the
project, the
optimal contract is not defined by 3 or p equal to 0.14 any more,
but rather by 3 or p equal to 0.70,
and
#
appendix
profit
of
FF
appendices #
4.3-13.
2,169,439;
the previous paragraph.
contract defined by
profits
equal to
information.
This best contract gives the
owner a
the
contract
type.
See
4.3-26 for a discussion equivalent to
What is interesting to note is that the
3
FF
# 4.3-4
whatever
to #
4.3-13
as shown in exhibit
or
p
equal
1,645,027
to
0.14
generates owner's
in the case of a high
level of
This profit is higher than for the first scenario,
but much lower than the profit got from the
best contract, which
generates
best
32%
more
profits.
With
contractor no longer chooses the E4
0.14
value of J or p,
this
level of
contract,
effort
the
as for the
but the E6 level; this increase in effort
is the explanation for the big increase in profits.
The difference is even
of information.
more striking for the
average level
The best contract, as said before, generates an
owner's profit of FF 1,509,740; whereas the contract defined by 1
or p equal to 0.70
best
contract
gives a profit of only FF
increases
profits
by
340%,
343,886.
Thus the
a
dramatic
quite
difference.
This simplified case shows the importance of well specifying
the contract's parameters according to the
for
the
contract.
included in
If
the contract
this
information
should
be
high,
information available
is
high, incentives
so as to ensure the
S
W
S0
SW
W
S
0
0S
S
Optimal Contract Determination
Average Level of Information
1.6
1.4
1.2
0.8
La.
La.
0.4
4-p
CA
0
5..
-x
0.2
0
Q..
H-
-N
0
In
5..
-X
0.6
-N
-0.2
w
3
--0.4
0
-0.6
-0.8
--1
-
-1.2
-1.4
0
0.2
0.4
x
0.6
0 and p Factors
Owner's Profit
0.8
I
I.
-97-
Exhibit 4.3-2
Construction Costs and Revenues are Fixed
Evaluation of Contracts - Average Level of Information
Contract Form:
P =
0.14 NPVd - F
5
Effort Level:
Payoffs to Contractor
E(NPV/Ej)
Franchise Fee F
2.172.954
(359,000)
Contractor Payoff P
Less: Effort
663,214
410,000
Contractor Profit
253,214
Contractor Utility
0.4010
Payoffs to Owner
E(NPV/Ej)
Less: Fixed Fee
Less: Effort
Less: Risk Premium
Plus: Franchise Fee
2,172,954
206,884
410,000
(312,670)
(359.000)
Owner Profit
1,509,740
Owner Utility
1,509,740
Total Risk Premium
46,330
-98-
Exhibit 4.3-3
Construction Costs and Revenues are Fixed
Evaluation of Stipulated Sum contracts - Average level of information
Contract Form:
P =
S - d*6*A
0
Effort Level:
j
=
5
Expected Delay:
d=
0.02
=
0.14
1,893.647
Payoffs to Contractor
Stipulated Sum (Bid)
E(Liquidated damages)
668,250
5,037
Contractor Payoff P
Less: Effort
663,213
410,000
Contractor Profit
253,213
Contractor Utility
0.4010
Payoffs to Owner
E(NPV/Ej)
Less: Fixed Fee
Less: Effort
Less: Risk Premium
Plus: Liquid. damages
2,172,954
206,884
410,000
51,366
5,037
Owner Profit
1,509.741
Owner Utility
1,509,741
Total Risk Premium
46,329
0
S
S
4P
S
S
S
S
0
S
0
aS
0
0
00
Optimal Contract Determination
High Level of Information
2.5
2
-r
1.5
Lz.
La.
I
4-,
U'
0
0
0:.5
-.4
a.
0
U'
S..
3
0
-0.5
-1
-1.5
-2
0
0.2
0.6
0 and IiFactors
Owner' s Profit
0.4
x
0.8
1
I.
'.0
-100-
maximum effort level.
On the contrary, if the information level
is only average, incentives should not be too high, otherwise the
risk premium will become greater than the incremental gains.
4.4
High
Level
of
Design
Information
-
Evaluation
of
Contracts:
When
different
construction costs
and revenues are
types of
are not equivalent
contract
not certain, the
anymore and it
becomes very important to choose the right type of contract.
The
ESIEE
project
is
characterized
the Paris Chamber of
contract for t he project.
superior
Commerce
in their
choice of a
In this case, we can conclude that the
Sum contract
Stipulated
a
This characteristic greatly
availability of design information.
influences
by
is
a better
contract
than the Profit
Sharing Contra ct, whereas the Maximum Cost plus fee contract - or
Cost Sharing
contract -,
contractor's
point of
for the ESIEE project.
for which revenues are fixed
view,
is probably the 'optimal contract'
This result
is very different
one gotten for the scenario of an average availability
information.
becomes a
In the latter
bet ter
Reasons for this
this
part.
contract
case,
than
the
the
fundamental conclusion
Thus,
from the
when variability in
from the
of design
profit sharing contract
Stipulated
Sum contract.
will be given
construction
later in
costs and
revenues is introduced in the model, the quantity and the quality
of design information plays a critical role in
of the 'optimal contract'.
the determination
-101-
We
consider
information.
appendices #
the
Please
4.4-1
scenario
of
high
see the exhibits
to
#
#
level
4.4-1
of
design
to # 4.4-7 and
Exhibits # 4.4-1 and # 4.4-2
4.4-12.
present the curves of the effort level spent by the contractor on
the project as a function of the profit sharing factor p
liquidated damages
factor,
factor
0.
The
the higher the effort level.
does not change continuously as a
necessary
that
the
sufficiently high
level
to
study,
The
higher
incentives
higher
function of p.
included
in
level.
Rather, it is
the
switch
contract
be
from an effort
As explained before in this
the behavior of the contractor is based on risk aversion.
risk
equally,
averse
contractor
level 4
does
not value
but instead values more heavily
at p and 0 equal to
0.24,
the
to effort level 5.
additional expected gain/loss.
to
cover the additional expenses.
and losses
For instance,
switches from effort
The contractor does
additional effort would be higher
profit/loss attributed
gains
losses.
contractor
effort before p and 0 reach this value,
the
profit sharing
However, the effort level
to make the contractor
the next
the
and the
not spend this
because the cost
than the utility
of the
value of the
This happens because the share of
the contractor is not
On the
enough to
contrary, the contractor
is better off by switching effort level at p and 0 = 0.24 than at
0.25,
because if not,
loss/gain
from
not
the utility cost to the contractor of the
switching
additional cost of effort.
averse contractor.
As
a
would
become
higher
This is not acceptable
consequence,
change of effort level at p equal to 0.04,
the
than
the
for the risk
contractor
has to
0.10 and 0.24 for the
S
S
S
S
0S
0U
OP
S
0S
eS
Stipulated Sum Contracts
High Level of Information
1.2
-
1.1
-
1 -
0.9
-
Li.
0.0
-
-.
0.7
-
0.6
-
H-
0
I-A
Ct
0
0.5
-
wi
0.4
-
0.3
-
0.2
-
0.1
-
'--~-
~--
tu
- -- * - -- - *
I-a
B
A 4..2
0
I
I
I
0.2
I
0.4
0
I
I
I
0.6
Liquidated Damages Factor 0
Effort Level Ej
0.8
I
0
t'J
0
0
0
0
0
0
4p
0
Profit Sharing Contracts
High Level of Information
450
-
400
-
350 -
300
Li.
-
'-a
0
250
200
--
0-
w
160100
-
a
.50 -
M
B
0
a
I
0
0.2
0.4
0
0.6
Profit Sharing Factor p
Effort Level Ej
0.8
1
0
-104profit sharing contract,
0.70
0 equal to 0.04,
and at
for the stipulated sum contract.
same points,
the
expected
0.10, 0.24 and
Obviously, at exactly the
net present
value
increases due to the additional effort put on
for
the project
the job,
as shown
in appendices # 4.4-5 and # 4.4-6.
For a given level of effort,
the profit
sharing
Please see exhibits
and
#
the
included
liquidated
4.4-3
for the owner's profit.
the owner's
and
#
damages
This happens because
level -
factors rise.
4.4-4, which give the curves
in the bids are increased with
whereas the effort
profit falls when
and the
the
the risk premiums
rising incentives.
expected NPV as a
result -
The best profit sharing contract is got at p equal
to 0.24,
remain constant.
effort
level E5 = FF 410,000.
of FF 2,680,451
This leads to a total expected NPV
and a profit to the owner of FF
total risk premium included in the
owner is
bid is FF 273,424.
in exhibit #
premium is computed as
disaggragated
in
five
1,790,143.
4.4-5
.
components,
The
The risk
The payoff to the
the
expected net
present value, the fixed fee to the contractor, necessary to meet
the contractor's no risk profit target,
effort,
the cost of contractor's
the franchise fee the contractor pays to win the auction
(negative in
this
case)
OP = NPV -
and the unadjusted risk
Fi -
Ej -
Ru +
premium.
Fr
OP = NPV - P
OP is the owner's profit and P is the payment to the contractor;
Fi
is
the fixed fee,
Ej
is
the cost
of
effort,
unadjusted risk premium and Fr is the franchise fee.
Ru
is the
4p
0
t
4p
a
WS
W
0
S
0
Stipulated Sum Contracts
High Level of Information
2.5
2.131.692
2
1.5
I
CA
0
0
0).5
1.4
C11
a.
0
Tn
WA
-1
-1.5
-2
I
0
I
0.2
I
.1
0.4
I
I
0.6
Liquidated Damages Factor 6
0 Owner's Prof i t
0.8
1
0
U,
40
0
a
a
4p
l
op
40
Profit Sharing Contracts
High Level of Information
2
1,790,143
1.5
1
-N
Li..
IL
0.5
-
0
5..
0
I-i
0
(t
0
0'~
I...
U,
--0.5
3
0
|
|
|
||
|N
0.6
0.8
- 1
-1.5
-2
0
0.4
0.2
o
Profit Sharing Factor p
Owner's Profit
1
-107-
Exhibit 4.4-5
Profit Sharing Contracts - Construction Costs and Revenues uncertain
Evaluation of Contracts - High Level of Information
----------------------------------------------------------------Contract Form:
P =
Effort Level:
j
=
0.24 NPVc.d.r - F
5
Payoffs to Contractor
E(NPV/Ej)
Franchise Fee F
2,680.451
(247,000)
Contractor Payoff P
Less: Effort
890,308
410,000
Contractor Profit
480,308
Contractor Utility
0.4011
Payoffs to Owner
E(NPV/Ej)
Less: Fixed Fee
Less: Effort
Less: Risk Premium
Plus: Franchise Fee
2,680,451
206,884
410,000
26,424
(247,000)
Owner Profit
1,790,143
Owner Utility
1,.790,143
Total Risk Premium
273.424
-108P = Fi + Ej + Ru - Fr
CP = P - Ej = Fi + Ru - Fr
CP is the contractor's profit.
Since we have also:
P = - NPV - Fr
OP = (i-p) NPV + Fr
we get
Ru = g NPV - Fi - Ej
The total risk premium is obtained by
fee to
the unadjusted
OP = NPV
R = Ru
risk
premium.
Fi - Ej - (Ru - Fr)
-
substracting the franchise
Fr
The owner is more concerned by the total risk premium than by the
unadjusted risk
premium,
because it
is the
total risk premium
that he finally will have to pay to the contractor.
If the franchise fee is positive, the contractor gives up some of
the payoffs he receives in order to win the contract.
franchise fee means that
meet
the contractor needs
his minimum utility,
in
which case
A negative
higher payoffs to
the
risk
premium is
increased by the absolute value of the franchise fee.
The best stipulated sum contract is got for 0 equal to 0.70,
an effort level equal to
expected net present
owner of
FF 429,555.
#4.4-6
,
liquidated
or FF 1,200,000.
value of FF 3,968,131
FF 2,131,692.
bid is
E6
is -0.93,
in
profit to the
included in the
as calsulated in exhibit
low despite the high
damages are negative
expected delay
and a
The total risk premium
The risk premium,
is relatively
This leads to an
this
0
value, because
case.
Actually, the
meaning the project is expected
to be
-109-
Exhibit 4.4-6
Construction Costs and Revenues uncertain
Evaluation of Stipulated Sum contracts - High level of information
Contract Form:
P =
S - d*S*A
8
=
Effort Level:
j =
6
Expected Delay:
d =
-0.93
0.70
1.893.647
Payoffs to Contractor
Stipulated Sum (Bid)
E(Liquidated damages)
Contractor Payoff P
Less:
Effort
Contractor Profit
Contractor Utility
605,000
(1,231,439)
1,836,439
1,200,000
636.439
0.4009
Payoffs to Owner
E(NPV/Ej)
Less:
Less:
Less:
Plus:
Fixed Fee
Effort
Risk Premium
Liquid. damages
3,968,131
206,884
1,200,000
(801,884)
(1,231,439)
Owner Profit
2,131,692
Owner Utility
2,131,692
Total Risk Premium
429,555
-110finished almost one semester ahead of schedule.
is obtained by
components,
cost
disaggragating the
payment to the
the expected net present value,
of effort,
The risk premium
owner in five
the fixed
the unadjusted risk premium and
fee, the
the liquidated
damages.
OP = NPV - Fi - EJ - Ru + LD
OP = NPV - P
LD are the liquidated damages; other notations are as before.
P = Fi + EJ + Ru - LD
CP = P - Ej = Fi + Ru - LD
Since we have also:
P = S - LD
OP = NPV - S + LD
we get
Thus the unadjusted risk premium can also be written as
Ru = S - Fi
The total risk
Ej.
-
premium is
equal to the
unadjusted risk premium
minus the liquidated damages.
