Course Content · Web viewCAPM, APT and WACC - Discussions - Interactive questions - Assignments 14-15 End of Semester Examination - Exams Written examination TEACHING METHODOLOGIES

HEP 3110: PROJECT TIME AND COST MANAGEMENT

Jomo Kenyatta University of Science and AgricultureMaster of Science in Project Management

Unit code: HEP 3110: Project Time and Cost ManagementLecture: Dr. Muchelule Yusuf, PhD

TABLE OF CONTENTSCourse Content................................................................................................................................................................4

Inputs required in sequence activities........................................................................................11Tools and methods used in sequence activities.........................................................................12Types of Dependency Determination in Project Management..................................................12Types of Dependencies or Logical Relationships.....................................................................14Schedule Network Diagrams.....................................................................................................15Arrow Diagramming Method (Activity on Arrow Method)......................................................15

Arrow Diagramming Method – Dummy Activity.................................................................16When to Use the Arrow Diagramming Method (ADM)...........................................................16How to Use the Arrow Diagramming Method (ADM).............................................................16

Summary................................................................................................................................17Leads and Lags..........................................................................................................................18Outputs of sequence activities...................................................................................................19Product-based planning.............................................................................................................19Detection of activities and dependencies in product-based planning........................................20

1.4 ACTIVITY RESOURCE ESTIMATION...............................................................................................................29

1.5 ACTIVITY DURATION ESTIMATING................................................................................................................31

Activity Duration Estimating technique include:......................................................................32a) Analogous Estimating.........................................................................................................32b) Parametric Estimating.........................................................................................................32c) Three-Point Estimating.......................................................................................................33

Basic concepts used in PERT and CPM.......................................................................................................................33

Step 1: Forward Pass Calculation..........................................................................................35Step 2: Backward Pass Calculation.......................................................................................35Step 3: Float Calculation for Each Activity / Arrow Diagramming Method Example.........36Step 4: Identifying the critical path / Arrow Diagramming Method Example......................36Summary................................................................................................................................36

Guidelines for construction of network diagrams.........................................................................................................37

Written and compiled by Dr. Muchelule Yusuf Wanjala Page 1

Time Estimates In Network Analysis...........................................................................................................................39

Critical Path Method.....................................................................................................................................................39

Advantages of CPM......................................................................................................................................................40

Drawbacks of CPM.......................................................................................................................................................40

PROJECT EVALUATION AND REVIEW TECHNIQUE (PERT)...........................................................................40

Summary................................................................................................................................43Advantages of PERT.....................................................................................................................................................45

Shortcomings of PERT.................................................................................................................................................46

Differences between PERT and CPM...........................................................................................................................46

Key Points..............................................................................................................................47d) Heuristic Estimating...........................................................................................................47e) Reserve Analysis................................................................................................................47f) Work Breakdown................................................................................................................47g) Historical.............................................................................................................................47h) Expert Judgment.................................................................................................................48i) Effort required....................................................................................................................48j) Units to produce..................................................................................................................48Activities in Control Schedule Process......................................................................................49Examples of potential cost driver..............................................................................................52Step 4 Plot the data on a graph..................................................................................................53Step 6: Test the reliability of the cost function..........................................................................53a) Engineering method...............................................................................................................54b) Account analysis (Inspection of accounts) method...............................................................54c) Work Breakdown Structure...................................................................................................54d) Resource Costing................................................................................................................54e) Unit Costs...........................................................................................................................54f) Historical Costing...............................................................................................................55Illustration 2.1............................................................................................................................55Solution......................................................................................................................................56Simple Regression.....................................................................................................................57Illustration 2.2............................................................................................................................59NET PRESENT VALUE...........................................................................................................60

Solution:.................................................................................................................................62PAY BACK PERIOD...................................................................................................................................................63

Formula......................................................................................................................................64


Decision Rule.............................................................................................................................64Examples....................................................................................................................................64Merits and demerits of payback period are as follows;.............................................................65

Accept or Reject Criteria of payback period.........................................................................65Advantages And Disadvantages Of Pay Back Period(PBP)..................................................66

