MANAGEMENTUL PROIECTELOR DE INVESTITII STRAINE DIRECTE

LECT.DR. ROXANA VOICU-DOROBANTU

STRUCTU

RA CURSU

LUI

PARTEA 1: MANAGEMENTUL PROIECTELOR

PARTEA 2: INVESTITIILE STRAINE DIRECTE

DETALII AD

MIN

ISTRATIVEDespre cursCursul urmăreşte:să familiarizeze studenţii cu conceptele, metodele şi tehnicile specifice managementului de proiect, cu precădere in contextul proiectelor investiţionale internaţionalesă ofere studenţilor un cadru specific de înţelegere a fenomenului investiţional global, atât din perspectiva investiţiilor străine directe, cât şi a celor de portofoliusă construiască şi să consolideze capacitatea studenţilor de analizare a tendinţelor şi caracteristicilor investiţiilor străine directe şi a celor de portofoliu din perspectiva motivaţiilor, strategiilor şi riscurilor specifice

Modulul de MPISD se desfăşoară pe parcursul a 7 intâlniri de curs şi 7 intâlniri de seminar pentru fiecare grupă :

CURSURI: Vineri, 5.10.2012 – orele 15.00 – 18.00 – sala 1201 - C1, C2Vineri, 12.10.2012 – orele 15.00 – 18.00 – sala 1201 – C3, C4Vineri, 19.10.2012 – orele 15.00 – 18.00 – sala 1201 – C5, C6Vineri, 26.10.2012 – orele 16.30 – 18.00 – sala 1201 – C7

Pentru planificarea seminariilor pe grupe, urmăriţi orarul.

Evaluare

Evaluarea se va face pe baza unui exercitiu de grup, ce va fi predat in ziua examenului.

Exercitiul se va realiza in grupe de 5 studenti, repartizati in ordine alfabetica.

Tema exercitiului: realizarea unui proiect de investitie straina directa pentru o companie prezenta pe piata din Romania pe o piata internationala.

Nu exista restrictii cu privire la forma sau dimensiunea exercitiului predat in scris. Acesta va trebui sa acopere toate informatiile relevante pentru un manager pentru a putea implementa proiectul.

Bibliografie

1. B Lientz, K P Rea – International Project Management, Butterworth Hienemann, 2003

2. JC Binder - Global project management : communication, ollaboration and management across borders, Gower, 2007

3. P Dinsmore, J Cabanis-Brewin – The AMA Handbook of project management, AMACOM, 2006

4. B Solnik – International Investments, McGraw-Hill, Reading, MA, 2004

5. A Horobeţ – Managementul riscului în investiţiile internaţionale, Editura AllBeck, Bucureşti, 2005

PARTEA 1: MANAGEMENTUL PROIECTELOR

STRUCTU

RA PARTII 11.1: Definire si Istoric

1.2: Principii fundamentale

1.3 Etapa 1: Pregatirea unui proiect

1.4 Etapa 2: Planificarea unui proiect

1.5. Etapa 3: Implementarea unui proiect

1.6. Proiecte globale

1.7. ?

THE “TEXTBO

OK ACCO

UN

T” OF PRO

JECT MAN

AGEM

ENT

1. Traditional Project Management Models2. Defining, Organizing, Planning, Executing, Monitoring, Finishing3. Purpose, Scope, Estimating, Budgeting, and Deadlines4. Work breakdowns, Dependencies, Key Resources5. Scheduling: PERT, CPM, GANNT6. Reporting, milestones, adjustments

TRADITIO

NAL PRO

JECT MAN

AGEM

ENT

Preparations for the project

Planning the ProjectManaging the Project In-Progress

Traditional PM Focus

PROD

UCT VS PRO

JECT LIFE CYCLES

Source: Dinsmore, 2006

THE ID

EA BEHIN

D FO

RMALIZIN

G PM

…Use structure to combat scale and complexityMake future possibilities more predictable, foresee problems, develop contingency plansThoroughness – Checklists as a way of being sureForces us to confront things that are hard to think about in detail

Helpful even when the details don’t unfold if expectedEisenhower: “The plan is nothing. Planning is everything.”