OP = NPV
R = Ru
Fi - Ej - (Ru - LD)
-
LD
Best contracts are
determined
exposed in section 4.2.
by
following
The best stipulated sum
the procedure
contract gives
FF 341,549 more profits to the owner than the best profit sharing
contract.
case
of
scenario,
This represents a difference of 19% in profits. In the
a
high
quality
and
quantity
of
design information
the stipulated sum contract is a better
contract type
-111-
than the profit sharing contract.
show
that
the Maximum Cost
Appendices # 4.4-9 to
plus
Fee contract
is
# 4.4-12
the optimal
contract type.
The precise definition of the contract is also
stipulated sum contract with a liquidated damages
to 0.24
leads to a profit to the owner of FF
equal to 0.70
leads to 7.5%
be much
higher
defined
by
contract.
0
with
=
is
Choosing 0 =
factor 0 equal
1,984,287.
Thus 0
more profits; this difference would
other values
0.24
important: a
of
actually
0.15
0
because
the
second
the contract
best possible
or 0 = 1.00 would lead to owner's
profits respectively equal to FF 1,604,111 and FF 1,483,933.
best contract gives 33%
and 44% more profits respectively.
The
Note
also that some values of 0 leads to negative expected profits for
the owner.
can
turn
contract.
This means that a potentially very profitable project
to
The
be
unprofitable
because
possibility for losses
profit sharing contract.
of
a
poorly
designed
is even greater
for the
For y equal to 0.70, profits fall to FF
113,135 or almost 19 times less than the optimal contract.
Risk premiums play a very
the optimal contract,
big role in the
as shown
profit sharing contract,
in
#
4.4-7.
For the
the risk premium increases dramatically
with the profit sharing factor p,
stipulated sum contract.
exhibit
determination of
whereas it stays lower for the
0
w
w
4P
4P
0
0
Total Risk Premiums
High Level of Information
A
.
35A
/
3.
7.
/
/
/
.7
-x
2.5
U1
.
7
0
7
7
9C.8
7
1.5
x
0
. 4.J
I
7
7-
-7
U. 5
a
0.2
0
xK
Prof it
Sharing
0.4
t and u Factors
v
0.6
0.8
Stipulated Sum
I
-113-
Let us analyze the risk structure in
consider
total
premiums.
premium,
risk
premiums
more
rather
details.
than
We now
unadjusted
risk
The risk premium is composed of the construction risk
the general
development risk premium
and the revenues
risk premium.
For the stipulated sum contract, the construction risk premium is
a constant,
since
the contractor bears
all construction risks;
For the high level of information scenario, this premium is equal
to
FF
37,200.
borne by
This
figure represents all
the contractor.
construction risks
For the profit
sharing contract, the
construction risk premium is equal to this
maximum premium times
the square of the profit sharing
Please
refer to
#
appendix
factor p (to
4.4-B for a
the first order).
demonstration of this
result and for precise expressions of risks premiums. Thus, for p
=
0,
the construction risk premium is 0, and for p = 0.50, this
risk premium equals FF 9,300.
for the profit
sharing
The premium will always be smaller
contract
than
for
the
stipulated sum
contract.
The revenues risk premium is zero for the stipulated sum contract
and rises rapidly with p for the profit
this premium is
easily compute
zero
the
for the stipulated
general
stipulated sum contract.
premium minus
development
It is simply
values ot
This
0.
sum
contract,
risk
premium
equal to
the construction risk premium.
general development risk premium is
37,200).
sharing contract.
risk premium
FF 392,355
we can
for the
the total risk
For 0
= 0.70 the
(FF 429,555 - FF
can be computed similarly
What is the value of the
Since
for all
general development risk
-114-
premium
for
the
profit
sharing
analysis done in the part
are fixed than
for
4.3
An Academic Case,
the
numerically
stipulated
contract?
According
to the
, Construction Costs and Revenues
this premium is
sum
contract.
equal because the liquidated
exactly the same
The
premiums
damages
lump
are
sum has
been set to the difference of NPVs from one delay scenario to the
next.
Thus the liquidated damages are exactly equal to the share
of profits/losses
the contractor
gets
with
the profit sharing
contract.
Note also that this identity of risk premiums is true
for
risk
total
premiums,
not
for
unadjusted
risk premiums.
Anyway, we are concerned with these total risk premiums.
Thus we
know
the construction
development risk premiums.
premium
is
zero
revenues risk
for the
risk
and
We also know that the
stipulated
premium for the profit
easy to compute.
premiums
It is simply
sum
the general
revenues risk
contract.
sharing
equal to the
Now, the
contract
is very
total risk premium
minus the construction risk premium minus the general development
risk premium.
1,539,849
For
p =
0.70,
the revenues risk premium
is FF
(FF 1,950,432 - FF 18,228 - FF 392,355). The following
table gives a summary of the previous results.
Table 4.4
Total Risk Premiums
Type of risk
1-Construction
risk
Stipulated Sum
constant CRP
FF 37,200
Profit Sharing
fraction of CRP
p^2 * CRP
-1152-General
Total premium - CRP
development
same as for SS
GDRP
GDRP
risk
3-Revenues
zero premium
risk
Total premium
FF 0
- u^2*CRP - GDRP
The striking fact is the rapidly rising revenues risk premium for
the profit sharing contract.
The next section examines the
the
ESIEE
project,
available is
but
lower.
The
which
the
study will
level
similar to
of information
emphasize the differences
just studied.
with the case we have
4.5
for
case of a project
Average Level of
Design
Information
-
Evaluation of
Contracts:
A project equivalent to the ESIEE project, but for which the
level of design information
available would be
only average, is
described by the results presented in exhibits # 4.5-1 to # 4.5-3
and appendices # 4.5-1 to # 4.5-16 .
The optimal contract is not
the stipulated sum contract anymore, but the commonly used profit
sharing
contract.
contract is
Interestingly
widely used in
enough,
the USA,
the
profit
sharing
whereas the stipulated sum
contract is more used in France.
For the scenario considered in this section, the best profit
sharing contract is defined by a profit sharing factor p equal to
0.14, an effort level ES or FF 410,000.
total expected
profit
to
the owner of
This contract leads to a
FF 1,427,605
out of an
-116-
expected NPV
of FF 2,172,954.
The risk premium is
The best stipulated sum contract
0.14.
is
FF 128,465.
also defined by 0
equal to
This contract leads to an effort level of E5 or FF 410,000
and an expected NPV of FF 2,172,954.
The owner's
profit is now
FF 1,012.991.
Therefore
the
contract with p =
the Maximum
optimal
0.14.
contract
contract.
Please
details).
This
the
profit
sharing
(More exactly, the optimal contract is
Cost plus Fee contract,
owner of FF 1.498,356.
is
which gives
profits to the
or FF 70,751 more than the profit sharing
see
profit
appendices
#
4.5-13
#
to
sharing contract gives
4.5-16 for
FF 414.614 more
profits to the owner than the best stipulated sum contract , or a
surplus of
about 41%.
sharing factor
is
The
determination of
essential,
the
right profit
because the profit
to
the owner
decreases dramatically when p diverges from the optimal
0.14,
as shown in exhibit # 4.5-1.
585,432
and
(1,471,678).
at
0.12
the
owner
At 0.13, profits are only FF
can
expect
a
loss
of
FF
When p increases, profits decrease from the optimal
value to FF 103,125
at p =
0.45
For the stipulated sum contract,
similar as
value of
shown in
exhibit
#
and FF (233,523)
the pattern of
4.5-2
.
at p = 0.50.
profits is very
However, the owner can
expect positive profits for a value of 0 between 0.13 and 0.65, a
somewhat larger
contract.
range of
values
than
The reason is simply that the
less rapidly in the case of
for
the
profit sharing
risk premium increases
the stipulated sum
contract than in
A
W
W
0
l
=
op
S
40
Profit Sharing Contracts
Average Level of Information
2
1 .427,605
m
I
0
U-
0
C
0
-1
a-
I
I-j
Lfl
N
I-
0
-4
-5
0
0.2
0.4
0.6
Profit Sharing Factor p
o Owner's Profit
0.0
1
W
0
0
0
W
op
0
W
Stipulated Sum Contracts
Average Level of Information
1.2
1,012,991
1
0.8
0.4
-
-N
0.*2
U.
F.
0
-
14-
0)
5..
0
_
-N
-N
-0.4
a.0
__N
-0.2
H-A
OD
I
-0.6
LJ1
-0.8
t~3
-1
-1.2
-1.4
-
-1.6
-1.8
-2
0
0.2
0.4
0.6
Liquidated Damages Factor 0
o Owner's Profit
0.8
1
a
w
w
a
a
w
0
0
w
Total Risk Premiums
Average Level of Information
-I
/
/
5-
/
/
LL
/
4
0)
M)
/
C
a.
A
7'
x
//
//
C-
V
I-.
i.0
-3N
24-I
0
(Ia
~
'7
0
~~q4~V
+T,
g
-
I
0.2
0
x
Profit Sharing
I
I
I
I
0.4
0.6
0.8
0 and p Factors
V
Stipulated Sum
I
-120-
the
case of the profit
the
contractor
sharing contract.
bears
no
revenue
This happens because
risk
in
stipulated sum contract. Please see exhibit
Why
is
stipulated
the
profit
sharing
sum contract,
despite
the
better
this
information.
case
Now,
of
average quality and quantity
the contractor has to
the profit
the value of Ii.
are FF 0
the
and FF 497,500
stipulated
sum
are very
of these
This share depends on
p and 0 are zero,
the risks premiums
respectively for the profit sharing and
contracts.
Because
difference and despite the fact that
more quickly -
the
bear all construction
sharing contract.
Thus when
than
of design
risks with the stipulated sum contract and only a share
risks with
the
previous considerations?
The main reason is the fact that the construction risks
large in
of
# 4.5-3.
contract
the
case
in percentage -
of
this
the risk
big initial
premium is rising
for the profit sharing contract,
the risk premium is much smaller at p and 0 equal to 0.14 for the
-
profit sharing contract
sum
contract
project,
the
-
-.
FF 543,079
better
The more
the profit
contractor does not have to
- than for the stipulated
FF 128,465
uncertainty
sharing contract,
for the
because the
bear all construction risks
in this
case.
Of course,
smaller expected
the
lower level of
NPV for
return to the owner.
the
design
project
and
information means a
a
smaller expected
The best contract leads to a project NPV of
FF 2,172,954 and an owner's profit of FF 1,427,605 in the average
level of
3,968,131
information scenario,
and FF 2,131,692
whereas
these
figures
were FF
respectively for the other scenario.
-121-
the probabilities of early or on time completion are less;
First,
and
second,
risk
the
accept the job are higher
the
429,555
and FF
because uncertainty is
the best
For
project.
128,465
contractor to
demanded by the
premiums
for
information respectively.
risk
contracts,
the
high
and
now higher for
premiums
average
are FF
levels of
As a percentage of total NPV
for the
project, these risk premiums represent 10.83% and 6.03%. The risk
premium
seems higher in the high
only because the best contract is
of 1 and p.
value
For
0 =
0.14,
for the profit
level of
information scenario
not defined by
the same value
which corresponds to the optimal p
sharing contract,
the risk premium
is FF
64,000 or only 3% of the FF 2,125,613 expected NPV.
The scenario studied in this section allowed us to
profit sharing contract is a better contract
sum
contract
when
the
quality
information is only average.
and
the
show that the
than the stipulated
quantity
The ESIEE project
of
design
provided a very
concrete example for this assertion.
4.6 Information Level & the Optimal Contract Type:
This thesis has demonstrated the critical role played by the
amount
of
contract
design
information available for
definition
process.
a
More precisely,
project
in the
if construction
costs are uncertain, then a well designed Stipulated Sum Contract
will
be
optimal
information is
when
high,
the
quantity
and
quality
of
whereas a Profit Sharing Contract
optimal when this information is poor or average.
design
will be
-122-
creates enough
optimal,
when it
to
incentives
the contractor by giving
him the
is
type
a contract
shown that
We have
The optimal contract will thus be
right amount of risk to bear.
designed so as to lead to the minimum risk premium
amount
attached
Since the
incentives.
of
to
the three types of
premium that the contractor will
sum
of
the
for the right
risks premiums
risk determines the
consider to make
final risk
his bid, this
thesis has demonstrated the following assertions.
For
a given level of
level of design information,
revenues uncertainty,
the higher the
the higher the probability that the
risk premium will be smaller for the Stipulated Sum contract than
for the Profit Sharing Contract.
For a given level
of
design
information,
the
higher the
the higher the probability that
the risk
premium will be smaller for the Profit Sharing Contract
than for
certainty of revenues,
the Stipulated Sum Contract.
4.7 Contract Parameter Determination:
In
this section,
real contracts, as
we shall evaluate the
they were determined for the ESIEE project.
the Chamber of Commerce was
The contract used by
a Stipulated Sum
contract, in which
Liquidated Damages were determined as follows:
-
from the first to the 6th day: FF 500
-
from the 7th to the 15th
the contract price,
day:
FF 1,000 plus 1/10,000 of
-123-
-
FF 1,500 plus 1/3,000 of the contract
from the 16th day:
price.
and the bid will
Since Base construction costs are FF 34,100,000
we can assume a total contract price of
be less than FF 700,000,
about
FF
34,800,000.
