chapter-2

Chapter Two

Project Planning and Control

Contents

Work Breakdown Structure

Project Organization

Bar Charts

Network Scheduling

Critical Path method

Program Evaluation and Review Techniques

S-curve

Project Crashing

Resource Allocation

Project Risks

Work Breakdown Structure (WBS)

It is a methodology for converting a large-

scale project into detailed schedules for its

thousands of activities for planning,

scheduling, and control purpose

The objective of developing a WBS is to

study the elemental components of a project

in detail

Using a WBS, a large project may be broken

down into smaller subprojects which may, in

turn, be further subdivided into another,

lower level of more detailed sub component

activities, and so on.

Eventually, all the tasks for every activity are

identified, commonalities are discovered, and

unnecessary duplication can be eliminated.

Thus by applying the WBS approach, the

overall project planning and control can be

improved.

Individual components in a WBS are referred

to as WBS elements and the hierarchy of

each is designated by a level identifier.

Elements at the same level of subdivision are

said to be the same WBS level.

Descending levels provide increasingly

detailed definition of project tasks. The

complexity of project and the degree of

control desired determine the number of

levels in the WBS.

Each WBS component is successively broken

down into smaller details at lower levels.

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Level 1: This level contains only the final

project purpose. This item should be

identifiable directly as an organizational

budget item.

Level 2: This contains the major

subcomponents of the project. This

subdivision is usually identified by their

contiguous location or by their related

purposes.

Level 3: Contains definable components of

the level 2 subdivisions.

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Subsequent levels are constructed in more

specific detail depending on the level of

control desired.

If a complete WBS becomes too crowded,

separate WBSs may be drawn for level 2

components.

Each WBS element is assigned a code that is

used for its identification throughout the

project life cycle.

Alphanumeric codes may be used to indicate

element level as well as component group.

Effective use of the WBS will graphically

outline the scope of the project and the

responsibility for each work package.

Designing the WBS requires a delicate

balance to address the different needs of

various disciplines and project occasions.

Necessarily there is no right or wrong

structure because what may be an excellent

fit for one discipline may be an awkward

burden for another.

Project Breakdown Structure

Project Organization

Like any organization, projects can be

managed and controlled by using different

type of organizational structure.

Before selecting an organizational structure,

the project team should assess the nature of

the job to be performed and its

requirements.

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The structure may be defined in terms of

functional specializations, departmental

proximity, standard management boundaries,

operational relationships, or product

requirements

Large and complex projects should be based

on well-designed structures that permit

effective information and decision processes.

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Formal and informal structures: The

formal organization structure represents

the officially sanctioned structure of a

functional area.

The informal organizations, on the other

hand, develop when people organize

themselves in an unofficial way to

accomplish an objective that is in line with

the overall project goals.

Both formal and informal organizations are

placed in every project environment.

Functional organization: This is the most

common type of formal organization,

whereby people are organized into groups

dedicated to a particular functions.

Depending on the size and the type of

auxiliary activities involved in the project,

several minor, but supporting, functional

units can be developed for a project.

The project home office or headquarters is

located in the specific functional

department.

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Product organization: Another approach to

organize a project is to use the end product

or goal of the project as the determining

factor for personnel structure.

This is often referred to as the pure project

organization or, simply, project organization.

The project is set up as a unique entity

within the parent organization.

It has its own dedicated technical staff and

administration.

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It is linked to the rest of the system

through process reports, organizational

policies, procedures, and funding.

The interference between product-

organized projects and other elements of

organization may be strict or liberal

depending on the organization.

This type of organization is common in large

project-oriented organizations or

organizations that have multiple product

lines.

Unlike the functional structure, the product

organization decentralizes functions. It

creates a unit consisting of specialized skills

around a given project or product.

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Matrix organization: the matrix

organization is a popular choice of

management professionals. A matrix

organization exists where there is multiple

managerial accountability and responsibility

for a job function.

It attempts to combine the advantages of

the traditional structure and the product

organization structure.

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In pure product organization, technology

utilization and resource sharing are limited

because there is no single group responsible

for overall project planning.

In the traditional organization structure,

time and schedule efficiency are sacrificed.

There are usually two chains of command:

horizontal and vertical.

The horizontal line deals with the functional

line responsibility while the vertical line

deals with the project line of responsibility.

The project manager has total responsibility

and accountability for the project success.

The functional managers have the

responsibility to achieve and maintain high

technical performance of a project.

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The project that is organized under a matrix

structure may relate to specific problems,

marketing issues, product quality

improvement, and so on.

The project line in the matrix is usually of

temporary nature while the functional line is

more permanent.

Matrix Organization Structure

Bar Charts or Milestone Charts

The history of project planning techniques

can be accurately traced back to World War

I when an American, Henry Gantt, designed

the barchart as a visual aid for planning and

controlling his projects.

The beginning and the end of each bar

represent the time of start and the time of

finish of that activity

Once the project has started the Gantt

chart can further be used as a tool for

project control.

This is achieved by drawing a second line

under the planned schedule to indicate

activity progress.

The relative position of the progress line to

planned line indicates percentage complete

and remaining duration, while the relative

position between the progress line and Time

now indicates actual progress against planned

progress.

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Example

Draw the bar chart for "finalization of

design and work orders" for a building

project.

Activity Description Time of

Completion

A Site selection and survey 4 weeks

B Design 6 weeks

C Preparation of drawings 3 weeks

D Preparation of specification

and tender document 2 weeks

E Tendering 4 weeks

F Selection of contractor 1 week

G Award of work order 1 week

Bar chart for a building Project

The benefits of Gantt chart can be clearly

seen not only are the calculations simple but

it combines all the above information on one

page.

Network Scheduling

The most common network scheduling

methods are Critical Path Method (CPM) and

Program Evaluation and Review Technique

(PERT).

Two approaches may be used for the

assessment of duration for activity

completion.

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The first approach is the deterministic

approach, in which we may assume that we know

enough about each job or operation, so that a

single estimate of their duration is sufficiently

accurate to give reasonable results.

The second approach is the probabilistic

approach, in which one may only be able to

state limits with-in which it is virtually certain

that the activity duration will lie. Between

these limits we must guess what the probability

of executing the activity is.

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Both methods (CPM and PERT) are

extensively used as dynamic control tools in

the management of a large project.

They give the project manager a

comprehensive picture of the project status

at any time.

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Network Diagram

For a project plan to be effective it must

equally address the parameters of activity

time and network logic.

As project becomes larger and more

complex, the Gantt chart was found to be

lacking as a planning and control tool,

because it could not indicate the logical

relationships between activities.

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This logical relationship is required to model

the effect schedule variance will have down

stream in the project.

In the 1950s feedback from industry and

commerce indicated that project cost and

time overruns were all too common.

It was suggested at the time that the

project estimates were on the optimistic

side in order to gain work. However, a more

important reason emerged which indicated

that the planning and control technique,

available to manage large complex projects,

were inadequate.

With these shortcomings in mind, network

planning techniques were developed

In network modeling of projects, the arrow

diagram is of primary importance. Some of the

advantages of network diagram or arrow

diagram are:

It clearly shows the inter-relationship between

events.