BENEFIT COST RATIO ANALYSIS......................................................................................67EARNED VALUE MANAGEMENT (EVM).............................................................................................................68

EVM - Basic Elements..................................................................................................................................................68

Planned Value............................................................................................................................69Actual Cost................................................................................................................................69Earned Value.............................................................................................................................69% Completed Planned................................................................................................................69% Completed Actual..................................................................................................................69

EVM - Cost Variance....................................................................................................................................................70

Cost Variance %........................................................................................................................70Cost Performance Indicator.......................................................................................................70To Complete Cost Performance Indicator.................................................................................71

EVM - Schedule Variance............................................................................................................................................71

Schedule Variance %.................................................................................................................72Schedule Performance Indicator................................................................................................72To Complete Schedule Performance Indicator..........................................................................73

EVM - Miscellaneous Formula.....................................................................................................................................73

Budget at Completion................................................................................................................73Estimate to Complete.................................................................................................................73Estimate at Completion..............................................................................................................74Variance at Completion.............................................................................................................74% Completed Planned................................................................................................................74% Completed Actual..................................................................................................................74

EVM - Examples...........................................................................................................................................................74


PURPOSE OF THE COURSE

The purpose of the course is to make the student understand the processes required to make the most effective use of time and costs involved in project.

COURSE OBJECTIVESAt the end of the course the student will be able to:

i. Determine how to effectively sequence activities.ii. Determine how to effectively estimate resource requirements and estimate durations.

iii. Develop an effective schedule.iv. Effectively utilize schedule controls to keep their projects on schedule.v. Effectively 'Crash' and 'Fast Track' their projects to meet time and cost requirements.

vi. Determine how to estimate costs.

Course ContentWk Topic Key Coverage Methodology Evaluation

1

Introduction - The Triple Constraint Theory (Time, Cost and Scope)

- Power Point Presentations- Discussions

- Interactive questions- Assignments

Written assignment

1. Critically evaluate the progress of major Jubilee government projects in relation to the triple constraint theory focussing much on time and cost since it took over power.

2. Discuss portfolio theory

- Research - To be submitted by end of the semester

1-2

Project Time and Cost Management Overview

- Project Management Processes- Initiate & Align the Project Team- Plan the Work- Endorse the Plan- Work the Plan- Transit ion & Closure



- Project Management Plan- Project Performance Baseline Management- Project Requirements (Scope) and Quality- Project Time (Schedule)- Project Costs (Budget) & Aging



- Work Breakdown Structure (WBS) - Power Point - Interactive


3-5Schedule Management

- Scheduled Activity (Task)- Schedule Milestone- Logical Relationship- Precedence Diagram (Network Diagram)- Critical Path- Float (Slack)

Presentations- Discussions

questions- Assignments

- Critical Path Method (CPM) Scheduling- Gantt Chart- Tracking Schedule “Actuals”

- Base Cost Percent completes- Schedule crashing- Schedule fast tracking- -“What-If” Scenario Analysis



6 CAT - Sit in CAT Written Examination

7-8

Resource Planning

- Resource Estimating- Expert Judgment- Bottom-up Estimating- Three point Estimating


Written Research Paper

- Resource Histogram- Resource conflict and balancing- Resource and Project Calendars- Resource Leveling

- Lecture- Discussions


9-10

Budget Management

- Budget Development- Analogous Est imating- Parametr ic Est imating- Bottom-up Est imating



- Cost Budgeting-Cost Basel ine- Cost Control- Cost Change Control System- Earned Value Management

- Group Work- Power Point Presentations

Oral Assessment

11-13

Portfolio theory - CAPM, APT and WACC - Discussions - Interactive questions- Assignments

14-15

End of Semester Examination

- Exams Written examination


TEACHING METHODOLOGIESLectures, Case Studies, Seminars, critiques, and Term Papers.

INSTRUCTIONAL MATERIALS/EQUIPMENTTexts, audio and video DVD’s, computer software, case studies

ASSESSMENTCoursework 40% Final Written Examination 60%Total 100 %

COURSE TEXTBOOKS

Gray, C. F., Larson, E. W. (2008). Project Management: The Managerial Process, (4th ed.). Boston: McGraw-Hill Irwin.