The danger…Structure can become an end in itself

Obsession with documents, milestones

A distraction or, worse, a constraint on the ability to adjust

STRATEGIC M

OD

EL FOR M

ANAG

ING

PROJECTS

Source: Dinsmore, 2006

CREATING

A PROJECT O

RGAN

IZATION

Define who is going to do whatDefine roles and responsibilitiesIdentify people, resources; ensure their commitment to projectIdentify a project leader, specify her/his authority and

responsibilitiesImportant questions:

• Who is the PM? What decisions are within PM’s area of authority? Is this authority sufficient to carry out the project?

• Who is on team? Full-time or part-time? What are their areas of expertise? Their roles?

• Who is the project sponsor? Is he or she at sufficiently high level in the organization to provide the project with support and a good chance of success?

PROJECT M

ANAG

EMEN

T PROCESS G

ROU

PS’ INTERACTIO

NS

Source: Dinsmore, 2006

THE PRO

JECT MAN

AGEM

ENT PLAN

1. Introduction/overview2. Mission and objectives

3.Work scope4. Planning basis: deliverables, requirements, constraints, approaches,

assumptions, exclusions5. Work breakdown structure

6. Organization development plan7. Resource plan

8. Procurement and logistics plan9. Logic and schedules

10. Cost estimates, budgets, and financial management11. Risk analysis and contingency plan

12. Quality and productivity plan13. Environmental, safety, and health protection plan

14. Security plan15. Project planning, control, and administration plan

16. Documentation and configuration management plan17. Appendix

DEFIN

ING

THE PRO

JECT’S OBJECTIVES AN

D SCO

PE

Make sure the proposed project is well understood an that all stakeholders agree on what it will accomplish

Clearly spell out expected outcomes, deliverables, objectivesAgree scope – what’s in, what’s not inDocument agreements formally, in writing, to surface/eliminate ambiguity in

different stakeholders’ expectationsImportant questions:

• What is the scope?• What does the project need to accomplish?• By when?

FORM

AL OBJECTIVE STATEM

ENT

A Formal Objective StatementShort, simple language, unambiguousShould Scope, Resources, and Schedule

A Famous Example: “Put a man on the moon and return him safely to Earth by the end of the decade at a cost of $9 billion.”

Scope – “Put a man on the moon and return him safely to Earth.”Schedule – “By the end of the decade.”Resources –”At a cost of $9 billion.”

The advantage in keeping it short and simple: Longer statements offer greater opportunity for people to come away with different understanding of what the project will accomplish while mistakenly assuming they have reached agreement

WH

AT’S IN/O

UT LIST FO

R PROJECT W

ORK PRO

DU

CTS

What’s In/Out List

List 1: Things included in the work product

List 2: Things excluded from the work product

Work Product Example: A Business PlanIs included: 30 pages + 10 pages of appendix, spiral bound, cover sheet with

300 word executive summary, one section must be financial projections, another must spell out marketing plans

Not included: Potential customer market segment analysis, a formal presentation

SETTING

UP PRO

JECT NO

RMS

Determine how the project will “operate” from day to daySet norms for meetings, updates, communicationEstablish “official” processes for logging, reviewing, updating progress on

issuesSet norms and escalation procedures for disagreements and unresolved

issuesImportant questions:

• What do we do when we encounter a new problem?• Who do we go to for help in making decisions?• How do we check progress on a known issue?

THE H

UM

BLE CHECKLIST

One of the most useful concrete tools in issue tracking

A running list of “open issues”Log issue, assign priority and problem

solving owner, current status, resources assigned to address

Revisit list on a regular basis (daily, weekly)

PROJECT “W

ORKBO

OK”

It’s a good idea to have a common collection point for all project documentation

Objective statementsOrganization definitions and rolesIssue checklistsEtc.

THE W

ORK BREAKD

OW

N STRU

CTURE

Need to identify all of the work required by a projectIdentify tasks and sub-tasksAssign “owners” for each taskEstimate how long each task will take

Important questions:• Are all tasks identified?• Do all tasks have owners?• How long will it take to do each task?

WBS – WORK BREAKDOWN STRUCTURE

Work breakdown structure, or the WBS = hierarchical structure defining tasks that can be completed independently of other tasks, facilitating resource allocation, assignment of responsibilities, and measurement and control of the project.