Thus the liquidated damages will
be the
encompassed
in the
various
following for the
delay
scenarios
study:
Table 4.7-1
ESIEE Contract
Incremental Liquidated Damages
Delay Scenario
One semester
FF
2,200,340
Two semester
FF
2,335,500
On time
FF
0
FF (1,167,750)
minus one semester
completes the
When the contractor
schedule, the
of
ahead
job
bonuses are only half of what would have been the penalties for a
delay
of
length.
the same
by
characterized
information,
we
a
have
contract was modelled
For the
high
quality
seen
that
by a
ESIEE
and
the
quantity
optimal
and a liquidated damages factor 0 equal to 0.70.
bonuses
of
This definition
and penalties
Table 4.7-2
Designed Optimal Contract
One semester
Incremental Liquidated Damages
FF
1,325,553
sum
FF 1,893,647
for the designed contract:
Delay Scenario
design
stipulated
liquidated lump sum of
of liquidated damages gives the following
which is
project,
-124-
Two semester
FF
1,325,553
On time
FF
0
FF (1,325,553)
minus one semester
The real
ESIEE contract
gives too much
thus
down-side and too little
on
the up-side.
given definition
of
damages factor 0
equal to 116%
incentives on the
On the downside, the
the penalties corresponds
to
a liquidated
much more than the
optimal 70%.
On the upside, the given definition of the bonuses corresponds to
a liquidated damages factor 0 equal to
62%,
a bit less than the
optimal 70%.
The first question to address is whether the contractor will
still choose the highest level
the ESIEE contract.
the second
of effort with
the definition of
Knowing the effort level of the contractor,
question to address is
how much
more the contractor
will bid for the project.
A higher bid will result, because the
deviation from the optimal
contract means a
included
in
the
contract.
Answers
to
higher risk premium
both
questions
are
presented in exhibit #4.7-1 and #4.7-2.
Because the incentives to complete the job ahead of schedule
the contractor chooses effort
are not enough anymore,
Indeed,
E6
level E5.
contractor's utility is higher choosing E5 than choosing
Thus the expected net present value is FF 2,680,451
by 0.08.
instead of
FF
3,968,131
for
the optimal
contract.
The risk
premium reaches a value of FF 318,116.
Total expected
contract are thus
than the higher
profits to
FF
1,198,490.
profits got with
the owner
with
These profits
the designed
the
real ESlEE
are much lower
contracts, since
-125-
Exhibit 4.7-1
The ESIEE Contract
Stipulated Sum Contract - With partial Liquidated Damages
Contract Form:
P =
S - LD
P is the payment to the contractor
S is the Stipulated Sum resulting from the bidding process
LD are the liquidated damages
LD are calculated as follows:
LD
Delay
2 semesters
2 *
0- * A
61 semester
On time
- 8+
-1 semester
A is a lump sum, d is the delay
* A
0
P =
A =
S - d*8*A
1,893,647
* A
and 0+
and 0-
0.62
=
=
1.16
Contractor's Utility Function
U = 1.016492 - 1.016492 exp[-0.00000241714*Y]
Y is the net profit; Y = S - LD - El
Minimum Fee to Hire Contractor is Umin =
.4
or a net profit of FF
206,884
Contractor's Action Choice
Variations in Construction Costs
Probability
0.25
0.50
0.25
Delta ( CC )
250,000
0
(250,000)
Contractor Utility Computations
Minimum Bid
Effort Level
935,000
El
935,000
E2
935.000
E3
935,000
E4
935.000
E5
935,000
E6
j =
Contractor chooses level of effort Ej,
Minimum Utility for Contractor is .4
Thus Minimum Bid over base construction costs is
Utility
-4510.3218
-1096.2897
-202.0343
-82.6646
0.4014
0.3291
5
935,000
Base construction costs are FF 34,100,000
d =
Expected completion delay is d,
Total Value of the project to the Owner is
E(NPV,Ej/Ej) - P =
-0.249
1,198,490
-126-
Exhibit 4.7-2
Evaluation of the ESIEE Stipulated Sum contract
Contract Form:
P =
0+ =
3- =
S - d*B*A
Effort Level:
I
=
5
Expected Delay:
d =
-0.25
0.62
1.16
1,893,647
Payoffs to Contractor
Stipulated Sum (Bid)
E(Liquidated damages)
935,000
(546,961)
Contractor Payoff P
Less: Effort
1,481,961
410.000
Contractor Profit
1,071,961
Contractor Utility
0.4014
Payoffs to Owner
E(NPV/Ej)
Less:
Less:
Less:
Plus:
Fixed Fee
Effort
Risk Premium
Liquid. damages
2,680,451
206,884
410,000
318,116
(546.961)
Owner Profit
1,198,490
Owner Utility
1,198.490
Total Risk Premium
865.077
-127-
the highest profits are FF 2,131,692.
as FF (933,202)
The difference is as high
or 44% less profits. The optimal contract brings
almost twice as much profits to the owner as the ESIEE contract.
The
ESlEE contract penalizes
reward enough early completion.
the thesis 'Incentives Design
may
well
not be a
delays too much and
does not
As we shall see in the
and the Legal
part of
Framework',
misunderstanding of the risk
reasons
allocation and
incentives design issues.
The
profit
other possible contract for the ESIEE
sharing contract
contract
is
modelled
maximum cost
equal
used
by a
by
This
in fact a
with a profit sharing
factor V
This contract would be very close to the optimal
profit sharing contract for which the profit sharing
0.24.
was the
government.
profit sharing contract,
plus fee contract,
to 0.25.
the French
project
factor p is
With this contract the owner can expect a profit of about
FF 1,790,000.
This real contract would thus be a better contract
for the ESIEE project than the ESIEE contract.
600,000
or
50%
more
profits
to
the
owner.
It would bring FF
This contract,
however, is still not optimal, as seen before, since it generates
FF 342,000 or 16% less profits than the optimal contract.
This section clealry shows that it
choose the right type of contract,
the
incentives included in
only to
but merely to design properly
the contract.
the contract parameters is thus
The determination of
an essential step in
of a good construction building contract.
one we have just studied,
is critical not
the design
In some cases like the
it can be more profitable to the owner
-128-
to choose the second best type of contract and
in an optimal
fail
way than to choose the optimal contract type but to
in the design of the contract incentives.
Our initial question was:
in the construction building
has given many
hints to
contract
and evaluate
steps.
all
design incentives
type
How to design an optimal contract
industry?
perform
this
This part of the thesis
task
incentives
well.
are the
Choose the
most
important
We have also seen that this was not an easy task anyway,
the more because the real
complexity
than
the
simple
world is characterized
model
used
in
by far more
this
study
can
encompass.
4.8 The trade-off between optimal and legal
incentives:
In the previous section of the thesis, we saw that the ESIEE
contract,
contract
though
to
not
a
the owner.
'bad'
contract,
was
Indeed the expected
project were far from the maximum possible
not
profits
an optimal
from the
profits. Although the
ESIEE contract was of the optimal type, a stipulated sum contract
in
this
case
information,
to
of
very
high
quality
and
quantity
of design
the contract did not include the optimal incentives
the contractor.
More
specifically,
little incentives on the up-side
the contract gives too
and too much
on the down-side.
Bonuses and penalties were defined by an equivalent 0 of 0.62 and
1.16 respectively, instead of the 0.70 optimal value.
-129-
The
1.16
0
figure
penalties of 1/3000
corresponds
approximatively
of the total contract value;
figure to daily bonuses of
1/6000
the legal
chosen by the owner when designing the
CCAG
('Cahier
stipulates
des
Clauses
the following
And the 0.62 0
of this contract value. These
penalties and bonuses are actually
The
to daily
limits
that can be
contract. More precisely,
Administratives
rules,
among
others,
Generales')
for
the delay
penalties and the early completion bonuses:
(1)
In
case
of
completion
penalty of 1/3000
otherwise
delays
the value of the contract is
stipulated
by
the
CCAP
Administratives Particulinres').
the
contractor
for public
as soon as
works, a delay
enforced, if not
('Cahier
des
Clauses
These penalties are incurred by
delays are recorded and
without any
compulsory pre-notification by the owner.
(2)
In the exceptional case when completion
and the works are not annoying
for the
collectivity,
penalties can be reduced by a particular
such
a case,
the
owner's
decision
justified in the market transaction
date is unimportant
clause of the
should
be
the delay
CCAP. In
documented and
report.
(3) The 1/3000 rate can be considered as an average minimum rate,
which can be raised if
particularly
urgent:
particularly
annoying
beginning of operations is
either
for
the
because
works
collectivity;
considered as
execution
or
because
is
a
completion delay implies losses of revenues for the project.
(4)
The total penalties for
limited upward.
a particular project
should not be
-130-
(5)
a completion
The agreement on
at
interests
contract
the
hand,
bonuses for early completion dates.
bonuses in the
include
two
situations:
usually taking various
date
should
normally not include
contract for early
when early
it is possible to
However,
completion
completion in either
diminish an
to
allows
excessive annoyance to the collectivity and when early completion
allows to get more revenues from the project.
(6)
they are usually
When bonuses are included in the contract,
set to
half
the delay
of
penalties.
Any
greater incentives
should be documented and justified.
The previous rules clearly show the difficulties in defining
an
optimal contract.
In
these rules naturally tend
little bonuses.
some
to
cases,
give
like the ESIEE project,
too much
penalties and too
This happens for two principal reasons: First, a
1/3000
ratio for a delay penalty is already a very high penalty,
though
considered
Second,
either
as
a minimum one by
induce the
not enough,
although the 1/3000
high.
or
too high
the 1/6000 ratio for bonuses was
ratio for penalties was already
The owner had the possibility to
the ratio for penalties up to 1/2315
bonus ratio,
penalties will
owner to choose too low bonuses
In the ESIEE case,
ratio of
French regulation.
the limitation of bonuses to half of the
penalties.
much too
the
raise further
in order to get the optimal
computed as 1/4630, or to choose an optimal penalty
1/4630
with
an
even
lower
bonus
ratio
of 1/9260.
Finally, any solution chosen by the owner was not optimal.
-131-
Obviously the fact
the bonus
that
the penalty
and
ratio
ratio are set to different values is not a drawback to the owner.
On the contrary,
these
ratios,
than when
if the owner had the complete liberty to choose
he could certainly get a
only
one common
ratio is
ratio is indeed an additional
therefore
cannot
do worse
higher
expected return
chosen. This supplementary
degree of
liberty to the
under this new
owner. He
assumption.
What is
annoying to him in the case of the French regulation, however, is
the fact that
these two ratios
that one should
be
half
of
are not independent,
the other.
clearly an example for which the
The
even more,
ESIEE project is
legislation does not provide the
optimal framework.
In any case,
strong
the
enough,
(sucessfully)
rigidity
hopefully,
of
to
French
preclude
legislation
the
owner
is not
from
trying to design and implement an optimal contract
in the construction building
industry.
The fact that the Paris
Chamber of Commerce chose the recommended figures
of
1/3000 and
1/6000
is
clearly an
for the
penalty
and
indication (although not 100%
the
bonus
ratios
certain) that no special study was
undertaken to specifying the optimal design for the
relevant
question,
Commerce
have
A
is what actions should the Chamber of
then,
taken in
contract.
order to
second question relates to
current French legislation.
sign
an
the possibility of
optimal contract. A
evolutions in the
-132-
4.9 Toward Optimal
The
Paris
Incentives Implementation:
of
Chamber
Commerce
should
used
have
the
possibilities for deviating from the generally accepted rules set
by the french regulation.
are
not compulsory,
the 1/3000 and 1/6000 ratios
Indeed,
although any deviation
complicates the contracting process.
had made a special study to
incentives,
it
been
optimal
a big
job
from
legislation argument
an
to
report and
this respect.
becomes weak to explain
the deviation
contract.
optimal
contract and
In
justify optimal ratios for the ESIEE project.
the
these figures
If the Chamber of Commerce
determine the
would not have
from
Specifying
best
the
contract
automatically gives the arguments to justify its design.
One could argue that the French administration
easily convinced
recommended
avoid
of
designs.
problems
in
the
But
would not be
optimality
of
large
the case
is
sufficiently simple to
most cases.
ratios are likely to be unoptimal
deviations from
However, since the recommended
values in almost
all cases, a
There is no
change in the legislation would be helpful.
justify deviations from legal ratios at all
times.
use to
Better would
be a system with the following characteristics:
(i)
Allow for the complete
independence
of
the bonus
and the
penalty ratios.
(ii)
ratio,
with a
for the bonus ratio,
with a
Allow for a range of values for the penalty
minimum set much lower than 1/3000.
(iii)
Allow for a range of
values
maximum set much higher than 1/6000.
-133-
(iv)
Require justifications only
when ratios are set
to values
outside of these allowed ranges.
This system, or a similar one, would give a higher
the owner and the contractor for maximizing
gotten from a construction project.
flexibility to
the investment value
-134-
5 Conclusion
'In Search of Optimal Contracts in the Construction Building
Industry'
was an
attempt
process is not to
to
prove
be neglected for
that
the
contract design
the project to
be a success
and the owner's investment to be valuable.
Some
factors
studied,
among
influencing
which
the
the
optimal
quantity
and
design
have
quality
of
information for the project appeared to be critical.
influenced by such
analyst
moral
is
information.
achieved when
problems
facing
the allocation
risks which
contract specifications is optimal.
incentives to
the risk bearing
contract so as
construction
of
sum contract
The role of the financial
to design the construction
hazard
design
Indeed the
choice of a profit sharing contract or a stipulated
was
been
to solve
projects.
results
This is
from the
Hence, the contract creates
contractor at the least
cost to
the owner.
The
complexity
of
the
real
world
is
even
much
more
challenging for the contract designer, who will have to deal with
a
very
large
number
successful designer will
of
often
contradictory
solve these issues,
attention to some basic principles.
issues.
The
while still paying
-135-
6 Appendices
0
0
0
0
W
W
W
W
0
Cash Flow Projections
Complete one semester ahead of schedule - Real Construction Costs = Estimated Costs.