Hopkinson, M. (2011). The project risk maturity model, (2nd). Farnham: Gower Publishers.

Chandra, P. (2009).Projects planning analysis, selection financing implementation and review, (7th ed.). New Delhi: Tata McGraw Hill.

REFERENCE TEXTBOOKS

Turner, R. (2008). Project Review Assurance and Governance. Farnham UK: Gower Publishers.

Hill, Gerard M. (2008). The Complete Project Management Office Handbook, Second Edition. New York, NY: Auerbach Publications.

PMBOK Guide (2008). Guide to the Project Management Body of Knowledge: Fourth Edition

COURSE JOURNALSJournal of Construction project management Journal of Construction project management and innovationPractical project management journal

REFERENCE JOURNALSProject Management connectionProject Management Journal


International Journal of Project Management

1.1 IntroductionCost and time estimation is crucial in project management. When getting started in a project, it is important to set accurate cost and timelines so that progress can be made and goals can be met successfully. When too much time is allocated for a project, things might not get done as quickly as they could have otherwise been. If enough time is not permitted, the team may get frustrated by constantly falling behind and work could suffer.

The ability to accurately forecast project schedule and cost is developed with experience and through trial and error. If time and cost is not managed successfully, resources or opportunities are to be wastes. The more time employees are spending on a specific project, the more expensive that project becomes. When a one-month project ends up taking two, the costs in some areas of the budget are likely to be doubled – potentially turning the success endeavor into failure. Its isn’t good enough in most cases to just get the project finished. Rather it needs to be finished and kept on time and on budget in order to be deemed a success. Thus, the need for proper time and cost estimation.What is time and cost estimation?

It is the process of forecasting or approximating the time and cost of completing project deliverables.

It is the task of balancing expectations of stakeholders and need for controls while the project is implemented.

Importance of Time and Cost Estimation• To support good decisions.• To schedule work.• To determine how long the project should take and its cost.• To determine whether the project is worth doing.• To develop cash flow needs.• To determine how well the project is progressing.• To develop time-phased budgets and establish the project baseline.

Factors Influencing the Quality of Estimatesa) Organization cultureb) Skills/experiencec) Project duration


d) Peoplee) Project structuref) Non-project factorsg) Planning horizon

Guidelines for Times, Costs and Resources Estimation1. Have people familiar with the tasks make the estimate.2. Use several people to make estimates.3. Base estimates on normal conditions, efficient methods, and a normal level of resources.4. Use consistent time units in estimating task times.5. Treat each task as independent, don’t aggregate.6. Do not make allowances for contingencies.7. Add a risk assessment to avoid surprises to stakeholders.

Refining Estimates (Reasons for Adjusting Estimates) Interaction/hidden costs. Normal conditions do not apply. Things go wrong on projects. Changes of project scope and plans. Time and cost estimates of specific activities are adjusted as the risks, resources, and

situation particulars become more clearly defined.

1.2 PROJECT TIME MANAGEMENT

IntroductionProject has to be done within a limited time. Furthermore, when it comes to the main constrains of the project, time, cost and scope require careful attention throughout the whole project life cycle; during planning phase, executing and monitoring and control before closing the project. Time management process happens mainly in the planning phase, although the project duration and the milestones are already decided in the initiation phase, but it is still the project manager’s responsibility to plan the project activities and to meet the set project duration within the planned budget.

Processes involved in project time management; Define Activities. Sequence Activities. Estimate Activity Resources. Estimate Activity Durations. Develop Schedule.

Project time management includes the processes required to ensure timely completion of the project. It involves the following major processes:


Activity Definition—identifying the specific activities that must be performed to produce the various project deliverables.

Activity Sequencing—identifying and documenting interactivity dependencies. Activity Duration Estimating—estimating the number of work periods which will be

needed to complete individual activities. Schedule Development—analyzing activity sequences, activity durations, and resource

requirements to create the project schedule. Schedule Control—controlling changes to the project schedule.