Task 1 Subtask 1.1 Work package 1.1.1Work package 1.1.2Work package 1.1.3

Subtask 1.2 Work package 1.2.1Work package 1.2.2

Task 2 Subtask 2.1 Work package 2.1.1Work package 2.1.2Work package 2.1.3Work package 2.1.4

Subtask 2.2 Work package 2.2.1Subtask 2.3 Work package 2.3.1

Work package 2.3.2

Terminology for Different Levels-tasks, sub-tasks, and work packages-phases, entries, and activities.

Organization by Deliverables or Phases•deliverables or phases of the project life cycle. •higher levels in the structure generally are performed by groups. •lowest level in the hierarchy often comprises activities performed by individuals, • a WBS that emphasizes deliverables does not necessarily specify activities.

Level of Detailfacilitates resource allocation and the assignment of individual responsibilities. ! Beware: micro-management OR tasks too large to manage effectively.

Defining tasks so that their duration is between several days and a few months works well for most projects.

THE 100%

RULE

The 100% rule states that the WBS includes 100% of the work defined by the project scope and captures all deliverables – internal, external, interim – in terms of the work to be completed, including project management.

The rule applies at all levels within the hierarchy: the sum of the work at the “child” level must equal 100% of the work represented by the “parent” and the WBS should not include any work that falls outside the actual scope of the project, that is, it cannot include more than 100% of the work…

It is important to remember that the 100% rule also applies to the activity level.

The work represented by the activities in each work package must add up to 100% of the work necessary to complete the work package.

TOP D

OW

N VS. BO

TTOM

UP

You can create a WBS top down or bottom up

Top down – Start with largest work groupings and break into smaller and smaller pieces

Bottom up – Brainstorm specific low level tasks, group them into larger groupings

ESTIMATIN

G IS D

ON

E IN M

ANY W

AYS…

Guestimates by task ownersGuestimates by a group, including experts who have “done this kind of work before”Other group consensus processesStatistical models that relate “size” of a project result to time and effort estimates

Suppose a project is expected to produce a software product with about 60,000 Lines of Code (written software)

According to statistical model: 60,000 Lines of Code translates into 200 person months of effort

200 person days of effort = it’ll take 20 people 10 months, or 10 people 20 months (or 2 people 100 months, etc.)

“BROO

KS’S LAW”

Frederick Brooks, author of The Mythical Man Month: “Adding more people to a late project makes it later”

“Adding more people to a late project helps less than you might think, and it helps less and less the more people you add ” -- 20 people for 10 months is not the equivalent to 10 people for 20 months (or 2 people for 100 months) –

The more people work on a project, the more overhead required to coordinate work (and the less spent on value-adding work)

Overall Productivity

Number of people

DEVELO

PING

A PROJECT SCH

EDU

LE

Given what you need to do, figure out when things will happen and when you’ll be finished (when you’ll deliver project results)

Identify dependencies between tasks (e.g., task A must be done before task B can be started)

Use task time estimates and dependencies to create a schedule, typically by generating a “Gantt Chart”

Important questions:Have all dependencies been identified?Is there a way to eliminate dependencies?Does estimated completion fit with project objectives?

PERT – PROGRAM EVALUATION AND REVIEW TECHNIQUE

PERT • 1957 - the Critical Path Method (CPM) was developed as a network model for project management. • a deterministic method that uses a fixed time estimate for each activity• does not consider the time variations that can have a great impact on the completion time of a complex project.

PERT = a network model that allows for randomness in activity completion times.

Assumptions to create the network diagram:an activity is a task that must be performed and an event is a milestone marking the completion of one or more activities.before an activity can begin, all of its predecessor activities must be completed. project network models represent activities and milestones by arcs and nodes.

STEPS IN TH

E PERT PLANN

ING

PROCESS

a. Identify the specific activities and milestones.b. Determine the proper sequence of the activities.c. Construct a network diagram.d. Estimate the time required for each activity.e. Determine the critical path.f. Update the PERT chart as the project progresses.

STEPS IN TH

E PERT PLANN

ING

PROCESS

a. Identify Activities and Milestones• The activities are the tasks required to complete the project. • The milestones are the events marking the beginning and end of one or

more activities. • It is helpful to list the tasks in a table that in later steps can be expanded to

include information on sequence and duration.

b. Determine Activity Sequence• This step may be combined with the activity identification step since the

activity sequence is evident for some tasks. • Other tasks may require more analysis to determine the exact order in which

they must be performed.