The project is seen as integrated whole, thus

making it easier for control.

It can be used even for highly complicated

projects consisting of a large number of

activities.

It directly indicates the time required in

between two activities.

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Event : it is defined to be an instant in time.

In a project, an event, may mark the initiation

of an activity, the completion of an activity, or

the time after which an activity may be

initiated.

Design completed, pipe line laid, electricity

installed, etc are examples of events. It is

represented by a circle o in a network which is also known as a node or connector.

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An event can be further classified into the

following categories:

Merge event: When more than one activity come

and join an event, such event is known as merge

event.

Burst event: When more than one activity leave

an event, such event is known as a burst event.

Merge and burst event: An activity may be a

merge and burst event at the same time as with

respect to some activities it can be a merge event

and with respect to some other activities it may

be a burst event.

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Different types of event formation

Activity: Any individual operation, which

utilizes resources and has a beginning and an

end, is called activity.

A project may be divided into activities that

are time consuming tasks or subprojects like:

assembly of parts, mixing of concrete,

preparing budget, etc.

Each activity in a project must be under the

direction of a single individual. The other

criterion is that an activity must be

performed in a single shop.

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A

k

An arrow representing an activity A whose

estimated duration is k unit of time.

Usually an activity can be classified into the

following four categories.

An arrow is commonly used to represent an

activity with its head indicating the

direction of progress in the project.

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Predecessor activity: Activities that must

be completed immediately prior to the start

of another activity are called predecessor

activities.

Successor activity: Activities that cannot

be started until one or more of other

activities are completed, but immediately

succeed them are called successor activities.

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Concurrent activities: Activities that cannot

be accomplished concurrently are known as

concurrent activities. It may be noted that

an activity can be a predecessor or

successor to an event or it may be

concurrent with one or more of the other

activities.

Dummy activity: An activity which does not

consume any kind of resource but merely

depicts the technological dependence is

called a dummy activity.

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It may be noted that the dummy activity is

inserted in the network to clarify the

activity pattern in the following two ways:

one is to make the activities with common

starting and finishing points distinguishable,

and

the other one is to identify and maintain the

proper precedence relationship between

activities that are not connected with

arrows

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For example, consider a situation where A

and B are concurrent activities, C is

dependent on A, and D is dependent on A and

B both.

Such a situation can be handled by using a

dummy activity

Dummy Activities

Another situation, consider a case where B

and C have the same job reference and they

can be started independently on completion

of A.

But, D could be started only completion of B

and C.

Dummy Activities

An event is that particular instant of time at

which some specific part of a project has

been or is to be achieved.

While an activity is actual performance of a

task. An activity requires time and resource

for its completion.

Correct & Incorrect Use of Network Dummies.

Rules for Drawing Network Diagram

In order to draw a network diagram, the

following general rules have to be

considered:

Each activity is represented by one and only

one arrow in the network:

This implies that no single activity can be

represented twice in the network.

This is to be distinguished from the case

where one activity is broken into segments.

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Sequence of Activity

No two activities can be identified by the

same events: For example, activities a and b

have the same end events. The procedure is

to introduce a dummy activity either

between a and one of end events or between

b and one of the events.

Modified representations after introducing a

dummy activity d is shown in figure

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As a result of using the dummy, activities a and

b can now be identified by unique end events.

It must be noted that a dummy activity does

not consume any time or resource.

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Dummy activities are also useful in

establishing logical relationship in the arrow

diagram which otherwise cannot be

represented correctly.

Suppose jobs a and b in a certain project must

precede the job c, on the other hand, the job

e is preceded by the job b only.

Shows the correct way since, though the

relationship between a, b and c are correct,

the diagram implies that the job must be

preceded by both the jobs a and b.

The correct representation using the dummy

d is shown that indicate precedence

relationships are justified.

Check the precedence relationship: In order

to ensure the correct precedence

relationship in the arrow diagram, the

following questions must be checked

whenever any activity is added to the

network.

What activity must be completed immediately

before this activity can start?

What activities must follow this activity?

What activities must occur simultaneously with

this activity?

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Apart from this, a few important suggestions

for drawing good networks are:

Try to avoid arrows which cross each

other.

Use straight arrows.

Do not attempt to represent duration of

activity by arrow length.

Use arrows from left to right (or right to

left). Avoid mixing two directions, vertical

and standing arrows may be used if

necessary.

Use dummies freely in rough draft but

final network should not have any

redundant dummies.

The network has only one entry point-

called the start event and one point of

emergence-called the end event.

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In many situations, all these may not be

compatible with each activity and some of

them are violated.

The idea of having a simple network is to

facilitate easy reading for all those who are

involved in the project.

Common Errors in Drawing Networks

Three types of errors are most commonly

observed while drawing network diagrams.

Dangling: To disconnect an activity before

the completion of all activities in a network

diagram is known as dangling.

As shown in the figure below, activities (b -

c) and (d - e) are not the last activities in

the network. So the diagram is wrong and

indicates the error of dangling.

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Drawing error diagram

Looping (or Cycling): Looping errors is also

known as cycling errors in a network diagram.

Drawing an endless loop in a network is known

as an error of looping as shown in the

following figure.

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Looping or cycling error diagram

Redundancy: Unnecessarily inserting the

dummy activity in a network diagram is known

as the error of redundancy as shown in the

following diagram.

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Redundancy Error

Critical Path Method (CPM)

The Critical Path Method (CPM) was

developed in 1957 by Remington Rand Univac

as a management tool to improve the planning

and control of a construction project

CPM was initially set-up to address the time

cost trade-off dilemma often presented to

project managers, where there is a complex

relationship between project time to

complete and cost to complete.

CPM enables the planner to model the effect

various project time cycles have on direct

costs.

Shortening the project duration will reduce

indirect costs, but may increase the direct

costs.

This technique is often called Project

crashing or acceleration,

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Time Estimate and Critical Path in Network Analysis:

Once the network of a project is

constructed, the time analysis of the

network becomes essential for planning

various activities of the project.

An activity-time is a forecast of the time an

activity is expected to take from its starting

point to its completion under normal

conditions.

The main objective of the time analysis is to

prepare a planning schedule of the project, which

should include the following factors:

Total completion time for the project.

Earliest time when each activity can start.

Latest time when each activity can be started

without delay of the total project.

Float for each activity, i.e., the amount of time by

which the completion of an activity can be delayed

without delaying the total project completion.

Identification of critical activities and critical

path.

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),( ji

iE E or T

jL L or T

Dij

ijSE )(

ijfE )(

ijSL )(

ijfL )(

The following notations are used for the basic scheduling computation techniques:

= Activity (i, j) with tail event i and head event j.

= Earliest occurrence time of event i.

= Latest allowable occurrence time of event j.

= Estimated completion time of activity (i , j)

= Earliest starting time of activity (i , j)

= Earliest finish time of activity (i , j)

= Latest starting time of activity (i , j)

= Latest finish time of activity (i , j)

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Thus the basic scheduling computation can be put

under the following three categories.

i) Forward Pass Computations: Before starting

computations, the occurrence time of initial

network event is fixed. Then, the forward pass

computation yields the earliest start and earliest

finish time for each activity (i, j), and indirectly the

earliest expected occurrence time for each event.