Year
0
I
2
Gross Operating Income
Less: Operating Expenses
Operations Loss/Gain
Net Operating Income
3.478.261
3.478,261
Plus: Sales Proceeds
Land Purchase
Design fees
Base Const. Costs
(6.500,000)
(3,100,000)
Before Tax Cash Flow
(9,600,000)
3
4
18.000.000
(10.000.000)
0
8.000,000
18.000.000
(10.000.000)
0
8.000,000
0'
(16,333,333)
(14,666,667)
0
(16,333,333)
(11, 188,406)
8.000. 000
8.000.000
'-A
L~)
Less: Interest Expenses
Less: Depreciation
Taxable Income
Less: Taxes 028%
After Tax Cash Flow
0
0
3.478.261
(973.913)
(9.600.000)
(16,333,333)
(12.162,319)
0
I
2
19,857,754
15, 751. 088
(DJ
(4.559.013)
(2,255.556)
1,185.432
(331,921)
(4.495.739)
(2.255.556)
1.248.705
(349.637)
7,668,079
7,650,363
Loan Cash Flows
Year
Funds received
Interest Payments
Loan's principal reduction
Total cash flows
19.857,754
15,751,088
3
4
(4,559,013)
(4,495,739)
(527.279)
(5,086,292)
(5,086,292)
(590.553)
0
a
0
Cash Flow Projections
One semester delay - Real Construction Costs = Estimated Costs.
Year
0
I
2
Gross Operating Income
Less: Operating Expenses
Operations Loss/Gain
Net Operating Income
3
0
0
Plus: Sales Proceeds
Land Purchase
Design fees
Base Const. Costs
(6,500,000)
(3,100,000)
Before Tax Cash Flow
(9,600,000)
4
18.000,000
(10,000.000)
(4,000,000)
4,000.000
18.000.000
(10.000.000)
0
8.000.000
(16, 333, 333)
(14,666,667)
0
(16.333,333)
(14,666,667)
4,000,000
8.000.000
(4,559,013)
(2,255.556)
(2,814,568)
788,079
(4,495,739)
(2,255,556)
4,788,079
7,650,363
>1
(AJ
Less: Interest Expenses
Less: Depreciation
Taxable Income
Less: Taxes 028%
After Tax Cash Flow
0
0
0
0
(9,600,000)
(16,333,333)
(14,666,667)
0
1
2
19,857.754
15,751,088
1,248,705
(349.637)
Loan Cash Flows
Year
Funds received
Interest Payments
Loan's principal reduction
Total cash flows
19,857.754
15,751,088
3
(4,559.013)
(527,279)
(5,086,292)
4
(4,495,739)
(590,553)
(5.086,292)
W
VS
V
W
Ll
W
SS
0
0
Cash Flow Projections
Two semester delay - Real Construction Costs = Estimated Costs.
Year
Gross Operating Income
Less: Operating Expenses
Operations Loss/Gain
Net Operating Income
0
0
Plus: Sales Proceeds
Land Purchase
Design fees
Base Const. Costs
(6.500,000)
(3.100.000)
Before Tax Cash Flow
(9,600.000)
4
3
2
1
0
18,000,OC 0
(10.000. 0C0)
(8.000.0C0)
0
(16.333.333)
(14,666,667)
0
(16,333,333)
(14,666,667)
0
18.000.000
(10.000.000)
0
8.000.000
8.000.000
1-
W
Less: Interest Expenses
Less: Depreciation
Taxable Income
Less: Taxes 028%
After Tax Cash Flow
0
0
0
0
(9.600,000)
(16.333,333)
(14,666,667)
0
I
2
(4.559,013)
(4.495.739)
(2.255.556)
(2.255.556)
(6.814.568)
1.908.079
1.248.705
(349.637)
1,908.079
7.650.363
Loan Cash Flows
Year
Funds received
Interest Payments
Loan's principal reduction
Total cash flows
19.857,754
19.857,754
3
4
15,751.088
15,751.088
(4,559,013)
(527.279)
(5,086,292)
(4.495,739)
(590.553)
(5.086.292)
W
-139-
6.2 Appendix # 3.10 - The Contract Type:
Cost plus Fee Contract:
For the Cost plus Fee contract,
the contractor receives the
following profits Yi:
Yi/Ej = F - Ej
F is
the Fee to
the contractor.,
EJ
is
the
effort
spent, or
overhead expenses.
For each level of effort, a complete system of event is described
by the unique fee F.
Ej is minimum.
Obviously,
the higher utility is got when
The optimal course of action
for the contractor
is to spend the ninimum level of effort.
Stipulated Sum Contract:
For the Stipulated Sum Contract, the contractor receives the
following profits Yi:
Yi/Ej = Yc,d/Ei = S - 0*d*A - SCC - Ej
S is
the Stipulated
factor,
A
is
Sum or
the
bid,
liquidated
0 is
damages
the
liquidated damages
lump
sum,
SCC
is the
variation of construction costs.
For each
level of
described by
effort
Ej,
a
complete system of
the four possible delay scenarios d
possible construction costs scenarios c.
(12)
events
and
Thus there
events is
the three
are twelve
possible events from the contractor's point of view.
are
mutually
exclusive
and
independent
These
according
to
previous hypotheses.
A particular
twelve
event is
possible
described by
couples.
a
{c;d)
among the
in the case
of a high
couple
For example,
level of information for the ESIEE project,
the possible couples
-140-
are
the
following:
1250,000;-1),
f250.000:2),
{0;2},
{0;1),
(250.000:1),
{0;0),
{0;-1).
1250,000;0),
((250,000)02),
{(250,000):1), {(250,000);0} and ((250,000);-1}.
Because events are independent, the probability that a particular
couple
of
events
probabilities that
occurs
is
the delay
simply
the
scenario
d
product
occurs
and
of
the
that the
construction cost scenario c occurs.
P({c:d))
= P(c) * P(d)
For a given level of effort j:
P(c,d)/Ej = Qcj
For instance,
Pdj
*
the probability that
the project be
construction costs lower by FF 250,000
on time with
in the case of an average
level of information and an effort level E4 is 0.376*0.25 = 0.094
or 9.4% chance of realization.
When determining the optimal effort
not
take
the Stipulated
constant determined
contract,
by
Sum
level,
into
the bid.
the
account,
Thus,
the contractor will choose
contractor will
because
it
is a
for the stipulated sum
the effort
level Ej which
maximizes the following expression:
Max
E
j
c,d
Uc(-O*d*A -9CC -EJ) * Pd, j*Qc,j
Maximum Cost plus Fee Contract:
For the
Maximum
Cost
plus
Fee
Contract,
receives the following profits Yi:
Yi/Ej = Yc,d/Ej = p*E('NPVc,d/Ej) - F - Ej
This can be written as:
Ycd/Ej = P*(NPVd/Ej - 9CC) - F - Ej
the contractor
-141-
p
is
the profit
sharing factor.
'NPVcd
is
the project's NPV
conditional on delay scenario d and construction cost scenario c,
F is a franchise fee.
For
each
level
of
effort,
a
described by the tour
possible
possible construction
cost
(12)
complete
system
of
delay scenarios d and
scenarios c.
events is
the three
Thus there are twelve
possible events from the contractor's point of view.
events
are
mutually
exclusive
and
independent
These
according
to
previous hypotheses.
A
particular
event is
twelve possible
described by
a couple
{c;dl
among the
couples, like for the stipulated sum contract.
With respect to probabilities of events, we have the same results
and properties than for the stipulated sum contract.
When
determining the optimal effort
level,
the contractor will
not take the franchise fee into account, because it is a constant
determined
contract,
by
the bid.
Thus,
the contractor will
for the maximum
choose the level
cost
plus fee
of effort which
maximizes the following expression:
Max
E
j
c,d
Uc(p*(NPVd/Ej - SCC) - Ej) * Pd, J*Qc,j
Profit Sharing Contract:
For the Profit Sharing Contract, the contractor receives the
following profits Yi:
Yi/Ej = Yc,d,r/Ej = p*NPVc,d,r/Ej - F - Ej
This can also be written as:
Yc.d,r/Ej = p*(NPVd.r/Ej - &CC) - F - Ej
-142-
p
is
the
profit
sharing
realized NPV conditional
factor,
NPVc,d,r
is
on construction cost
the project's
scenario c. delay
scenario d and revenue scenario r, F is the franchise fee.
For
each
level
described by
of
effort,
the four
a
complete
possible
delay
system
of
events is
scenarios
d.
the three
construction cost scenarios c and the eleven revenue scenarios r.
Thus there are one hundred
and thirty two
from the contractor's point of
view.
(132) possible events
These events are mutually
exclusive and independent according to previous hypotheses.
A particular event is
132
described by
possible triplets.
of information for
a triplet fc;d;r)
among the
For example, in the case of a high level
the
ESIEE
project,
a
possible
triplet is
{(250.000):1;7).
Because events are independent, the probability that a particular
triplet
of
events
probabilities
that
occurs
the
is
delay
simply
the
scenario
d
product
occurs,
of
the
that
the
construction cost scenario c occurs and that the revenue scenario
r occurs.
P((c;d;r))
= P(c) * P(d) * P(r)
For a given level of effort j:
P(c,d,r)/Ej = Qc, j * Pd, j * Rr, j
For
instance,
{(250,000);1;7)
the
probability
occurs,
meaning
that
the
completion
with construction costs lower by FF 250,000
FF
1,118,525
(not
including
the
previous
triplet
one semester late,
and revenue scenario
variability
in construction
costs) for an effort level E5 and average level of information is
0.25*0.192*0.1747 = 0.0083856 or a 0.84% chance of realization.
-143When
determining the
optimal
contractor will not take
it
is a
effort
for
the franchise fee into
constant determined by
sharing contract,
level
the bid.
the
job,
the
account because
Thus, for the profit
the contractor will choose the level of effort
which maximizes the following expression:
Max
E
j
c,d,r
For
each
Uc(.*(NPVd,r/Ej - &CC) - EJ) * Pd,J*Qc,j*Rr,j
type of contract,
we now know
the exact process
under which the contractor will choose his course of
action. The
last thing to do for the contractor is to evaluate and submit his
bid.
-144-
6.3 Appendix # 3.11 - Submitting a bid:
We assume that the contractor has chosen effort level Ejo
For the Cost
plus
Fee contract,
the fee F will be
set so
that:
Ucmin = 0.4 = Uc (F - Ejo)
For the Stipulated Sum
Contract,
the Stipulated Sum S will
be set so that:
Ucmin = 0.4
E
Uc(S -O*d*A - &CC - Ejo) * Pd,jo*Qc,jo
c,d
For the Maximum Cost plus Fee Contract,
the franchise fee F
will be set so that:
Ucmin = 0.4 =
Uc(p*(NPVd/Elo - &CC) - F - Ejo) * Pd,jo*Qc,jo
E
c.d
For the Profit Sharing Contract, the franchise fee F will be
set so that:
Ucmin= 0.4=
E Uc(p*(NPVd.r/Ejo -&CC) -F -Ejo) *Pd,jo*Qc,jo*Rrjo
c,d,r
The simple
fees F will
be
contract type.
fee F,
the stipulated sum S
and the franchises
the contractor
for each
These bids will depend on the contract
type and
the bids
submitted by
on the level of information available for the ESIEE project.