3. Construct the Network Diagram• You may use software for this step

STEPS IN TH

E PERT PLANN

ING

PROCESS

d. Estimate Activity Times• Weeks are a commonly used unit of time for activity completion, but any

consistent unit of time can be used.• For each activity, the model usually includes three time estimates:

• Optimistic time - generally the shortest time in which the activity can be completed. It is common practice to specify optimistic times to be three standard deviations from the mean so that there is approximately a 1% chance that the activity will be completed within the optimistic time.

• Most likely time - the completion time having the highest probability. Note that this time is different from the expected time.

• Pessimistic time - the longest time that an activity might require. Three standard deviations from the mean is commonly used for the pessimistic time.

• PERT assumes a beta probability distribution for the time estimates. For a beta distribution, the expected time for each activity can be approximated using the following weighted average:• Expected time = ( Optimistic + 4 x Most likely + Pessimistic ) / 6

• This expected time may be displayed on the network diagram.• To calculate the variance for each activity completion time, if three standard

deviation times were selected for the optimistic and pessimistic times, then there are six standard deviations between them, so the variance is given by:• [ ( Pessimistic - Optimistic ) / 6 ]2

STEPS IN TH

E PERT PLANN

ING

PROCESS – CRITICAL PATH

e. Determine the Critical Path• That sequence of tasks that are the “bottleneck” in the schedule•The critical path is determined by adding the times for the activities in each sequence and determining the longest path in the project. • The critical path determines the total calendar time required for the project. • If activities outside the critical path speed up or slow down (within limits), the total project time does not change. • The amount of time that a non-critical path activity can be delayed without delaying the project is referred to as slack time.

If the critical path is not immediately obvious, it may be helpful to determine the following four quantities for each activity:

ES - Earliest Start timeEF - Earliest Finish timeLS - Latest Start timeLF - Latest Finish time

STEPS IN TH

E PERT PLANN

ING

PROCESS – CRITICAL PATH

ES - Earliest Start time EF - Earliest Finish timeLS - Latest Start time LF - Latest Finish time

• These times are calculated using the expected time for the relevant activities.

• The earliest start and finish times of each activity are determined by working forward through the network and determining the earliest time at which an activity can start and finish considering its predecessor activities.

• The latest start and finish times are the latest times that an activity can start and finish without delaying the project. LS and LF are found by working backward through the network.

• The difference in the latest and earliest finish of each activity is that activity's slack.

• The critical path then is the path through the network in which none of the activities have slack.

CRITICAL PATH - EXAM

PLE

Source: syque.com

STEPS IN TH

E PERT PLANN

ING

PROCESS – CRITICAL PATH

The variance in the project completion time can be calculated by summing the variances in the completion times of the activities in the critical path.

Given this variance, one can calculate the probability that the project will be completed by a certain date assuming a normal probability distribution for the critical path.

The normal distribution assumption holds if the number of activities in the path is large enough for the central limit theorem to be applied.

Since the critical path determines the completion date of the project, the project can be accelerated by adding the resources required to decrease the time for the activities in the critical path.

Such a shortening of the project sometimes is referred to as project crashing.

CRITICAL PATH “W

HAT IF” AN

ALYSIS

The results of this process for arriving at a project schedule are often poorly received“That project completion date is far too late!”

So a “what if” exercise ensuesTo shorten a project’s overall duration (to be “done” sooner), you must shorten

tasks on the Critical Path (“What if task 14, on the critical path, could be done faster?) or remove tasks from the Critical Path (Does task 15 really depend on task 14 – what if we can, by making an adjustment, do them at the same time, thus moving task 14 off the Critical Path?)

Sometimes when you shorten the Critical Path, a different sequence of tasks becomes the new Critical Path (the “bottleneck” shifts) – that is, you’ve shortened the old Critical Path to a point where it is no longer the Critical Path

STEPS IN TH

E PERT PLANN

ING

PROCESS

f. Update as Project ProgressesMake adjustments in the PERT chart as the project progresses. As the project unfolds, the estimated times can be replaced with actual times. In cases where there are delays, additional resources may be needed to stay on schedule and the PERT chart may be modified to reflect the new situation.