This is mainly done by using the following steps:

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iijS EE )(

ijijSijf DEE )()(

ijiijf DEE )(

Step 1. The computations begin from the start node and move towards the end node.

Step 2. a) Earliest starting time of activity (i, j) is the earliest event time of the tail end event i.e.,

b) Earliest finish time of activity (i, j) is the earliest starting time

plus the activity time. i.e.,

or

]D[Emax.E ]or j)(i, of rpredecesso immediate all for)[(Emax.E ijiijijfij

c) Earliest event time for event j is the maximum of the earliest finish

times of all activities ending into that event. That is,

The computed E values are put over the respective circles representing each event.

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ii) Backward Pass Computations

The latest event time, (L) indicates the time

by which all activities entering into that

event must be computed without delaying the

computation of the project. These can be

computed by reversing the method of

calculation used for earliest event times.

This is done in the following steps:

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LE

LL ijf )(

Step 1. For ending event assume

Remember that all Es have been computed by forward pass computations.

Step 2. Latest finish time of activity (i, j) is equal to the latest event time of

event j. i.e.,

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ijijfijS DLL )()(

ijjijS DL)L(

Step 3. Latest starting time of activity (i , j) = the latest completion time of

activity (i , j) the activity time, or

or

Step 4. Latest event time for event I is the minimum of the latest start time

of all activities originating from the event, i.e.,

]DL[min.]D -)[(Lmin. j)] (i, of s successorimmediate all for)[(L.inmL ijjjijijfjijSji

The computed L values are put over the respective circles representing each event.

iii) Determination of Floats and Slack Times

When the network diagram is completely

drawn, properly labeled, and earliest (E) and

latest (L) event times are computed as

discussed so far, the next objective is to

determine the float and slack times of a

project.

There are mainly five kinds of floats.

Total float: The amount of time by which

the completion of an activity could be

delayed beyond the earliest expected

completion time without affecting the

overall project duration time.

Mathematically, the total float of an activity

(i , j) is the difference between the latest

start time and the earliest start time of

that activity. Hence the total float for an

activity (i , j), denoted by

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ijfT )(

)()( startEarliest startLatestT ijf

can be calculated by the formula:

for activity (i - j)

ijSijSijf ELT )()()(

iijjijf E)DL()T(

or

Free float: The time by which the

completion of an activity can be delayed

beyond the earliest finish time without

affecting the earliest start of a subsequent

(succeeding) activity.

ijfF )(

ijijijf DEEF )()(

)j,i(for timeActivity )i event for time Earliestj event for time Earliest()j,i(for float Free

Mathematically, the free float for activity (i, j), denoted by

can be calculated by the formula :

In other words,

This float is concerned with the commencement of subsequent activity.

Independent float: The amount of time by

which the start of an activity can be delayed

without affecting the earliest start time of

any immediately following activities,

assuming that the preceding activity has

finished at its latest finish time.

ijFI )(

ijijijF DLEI )()(

Mathematically, independent float of an activity (i, j), denoted by

, can be calculated by the formula :

The negative independent float is always taken zero. This float is concerned with prior and subsequent activities.

Interfering float: Utilization of float of an

activity may affect the float time of the

other activity in the network. Interfering

float is that part of total float which causes

a reduction in the float of successor

activities.

It is the difference between the latest

finish time of activity in question and the

earliest starting time of the following

activity or zero whichever is larger.

Event slacks: For any given event, the

event slack is defined as the difference

between the latest event and earliest event

times. Mathematically, for a given activity (i,

j),

jj EL slackevent Head

ii EL slackevent Tail

ijij DELfloat Total

All the floats defined earlier can be represented in times of head and tail event slacks also.

)()(float Free jjijijijij ELDELDEE

slackevent Head -float Total

)()( iiijijijij ELDEEDLEfloat tIndependen

slackevent Tail -float reeF

iv) Time Scale Representation of Floats and

Slacks

The various floats and slacks for an activity

(i, j) can be represented by the following

time scale figure

Time scale representation of float and slacks

Value of total float

Determination of the Critical Path

ii ELiSlack )(

ii LE

Critical event: Since the slack of an event is the difference between the latest and earliest event times. i.e.,

the events with zero slack times are called critical events. In other words, the event i is said to be critical if

ii) Critical activity: Since the difference

between the latest start time and earliest

start time of an activity is usually called as

total float, the activities with zero total

float are known as critical activities. In

other words an activity is said to be critical

if a delay in its start will cause a further

delay in the completion date of the entire

project.

Obviously, a non-critical activity is such that the time between its earliest start and its latest completion dates (as allowed by the project) is longer than its actual duration. In this case, non-critical activity is said to have a slack or float time.

iii) Critical path: The sequence of critical

activities in a network is called the critical

path. The critical path is the longest path in

the network from the starting event to

ending event and defines the minimum time

required to complete the project. By the

term path we mean a sequence of activities

such that it begins at the starting event and

end at the final event. The length of the

path is the sum of the individual times of the

activities lying on the path.

If the activities on a critical path are

delayed by a day, the project would

also be delayed by a day unless the

times of the future critical activities

are reduced by a day by different

means.

The critical path is denoted by double

or darker lines to make distinction

from the other non-critical paths.

Thus the critical path has two features:

If the project has to be shortened, then

some of the activities on that path must also

be shortened. The application of additional

resources on other activities will not give the

desired result unless that critical path is

shortened first.

The variation in actual performance from the

expected activity duration time will be

completely reflected in one-to-one fashion in

the anticipated completion of the whole

project.

The critical path identifies all critical

activities of the project. The method of

determining such a path is explained by the

following numerical example.

Example 12.2:

Consider the following project to

manufacture a simple mobile stone crasher.

The list of each activities, their relationship,

and the time required to complete them are

given in the following table. We are

interested to find the time it will take to

complete this project. What jobs are critical

to the completion of the project in time,

etc?

List of Activities

Activity Symbol Duration

(weeks)

Restriction

Preliminary design A 3 A < B, Cl

Engineering analysis B 1 B < Dl, F, H

Prepare layout I Cl 2 Cl < C2, Dl

prepare layout II C2 2 C2 < E

Prepare material request Dl 1 Dl < D2

Receive requested material D2 1 D2 < E

Fabricate Parts E 4 E < J

Requisition Parts F 1 F < G

Receive Parts G 2 G < J

Place subcontracts H 1 H < I

Receive subcontracted parts I 5 I < J

Assemble J 2 I < K

Inspect and test K 1

Solution:

First the network diagram is constructed

Then, it is necessary to find out the earliest

and latest completion time of for each

activity in the net work.

The earliest and the latest times are re-

calculated by using forward pass and

backward pass computations, respectively.

The solution now starts by the forward pass

computation.

Step1. Determination of Earliest Time )( jE

Forward Pass Computation

The purpose of the forward pass computation is to find out

earliest start times for all the activities.

For this, it is necessary to assign some initial value to the

starting node 10.