These processes interact with each other and with the processes in the other knowledge areas as well. Each process may involve effort from one or more individuals or groups of individuals based on the needs of the project. Each process generally occurs at least once in every project phase. Although the processes are presented here as discrete elements with well-defined interfaces, in practice they may overlap and interact in ways not detailed here. On some projects, especially smaller ones, activity sequencing, activity duration estimating, and schedule development are so tightly linked that they are viewed as a single process (e.g., they may be performed by a single individual over a relatively short period of time). They are presented here as distinct processes because the tools and techniques for each are different.

At present, there is no consensus within the project management profession about the relationship between activities and tasks:• In many application areas, activities are seen as being composed of tasks. This is the most common usage and also the preferred usage.• In others, tasks are seen as being composed of activities. However, the important consideration is not the term used, but whether or not the work to be done is described accurately and understood by those who must do the work.

1. ACTIVITY DEFINITIONThis process includes defining the activities need to be implemented to achieve the project deliverables. Activity definition involves identifying and documenting the specific activities that must be performed in order to produce the deliverables and deliverables identified in the work breakdown structure. Implicit in this process is the need to define the activities such that the project objectives will be met.

The main tools and techniques used in defining activities process are;

Decomposition. Rolling wave planning. Templates. Expert judgment.


Decomposition in project management means to divide the project into smaller pieces that can be easily managed and controlled. It is a technique used in Work Breakdown structure (WBS) creation and to define the required activities.

Decomposition of project scope generally involves the following activities: Gather information on major project deliverables and analyze related tasks. Start development of work breakdown structure (WBS) at the highest level. Decompose the upper WBS levels into lower level detailed components. Identify each work package & WBS components with unique code, and Verify if the

degree of decomposition of the work is necessary and sufficient. Any of Levels of WBS need not be the same for all deliverables.

The work breakdown structure (WBS) is a checklist of every activity that must be performed to create the end product. This checklist becomes the foundation for the schedule, resource allocation, and budget plans. WBS is created using questionnaire, one-to-one personal interviews, or group sessions.

Rolling Wave Planning is a technique that enables you to plan a project as it unfolds. This technique, then, requires you to plan iteratively. Essentially, when you use Rolling Wave Planning, plan until you have visibility, implement, and then re-plan. It is usually be used when you have clarity for the activities of the first months of the project

Inputs to Activity Definitiona. Work breakdown structure (WBS). The work breakdown structure is the primary input

to activity definition.b. Scope statement. The project justification and the project objectives contained in the

scope statement must be considered explicitly during activity definitionc. Historical information. Historical information (what activities were actually required on

previous, similar projects) should be considered in defining project activities. d. Constraints. Constraints are factors that will limit the project management team’s

options.e. Assumptions. Assumptions are factors that, for planning purposes, will be considered to

be true, real, or certain. Assumptions generally involve a degree of risk and will normally be an output of risk identification

2. ACTIVITY SEQUENCINGActivity sequencing involves identifying and documenting interactivity dependencies. Activities must be sequenced accurately in order to support later development of a realistic and achievable schedule. Sequencing can be performed with the aid of a computer (e.g., by using project management software) or with manual techniques. Manual techniques are often more effective on smaller projects and in the early phases of larger ones when little detail is available. Manual and automated techniques may also be used in combination. The relationships between the


activities of a project can be detected and documented in a process known as Sequence Activities, which are capable of considering the rational sequence of work and all project limitations to achieve the highest efficiency. At least a predecessor having a logical relationship of finish-to-start or start-to-start as well as minimum one successor having a logical relationship of finish-to-start or finish-to- finish in every activity and milestone, except for the first and last ones. A realistic and achievable project schedule should be considered in the design of logical relationships, which might be essentially supported using lead or lag time between the activities. In this context, project management software or manual or automated approaches can be beneficial in sequencing.

Inputs required in sequence activities

1. Schedule Management Plan (SMP): The SMP is a pre-project preventive thinking to identify several points, including the scheduling process involved in the project, thus helping the sequence activities.

2. Activity List : The activity list contains a critical pathway and basically a detailed documentation of all schedule activities required and sequenced for a particular project. The sequence activities can be affected by the dependencies and limitations that exist on the path to these activities.

3. Activity Attributes : Activity attributes generally refer to active components associated with an activity, which may be pivotal for sequencing for details like events, predecessors or successor.