PERTBenefitsExpected project completion time.Probability of completion before a specified date.The critical path activities that directly impact the completion time.The activities that have slack time and that can lend resources to critical path activities.Activity start and end dates.

LimitationsThe activity time estimates - subjective and depend on judgement. Even if the activity times are well-estimated, PERT assumes a beta distribution for these time estimates, but the actual distribution may be different.Even if the beta distribution assumption holds, PERT assumes that the probability distribution of the project completion time is the same as the that of the critical path. Because other paths can become the critical path if their associated activities are delayed, PERT consistently underestimates the expected project completion time.The underestimation of the project completion time due to alternate paths becoming critical is perhaps the most serious of these issues. To overcome this limitation, Monte Carlo simulations can be performed on the network to eliminate this optimistic bias in the expected project completion time.

CRITICAL PATH “W

HAT IF” AN

ALYSIS

The results of this process for arriving at a project schedule are often poorly received“That project completion date is far too late!”

So a “what if” exercise ensuesTo shorten a project’s overall duration (to be “done” sooner), you must shorten

tasks on the Critical Path (“What if task 14, on the critical path, could be done faster?) or remove tasks from the Critical Path (Does task 15 really depend on task 14 – what if we can, by making an adjustment, do them at the same time, thus moving task 14 off the Critical Path?)

Sometimes when you shorten the Critical Path, a different sequence of tasks becomes the new Critical Path (the “bottleneck” shifts) – that is, you’ve shortened the old Critical Path to a point where it is no longer the Critical Path

ASSIGN

ING

PROJECT RESO

URCES

With tasks and dependencies identified, assign people and other resources (e.g., specialized equipment) to tasks

Allocate resources across tasksMake sure resources available can cover tasksMake sure key there are no conflicts for key resources (same

person/machine can’t be two places at once)Analyze the merits of different ways of allocating resourcesRe-examine scope, schedule, and resources

Important questions:Is work spread reasonably across resources?Should we make adjustments to scope, schedule, or resources?

Assigning more resources is one way of shortening the CP

KEY RESOU

RCES AND

“SWITCH

ING

COST”

A very common problem: Some resources are over allocated while others are under allocated

People working on some tasks are overwhelmed, while others have nothing much to do

Over allocated resources end up being asked to multi-taskLiterally, work on more than one task at onceTheir time gets allocated in smaller and smaller fractions

But there are big hidden costs in doing this…Switching tasks takes effortPeople work more hoursBurn out, morale issues Worst for key people

Value-add time on

each task

Number of tasks

THE G

ANTT CH

ART – EXAMPLE A SH

EDU

LE

THE G

ANTT CH

ART – AN EXCEL EXAM

PLE

GAN

TT CHARTS

Gantt charts illustrate the start and finish dates of the terminal elements and summary elements of a project. Terminal elements and summary elements comprise the work breakdown structure of the project. Some Gantt charts also show the dependency (i.e., precedence network) relationships between activities.

Pitfalls:Attempt to define the project work breakdown structure at the same time that they define schedule activities. the WBS should be fully defined to follow the 100% Rule, then the project schedule can be designed.Difficult to grasp for projects with more than 30 activitiesThe equal horizontal dimension of activities does not take into consideration the resource load of each activity

MAKIN

G TRAD

EOFFS

With tasks, CP, and resource assignments in place, you are positioned to make explicit planning tradeoffs

Analyze the impact on schedule of different feasible allocations of available resources

Determine impact on schedule and budget of adding (or subtracting) resources (keeping in mind Brooks’s Law)

Determine impact of changes in project scopeImportant questions:

Are schedule and cost consistent with project objectives?If not, can they be made so?Or should we change the objectives?Can we eliminate dependencies by working differently? Are we trying to do too much?

PROJECT STRU

CTURE – H

OW

MAN

Y “CHU

NKS”?

In considering scope, resource, and schedule tradeoffs, often the question of how you might “chunk” the project comes up

What if we divide this project into smaller projects?Can improve fit between available resources and scheduleMight allow most important objectives to be delivered sooner, at the cost of

waiting longer for some other, less important objectives

Can also have budget implications – dividing a project up into smaller chunks can make it appear more expensive

Although it can sometimes turn out cheaper if the smaller projects have fewer problems than the big one would have…

Which brings us to…

PLANN

ING

FOR PRO

JECT RISKS

As much as possible during planning stages of a project, draw attention to project risks and develop plans for managing them.