Usually this value is taken to be zero so that the subsequent

earliest time could be interpreted as the project duration up to

that point in question.

Rules for the computation are as follows:

010 E

jE

].[ ijij DEMaxE

Rule 1. Initial event is supposed to occur at time equal to zero, that is,

Rule 2. Any activity can start immediately when all preceding activities are completed.

for node j is given by

010 E

].[ 2020 ii DEMaxE

10i

Rule 3. Repeat step2 for the next eligible activity until the end node is reached.

and

For node 20, node 10 is the only predecessor and hence

contains only one element. Therefore,

].[ ijij DEMaxE

33020,101020 DEE

,

,

,

52321,202021 DEE

41330,202030 DEE

51450,303050 DEE

51460,303060 DEE

5]404,505.[ 31,303031,212131 DEDEMaxE

32E

61532,313132 DEE

The collection i consists of node 21 and 30 that are preceding node 31, Therefore,

and values of can be computed as:

Once again, for node 40 and 70;

].[ 31,31 ii DEMaxE

Consider node 31, where there are two emerging activities, i.e.

7]716,725.[ 40,323240,212140 DEDEMaxE

11]1055,725,1147.[ 70,606070,505070,404070 DEDEDEMaxE

80E 90E

1321180,707080 DEE

1411390,808090 DEE

and values of , and can be computed as:

From this computation, it can be inferred that this job will take 14

days to finish as this the longest path of the network.

Activities along this longest path are: 10 20 21 40 70 80

90. This longest path is called the critical path. In any network, it

is not possible that there can be only one critical path.

For example, if in the above network, let

530 E

days, then 10 20 30 60 70 80 90 can be also

critical, in that case two critical paths exist having the

same duration for completion of the project.

Step2. Determination of Latest Time )( iL

Backward Pass Computation

In forward pass computation, the earliest time when a

particular activity will be completed is known.

It is also seen that some activities are not critical to

the completion of the job.

The question a manager would like to ask is: Can their

starting time be delayed so that the total completion

time is still the same?

Such a question may arise while scheduling the resources

such as manpower, equipment, finance and so on.

If delay is allowable, then what can be the maximum

delay? For this, the latest time for various activities

desired.

The backward pass computation procedure is used to

calculate the latest time for various activities.

In forward pass computation, assignment of was

arbitrary, likewise for the backward pass computation, it

is possible to assign the project terminal event the date

on which the project should be over.

If no such date is prescribed, then the convention is of

setting latest allowable time determined in forward pass

computation.

Sii T or EL

ST

iE

][. ijjji D-LMinL

Rule 1. Set

Where is the scheduled date for completion and

is the earliest terminal time.

i.e. the latest time for activities is the minimum of the latest time of all succeeding activities reducing their activity time.

Rule 3. Repeat rule 2 until starting activity reached.

Rule 2.

14L90

80L

70L

60L

50L

40L

32L

31L

Latest times for activities of the network are calculated below: By rule1, set

. Applying rule 2, it is to determine

90j for 13114}D-{LMin.L j80,jj80

11231D-}D-{LMin.L 70,8080j70,jj70 L

6511D-L}D-{LMin.L 60,7070j60,jj60

9211D-L}D-{LMin.L 50,7050j50,jj50

(j contains only one node 80)

(j contains node 70)


7411D-L}D-{LMin.L 40,7040j40,jj40

617D-L}D-{LMin.L 32,4032j32,jj32

516D-L}D-{LMin.L 32,3231j31,jj31



(j contains node 32) Now consider node21, for this node, there are two succeeding activities, namely 21 40, and 21 31. Hence,

5505

527..

31,2131

40,2140

Min

DL

DLMin}D-{LMin.L j21,j40) (31,j21

3314

325..

30,2030

21,2021

Min

DL

DLMin}D-{LMin.L j21,j30) (21,j20

4

415

415

505

..

31,6031

31,5031

31,3031

Min

DL

DL

DL

Min}D-{LMin.L j30,j60) 50, (31,j30

Similarly, for node 20, and 30,

03D-L}D-{LMin.L 10,20j10,jj10 320

0L10

EL ii

0L10

and like the other one, for node 10,

The minimum value of

is no surprising result. Since, started with

, it is always possible to have

If this is not so, it means that some error is made in calculations of forward pass or backward pass values.

Network diagram with critical path

Recall that path 10 20 21 40 70 80 90

was defined as the critical path of this network.

Along this path, it is observed that the latest

and earliest times are the same implying that any

activity along this path cannot be delayed

without affecting the duration of the project.

Step 3. Computation of Float )( fL

By definition, for activity 60 70, the float is one day

1566060 EL

This float represents the amount by which this particular activity

can be delayed without affecting the total time of the project.

Also, by definition, free float, if any will exist only

on the activities merge points.

To illustrate the concept of free float, consider

path 10 20 30 50 70, total float on activity 50

- 70 is four days and since this is the last activity

prior to merging two activities, this float is free

float also.

Similarly, consider the activity 30-50 which has a

total float of 4 days but has zero free float

because 4 day of free float is due to the activity

50-70.

If activity 30-50 is delayed up to four days, the early start time of no activity in the network will be affected.

Therefore, the concept of free float clearly states that the use of free float time will not influence any succeeding activity float time.

Step 4. To Identify Critical Path

Identifying the critical path is a byproduct

of boundary time calculations. A critical

activity has no leeway in scheduling and

consequently zero total float. It is important

to note that the value of slack, associated

with an event, determines how critical that

event is. The less the slack, the more critical

an event is.

The earlier calculation shows that the path or paths which have zero float are called the critical ones or in other words, a critical path is the one which connects the events having zero total float or a minimum slack time.

If this logic is extended further more, it would provide a guide rule to determine the next most critical path, and so on.

Such information will be useful for managers in the control of project. In this example, path 10 20 30 60 70 80 - 90 happens to be next to critical path because it has float of one day on many of its activities.

Activity Duration

Start Finish Total Float

Earliest Latest Earliest Latest

(1) (2) (3) (6)

A 3 0 0 3 3 0

B 1 3 4 4 5 1

C1 2 3 3 5 5 0

C2 2 5 5 7 7 0

D1 1 5 5 6 6 0

D2 1 6 6 7 7 0

E 4 7 7 11 11 0

F 1 4 8 5 9 4

G 2 5 9 7 11 4

H 1 4 5 5 6 1

I 5 5 6 10 11 1

J 2 11 11 13 13 0

K 1 13 13 14 14 0

iE (2)-(6)(4) (2)(3)(5) (3)-(4)(7)

ijDj)-(i

Boundary Times Duration for the Start and Finish of Activities

Program Evaluation and Review Techniques (PERT)

The US Navy set up a development team with

the Lockheed Aircraft Corporation, and a

management consultant Booz Allen &

Hamilton, to design PERT as an integrated

planning and control system to manage their

Polaris Submarine project.

The PERT technique was developed to apply a

statistical treatment to the possible range of

activity time durations

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0t

pt

lt

Optimistic time limit of completion time if every thing goes all-right.

limit of completion time if every thing goes all-wrong (in case climatic conditions, explosions, accidents, etc., come into effect to retard the activity).

the duration that would occur most often if the activity was repeated many times under the same conditions.