-145-
6.4 Appendix 4.3 - Optimal
Ontracts with no uncertainty
Appendix 4.3-1
Summary of Results - Optimal Contract Determination
No uncertainty
Contract Form:
P = a NPVd - F
Average Level of Information
Profit Sharing
Factor
pi
0.00
0.05
0.10
0.12
0.13
0.14
0.15
0.20
0.30
0.40
0.50
0.60
0.70
0.80
0.81
0.82
0.85
0.90
1.00
Effort Level
Ej
0
0
0
0
250,000
410,000
410,000
410,000
410,000
410,000
410,000
410,000
410,000
410,000
410,000
1,200,000
1,200,000
1,200.000
1,200,000
E(NPV/Ej)
(1,176.907)
(1,176,907)
(1,176,907)
(1,176,907)
1,190,151
2,172,954
2,172,954
2,172,954
2,172,954
2,172,954
2,172,954
2,172,954
2,172,954
2,172,954
2,172,954
2,638,791
2,638,791
2,638,791
2,638,791
Contractor Profit
206.884
209,155
215,309
218.771
271,720
253,214
259,943
302,591
427,886
608,182
839,477
1,112,772
1,419,068
1,748.363
1,782,093
1,399,809
1,492,972
1,655,912
2,002,791
-146-
Appendix 4.3-1
Summary of Results - Optimal Contract Determination
No uncertainty
Contract Form:
P = P NPVd - F
Average Level of Information
Profit Sharing
Factor
p
Total Risk
Owner Profit
Premium
0.00
0.05
0.10
0.12
0.13
0.14
0.15
0.20
0.30
0.40
0.50
0.60
0.70
0.80
0.81
0.82
0.85
0.90
1.00
0
2,271
8.425
11,887
64, 836
46,330
53,059
95,707
221,002
401,298
632,593
905,888
1,212,184
1,541,479
1,575,209
1,192,925
1,286,088
1,449,028
1,795,907
(1,383.791)
(1,386,062)
(1,392,216)
(1,395.678)
668,432
1,509,740
1,503,011
1,460.363
1,335.068
1,154,772
923,477
650, 182
343,886
14,591
(19,139)
38,982
(54.181)
(217,121)
(564,000)
-147-
Appendix 4.3-2
Construction Costs and Revenues are Fixed
Maximum Cost Plus Fee Contract (Profit Sharing) With Partial Liquidated Damages
Contract Form:
P =
0.14
u NPVd - F
P is the payment to contractor
NPVd is the Project Net Present Value for Delay Scenario d
u is the profit sharing factor
F is the Fee reserved by the Owner
Contractor's Utility Function
U = 1.222 - 1.222 exp[-IOE-6*YJ
Y is the net profit; Y = u NPV - Ei
Minimum Fee to Hire Contractor is Umin = .4
206,884
or a net profit of FF
Contractor's Action Choice
Contractor Utility Computations
Average Level of Information
Before Fee
E(U(NPV.E1)/E1)
E(U(NPV.E2)/E2)
E(U(NPVE3)/E3)
E(U(NPV.E4)/E4)
E(U(NPV.E5)/E5)
E(U(NPV,E6)/E6)
=
=
=
=
=
=
-0.5528
-0.5606
-0.5352
-0.4712
-0.4493
-7.1194
Contractor chooses level of effort Ej,
Minimum Utility for Contractor is .4
Thus Maximum Fee for franchise is
Total Value of the project to the Owner is
F + (1-u) E(NPV,Ej/Ej) =
After Fee
0.357555571
0.3542929495
0.3649287686
0.391833381
0.4010247681
-2.3997342861
5
(359,000)
1,509,740
-148-
Appendix 4.3-3
Stipulated Sum Contract - With partial Liquidated Damages
Contract Form:
P =
S - LD
P is the payment to the contractor
S is the Stipulated Sum resulting from the bidding process
LD are the liquidated damages
LD are calculated as follows:
LD
Delay
2 semesters
2 * 3 * A
P = S - d*0*A
I semester
13*A
0
A =
1,893,647
On time
-1 semester
- 6 * A
0.14
A is a lump sum, d is the delay and 3 =
Contractor's Utility Function
U = 1.016492 - 1.016492 exp[-0.00000241714*YJ
Y is the net profit; Y = S - LD - Ei
Minimum Fee to Hire Contractor is Umin = .4
206,884
or a net profit of FF
Contractor's Action Choice
Contractor Utility Computations
Average Level of Information
Effort Level
El
E2
E3
E4
E5
E6
Minimum Bid
668,250
668,250
668,250
668,250
668,250
668,250
j=
Contractor chooses level of effort Ej,
is
.4
Contractor
Minimum Utility for
Thus Minimum Bid over base construction costs is
Base construction costs are FF 34,100.000
d =
Expected completion delay is d,
Total Value of the project to the Owner is
E(NPV,Ej/Ej) - P =
Utility
0.3576
0.3543
0.3649
0.3918
0.4010
-2.3997
5
668,250
0.019
1,509,741
-149-
Appendix 4.3-4
Construction Costs and Revenues are Fixed
Maximum Cost Plus Fee Contract (Profit Sharing) With Partial Liquidated Damages
Contract Form:
P =
P is
NPVd
u is
F is
u NPVd - F
0.70
u
the payment to contractor
is the Project Net Present Value for Delay Scenario d
the profit sharing factor
the Fee reserved by the Owner
Contractor's Utility Function
U = 1.222 - 1.222 exp[-10E-6*YJ
Y is the net profit; Y = u NPV - El
Minimum Fee to Hire Contractor is Umin = .4
206,884
or a net profit of FF
Contractor's Action Choice
Contractor Utility Computations
Average Level of Information
Before Fee
E(U(NPV,E1)/E1)
E(U(NPV,E2)/E2)
E(U(NPV,E3)/E3)
E(U(NPV.E4)/E4)
E(U(NPV,E5)/E5)
E(U(NPV,E6)/E6)
=
=
=
=
=
=
-10.9820
-9.7743
-5.7764
-4.2783
-0.2788
-0.6478
j
Contractor chooses level of effort Ej,
.4
is
Minimum Utility for Contractor
Thus Maximum Fee for franchise is
Total Value of the project to the Owner is
F + (1-u) E(NPV,EJ/Ei) =
After Fee
-4.6825945119
-4.1089454119
-2.2099909739
-1.498449726
0.4012552931
0.225984663
5
(308.000)
343,886
-150-
Appendix 4.3-5
Construction Costs and Revenues are Fixed
Evaluation of Contracts - Average Level of Information
----------------------------------------------------------0.70 NPVd - F
P =
Contract Form:
5
Effort Level:
Payoffs to Contractor
E(NPV/Ej)
Franchise Fee F
2,172,954
(308,000)
Contractor Payoff P
Less: Effort
1,829,068
410,000
Contractor Profit
1,419,068
Contractor Utility
0.4013
Payoffs to Owner
E(NPV/Ej)
Less: Fixed Fee
Less: Effort
Less: Risk Premium
Plus: Franchise Fee
2,172,954
206,884
410,000
904,184
(308,000)
Owner Profit
343,886
Owner Utility
343,886
Total Risk Premium
1,212,184
-151-
Appendix 4.3-6
Stipulated Sum Contract - With partial Liquidated Damages
-----------------------------------------------------------------Contract Form:
P =
S - LD
P is the payment to the contractor
S is the Stipulated Sum resulting from the bidding process
LD are the liquidated damages
LD are calculated as follows:
Delay
LD
2 semesters
2 * 0 * A
1 semester
8 * A
P = S - d**A
On time
0
A =
1.893.647
-1 semester
- 0 * A
A is a lump sum. d is the delay and 1
0.70
Contractor's Utility Function
U = 1.016492 - 1.016492 exp[-0.00000241714*Y
Y is the net profit; Y = S - LD - Ei
Minimum Fee to Hire Contractor is Umin = .4
or a net profit of FF
206,884
Contractor's Action Choice
Contractor Utility Computations
Average Level of Information
Effort Level
Minimum Bid
El
E2
E3
E4
E5
E6
Utility
-4.6826
-4.1090
-2.2100
-1.4985
0.4013
0.2260
1,854,253
1.854,253
1,854.253
1,854,253
1,854.253
1,854,253
Contractor chooses level of effort Ej,
j =
Minimum Utility for Contractor is .4
Thus Minimum Bid over base construction costs is
Base construction costs are FF 34,100,000
Expected completion delay is d,
d =
5
1,854,253
0.019
Total Value of the project to the Owner is
E(NPV,EJ/Ej)
- P =
343, 886
-152-
Appendix 4.3-7
Construction Costs and Revenues are Fixed
Evaluation of Stipulated Sum contracts - Average level of information
Contract Form:
P =
S -
0 =
d*0*A
Effort Level:
1
=
5
Expected Delay:
d=
0.02
0.70
1,893.647
Payoffs to Contractor
Stipulated Sum (Bid)
E(Liquidated damages)
1,854,253
25,186
Less: Effort
1,829,067
410,000
Contractor Profit
1,419,067
Contractor Payoff P
Contractor Utility
0.4013
Payoffs to Owner
E(NPV/EJ)
Less: Fixed Fee
Less: Effort
Less: Risk Premium
Plus: Liquid. damages
2,172,954
206,884
410,000
1,237,369
25.186
Owner Profit
343,886
Owner Utility
343,886
Total Risk Premium
1,212,184
Optim al Contrac t Determination
Information
Average Level of
1.2
1.1 -4
I
0.9 L.
7;
-
0.811,
C
0
0.7 H-,
0.6-
0
L&)
OD
0.5 -
w
8~
e
U.3
0.2
0.1
0
I
-f
0
0
0.4
.2
1
I
I
0.6
0 and m Factors
Effort Level Ej
I
I
0.8
I
1
w
0
w
0
0
0
0
Optimal Contract
Average Level
of
V
w
w
w
Determination
Information
2.5
2-
1.5
-In
0
F-
z
110
a
-0.5
-1
-1.5
I
i
0
0.4
0.2
0
0 and p Factors
+
E(NPV/Ej)
(FF)
0.8
1
U,
0
a
w
0
w
a
0
0
L71
0
Optimal Contract Determination
1
Average Level of Information
8
/
/
1.4
1.3La.
La.
/
1.2-
U
U
0
a,
0..
x
/
/
/
1/
/
/
~1...
/
IQ-, 0.9
/
0.8-
oJ
H-
x
/
/
in
(A)
I-A
0.6-
0
0.5-
0.40.3
-
0).2
-
7
7
7
/
0.1
0
I2
0.2
I
0.4
0.6
0 and p Factors
Risk Premidm
I
0.8
I
1
Ln
U,
w
w
w
,
a
w
l
4P
40
410
S
Optimal Contract Determination
Average Level of
Information
2
1.91.81.7
/
1.6
IL.
La.
A
/
/
1.5
1.4
1.3
/
0
7
1.2
FA
/
/
/
Iy
/
QJ
H-
0
I'l0
I4
-
0
Q
x
/
0
4j3
LAJ
7
I-A
0.6
0.830.-
A
0.4
-
0.20.1
-
u
0
0.4
0.2
o
0 .6
0 and p Factors
Contractor's Profit
0.8
1
U,
0ON
0
0
0
0
0
ul
W
Optimal Contract Determinc tion
Av erage Level of Information
1.5
25
01,
0
.
1
0
QJ
x
1
0.5
-J.
-4
10
0
I-a
t%)
-1.15
TN
-1
-1.5
I
0
I
0.2
I
I
I
04
0.6
0.8
0 and p Factors
OContractor's Profit
x Owner's Profit
I
Lfl
-158-
Appendix 4.3-13
Summary of Results - Optimal Contract Determination
No uncertainty
Contract Form:
High Level of
Profit Sharing
Factor p
0.00
0.03
0.04
0.09
0.10
0.15
0.20
0.23
0.24
0.30
0.40
0.50
0.60
0.69
0.69
0.70
0.80
0.90
1.00
Effort Level
Ej
0
0
50,000
50,000
250,000
250,000
250,000
250,000
410,000
410,000
410,000
410,000
410,000
410,000
1,200,000
1,200,000
1,200,000
1,200,000
1,200,000
P = p NPVd - F
Information
E(NPV/Ej)
(1,479,890)
(1,479,890)
(12,314)
(12,314)
2,125,613
2,125,613
2,125,613
2,125.613
2,680,451
2,680,451
2,680,451
2,680,451
2,680,451
2,680,451
3,968,131
3,968,131
3,968,131
3,968,131
3,968,131
Contractor Profit
206,884
207,603
208.507
214,892
218.561
234,842
257,123
274,891
249,308
270,135
312,180
363,226
422,271
484,511
583,010
598,692
775,505
993,318
1,247,131
-159Appendix 4.3-13
Summary of Results - Optimal Contract Determination
No uncertainty
Contract Form:
P = u NPVd - F
High Level of Information
Profit Sharing
Factor u
0.00
0.03
0.04
0.09
0.10
0.15
0.20
0.23
0.24
0.30
0.40
0.50
0.60
0.69
0.69
0.70
0.80
0.90
1.00
Total Risk
Premium
0
719
1,624
8,008
11,617
27,958
50,239
68,007
42,424
63,251
105,297
156,342
215,387
277,627
376,127
391,808
568,621
786,434
1,040,247
Owner Profit
(1,686,774)
(1,687,494)
(270,821)
(277,206)
1,657.051
1,640,771
1,618,490
1,600,722
2,021,143
2,000,316
1,958,271
1,907,226
1,848,180
1,785,940
2,185,121
2,169,439
1,992,626
1,774,813
1,521,000
-160-
Appendix 4.3-14
Construction Costs and Revenues are Fixed
Maximum Cost Plus Fee Contract (Profit Sharing) With Partial Liquidated Damages
Contract Form:
P
P is
NPVd
u is
F is
0.70
u=
u NPVd - F
the payment to contractor
is the Project Net Present Value for Delay Scenario d
the profit sharing factor
the Fee reserved by the Owner
Contractor's Utility Function
U = 1.222 - 1.222 exp[-1OE-6*Y]
Y is the net profit; Y = u NPV - El
Minimum Fee to Hire Contractor is Umin = .4
206,884
or a net profit of FF
Contractor's Action Choice
Contractor Utility Computations
High Level of Information
After Fee
Before Fee
E(U(NPVEI)/EI)
E(U(NPVE2)/E2)
E(U(NPVE3)/E3)
E(U(NPVE4)/E4)
E(U(NPVE5)/E5)
E(U(NPVE6)/E6)
=
=
=
=
=
=
-148.00325398
-40.034437071
-11.8480826784
-3.3686897936
0.3929155677
0.4000600446
-12.9645
-2.8349
-0.1905
0.6051
0.9580
0.9587
j
Contractor chooses level of effort Ej,
Minimum Utility for Contractor is .4
Thus Maximum Fee for franchise is
Total Value of the project to the Owner is
F + (1-u) E(NPV,EJ/Ej) =
=
6
979,000
2,169,439
-161-
Appendix 4.3-15
Construction Costs and Revenues are Fixed
Evaluation of Contracts - High Level of Information
Contract Form:
P =
Effort Level:
j
=
0.70 NPVd - F
6
Payoffs to Contractor
E(NPV/Ej)
Franchise Fee F
3,968,131
979.000
Contractor Payoff P
Less: Effort
1,798,692
1,200,000
Contractor Profit
Contractor Utility
598,692
0.4001
Payoffs to Owner
E(NPV/Ej)
Less: Fixed Fee
Less: Effort
Less: Risk Premium
Plus: Franchise Fee
3,968, 131
206,884
1,200,000
1,370,808
979,000
Owner Profit
2,169,439
Owner Utility
2,169.439
Total Risk Premium
391,808
-162-
Appendix 4.3-16
Stipulated Sum Contract - With partial Liquidated Damages
-----------------------------------------------------------------Contract Form:
P =
S - LD
P is the payment to the contractor
S is the Stipulated Sum resulting from the bidding process
LD are the liquidated damages
LD are calculated as follows:
LD
Delay
2 * 0 * A
2 semesters
P = S - d*3*A
0*A
I semester
1,893,647
A =
0
On time
- 0 * A
-1 semester
0.70
A is a lump sum, d is the delay and 3 =
Contractor's Utility Function
U = 1.016492 - 1.016492 exp[-0.00000241714*YJ
Y is the net profit; Y = S - LD - Ei
Minimum Fee to Hire Contractor is Umin = .4
206.884
or a net profit of FF
Contractor's Action Choice
Contractor Utility Computations
High Level
of
Information
Effort Level
Utility
Minimum Bid
El
E2
E3
E4
E5
E6
-148.0035
-40.0345
-11.8481
-3.3687
0.3929
0.4001
567,253
567,253
567,253
567,253
567,253
567,253
Contractor chooses level of effort EJ,
j =
6
Minimum Utility for Contractor is .4
Thus Minimum Bid over base construction costs is
Base construction costs are FF 34,100,000
Expected completion Delay is d.