4. Milestone List : The milestone list as a project management document may schedule all specific project milestones influencing sequence activities.

5. Project Scope Statement: The project scope statement is a good mean to describe the key deliverables of a project, including product properties involved in sequence activities like physical lineament of a project being implemented or the nature of a software project. Other scope statements of project can detail constraints and assumptions associated with sequence activities. Although these are mostly recorded in the activity list, their accuracy is explored as product scope description.

6. Enterprise Environmental Factors: The success of sequence activities is depended on either internal or external enterprise environmental factors (EEFs), including government regulations,


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industry conditions, project management information system (PMIS), scheduling tool, or work authorisation system (WAS).

7. Organizational Process Assets : Another factor contributing to the sequence activities is the organizational process assets (OPAs), including project plans of the corporate, formal or informal policies, procedures, processes, scheduling methods to developing logical relationships, and templates required for providing networks of project activities. Sequence activities can benefit from additional descriptive data provided by information related to activity characteristics in templates.

Tools and methods used in sequence activities

Project Dependencies

Dependencies in project management are well-defined as connections among the projects that decide the sequence in which project management activities should be executed. These tasks might be multiple preceding tasks which mean that two activities can be appropriate at the same time. Furthermore, they are described by the four types of dependencies such as discrete, mandatory, external and internal dependency. Dependency is a method utilized in recognizing the proper sort of dependency that is used to make the relationship between two activities. The activities are named as predecessor (which alludes to the principal action) and successor (the work that goes before the first).

Types of Dependency Determination in Project Management

One of the most critical aspects of creating a strong project schedule is to understand the types of dependencies that are inherent in the workspace. Characterized into mandatory or discretionary, internal or external dependency determination attributes can be utilized at the same time in the following ways:

1. Mandatory dependencies are those that are lawfully necessary as an integral part of the workplace. Regularly involving physical impediments, the project team figures out the dependencies that are required to implement amid the process of sequencing the tasks. Mandatory Dependencies also denoted as hard logic, or hard dependencies should not be mistaken for relegating plan imperatives in the scheduling tool.

Examples of this logic include:


https://www.invensislearning.com/resources/pmp/how-to-develop-a-schedule-in-a-project

Two activities must be performed at the same time (starting and/or finishing at the same time)

An activity cannot begin until another activity is completed2. Discretionary dependencies also referred as preferential logic, are set up based on the

learning of best practices inside a specific application area of the project where a particular sequence is needed, even though there might be other sequences that are adequate. Discretionary dependencies can make random float values that can restrict advanced scheduling options, hence, needs to be documented.

Discretionary dependencies must be audited and considered for modifications when optimizing systems are in use. The project team figures out which dependencies are optional amid the way toward sequencing the tasks.

Examples of this logic include:

Activity will take place at the same time along with another group of activities Activity will begin after few days of the completion of another activity3. External dependencies include a connection between project activities and non-task

activities. Mostly outside the project team’s control, the project management group figures out which dependencies are external during the process of sequencing the tasks.

Examples of External dependencies include:

Get approval from the external organization must be gotten before beginning an activity. Finishing of a project milestone is connected to the completion of a milestone within

another project.

Developing external dependencies in your project schedule can be cultivated in diverse ways:

Embed an achievement that reflects the accomplishment of the external dependency. Embed a planning segment that reflects the scheduling of the external dependency. Associate definite activities in other project plans that require utilization of big business

planning tools4. Involving a precedence relationship between project activities Internal Dependencies are

generally within the control of the project team. The project management team figures out which conditions are inward amid the way toward sequencing the activities.

For instance,


https://www.invensislearning.com/resources/pmp/the-purpose-of-sequence-activities-in-a-project

Types of Dependencies or Logical Relationships

The Precedence Diagramming Method (PDM) includes four types’ dependencies, and each one has its specific area of application.

Finish-to-Start Finish-to-Finish Start-to-Start Start-to-Finish

Finish-To-Start: Until the predecessor activity is complete, the successor activity cannot start.

Finish-To-Finish:The successor activity can't be completed until the point that a predecessor activity is complete.