Pessimistic time

Most likely time

A three time probabilistic model was developed, this includes:

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The three times were imposed on a normal

distribution to calculate the activitys

expected time te as,

6

t4ttt

plo

e

)(

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Normal Probability distribution

Each activity in a PERT network also has a

variance with its completion of time. This

variance measures the dispersion of possible

duration. A large variance means a wide

variation in the outside limits of estimate and

indicates less confidence in estimating:

2

2

6

op tt

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3et

2et

et

99.7 % within

95.0 % "

68.0 % "

A contractor has received order for

constructing a cottage on a sea side resort.

The delivery of materials must be planned and

the complete job finished in 13 weeks. The

work involves and the time required to

complete each activities are given in the table

below.

ot lt pt

Job Description Time, days

A Buying bricks and cement 8 10 14

B Roof tiles 20 24 30

C Preparing foundation 12 14 16

D Erecting shell structure of building 18 20 24

E Laying drains 12 14 15

F Wiring for electrical 16 20 26

G Constructing roof 8 8 10

H Plastering 12 12 18

I Landscaping 4 4 6

J Painting and cleaning 10 12 14

K Laying pathway 4 4 4

L Installing doors and fittings 4 4 4

M Plumbing 20 24 30

N Flooring 8 10 12

a) construct a logical PERT diagram.

b) find the critical path and project duration.

c) determine whether the project is completed

within the planed estimated time or not?

Question

Solution:

Before constructing the PERT diagram, the

expected time (te) for each of the activities

has to be calculated by using the following

formula

6t4ttt

plo

e

)(

ot

lt

pt

where

= optimistic time

= most likely time

= pessimistic time

and also the precedence of the activities has to be determined.

Job Description Immediate predecessors

Time, days

A Buying bricks and cement - 8 10 14

B Roof tiles buying D 20 24 30 24

C Repairing foundation A 12 14 16 14

D Erecting shell structure of building

C 18 20 24 20

E Laying drains C 12 14 15 14

F Wiring for electrical G 16 20 26 20

G Constructing roof D 8 8 10 8

H Plastering G 12 12 18 13

I Landscaping K 4 4 6 4

J Painting and cleaning B,F,I,N 10 12 14 12

K Laying pathway E 4 4 4 4

L Installing doors and fittings G 4 4 4 4

M Plumbing G 20 24 30 24

N Flooring H,L,M 8 10 12 10

6

t4ttt

plo

e

)(

ot ptlt

Network Diagram

j)-(iijD

iE (2)-(6)(4) (2)(3)(5) jL

(3)-(4)(7)

Activity

Duration

(3) (6)

Start Finish Total Float

Earliest Latest Earliest Latest

(1) (2)

A 0 0 10 10 0

B 24 0 20 24 44 20

C 14 10 10 24 24 0

D 20 24 24 44 44 0

E 14 24 64 38 78 40

G 8 44 44 52 52 0

H 13 52 63 65 76 11

I 4 42 82 46 86 40

J 12 86 86 98 98 0

K 4 38 78 42 82 40

L 4 52 72 56 76 20

M 24 52 52 76 76 0

N 10 76 76 86 86 0

S- Curve

An S curve is a graph of the cumulative value

of manhours, percentage complete, or cost,

against time.

In an S-curve, the vertical scale represents

manhours or cost, or the percentage of

planned manhours or budgeted cost, that is,

percentage completed and the horizontal

scale represents the total time available, or

time spent for a specific activity.

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This graph generally takes the form of an S because most projects have a slow start, followed by a longer period of relatively constant activity at a higher rate of activity, and finally a falling off of this rate of activity to give a slow finish.

The S curve is a very sensitive tool for the

analysis and control of progress, whether it

could be based on manhours or cost.

The big advantage of S curves is that they

can be used to identify trends at an early

stage, because they can monitor both the

rate of progress, and also the acceleration or

deceleration of this rate.

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In manpower analysis the slope of the curve represents the rate of expenditure of manhours, that is the velocity, and the rate of change of the curve represents the rate of build up or run down of the momentum of the work on the project, that is, the acceleration or deceleration of the place of work.

In order to plot S curve for effective control

of manhours, three elements of data are

required. These are:

The planned cumulative expenditure of manhours

against time.

The actual cumulative expenditure of manhours

against time.

The cumulative manhours equivalent of actual work

completed, that is, earned value.

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The slope of the curve at the start represents the initial rate of work on the project.

If the gradient of the actual manhours curve is less than planned, then it is obvious that there is too slow at a start.

Thereafter the first critical point is where the curve should turn up at the bottom of the S.

If this critical acceleration of work on the project dose not turn upwards, the project is going to be delayed, no matter what is done.

Once the curve does turn up, the slope of the curve shows the rate of progress.

If work is not progressing as fast as planned,

the slope of the actual curve vary quickly and

obviously becomes less than that of the

planned work curve.

At the top of the curve if the work does not

decelerate as planned then there is going to

be an overshoot.

This is because it is generally not possible to

finish off a project without the slowing down

of the project of work, as is represented by

the top of the S.

Consider the following case, where an activity is scheduled for an electrical design and design of drawing offices.

The list of activities with their respective estimated times are listed.

Activity Description Predecesso

r

Schedule Actual %

completion

Forecast Completion

Start

Finish

Start

Finish

1 Basic design - 0 8 0 9 - -

2 Electrical design I 1 8 12 9 14 - -

3 Specify electrical motors

2 12 16 14 18

- -

4 Electrical design II 2 12 20 14 22 - -

5 Mechanical drawing office

- 18 24 18 -

90 25

6 Instrument design 2 20 28 23 - 10 32

7 Electrical drawing office

4 20 32 22 -

15 34

8 Instrument drawing office

6 24 32 - -

- 33

Time Analysis for Electrical Design and Design of Drawing Offices

S curve for electrical design

1) Week 10: The activity labeled basic design is

just complete and 14 men were employed on it

for 10 weeks, instead of 16 men for the eight

weeks as planned. The S curve clearly shows

this deviation from plan, together with a

poorer than estimated performance and can

be calculated as follows

1016 i.e. 160

1014 i.e. 140

816 i.e. 128

Planned cumulative manweeks

Actual cumulative manweeks

Earned value

In this case the earned value is the planned

manweeks to complete basic design.

The horizontal difference between the

earned curve and the planned curve also

shows any deviation from schedule; in this

case the project is already two weeks behind

schedule.

Week 15: The first stage of electrical design

is now complete and 16 men were employed, as

planned, although this activity took one week

longer than planned.

Thus the slope of the actual curve is the

same as the planned curve for that stage of

the work, but the earned curves slope is less

than that of the actual.

This clearly identifies performance less than

planned, and brings it to the attention of the

project manager for further investigation.

290

220

192

The project is now three weeks late, as shown by the horizontal difference between curves and performances can be calculated as follows


Earned value

It is also observed at a glance that the pace of work has not accelerated as planned and that the deviation between the curves is increasing.


Week 17: Although the slopes of the actual

and earned value curves have increased, they

are still less than that of the planned curve.