Identify likely sources of riskDevelop plans to minimize probability that risks will materialize

Might result in new tasks being identified, which will require additional resource requirements

Develop plans to minimize impact if risks do materializeImportant questions:

Have we identified all the risks we can?Which should we worry most about (because the are very likely or would have

major impact on the project)?

PROJECT STRU

CTURE AN

D RISK

There is a relationship between project structure and riskIn general, larger projects involve greater risks than a series of smaller projects

(smaller projects are less complex and constitute smaller failures even when something does go wrong)

An additional advantage in “chunking” large projects into smaller ones: Can incorporate learning from early chunks into later chunks

Certain projects have characteristics that make risks harder to anticipate and make smaller chunks more beneficial

If project outcomes are difficult to specify in advance (thus must be “discovered” to some extent – such as when a user of a product can’t easily envision how the product might be used differently)

If project objectives are likely to change while the project is in progress (due to changes in technology, moves by competitors, etc.)

ON

GO

ING

STATUS M

ON

ITORIN

G

The challenge is to keep the PM and project team focused on areas that that provide the best indication of project progress, and to maintain access to high quality information about the progress of the project

Important questions:How will status information be collected?What will be monitored and how?Are we confident in the quality of our measures of progress?

The problem of open communication: To do a good job of collecting status information, you need people to be really honest about the problems they’re seeing

“SWEEPIN

G TH

ING

S UN

DER TH

E RUG

”

A very common sequence of events on projectsTeam members discover problems that will delay the projectPM and senior managers are not happy to hear of the delay and convey the

impression (often unintentionally) that the person who discovered the problem is to blame for the delay

People get the idea that identification of problems that result in project delays is an unwelcome behavior

They start “sweeping things under the rug”After problems accumulate “under the rug” for some time, something goes

terribly wrong with the project…

IN PRO

GRESS ADJU

STMEN

T AND

ADAPTATION

…

In every project, there is a need to adjust the ongoing project to account for unexpected problems (or opportunities)

A continuation of the process of making planning tradeoffsChange scope, eliminate dependencies, or add resourcesManage “scope creep” – enlarging project scope without really acknowledging

that the project is getting bigger, and without assigning additional resources or otherwise accounting (e.g., moving deadline later) for the increase in work that accompanies the increase in scope

Important questions:Are mid-project requests for changes really requirements?Should we make adjustments to the project?Should we abandon the project?

LEARNIN

G FRO

M PRO

JECT EXPERIENCES

Important to capture key learning that will improve management of future projectsConduct “post mortem” meetingsCapture and communicate key learning to others on other projects and

throughout the larger organizationOften not done, so learning gets lostImportant questions:

What worked?What didn’t?Have we acknowledged and celebrated good work?

THE TH

REE MAIN

“LEVERS” OF PM

ScopeAdjust what is included in the projecte.g., decide to drop Feature 7 from the project objectives

ResourcesAdjust who is working on a projecte.g., decide to add two more people to the project

ScheduleAdjust target completion targete.g., decide to allow another month to complete the project

You decide these things as you plan, then revisit during a project

COSTS AND SCHEDULE

PROJECT CO

NTRO

L COST BASELIN

E

Develop a project cost control baseline from the project cost estimateImportant questions:

+How many individual cost elements can the office and field personnel be expected to break actual project costs into for reporting purposes?

+How many individual cost elements can the project management team effectively review and monitor?

+How can Pareto’s Law be taken into account—that 80 percent of the total project cost is probably represented by only 20 percent of the cost items?

! Beware: cost escalation

ESTIMATIN

G CO

STS – BASIC TECHN

IQU

ES1. Expert opinion2. Analogy - reviewing costs from previous, similar projects

Costproposed = Costanalogy x (Capacityproposed/Capacityanalogy)

3. Parametric - an estimate derived from an empirical or mathematical relationship – eg. a multiple regression model that links material cost to floor space to receiving docks in a building

4. Cost engineering - detailed cost analysis of individual cost categories at the work package or task level. It is a bottom-up approach.