Total Value of the project to the Owner is
E(NPV,Ej/Ej) - P =
d =
567,253
-0.929
2,169,439
-163-
Appendix 4.3-17
Construction Costs and Revenues are Fixed
Evaluation of Stipulated Sum contracts - High level of information
Contract Form:
P =
0.70
1,893.647
S - d*O*A
Effort Level:
j
=
6
Expected Delay:
d =
-0.93
Pavoffs to Contractor
Stipulated Sum (Bid)
E(Liquidated damages)
Contractor Payoff P
Less: Effort
Contractor Profit
Contractor Utility
567,253
(1,231,439)
1,798,692
1,200,000
598,692
0.4001
Payoffs to Owner
E(NPV/Ej)
Less: Fixed Fee
Less: Effort
Less: Risk Premium
Plus: Liquid. damages
3,968,131
206.884
1,200,000
(839,631)
(1,231,439)
Owner Profit
2,169,439
Owner Utility
2,169,439
Total Risk Premium
391,808
-164-
Appendix 4.3-18
Construction Costs and Revenues are Fixed
Maximum Cost Plus Fee Contract (Profit Sharing) With Partial Liquidated Damages
Contract Form:
P =
P is
NPVd
u is
F is
u NPVd - F
0.14
u
the payment to contractor
is the Project Net Present Value for Delay Scenario d
the profit sharing factor
the Fee reserved by the Owner
Contractor's Utility Function
U = 1.222 - 1.222 exp[-10E-6*YJ
Y is the net profit; Y = u NPV - El
Minimum Fee to Hire Contractor is Umin =
.4
or a net profit of FF
206,884
Contractor's Action Choice
Contractor Utility Computations
High Level of Information
Before Fee
E(U(NPV,E1)/Ei)
E(U(NPV,E2)/E2)
E(U(NPV,E3)/E3)
E(U(NPV,E4)/E4)
E(U(NPV.E5)/E5)
E(U(NPV.E6)/E6)
=
=
=
=
=
=
After Fee
-0.6757
-0.1872
-0.1902
0.0578
-0.1308
-3.8931
Contractor chooses level of effort Ej,
j
Minimum Utility for Contractor is .4
Thus Maximum Fee for franchise is
Total Value of the project to the Owner is
F + (1-u) E(NPV,EJ/Ej) =
-0.0707948532
0.2431004015
0.2411526729
0.4004740524
0.2793070814
-2.1380529823
=
4
(183,000)
1,645,027
-165-
Appendix 4.3-19
Construction Costs and Revenues are Fixed
Evaluation of Contracts - High Level of Information
Contract Form:
P =
Effort Level:
j
=
0.14 NPVd - F
4
Payoffs to Contractor
E(NPV/Ej)
Franchise Fee F
2,125.613
(183.000)
Less: Effort
480,586
250,000
Contractor Profit
230,586
Contractor Payoff P
Contractor Utility
0.4005
Payoffs to Owner
E(NPV/Ej)
Less:
Less:
Less:
Plus:
Fixed Fee
Effort
Risk Premium
Franchise Fee
2,125,613
206.884
250.000
(159,298)
(183.000)
Owner Profit
1,645,027
Owner Utility
1,645,027
Total Risk Premium
23,702
-166-
Appendix 4.3-20
Stipulated Sum Contract - With partial Liquidated Damages
Contract Form:
P =
S - LD
P is the payment to the contractor
S is the Stipulated Sum resulting from the bidding process
LD are the liquidated damages
LD are calculated as follows:
Delay
LD
2 semesters
2 * 3 * A
I semester
6 * A
P = S - d*6*A
On time
0
A =
1,893,647
-1 semester
- 1 * A
A is a lump sum, d is the delay and 1=
0.14
Contractor's Utility Function
U = 1.016492 - 1.016492 exp[-0.00000241714*Y)
Y is the net profit; Y = S - LD - Ei
Minimum Fee to Hire Contractor is Umin = .4
or a net profit of FF
206,884
Contractor's Action Choice
Contractor Utility Computations
High Level of Information
Effort Level
El
E2
E3
E4
E5
E6
Minimum Bid
492.250
492,250
492,250
492,250
492,250
492,250
Contractor chooses level of effort Ej,
=
Minimum Utility for Contractor is .4
Thus Minimum Bid over base construction costs is
Base construction costs are FF 34,100,000
Expected completion Delay is d,
d =
Total Value of the project to the Owner is
E(NPV,EJ/Ej) - P =
Utility
-0.0708
0.2431
0.2412
0.4005
0.2793
-2.1381
4
492,250
0.044
1,645,028
-167-
Appendix 4.3-21
Construction Costs and Revenues are Fixed
Evaluation of Stipulated Sum contracts - High level of information
Contract Form:
P =
S - d*0*A
0.14
1,893,647
Effort Level:
j
=
4
Expected Delay:
d=
0.04
Payoffs to Contractor
Stipulated Sum (Bid)
E(Liquidated damages)
492,250
11,665
Less: Effort
480.585
250,000
Contractor Profit
230,585
Contractor Payoff P
Contractor Utility
0.4005
Payoffs to Owner
Less: Risk Premium
Plus: Liquid. damages
2,125,613
206,884
250,000
35,366
11,665
Owner Profit
1,645,028
Owner Utility
1, 645, 028
EtNPV/Ej)%
Less: Fixed Fee
Less: Effort
Total Risk Premium
23,701
qp
0
0
w
0
w
0
Optim IlContract Determi nation
High Level of
Information
RR
1.2-
1.1
R
H
-
100.9La.
W
FA
0.8
-
0.7
-
-
oJ
00.6 -
x
0
0.5
-
LiJ
wa
0.4
-
0.3
-
o.2
-
I-i.
r~3
t~3
to
CM
c
0.1
00
0.4
0.2
0
0.6
0 and p Factors
Effort Level Ej
0.8
1
I-.
w
0
0
0
Sw
w
0
0
0
Optim al Contract Determination
High Level of Information
4
mo m&
3-
E
2-
LL.
0
w
QJ
I.-'.
x
1
z
wi
(JJ
0
N)
-t
L~)
-1
-2
.
0
I
0.2
0.4
O.G
0 and p Fac tors
+ E(NPV/Ei)
(FF)
0.8
1
I
0
0
0
0
w
w
a
Optimal Contract Determination
High Level of Information
1.1
/
n.9
/
/
/
/
0.8
K
-
LL
La.
0.7
U
U
-
U,
/
0
a'
I..
aU,
/
1.6i
0.5
-
0.4
-
0.3
-
u.2
-
/
I
/
/
0.1 -A
0
--
Q4
i
i
0.2
0.4
4
i
I
0.6
0 and u Factors
Risk Premium
I
~~4
-A)
0
/
I
0.8
I
1
0
a
0
w
IV
w
w
a
0
Optima 1 Contract Determination
High Level of Information
1 3
A
1.2
/
/
/
LL.
/
LL.
/
/
/
0.9-
0
9.4
CL
'A
/
0.8-
0
0
/
0.7-
/
/
/
x
/
(Ji
0.5
-
0.4
-
0.3
-
0.2 'I
0
I
0. 2
0.4
9
0.6
0 and p Factors
Contractor's Profit
-I
I-A
(A
/
o.6-
'-I
0.8
1
W
0
0
W
W
0
W
W
Optima I Contract Determination
2.5
High Level of Information
-
2
1.5
-
........
in
U
(U 0
a-
:0
1%)
0.5
La.
-c
(J6
U
0
a'
'-I
La.
-0.5
.................... III
-1
-1.5
0
0.2
0.4
6 and p Factors
OContractor's *Conractr~sProft
Profit
0.6
) Owner's
0.8
Profit
I
-173-
6.5 Appendix 4.4A - Optiuml Contracts - High Level of Inf.
Appendix 4.4-1
Summary of Results - Optimal Contract Determination
Construction Costs and Revenues are uncertain
Stipulated Sum Contracts - High level of information
Contract Form:
Liquidated Damages
Factor 0
0.00
0.03
0.04
0.09
0.10
0.15
0.20
0.23
0.24
0.30
0.40
0.50
0.60
0.68
0.69
0.70
0.80
0.90
1.00
Effort Level
El
0
0
50,000
50,000
250.000
250.000
250,000
250,000
410.000
410,000
410.000
410,000
410,000
410,000
410.000
1,200,000
1,200,000
1,200,000
1.200,000
P = S - 0*d*LD
Bid
S
244.100
355.000
385.000
502.000
514.000
534,000
561,000
581,000
583,000
576,000
571,000
574,000
587,000
604,000
606,000
605,000
606,000
647,000
725,000
E(NPV/Ei)
(1.479.890)
(1,479.890)
(12,314)
(12.314)
2,125,613
2.125,613
2,125,613
2,125,613
2,680,451
2,680,451
2,680.451
2,680.451
2,680,451
2.680,451
2,680,451
3,968,131
3,968,131
3,968,131
3,968,131
-174-
Appendix 4.4-2
Summary of Results - Optimal Contract Determination
Construction Costs and Revenues are uncertain
Stipulated Sum Contracts - High level of information
Contract Form:
P =
S - O*d*LD
Owner Profit
Total Risk
Liquidated Damages Contractor Profit
Premium
0
Factor
-----------------------------------------------------------------(1,723,990)
37,216
244,100
0.00
(1,724,226)
37,451
244,335
0.03
(308.464)
39,266
246,150
0.04
(314,402)
45,204
252,088
0.09
1,619,945
48,784
255,668
0.10
1,604.111
64,618
271,502
0.15
1,581,277
87,452
294,336
0.20
1,563,776
104.952
311,836
0.23
1,984.287
79,280
286,164
0.24
1,962,996
100.571
307,455
0.30
1,920,844
142,723
349,607
0.40
1,870,692
192,875
399,759
0.50
1,810,540
253,027
459,911
0.60
1,755,819
307,748
514,632
0.68
1,749,104
314,463
521,347
0.69
2,131,692
429,555
636,439
0.70
1,954,773
606,474
813.358
0.80
1,737,853
823.394
1,030,278
0.90
1,483,933
1,077,314
1,284,198
1.00
-175-
Appendix 4.4-3
Summary of Results - Optimal Contract Determination
Construction Costs and Revenues are uncertain
Profit Sharing Contracts - High level of information
Contract Form:
Profit Sharing
Factor p
0.00
0.03
0.04
0.09
0.10
0.15
0.20
0.23
0.24
0.30
0.40
0.50
0.60
0.68
0.69
0.70
0.80
0.90
1.00
Effort Level
Ej
0
0
50,000
50,000
250,000
250,000
250,000
250,000
410,000
410,000
410,000
410,000
410,000
410,000
410,000
410,000
410,000
410.000
410,000
P = u NPVcd,r - F
Franchise Fee
(206.884)
(256,000)
(266,000)
(300,000)
(297,000)
(256,000)
(242,000)
(247,000)
(247,000)
(232,000)
(265,000)
(360,000)
(505,000)
(651,000)
(671,000)
(691,000)
(914,000)
(1,169,000)
(1,456,000)
E(NPV/Ej)
(1,479,890)
(1,479,890)
(12,314)
(12,314)
2,125,613
2.125,613
2,125,613
2,125,613
2,680,451
2,680,451
2,680,451
2,680,451
2,680,451
2,680,451
2,680,451
2,680,451
2,680,451
2,680,451
2,680,451
-176-
Appendix 4.4-4
Summary of Results - Optimal Contract Determination
Construction Costs and Revenues are uncertain
Profit Sharing Contracts - High level of information
Contract Form:
Profit Sharing
Factor p
0.00
0.03
0.04
0.09
0.10
0.15
0.20
0.23
0.24
0.30
0.40
0.50
0.60
0.68
0.69
0.70
0.80
0.90
1.00
Contractor Profit
206,884
211,603
215,507
248,892
259,561
324,842
417,123
485.891
480.308
626.135
927,180
1.290,276
1,703,271
2,063,707
2,110,511
2,157,316
2.648,361
3,171,406
4,136,451
P = P NPVcd,r - F
Total Risk
Premium
0
4,719
8,624
42,008
52,677
117,958
210.239
279,007
273.424
419,251
720,297
1,083,342
1.496,387
1,856,823
1,903,627
1,950,432
2.441,477
2,964,522
3,929,567
Owner Profit
(1,686.774)
(1,691.494)
(277,821)
(311.206)
1,616,051
1,550,771
1,458,490
1.389.722
1,790.143
1,644,316
1,343,271
980.226
567,180
206,744
159.940
113,135
(377,910)
(900,955)
(1,456,000)
40
w
0
VP
w
w
w
Stipulated Sum Contracts
High Level of
Information
4
3
2
01
z
0
I-h
-J
1
-.1
+j
xn
E
0
S..
Q.