The project is now approximately four weeks

behind schedule and an extrapolation of

present performance can now be made to

forecast the completion date of this

assignment of the project and the number of

manweeks that will be required.

350

275

235

value Actual

value Earnedindex eperformanc Manpower

The results to date can be calculated as follows


Earned value

If performance is unchanged it can be estimated from the curves that

this segment of work will take 26 weeks instead of 20 as planned, and 505

manweeks instead of 432.


0.85275

235

index eperformanc Manpower

manweeks Plannedmanweeks total Estimated 055

0.85

432

It is obvious that not only are the promised

number of men not being committed to the

work but that these men are not achieving the

expected performance.

The S curve being a cumulative curve is

sensitive to deviations which although small in

themselves in any one period, can build up to a

significant deviation. When the data for all

the activities on a project are considered, S

curve analysis gives a concise and clear

picture of performance on a project

575,1

1,250

1,025



Earned value

The project is approximately 6 weeks behind

schedule because in the 24 weeks, fewer men

were committed to the work than planned and

they did not achieve the estimated

performance.

The acceleration of work into the main phase

of the project was 4 weeks behind schedule

and though the planned number of men is now

being committed to the work, they are still

not achieving the required performance.

1,250

1,025date to project on index eperformanc Manpower 0.82

875-1,250

750-1,025phase main on index eperformanc Manpower 0.85

The manpower performance index can be calculated on three bases, that is,

on the project to date, on the main phase of the project, that is, week 28 to

week 32, and for individual segments as describes above. For example

If the earned value curve is extracted, it forecasts

the project completion will be 13 weeks late.

If the manpower is unchanged it forecasts that

either 4,604 or 4,442 manweeks will be required to

complete the project instead of the planned 3,776

manweeks.

Thus these S curves and the information they

represent can be used at any time to determine how

much work is actually completed, the efficiency of

working, the rate of working and to forecasts the

time to completion and the actual manpower required.

One of the skills a project manger must to

have is the ability to recognize trends, or

deviations from plan or budget, at an early

stage.

Everyone can recognize a trend or deviation

when it is well established, but by the time in

most cases it is too late to do anything about

it.

To be able actually to influence the success of the project, rather than be carried along by its momentum, a project manager must be able to recognize a trend at an early enough stage to be able to do something about it.

This may be partly an intuitive skill, but this can be enhanced by the intelligent use of the analytical techniques available, of which the S chart is one of the simplest, but one of the most useful.

Project Crashing

The crash time estimate is the shortest time

that could be achieved if all effort were made

to reduce the activity time. The use of more

workers, better equipment, overtime, etc,

would generate higher direct cost for

individual activities.

The following are sequence of steps required

to crash an activity:

Step1. Identify the activities that need to be

crashed (where an activity has negative float

for instance). This can happen at any time

from the initial project planning phase to

project completion.

Step 2. Identify the critical path. To crash

non-critical activities is a waste of financial

resource because it will simply increase the

float on that activity without affecting the

end date of the project. See figure 11.25.

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Step 3. Prioritize the activities to be crashed. When there are many activities which can be crashed, it is necessary to know which activity will be crashed first? This can be done by selecting the activity

with the least cost per day to crash. that is the easiest to crash. which can be crashed soonest to bring the project

back on course. As project manager you do not want to approach

the end of the project with a number of activities running behind schedule and the prospects of further problems during commissioning

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Step 4. Crash activities one day at a time, then re- analyze the network to see if any other activities have gone critical.

Continue this iterative process until there are no activities with negative float. These crashing steps may vary with the different types of projects.

Time Cost Trade-off Theory

Before discussing the time cost trade-off

concept, it is necessary to define some

terminologies used.

Normal Time: This is the normal office hour,

for example eight hour a day, and six days a

week.

Normal Cost: The cost of activity working on

normal time.

Direct Cost: Costs attributed directly to

the project labor and materials. These costs

usually group when the activity is crashed due

to overtime, shift allowance, etc.

Indirect Cost: This is overhead cost which

can not be directly attributed to the project,

for example, office rent, and management

salaries. These costs are usually linear with

time, therefore, if the time reduces, the

indirect costs also reduce.

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Crash Time: The duration the activity can

be reduce to, by crashing the activity.

Crash Cost: The new cost of the activity

after crashing.

i) Crashing direct cost: The duration has been

reduced but the costs have increased. These

additional costs are caused by overtime, shift

work and a reduction in productivity

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Crashing Direct Costs

ii) Crashing indirect cost: The duration has

been reduced but the time and the costs have

also reduced. The benefit has come from

reduced office rental, equipment hire etc.

Unfortunately project costs are usually split

80% direct, and 20% indirect cost, so the

advantage of crashing indirect costs is usually

overwhelmed by the far greater direct costs

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Crashing indirect costs

When the direct costs and indirect costs are

combined on the same graph an optimum

position is derived.

Combined direct and indirect costs

Time cost trade-off: The time cost trade-

off figure outline graphically four different

time costs positions.

The time cost trade-off

cpNtotal dmCC total

totalNC

cpd

where

= total sum of normal cost m = indirect cost slope

= number of days in critical path.

The total cost of the project can be calculated by:

Example:

The following example depicts how direct

costs increase while indirect costs reduced

during crashing. Consider the following

activity to manufacture a motor driven hollow

block machine.

When working normal time the activity will

take;

Five men working eight hours per day,

Six days per week for five weeks =1,200 man hrs.

The activitys normal costs will be:

Labor at 5 birr per hour x 1200 man hours =6,000 Birr.

Material = 4,500 Birr

Administration and office expense Birr 1000 per week

Birr 1000 x 5 weeks = 5000 Birr

Total=15,500 Birr

If the client now wants to manufacture the

machine in less time, the crash cost can be

quantified in steps of one day. To reduce the

duration the men will have to work overtime,

say 10 hours per day (2 hours overtime which

is calculated with one and a half time).

Assume the additional hours do not affect

the productivity.

The total man hours will still be the same i.e.

weeks4 or days 24

day per hours 10men 5

hours man 1200

hrs 8men 5 days 24 Birr 5 time) (normal Birr 4800

time) (over 1.5hrs 2men 5 days 24 Birr 5 time) (over Birr 1800

The extra hours worked per day will reduce the duration from 30 working days to 24 working days. The crashing costs will be: Labor:

=

=

change) (no Birr 5000

weeks4 Birr 1000

)(reduction Birr 4000

Birr 15,600

time) in e(Differenc

cost) in e(Differenc day per cost crash Additional

24) - (30

15500) - (15,600 day per Birr 1 7

Material =

Adm. and Off. expense :

___________ Total =

With this information calculate the additional cost to crash the activity by on day, will be

This example clearly shows that to reduce the

project by one week or six days the direct

costs will increase while the indirect costs

reduce. The overall effect is to increase the

costs by 17 Birr per day.

The project time-cost model seeks to shorten

the length of a project to the point where the

saving in direct project costs is offset by the

increased direct expenses.

Resource Allocation

While developing the PERT and CPM networks

we have generally assumed that sufficient

resources are available to perform the

various activities.