Start-To-Start:Unless the predecessor activity has not started a successor activity cannot start.

Start-To-Finish:Until the predecessor activity has not begun, a successor activity cannot finish.

To show interdependencies, network diagrams are used.

Network Diagrams A network diagram is a schematic display of the logical relationships among, or

sequencing of, project activities. Network diagrams are the preferred technique for showing activity sequencing. The two main formats are the arrow and precedence diagramming methods

Arrow Diagramming Method (ADM Also called activity-on-arrow (AOA) network diagrams Activities are represented by arrows Nodes or circles are the starting and ending points of activities Can only show finish-to-start dependencies Can omit activities that have no dependencies


https://www.invensislearning.com/resources/pmp/precedence-diagramming-method

Schedule Network DiagramsA project network diagram of a work schedule demonstrates the logical order that the activities will follow. It shows a sequence of activities required to complete the project. Basically, there are two common techniques to create network diagrams. These techniques are Arrow Diagramming Method (ADM) (or Activity on Arrow) and Precedence Diagram Method (PDM) (or Activity on Node). Network diagrams enable to determine the critical path of the project. The critical path is the longest path where a delay on it results in a project delay.

Arrow Diagramming Method (Activity on Arrow Method)Arrow diagramming method (ADM) is a network diagramming technique like the Precedence Diagram Method (PDM). In this method, activities are shown as arrows on the diagram. It has been used a long time to determine the critical path and identify resource problems and feasible solutions when the approximate duration and resource requirement of all the activities of the network diagram are known. There are two main elements of the Arrow Diagramming Method (ADM) which are arrows and nodes. One arrow represents one activity to be performed. The starting point of the arrow represents the start of the activity and the ending point of the arrow represents the end of the activity. The length of the arrow represents the duration of the activity. For better understanding lets analyze the schema below.

The circles numbered 1, 2, 3 and 4 are the nodes of this network system. They are the definable achievement in the project. Nodes have neither duration nor resource. Activities A, B, C, D are represented by the arrows. Each activity has a duration and allocated resource.

Arrow Diagramming Method – Dummy ActivityA dummy task which is not a real activity is added to represent dependency between tasks. It can be used to separate tasks or to keep the sequence correct. Duration of a dummy task is often zero.

When to Use the Arrow Diagramming Method (ADM)Arrow Diagramming Method (ADM) shows the logical order of activities that helps to determine the critical path and identify the problems related to resources. From this aspect, it can be used for schedule compression practices such as fast tracking and crashing. Arrow Diagramming Method (ADM) can be used to plan and track the activities within a complex schedule with many


https://www.projectcubicle.com/schedule-compression-fast-tracking-vs-crashing/

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resources. For a successful implementation, activity durations, their sequences and project execution strategy must be clear.

How to Use the Arrow Diagramming Method (ADM)Below steps are used in Arrow Diagramming Method (ADM)

Identify all the activities required to complete the project and list them. Estimate the activity durations considering the crews and quantity of work. Estimating

activity durations is an important process because activity durations affect the length of the critical path. There are some techniques to estimate activity durations. Expert judgment, analogous estimating, parametric estimating and three-point estimating are the techniques widely used to estimate the activity durations. Unlike other techniques, three-point estimates provide most likely, optimistic and pessimistic estimates that are used for the PERT method.

Determine the predecessor, successor activities and logical sequences. While performing this step ask the questions below while using the arrow diagramming method;

– Which activity will start first?– Which activities will be performed simultaneously?– Which activity will finish after this activity?– Which activity will start after this activity?Creating a table and organizing the columns with this information may be useful to save time.

Draw the network diagram by using the data created in former steps. Draw the nodes for events that represent the beginning or end of an activity. These nodes separate the activities. Use dummy activities when needed and show them as dashed lines.

Determine the critical path of the network diagram by performing forward pass and backward pass calculations.

Calculate the ES (Earliest Start), EF (Earliest Finish), LS (Latest Start), LF(Latest Finish) dates for each activity.

Calculate the Total Float and Free Float for each activity. Total float is the duration that a task (or an activity) can be postponed without delaying the project. Free float is the duration that a task can be postponed without delaying the ES of the successor activity. Float is also known as slack.