0
-1
-2
I0
0
I
I
0.2
I
I
0.4
I
I
I
0.6
Liquidated Damages Factor 0
+E(NPV/Ej)
I
0.8
I
0
9
w
v=
9
9
Profit Sharing Contracts
High Level of
Information
3
~I
I I
I
I
ii
2.62La.
i.
1.5I-
-o
05
-1
-
01..J
-0.5
0
0.2
0.4
0.0
Profit Sharing Factor p
+ E(NPV/Ej)
0.3
w
w
w
-179-
Appendix 4.4-7
Stipulated Sum Contract - With partial Liquidated Damages
Contract Form:
P =
S - LD
P is the payment to the contractor
S is the Stipulated Sum resulting from the bidding process
LD are the liquidated damages
LD are calculated as follows:
Delay
LD
2 semesters
2 * 0 * A
I semester
0 * A
P = S - d*8*A
On time
0
A =
1,893,647
-1 semester
- 0 * A
0.70
A is a lump sum, d is the delay and 1
Contractor's Utility Function
U = 1.016492 - 1.016492 exp[-0.00000241714*YJ
Y is the net profit; Y = S - LD - Ei
Minimum Fee to Hire Contractor is Umin = .4
206,884
or a net profit of FF
Contractor's Action Choice
High Level of information
Variations in Construction Costs
Delta ( CC )
Probability
250,000
0.25
0
0.50
0.25
(250,000)
Contractor Utility Computations
Effort Level
El
E2
E3
E4
E5
E6
Minimum Bid
605,000
605,000
605,000
605,000
605,000
605,000
j =
Contractor chooses level of effort EJ,
is
.4
for
Contractor
Utility
Minimum
Thus Minimum Bid over base construction costs is
Base construction costs are FF 34,100,000
d =
Expected completion delay is d,
Total Value of the project to the Owner is
E(NPV,EJ/Ej) - P =
Utility
-147.8091
-39.9809
-11.8313
-3.3630
0.3937
0.4009
6
605,000
-0.929
2,131,692
-180-
Appendix 4.4-8
Construction Costs and Profits are uncertain
Profit Sharing Contract (Maximum Cost Plus Fee) With Partial Liquidated Damages
Contract Form:
P=
u NPVc,d,r - F
u=
0.24
P is the payment to contractor
NPVc,dr is the Project Net Present Value for construction cost
scenario c. delay scenario d and profit level r
u is the profit sharing factor
F is the Fee reserved by the Owner
Contractor's Utility Function
U = 1.222 -
1.222 exp[-10E-6*YJ
Y is the net profit; Y = u NPV - Ei
Minimum Fee to Hire Contractor is Umin = .4
or a net profit of FF
206.884
Contractor's Action Choice
High Level of
Information
Variations in Construction Costs
Delta ( CC )
Probability
1
2
3
0.25
0.50
0.25
250,000
0
(250,000)
Variations in Project Net Present Values
(See the NPV - Delay Probability Matrix)
Contractor Utility Computations
Before Fee
E(U(NPV,EI)/E1)
E(U(NPV.E2)/E2)
E(U(NPV,E3)/E3)
E(U(NPV,E4)/E4)
E(U(NPV.E5)/E5)
E(U(NPV.E6)/E6)
=
=
=
=
=
=
After Fee
-3.7617
-1.3929
-0.9064
-0.1135
-0.1015
-2.7246
Contractor chooses level of effort Ej,
1
Minimum Utility for Contractor is .4
Thus Maximum Fee for franchise is
Total Value of the project to the Owner is
F + (1-u) E(NPV,EJ/Ej) =
-1.6136426507
-0.3097310178
-0.0419298757
0.3944914059
0.4011175729
-1.0427721659
=
5
(247,000)
1,790, 143
-181-
Appendix 4.4-9
Summary of Results - Optimal Contract Determination
Construction Costs and Revenues are uncertain
Maximum Cost plus Fee Contracts - High level of information
Cost Sharing
Factor p
0.00
0.03
0.04
0.09
0.10
0.15
0.20
0.23
0.24
0.30
0.40
0.50
0.60
0.68
0.69
0.70
0.80
0.90
1.00
Contract Form:
P = P NPVc,d - F
Effort Level
Ej
Franchise Fee
0
0
50,000
50,000
250,000
250.000
250.000
250.000
410,000
410,000
410,000
410,000
410,000
410,000
410,000
1,200,000
1,200,000
1,200,000
1,200,000
(206,884)
(251,550)
(259.487)
(266,286)
(256,268)
(166,294)
(83,507)
(37,725)
(17,813)
120,502
343,761
558,276
762,053
917,948
937,528
960,099
1,174,423
1,348,034
1,483,942
E(NPV/Ej)
(1,479.890)
(1,479,890)
(12,314)
(12,314)
2,125.613
2,125,613
2,125,613
2,125,613
2,680,451
2,680,451
2,680,451
2,680,451
2,680,451
2,680,451
2,680,451
3,968,131
3,968,131
3,968,131
3,968,131
-182-
Appendix 4.4-10
Summary of Results - Optimal Contract Determination
Construction Costs and Revenues are uncertain
Maximum Cost plus Fee Contracts - High level of information
Contract Form:
Cost Sharing
Factor p
0.00
0.03
0.04
0.09
0.10
0.15
0.20
0.23
0.24
0.30
0.40
0.50
0.60
0.68
0.69
0.70
0.80
0.90
1.00
Contractor Profit
206,884
207.153
208,994
215,178
218.830
235,135
258,630
276,616
251,122
273,633
318,419
371,949
436,218
494,758
501,983
617,593
800,082
1,023,284
1,284,189
P = p NPVc,d - F
Total Risk
Premium
Owner Profit
0
269
2,110
8,294
11,946
28,251
51,746
69,732
44,238
66,749
111,535
165,065
229,334
287,874
295,099
410,709
593,198
816,400
1,077,305
(1.686.774)
(1,687,043)
(271,308)
(277,492)
1,656,783
1,640,478
1,616,983
1,598,997
2,019,329
1,996,818
1,952,032
1,898,502
1,834.233
1,775,693
1,768.468
2,150,538
1,968,049
1,744,847
1,483.942
L-
w
a
0
0
e
0
0
0
Total Risk Premiums
High Level of Information
4
/
/
3.15
//*//
7/
3
La.
U
7
2.5
H-
7
M
U
ii
7
0
x
7
4
1.5
7
0
I--
x
I
7
7-
7u.5
0
I -. 0
Cost Sharing
II
II
0.2
I
0.4
.
0 and a Factors
Profit Sharing
I
I
I
0.0
0.8
V
I
1
Stipulated Sum
OD
w~
0
0
0
a
e
0
0
.0
Sp
Maximum Cost plus Fee Contracts
High Level of Information
2.5
2,150,538
2
1.5
LL
I
LL
4
4.,
0
0
u.6
Z-
S..
OD
a..0:
In
I I
S..
a'
-0.6
0
-1
-1.5
I
0
I
I
0.4
0.2
o
I
I
0.6
Cost Sharing Factor 'i
Owner's Profit
I
0.3
1
-185-
6.6 Appendix # 4.4-B - Risk Premiums:
In
this section
we compute the
construction risk premiums
for the stipulated sum contract and the
profit sharing contract.
Stipulated Sum Contract:
Let be So the contractor's
bid when
construction costs are
certain and S his bid when these costs are
things being identical.
The
difference
uncertain,
between
S
all other
and
So is
exactly equal to the construction risk premium &S.
S = So + S
In both cases the contractor will
submit a bid
so that his
utility is equal to the minimum acceptable utility value Umin.
Umin = E
Pd,jo * U(So - LDd - Ejo)
d
= E
Pd,jo * {E Qc,jo * U(So + £S
d
LDd
-
Ejo - &CCc))
-
c
Thus, we should have:
U(So
LDd - Ejo) = E Qc,jo * U(So + ES
-
-
LDd
-
Ejo - 9CCc)
C
= a
a * E Qc,jo expi-b(So + £S
-
-
LDd
-
Ejo
-
9CCc))
c
= a
a * exp{-b(So - LDd
-
-
Ejo)) * (E Qc,jo exp{-b(9S - &CCc)))
c
Since we have also:
U(So
-
LDd - Ejo) = a - a * exp{-b(So - LDd - Ejo))
we get:
E Qcjo * exp{-b(&S - &CCc)) = I
c
-186-
expfb * 9S) = E Qc,jo exp(b * 9CCc)
C
The construction risk premium is therefore:
&S = (1/b) * Log (E Qc exp(b &CCc))
c
&S = FF 37,206 in the high information level case.
Using a limited development, we get:
SS = b E Qc &CCc^2 + b^3 * 1/24 * E Qc &CCc^4
c
-
2
b^3 * 1/8 *
c
(E Qc * 9CCc^2)^2
c
Maximum Cost plus Fee Contract:
Using the same method than for the
stipulated sum contract.
we can compute the construction risk premium for the maximum cost
plus
fee
contract
and
the
construction risk premium is
profit
sharing
now equal to
contract.
minus the incremental
franchise fee SF.
F = Fo + CF
We get the following result:
SF = (-1/b) * Log (E Qc
*
exp(b*p*CCCc))
c
Using a limited development, we get:
CF = -b E Qc (P^2*&CCc^2 + b^2*p^4*SCCc^4)
c
2
4!
+ (b/2) (E Qc u^2*CCc^2)^2
c
2
The
-187-
Thus to the first order, we have:
- SF = P^2 * SS
The construction risk premium for the profit sharing
equal
to
the construction
risk premium for
contract is
the stipulated sum
contract times the square of the profit sharing factor
p.
-188-
6.7 Appendix 4.5 - Optimal Contracts - Average Ievel of Inf.
Appendix 4.5-1
Summary of Results - Optimal Contract Determination
Construction Costs and Revenues are uncertain
Stipulated Sum contracts - Average level of information
Liquidated Damages
Factor 8
0.00
0.05
0.10
0.12
0.13
0.14
0.14
0.15
0.20
0.30
0.40
0.45
0.50
0.60
0.68
0.69
0.70
0.80
0.81
0.82
0.85
0.90
1.00
Contract Form:
P = S - O*d*LD
Effort Level
Ej
Bid
S
0
0
0
0
250,000
250,000
410.000
410,000
410.000
410,000
410,000
410,000
410,000
410,000
410,000
410,000
410,000
410,000
410,000
1,200,000
1,200,000
1,200,000
1,200,000
704,500
876,000
1,051,000
1,122,000
1,151,000
1,161.000
1,165,000
1,172,000
1,217,000
1,346,000
1,530,000
1,641,000
1,765,000
2,041,000
2,287,000
2,319,000
2,351,000
2,684,000
2,718,000
2,745,000
2,826,000
2,967,000
3,271,000
E(NPV/Ej)
(1,176,907)
(1.176.907)
(1,176,907)
(1,176,907)
1,190,151
1,190,151
2,172.954
2.172.954
2,172,954
2,172,954
2,172,954
2.172,954
2,172,954
2,172,954
2,172,954
2,172,954
2,172,954
2,172,954
2,172,954
2,638,791
2,638,791
2,638,791
2,638,791
-189-
Appendix 4.5-2
Summary of Results - Optimal Contract Determination
Construction Costs and Revenues are uncertain
Stipulated Sum contracts - Average level of information
Contract Form:
Liquidated Damages Contractor Profit
Factor 6
0.00
0.05
0.10
0.12
0.13
0.14
0.14
0.15
0.20
0.30
0.40
0.45
0.50
0.60
0.68
0.69
0.70
0.80
0.81
0.82
0.85
0.90
1.00
704,037
706,708
712,416
715,699
768,558
773,464
749,963
756,603
799,804
925,206
1,105,608
1,214,809
1,337,010
1,609,412
1,852,534
1,884,174
1,915,814
2,245,217
2,278,857
1,897,483
1,991,379
2,153,872
2,500,858
P = S - B*d*LD
Total Risk
Premium
Owner Profit
497,153
499,824
505,532
508.815
561,674
566,580
543,079
549,719
592,920
718.322
898,724
1,007,925
1,130,126
1,402,528
1,645,650
1,677,290
1,708,930
2,038,333
2,071,973
1,690,599
1,784,495
1,946,988
2,293,974
(1,881,407)
(1,883,615)
(1,889.323)
(1,892,606)
171,593
166,687
1,012,991
1,006,351
963,150
837,748
657.346
548,145
425,944
153,541
(89,580)
(121,220)
(152,861)
(482,263)
(515,903)
(458,693)
(552,588)
(715,081)
(1,062,067)
-190-
Appendix 4.5-3
Summary of results - Optimal Contract Determination
Construction Costs and revenues are uncertain
Profit Sharing Contracts - Average level of information
Contract Form:
Profit Sharing
Factor p
0.00
0.05
0.10
0.12
0.13
0.14
0.14
0.15
0.20
0.30
0.40
0.45
0.50
0.60
0.68
0.69
0.70
0.80
0.81
0.82
0.85
0.90
1.00
Effort Level
Ej
0
0
0
0
250.000
410,000
410,000
410,000
410,000
410,000
410,000
410,000
410,000
410,000
410,000
1,200,000
1,200,000
1,200,000
1,200,000
1,200,000
1,200,000
1,200,000
1,200,000
P = p NPVcd,r - F
Franchise Fee
(206,884)
(282,000)
(386,000)
(436,000)
(450,000)
(452,000)
(450,000)
(449,000)
(464,000)
(606.000)
(895,000)
(1,092,000)
(1,320,000)
(1,853,000)
(2,337,000)
(2,395,000)
(2,448,000)
(3,020,000)
(3,081,000)
(3,143,000)
(3,332,000)
(3,659,000)
(4,343,000)
E(NPV/Ej)
(1,176,907)
(1,176,907)
(1,176,907)
(1,176,907)
1,190,151
2,172,954
2,172.954
2, 172,954
2.172.954
2,172,954
2,172,954
2,172,954
2,172,954
2,172,954
2,172,954
2,638,791
2,638,791
2,638,791
2,638,791
2,638,791
2,638,791
2,638,791
2,638,791
-191-
Appendix 4.5-4
Summary of results - Optimal Contract Determination
Construction costs and revenues are uncertain
Profit Sharing Contracts - Average level of information
Contract Form:
Profit Sharing
Factor
Contractor Profit
p
0.00
0.05
0.10
0.12
0.13
0.14
0.14
0.15
0.20
0.30
0.40
0.45
0.50
0.60
0.68
0.69
0.70
0.80
0.81
0.82
0.85
0.90
1.00
206,884
223,155
268,309
294,771
- 354,720
335,349
344,214
364,943
488.591
847,886
1,354,182
1,659,829
1,996,477
2,746,772
3,404,609
3,015,791
3,095,154
3,931,033
4,018,421
4,106,809
4,374,972
4,833,912
5,781,791
P = p NPVcd,r - F
Total Risk
Premium
0
16,271
61,425
87,887
147,836
128,465
137,330
158,059
281,707
641,002
1,147,298
1,452,945
1,789,593
2,539,888
3,197,725
2,808,882
2,888,270
3,724,149
3,811,537
3,899,925
4,168,088
4,627,028
5,574,907
Owner Profit
(1,383,791)
(1,400,062)
(1,445,216)
(1,471,678)
585,432
1,427,605
1,418,740
1,398,011
1,274,363
915.068
408,772
103,125
(233,523)
(983.818)
(1,641,655)
(1,576.975)
(1,656,363)
(2,492,242)
(2,579,630)
(2,668,018)
(2,936,181)
(3,395,121)
(4,343,000)
0
0
4p
w
w
4p
Stipulated
0
173
0
Sum Contracts
Average Level of Information
'3 3
1.2
E3
1.1
i
0.9
0.8
La)
-
M
w
o.7
~1
0
I~1.