In every production enterprise, resources are

always limited and the management always

wants to assign these various activities in

such a manner that there is best possible

utilization of available resources.

At a certain time the demand on a particular resource is the cumulative demand of that resource on all the activities being performed at that time.

Proceeding according to the developed plan, the demand on a certain type of resource may fluctuate from very high at one time to very low at another.

If it is material or unskilled labor which has to be procured from time to time, the fluctuation in demand will not affect the cost of the project much.

But, if it is some personnel who cannot be hired and fired during the project or machines which are to be hired for the entire duration of the project, the fluctuation in their demand will affect the cost of the total project due to high idle time.

In order to reduce the idle time, the activities on non-critical paths are shifted by making use of the floats and alternative schedule is generated comparing the more important resources with the objective of smoothening the demand on resources.

Depending upon the type of constraints the

resource allocation procedure can be

categorized into two main activities: resource

smoothing and resource leveling.

Resource Smoothing

If the constraint is the total project

duration, then the resource allocation only

smoothens the demand on resources in order

that the demand of any resource is as uniform

as possible.

The periods of maximum demand for

resources are located and activities according

to their float values are shifted for balancing

the availability and requirement of resources.

So the intelligent utilization of floats can

smoothen the demand of resources to the

maximum possible extent. Such type of

resource allocation is called Resource

smoothing or Load smoothing.

Resource Smoothing Steps.

The following are steps which are used to

smoothen the resources of a project.

Step1. The first step in resource smoothing

is to determine the maximum requirement.

One way is to draw the time scale version of

the network and assign the resource

requirements to activities.

Step2. Then, below the time scaled network,

the cumulative resource requirements for

each time unit are plotted.

Step3. The resource histogram is plotted on the basis of the early start times or the late start times of the activities. These resource histograms establish the frame work under which the smoothing or leveling must occur.

Resource Leveling

There are various activities in a project

demanding varying levels of resources. The

demand on certain specified resources should

not go beyond the prescribed level. This

operation of resource allocation is called

Resource Leveling or Load Leveling.

Although the overall resources of the

organization are limited, but these should not

go below the amount required to perform an

activity among all the activities in the

process, otherwise that particular activity

cannot be computed.

In the process of resource leveling, whenever

the availability of a resource becomes less

than its requirement, the only alternative is

to delay the activity having large float.

Incase, two or more activities require the

same resources, the activity with minimum

duration is chosen for resource allocation.

To illustrate the resource smoothing

operation, let us consider the following

example:

Example: Resource Leveling

Consider the activities of a project given in

the table below. For simplicity, only one kind

of resource, manpower required, has been

considered.

And the manpower required for each activity

is also given in the table.

Level the resource for the activities if the

total man power required is equal to 12

Activity Crew Size

0-1 2

0-3 6

0-5 9

0-7 3

1-2 4

2-6 0

3-4 5

4-6 1

5-4 0

6-8 8

7-8 0

Solution:

In order to level the resource with the

available manpower, we have to shift all jobs

with a slack and which can make a difference

in the manpower allocation.

Thus, job 3 has a slack of 7 days, shift job 3

to the right by 6 days. Then shift job 4 and

job 9 to the right by 2 days. By so doing the

resource will be leveled with an extra man-

hour of (2x2 = 4).

Project Risks

However small the percentage may be, there

is always uncertainty in any venture.

Identification and management of risks is

fundamental to any project.

Before undertaking a project, all participants

want to identify the risks involved, as well as

the steps that may be taken to manage them.

There is direct relation between the project risk and expectation of return.

If the risk of the project is in line with the average risk of the company, then the expected rate of return would be the weighted average cost of capital of the firm.

If the risk is higher the expected rate of return would be higher.

The expected rate of return is determined by comparing it against similar project of other companies

It is difficult to generalize about the risk

characteristics of projects.

Each host country and in deed each specific

project has its own risk profile.

i) General (or country) Risks: General or

country risks refer to the ones that affect

the overall sectors of the country.

Factors such as a countrys economic growth,

its political environment, the tax code, the

legal system and the prevailing currency

exchange rate are classified under this

category.

The general risks may be divided into three

major divisions. The importance of these risks

can vary substantially from country to country

and from project to project.

Political risks: These are related to the

internal and external political situation and

the stability of the host country. These risks

include the governments attitude towards

allowing private sector profits from projects,

changes in the host countrys fiscal regime,

including taxation, the risk of expropriation

and nationalization of the projects by the

host country, cancellation of the concession,

and similar factors.

Country commercial risks: These are risks

related to the convertibility of revenue from

the project into foreign currencies, foreign

exchange and interest fluctuation and

inflation.

Country legal risks: The risks to sponsors

and lenders is that legislation that is relevant

to the project (for instance, environmental

legislation or property legislation) may change

after a project has been implemented

ii) Special Project Risks: In addition to the general risks discussed above, sponsors and lenders face specific project risks that may be generally within the control of the sponsors. The specific project risks may be broadly divided into the following three categories in accordance with phases of a project cycle.

Development risks: These are risks

associated with the bidding competition that

occurs in the initial stage of the process. The

development risks also include losses caused

by delays in planning and approval, which can

be particularly acute in the case of

transnational projects, where project

sponsors have to deal with the authorities of

two or more governments.

Construction/completion risks: The primary

risks here are the following:

The actual cost of construction may be higher

than projected (cost overruns).

Completion takes longer than projected

(completion delays).

The construction of the project may not be

completed at all.

Operating risks: operating risks result from

insufficiency in performance, revenue income,

material supply etc. and from higher than-

expected operating costs. They may be

divided into six main categories:

Associated-infrastructure risks: These risks

are associated with facilities outside the

project, such as approach roads and

transmission lines, for which construction

responsibility lies with third parties rather

than the project sponsors themselves.

Technical risks: These include design defects

and latent defects in project equipment.

Demand risks: Most projects that rely on

market-based revenues face demand risks

related to volume and/or prices, thereby

lowering the rate of return of the project.

Supply risks: Because they are also market

risks, supply risks have two components,

volume and prices.

Management risks: The quality of

management in every project is always a

critical success factor.

Force major risks: Force major risks denote

losses from certain exceptional types of

events beyond the control of the parties to

the project that impeded the performance of

their obligations.

Risk Identification Check List

General or Country Risks

Political Risks

Political support risks

Taxation risks

Expropriation/nationalization risks

Forced buy-out risks

Cancellation of concession

Import/export restrictions

Failure to obtain or renew approvals

Country Commercial Risks

Currency inconvertibility risks

Foreign exchange risks

Devaluation risks

Inflation risks

Interest rate risk

Country Legal Risks

Changes in laws and regulations

Law enforcement risk

Delays in calculating compensation

Specific Project Risks

Development Risks

Bidding risks

Planning delay risks

Approval risks

Transnational risks

Construction/Completion Risks

Delay risk

Cost risk

Re-performance risk

Completion risk

Force major risk

Loss or damage to work

Liability risk

Operating Risks

Associated infrastructure risks

Technical risks

Demand risk (volume and price)

Cost escalation risks

Management risks

Force major risk

Loss or damage to project facilities

Liability risk

Risk Management

When designing the risk allocation and

management structure of a project three

overriding considerations have to be made.