DETERM

ININ

G EARN

ED VALU

E1. Units completed:

For example, suppose that 420 linear feet (LF) of 4-inch diameter steel pipe has been installed. If the total project requires 2,100 LF of pipe, then the percentage of completion is 20 percent (420 LF divided by 2,100 LF).

2. Incremental milestones:

When the work task involves a sequential series of subtasks, the percentage of completion may be estimated by assigning a proportionate percentage to each of the subtasks.

For example, the installation of a major item of equipment might be broken down as follows: Construct foundation pad 10 percent Set equipment on foundation 60 percent Connect mechanical piping 75 percent Connect electrical 90 percent Performance testing and start up 100 percent.

Percentage of completion is estimated by determining which of the milestones have been reached. The accuracy of this procedure depends upon a fair allocation of percentage to the subtask in relation to costs.

DETERM

ININ

G EARN

ED VALU

E3. Cost to complete:The cost to complete the remaining work for a given task is first estimated. This detailed cost estimate utilizes both the original cost estimate and any historical cost data acquired so far on the project.

For example, if the actual cost to date for structural steel erection is $18,500 and theestimated cost to complete the task is $6,500, the percentage of completion is 74%.

Earned value = % of completion x original budget cost for the task

EXAMPLE O

F COST CO

NTRO

L STATUS REPO

RT

ELEMEN

TS OF A CO

ST CON

TROL SYSTEM

DO NOT FORGET ABOUT VALUE!

COST CO

NTRO

L SYSTEMS

-Based on the variance in costs, caused by• Resources used to accomplish the work have been paid more than was

planned.• Resources used to accomplish the work have been consumed in more

quantity than was planned.

COST M

ANAG

EMEN

T IND

ICES

Implementing change

INVESTMENTS AS REAL OPTIONS

INTRODUCERE ÎN ARBORI BINOMIALI

EVALUAREA OPŢIUNILOR

Factorii care influenţează preţul unei opţiuniPreţul actual al activului de bazăTimpul până la expirarea opţiuniiPreţul de exercitareRata de dobândă pe piaţăCaracteristicile aleatoare ale preţului activului de bază

Preţurile opţiunilor sunt determinate prin intermediul unor modele care au la bază ipoteze cu privire la procesul stocastic care guvernează preţul activului de bază la expirarea opţiunii.

ABORDĂRILE DOMINANTE

1. Preţul are o distribuţie lognormală: logaritmul preţului viitor urmează distribuţia normală. Aceasta este ipoteza de bază a modelului de evaluarea a opţiunilor Black-Scholes-Merton.

2. Preţul activului are a distribuţie în timp discret, conform căreia în fiecare perioadă randamentele activului de bază pot lua numai două valori posibile. Aceasta este esenţa modelului binomial.

ABORD

ĂRILE DO

MIN

ANTE

(CON

T.)Ambele modele (Black-Scholes-Merton şi modelul binomial) pot determina un preţ al opţiunii numai

pe baza argumentului lipsei de arbitraj (free lunch). Alte distribuţii necesită ipoteze adiţionale.

UN

MO

DEL BIN

OM

IAL SIMPLU

Preţul acţiunii este în prezent $20În trei luni va ajunge fie la $22 fie la $18

Preţul acţiunii = $22

Preţul acţiunii = $18

Preţul acţiunii = $20

Preţul acţiunii = $22Preţul opţiunii = $1

Preţul acţiunii = $18Preţul opţiunii = $0

Preţul acţiunii = $20Preţul opţiunii=?

O O

PŢIUN

E CALL

O opţiune call la 3 luni pe această acţiune are un preţ de exercitare de 21.

Fie portofoliul:long D acţiuni short o opţiune call

Portofoliul este fără risc dacă 22 D – 1 = 18D adică D = 0.2522 D – 1

18D

CONST

RUCŢIA U

NU

I PORTO

FO

LIU

FĂRĂ RISC

EVALUAREA PO

RTOFO

LIULU

I

(RATA FĂRĂ RISC ESTE 12%)

Portofoliul fără risc este: long 0.25 acţiuni

short 1 opţiune callValoarea portofoliului în 3 luni este 22´0.25 – 1 = 4.50Valoarea portofoliului astăzi este 4.5e – 0.12´0.25 = 4.3670