>4
0.G
-j
-. 4
4.8
94
0
w
-3
a
(.11
p
Lfl
0.4
0.3
0.2
0.1
U
0
0.2
0.4
0.6
Liquidated Damages Factor 0
0 Effort Level Ej
0.8
I
'.0
r\)
is
V
w
w
Stipulated Sum Contracts
Average Level of Information
3
2.6
.1
La.
1.5
a. o
Z
-
I1'.0
-
(A)
QJ
I-'
0.5-4
0
1.
'l
U
-0.5
-
--1 -
I
0
I
0.2
I
I
0.4
I
I
I
0.6
Liquidated Damages Factor 0
+ E(NPV/Ej)
I
0.8
i
1
0
0
w
0
IV
w
0
0
S
e
Profit Sharing Contracts
Average Level of Information
1.2
-
I.W.1
rq
1.1
10.9
0.8-
4J
-4
0'
0
>0
0.6 -
'-a
'.0
0
Ie
14"
0.5-
'.4
0
I
0.4 -
-4
0.3 0.2 0.1 0
I
0
0.2
0.4
0
I
I
0.6
Profit Sharing Factor p
Effort Level Ej
I
I
0.8
I
0
0
0
a
w
f
0
40
14
0
Profit Sharing Co ntra cts
3
Average Level of Information
-
2.6
1.5
LL.
LL.
z
In
0
U,
0.5
Ln
0
C"
0L
ID
0
-0.5
-1
-'.5
,
0
0.2
0.4
0.0
Profit Sharing Factor p
+ E(NPV/Ej)
0.8
I
-196-
Appendix 4.5-9
Stipulated Sum Contract - With partial Liquidated Damages
Contract Form:
P =
S - LD
P is the payment to the contractor
S is the Stipulated Sum resulting from the bidding process
LD are the liquidated damages
LD are calculated as follows:
Delay
LD
2 semesters
2 * 3* A
P = S - d*0*A
I semester
13 * A
1,893,647
On time
0
A =
- 0 * A
-1 semester
0.14
A is a lump sum, d is the delay and 1 =
Contractor's Utility Function
U = 1.016492 - 1.016492 exp[-0.00000241714*YJ
Y is the net profit: Y = S - LD - El
Minimum Fee to Hire Contractor is Umin = .4
206.884
or a net profit of FF
Contractor's Action Choice
Average Level of information
Variations in Construction Costs
Delta ( CC
Probability
1,000,000
0.25
0
0.50
(1.000.000)
0.25
Contractor Utility Computations
Effort Level
El
E2
E3
E4
E5
E6
Minimum Bid
1,165,000
1,165,000
1,165,000
1,165,000
1,165.000
1,165.000
j =
Contractor chooses level of effort Ej,
Minimum Utility for Contractor is .4
Thus Minimum Bid over base construction costs is
Base construction costs are FF 34,100,000
d =
Expected completion delay is d,
Total Value of the project to the Owner is
E(NPV,Ej/Ej) - P =
Utility
0.3569
0.3536
0.3643
0.3912
0.4004
-2.4031
5
1,165.000
0.019
1,012,991
-197-
Appendix 4.5-10
Construction Costs and Revenues are uncertain
Evaluation of Stipulated Sum contracts - Average level of information
Contract Form:
P =
S - d*0*A
6
=
Effort Level:
j
=
5
Expected Delay:
d =
0.02
0.14
1,893.647
Payoffs to Contractor
Stipulated Sum (Bid)
E(Liquidated damages)
Contractor Payoff P
Less: Effort
Contractor Profit
Contractor Utility
Payoffs
1,165,000
5,037
1,159,963
410,000
749,963
0.4004
to Owner
Less: Risk Premium
Plus: Liquid. damages
2,172,954
206,884
410,000
548,116
5,037
Owner Profit
1,012,991
Owner Utility
1,012.991
E(NPV/Ej)
Less: Fixed Fee
Less: Effort
Total Risk Premium
543.079
-198-
Appendix 4.5-11
Construction Costs and Profits are uncertain
Profit Sharing Contract (Maximum Cost Plus Fee) With Partial Liquidated Damages
Contract Form:
P
u NPVc,dr - F
u
0.14
P is the payment to contractor
NPVc,d,r is the Project Net Present Value for construction cost
scenario c, delay scenario d and profit level r
u is the profit sharing factor
F is the Fee reserved by the Owner
Contractor's Utility Function
U = 1.222 - 1.222 exp[-10E-6*YJ
Y is the net profit; Y = u NPV - El
Minimum Fee to Hire Contractor is Umin = .4
or a net profit of FF
206.884
Contractor's Action Choice
Average Level of Information
Variations in Construction Costs
Delta ( CC )
Probability
1
2
3
0.25
0.50
0.25
1,000,000
0
(1,000,000)
Variations in Project Net Present Values
(See the NPV - Delay Probability Matrix)
Contractor Utility Computations
Before Fee
E(U(NPV,E1)/E1)
E(U(NPV,E2)/E2)
E(U(NPV.E3)/E3)
E(U(NPV,E4)/E4)
E(U(NPV,E5)/E5)
E(U(NPV.E6)/E6)
=
=
=
=
=
=
-0.9350
-0.9425
-0.9031
-0.8335
-0.8176
-9.2533
Contractor chooses level of effort Ej,
Minimum Utility for Contractor is .4
Thus Maximum Fee for franchise is
Total Value of the project to the Owner is
F + (1-u) E(NPV,Ej/Ej) =
After Fee
0.3620438112
0.3595266535
0.372728795
0.3960820059
0.4014012347
-2.4275866936
5
(452,000)
1,427,605
-199-
Appendix 4.5-12
Profit Sharing Contracts - Construction Costs and Revenues uncertain
Evaluation of Contracts - Average Level of Information
----------------------------------------------------------Contract Form:
P =
0.14 NPVcd~r - F
Effort Level:
1 =
5
Payoffs to Contractor
E(NPV/Ej)
Franchise Fee F
2,172,954
(452,000)
Contractor Payoff P
Less: Effort
745,349
410.000
Contractor Profit
335,349
Contractor Utility
0.4014
Payoffs to Owner
E(NPV/Ej)
Less: Fixed Fee
Less: Effort
Less: Risk Premium
Plus: Franchise Fee
2,172,954
206,884
410,000
(323,535)
(452,000)
Owner Profit
1,427,605
Owner Utility
1,427,605
Total Risk Premium
128,465
-200-
Appendix 4.5-13
Summary of Results - Optimal Contract Determination
Construction Costs and Revenues are uncertain
Maximum Cost plus Fee Contracts - Average level of information
Cost Sharing
Factor
p
0.00
0.05
0.10
0.12
0.13
0.14
0.14
0.15
0.20
0.30
0.40
0.45
0.50
0.60
0.68
0.69
0.70
0.80
0.81
0.82
0.85
0.90
1.00
Contract Form:
P = p NPVcd - F
Effort Level
Ei
Franchise Fee
0
0
0
0
250.000
250.000
410.000
410,000
410,000
410,000
410.000
410.000
410,000
410.000
410,000
410,000
410,000
410,000
410,000
1,200,000
1,200,000
1,200,000
1,200,000
(206,884)
(269,910)
(338,982)
(368,446)
(376,856)
(376,605)
(370,384)
(357,029)
(302,000)
(239.401)
(242,412)
(266,599)
(306.064)
(419,273)
(540,451)
(557,155)
(573,923)
(757,930)
(777,340)
(789,802)
(827,496)
(897,280)
(1,062,067)
E(NPV/Ej)
(1,176.907)
(1,176,907)
(1.176,907)
(1,176,907)
1,190,151
1,190,151
2,172,954
2,172,954
2,172.954
2.172,954
2.172.954
2,172.954
2,172.954
2,172,954
2,172,954
2,172,954
2,172,954
2,172,954
2,172,954
2,638,791
2,638,791
2,638.791
2,638,791
-201-
Appendix 4.5-14
Summary of Results - Optimal Contract Determination
Construction Costs and Revenues are uncertain
Maximum Cost plus Fee Contracts - Average level of information
Contract Form:
Cost Sharing
Factor p
0.00
0.05
0.10
0.12
0.13
0.14
0.14
0.15
0.20
0.30
0.40
0.45
0.50
0.60
0.68
0.69
0.70
0.80
0.81
0.82
0.85
0.90
1.00
Contractor Profit
206,884
211,065
221,291
227,217
281,576
287,276
264,598
272,973
326,591
481,287
701,594
834,428
982,541
1,313,045
1,608,060
1,646,493
1,684,991
2,086,293
2,127,432
1,753,611
1,870,468
2,072,192
2,500,858
P
=
p NPVcd - F
Total Risk
Premium
Owner Profit
0
4,181
14,407
20,333
74,692
80,392
57,714
66,089
119,707
274.403
494,710
627,544
775,657
1,106,161
1,401,176
1,439,609
1,478,107
1,879,409
1,920,548
1,546,727
1,663,584
1,865,308
2,293,974
(1,383.791)
(1,387,972)
(1,398,198)
(1,404,124)
658,575
652,875
1,498.356
1,489,981
1,436,363
1,281,667
1,061,360
928,526
780,413
449,909
154,894
116,461
77,963
(323,339)
(364,478)
(314.820)
(431,677)
(633,401)
(1,062,067)
ra
=
0
0
0
U
VSUUU
9
0
U
0
Total Risk Premiums
Average Level of Information
A
/
2
/
4-
'7
La.
-V
U)
CA
0
7
/ 2\x
7
/
I\
/
0
-a-4---
2-
A.
--
7
~
"<'p
-r~A'
26
1-
--
4*-
~
V -r
0
Cost Sharing
-
'
I
I
I
0.2I
0.4
0 and p Factors
CSProfit SharingS
I
0.6
0.8
v
Stipulated
I
1
Sum
I
W
W
l
0
0
e
0
S
Maximum Cost plus Fee Contracts
Aver age Level of Information
I ,498,366
1.6
-
Li.
.
l.5
0
0
0
Lii
'N
'N
0
-0.5
N.
'N
'N
N
-t
-1.5
I
0
I
0.2
0.4
<9
0.6
Cost Sharing Factor p
Owner's Profit
I
I
0.8
I
I
-204-
Bibilography
1- Ronald Pastore
"Construction Contracts and the Investment
Value of Commercial Real Estate Developments". MIT Sloan School
of Management thesis. 1988.
2- Philip Hampson - "Optimal Profit Sharing Rules for Petroleum
Exploration and Develoment in Jordan", MIT Sloan School of
Management thesis, 1988.
3- John Parsons - "Financial Contracting & Moral Hazard", MIT
Sloan School of Management, Cambridge MA, October 1987.
4- Preston McAfee and John McMillan - "Auctions and Bidding",
Journal of Economic Litterature, June 1987.
5- Charles Blitzer, Donald Lessard and James Paddock - "Risk
Bearing and the Choice of Contract Forms for Oil Exploration and
Develoment", Energy Laboratory and Sloan School of Management,
MIT, Cambridge, MA, 1984.
6- Mark Wolfson - "Empirical Evidence of Incentive Problems and
their Mitigation in Oil and Gas Tax Shelter Programs", Harvard
Business School Press, Cambridge MA, 1985.
7- Chambre de Commerce et d'Industrie de Paris - "Cahier des
Clauses Administratives Particulteres pour l'Ecole Superieure
d'Ingenieurs en Electrotechnique et Electronique", Paris, 1984.
8- Centre de l'lndustrie Frangaise des Travaux Publics - "TP
Annuaire 1987 - 1988. Marches at Reglementations Diverses",
Paris, 1987.
-