First, it is the cost of the project in its

entirety that should decide any particular risk

allocation. A particular risk should be borne

by the party most suited to deal with it, in

terms of control or influence and costs

In some cases, the party in the best position

to financially bear a particular risk may

prefer some method of risk allocation that, in

the interest of the project, does not reduce

the other partys incentive to perform

efficiently.

Secondly, since the solutions to the risk

management of a project do not in principle

rely on unconditional guarantees from any one

party alone, the financial structure of the

project must consider the following

requirements

All substantial project risks have to be identified, allocated and managed; and the project risks have to be managed by a combination of financial resources and firm contractual commitments. Thirdly, the risk structure has to be sufficiently sound to withstand the ups and downs of a project implementation.

In this section we will see how to manage some of the risks encountered in the financial aspect. A wide range of capital market instruments, such as swaps, options and futures, are now available for management and hedging of currency and interest rate risks. What these instruments offer are the following.

Forward Market: Forward Rate is an agreed rate between the bank and a customer for a specific sum to be traded in a specific time in the future. By entering in forward agreement, a company eliminates its potential foreign exchange loss. However, it also eliminates its potential gain in case exchange rate goes in its favour.

The rate that dealers buy currency is called bid, the rate they sell currency is called offer. Difference between spot and forward is shown as point. If bid is greater than offer in point, currency is in premium as may be seen in the following data, but if offer is greater than bid in point, currency is in discount as can be seen in the following example.

Bid Offer

Spot 1.8215 1.8225

Three months 1.8040 1.8056

Points 175 169

Options: In the option market an individual has a right to buy (or sell) currency at a certain rate.

The risk would be the cost of the option, while potential gain is infinite

A call option is the right to buy at a certain rate, a put option is the right to sell at a certain rate. Strike price is the price that option can be exercised. Break-even point is the exercise price plus the premium.

Call Options

iii) Money Market Hedge: The firm borrows (deposites) in the foreign market equivalent of their receivable(payable). Fund then is exchanged to home currency at the spot rate. The future value of the fund indicated the actual receivable. To consider the future value the deposit rate is used if the company is cash rich and Weighted Average Cost of Capital (WACC) is used if the company is cash poor.

rdtreWACC VDVE )1(

re

rfrmrf

rf

rm

Where E = value of equity D = value of debt V = value of firm (debt + equity) rd = cost of debt t = tax rate

cost of equity

risk free interest rate

market rate rate of return

= risk factor particular to the company.

iv) Other Methods a) Reinvoicing Centre and Netting Process: All

projects and subsidiaries would settle their exchange rate exposure with the headquarters. The reinvoicing centre would hedge the residual. This would minimize firms cost of exchange rate hedging.

b) Leading and Lagging: The fund transfer between the headquarters and the project could be adjusted based on the sort term interest rate change. For example, if there is expectation of foreign currency devaluation, parent company would slow down sending fund to the project. At the same time, fund transfer from project to parent company would be speeded up.

The forgoing methods can best be explained using the following example.

Financial Strategy in Dealing with Exchange Rate Risk

A company, MH, is awarded a contract to build a number of constructions in Addis Ababa. The project is cost plus, which means that after all expenses are paid, MH will have a 6.25 million Birr profit, which it will bring back to its U.S. headquarters (all costs are in Birr).

The contract was awarded on January 1st and is expected to be completed by December 31st of the same year. The exchange rate on January 1st was 0.16 $/Birr and is expected to become 0.156 $/Birr for December 31st. MH can borrow or lend money in Ethiopia at the rate of 8% and in the U.S. at the rate of 3%.

Example

Financial Strategy in Dealing with Exchange

Rate Risk

A company, MH, is awarded a contract to

build a number of constructions in Addis

Ababa. The project is cost plus, which means

that after all expenses are paid, MH will have

a 6.25 million Birr profit, which it will bring

back to its U.S. headquarters (all costs are in

Birr).

The contract was awarded on January 1st and is expected to be completed by December 31st of the same year. The exchange rate on January 1st was 0.16 $/Birr and is expected to become 0.156 $/Birr for December 31st. MH can borrow or lend money in Ethiopia at the rate of 8% and in the U.S. at the rate of 3%.

i) Unhedged Position: When no action is taken

on covering the currency exposure, it is called

open exposure. This is highly risky, since

events could change future exchange rates.

In this case, the company is highly exposed.

With an unhedged risk:

Today Birr 6.25 x 106 x 0.16 = $1 Million

is the value that MH owns

By the end of the year the value in dollar that

MH will have is

Birr 6.25 x 106 x 0.156 = $ 0.975 Million or

$975,000, which is a 2.56% decline.

However, if the Birr goes down to 0.144, the

impact would be even more substantial.

Birr 6.25 x 106 x 0.144 = $0.9 Million or

$900,000 which is 11% lower than todays

return.

ii) Forward Market Hedge: At Dollar/Birr rate

of 0.1528, it is possible to hedge the risk by

buying dollars in the forward market. Birr

6.25 x 0.1528 = $0.955 or $955,000

While this is $20,000 less than an unhedged

position, it is $55,000 higher than if

exchange rate goes to 0.144 $/Birr. In

essence, $20,000 is the cost of buying

insurance against a decline of the Birr.

iii) Option Market Hedge: Buying out option (to

sell Birr) on December 31st is another

alternative. Assuming the cost/Birr is 0.8

cents or $0.008, then the total cost of

hedge is:

6,250,000 x 0 .008 = $50,000

At the end of the year, MH is assured

6,250,000 x 0.16 - $50,000 = $950,000

While this cost is higher than using a forward

market hedge or a money market hedge, it

provides an opportunity for company to have

substantial gain in case the Birr becoming

stronger, relative to the dollar by the end of

the year, since MH has bought a right to sell

Birr at 0.16 Birr without having an obligation

to do so.

iv) Money Market Hedge: In money market

hedge, funds are borrowed in the country

where the company is expected to receive

payment in the future. In the example,

borrowing takes place in Ethiopia. Funds are

then exchanged to home currency at the

prevailing rate and are put in an interest-

yielding instrument for the duration of the

project (or longer). Upon receiving payment

in foreign currency, debt is paid.

Firms can actually use the money for working capital or capital investments as opposed to putting it in an interest-yielding instrument. In this case, the opportunity cost of money should be considered as opposed to the interest.

Borrow present value of Birr 6.25 at market

rate of interest 8%

Present value Birr 6.25/1.08 = 5.787

Change the amount to dollar

5.787 x 0.16 = 0.926 or $926,000

Put the $926,000 in an interest yielding

instrument at 3% annually

926,000 x 1.03 = $953,780

So at the end of the year, MH will have

$953,780 compared to an unhedged position

of $975,000 or forward market hedge of

$955,000.

While both forward and money market hedges

eliminate risk, in this case, a forward market

hedge is less expensive. Everything being

equal, this instrument is prepared.

chapter-2

Documents

wbs level

large project

project occasions

largescale project

project team

complexity of project

wbs component

wbs elements