EVALUA

REA U

NEI

OPŢIU

NI

Portofoliullong 0.25 acţiuni

short 1 opţiune valorează 4.367Valoarea acţiunilor din portofoliu este

5.000 (= 0.25´20 )Astfel, valoarea opţiunii va fi

0.633 (= 5.000 – 4.367 )

GEN

ERALIZARE

Un produs derivat durează până la momentul T şi este dependent de preţul acţiunii

S0u ƒu

S0d ƒd

S0

ƒ

GEN

ERALIZARE

(CON

T)

Să considerăm portofoliul care constă din o poziţie long pe D acţiuni şi o poziţie short pe 1 derivat

Portofoliul este fără risc dacă S0u D – ƒu = S0d D – ƒd, adică

ƒu df

S u S d0 0

S0 u D – ƒu

S0d D – ƒd

ΔS0– f

GE

NE

RALIZARE(CON

T)

Valoarea portofoliului la momentul T esteS0u D – ƒu

Valoarea portofoliului astăzi este (S0u D – ƒu )e–rT

O altă expresie pentru valoarea portofoliului de astăzi este S0 D – f

Prin urmare ƒ = S0 D – (S0u D – ƒu )e–rT

GEN

ERALIZARE

(CON

T)

Înlocuind pe D vom obţine

ƒ = [ p ƒu + (1 – p )ƒd ]e–rT

unde

pe d

u d

rT

MED

IA RANDAM

ENTELO

R ACTIVULU

I DE BAZĂ ESTE N

ERELEVANTĂ

Când evaluăm o opţiune în funcţie de activul de bază, randamentul aşteptat (mediu) nu apare în analiză

EVALUA

REA N

EUTRĂ

LA RISC

ƒ = [ p ƒu + (1 – p )ƒd ]e-rT

Variabilele p şi (1 – p ) pot fi interpretate ca fiind probabilităţi neutre la risc pentru mişcările în sus şi în josValoarea unui produs financiar derivat este dată de câştigul aşteptat într-o lume neutră la risc, actualizat cu rata fără risc

S0u ƒu

S0d ƒd

S0

ƒ

p

(1 – p )

REVIZITAREA EXEM

PLU

LUI

INIŢI

AL

Cum p este o probabilitate neutră la risc20e0.12 ´0.25 = 22p + 18(1 – p );

p = 0.6523Sau, putem folosi formula

6523.09.01.1

9.00.250.12

e

du

dep

rT

S0u = 22 ƒu = 1

S0d = 18 ƒd = 0

S0

ƒ

p

(1 – p )

EVALUAREA U

NEI

OPŢIU

NI

Valoarea opţiunii estee–0.12´0.25 [0.6523´1 + 0.3477´0] = 0.633

S0u = 22 ƒu = 1

S0d = 18 ƒd = 0

S0

ƒ

0.6523

0.3477

EXEMPLU

CU

D

OI

PAŞI

Fiecare pas are 3 luni

20

22

18

24.2

19.8

16.2

EVALUAREA U

NEI

OPŢIU

NI

CALL

Valoarea în nodul B = e–0.12´0.25(0.6523´3.2 + 0.3477´0) = 2.0257

Valoarea în nodul A = e–0.12´0.25(0.6523´2.0257 + 0.3477´0)

= 1.2823

201.2823

22

18

24.23.2

19.80.0

16.20.0

2.0257

0.0

A

B

C

D

E

F

EXEMPLU

CU O

PŢIUN

E PUT; K=52

504.1923

60

40

720

484

3220

1.4147

9.4636

A

B

C

D

E

F

DAR DACA OPŢIU

NEA ESTE AM

ERICANĂ...

505.0894

60

40

720

484

3220

1.4147

12.0

A

B

C

D

E

F

DELTA

Delta (D) este elasticitatea preţului unei opţiuni la o modificare a preţului activului de bazăValoarea lui D variază de la nod la nod

ALEGEREA LU

I U ŞI D

O modalitate de alegerea a volatilităţii este să considerăm că

unde s este volatilitatea şi dt este dimensiunea pasului în timp. Este abordarea folosită de Cox, Ross şi Rubinstein

u e

d e

t

t

OPTIO

N PRICIN

G – BLACK SCH

OLES M

ERTON

PARTEA 2: INVESTITII STRAINE DIRECTE