Total Float (TF) :LS – ES , LF – EFFree Float (FF) : ES (of successors) – EF of current activity -1

SummaryThe Arrow Diagram was a common visible and practical network diagramming method used in the past which was developed after the Gantt Charts (or bar charts). It was widely used in the


https://www.projectcubicle.com/total-float-versus-free-float-scheduling/

https://www.projectcubicle.com/pert-method/

past to identify the critical path of a complex project. As a traditional project management technique, Arrow Diagramming Method (ADM)’ s popularity has fallen away because of the introduction of software solutions that can calculate the critical path of a project schedule easily and automatically. In this post, we make a short review of this important network diagramming method in scheduling. It is critical to understand the logic of network diagrams to create better schedules.

Precedence Diagramming Method (PDM)

The PDM is a common visual tool to draw a diagram of project schedule network, which depicts graphical rectangles known as nodes, connected by one or more logical relationships to represent activities in these boxes. A precedence diagram is shown with the aid of activity-on-node (AON) strategy that is applied frequently within project management software. There are four logical relationships or dependencies in the package of PDM, including finish-to-start (FS), finish-to-finish (FF), start-to-start (SS), and start-to-finish (SF), containing a predecessor activity depicted logically prior to a dependent activity of a schedule, and a successor activity as a dependent activity depicted logically after another activity of a schedule.

Figure 3: Four types of dependency in PDM. Inspired by PMBOK[2]

In a logical relationship of FS, a successor activity can be advanced when the predecessor activity has finished; for instance, the ceremony of awards (the successor activity) can be advanced when the competition (the predecessor activity) has elapsed.

In a logical relationship of FF, a successor activity can finish when a predecessor activity has finished; for instance, a document editing (the successor activity) can end when a document writing (the predecessor activity) has finished.


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In a logical relationship of SS, a successor activity can be advanced when a predecessor activity has advanced; for instance, Level concrete (the successor activity) can be advanced when a pour foundation (the predecessor activity) has advanced.

In a logical relationship of SF, a successor activity can be ended when a predecessor activity begins; for instance, the first shift of security guard (the successor activity) can be ended when the second shift of security guard (the predecessor activity) begins.

The most and the least commonly used logical relationships in the PDM are FS and SF, respectively. However, all of these logical relationships are present in a complete list of the PDM.

PDM SUMMARY

More popular than ADM method and used by project management software Activities are represented by boxes Arrows show relationships between activities Better at showing different types of dependencies

Leads and Lags

Figure 4: Lead and lag in sequence activity. Inspired by PMBOK[3]

The time required for starting a successor activity regarding a predecessor activity is called as a lead. For example, scheduling a landscaping in a construction project of office building can begin two weeks before the completion of the scheduled punch list. Lead is often planned as a negative amount for lag in scheduling. The time required for delaying a successor activity regarding a predecessor activity is called as lag. For instance, a technical writing team has a 15-day delay time to edit a draft of a large document after writing, meaning a 15-day lag plus SS relationship (SS+10). Lag can be appeared in diagrams of project schedule network plotted for the relationship between H and I activities in spite of unclear offset relative to a timescale. Determination of the need for a lead or a lag in the dependencies is undertaken by the project management team in the exact process of defining the logical relationship. The schedule logic


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should not be changed following the use of leads and lags. it is essential to document the activities and corresponding assumptions. [2]

Outputs of sequence activities

1. Project Schedule network diagrams: The logical relationships are graphically drawn called as project schedule network diagram, also referred to as dependencies among the project schedule activities, which is prepared by manual manner or project management software. The diagram can represent full details or summarized activities of the project. A summary narrative can be illustrated with a diagram to show the used fundamental strategy in sequencing the activities, and to describe any abnormal sequence of activity on the network.[2]

2. Updates of project documents: There are needs to update the project documents, such as activity lists, activity attributes, milestone list and risk register.

Only, the project product description should be prepared for a small project. Careful thinking is necessary to achieve quality criteria in order to distinguish whether a

product is acceptable or not. A way to test quality criteria is to scrutinise the distinction between completed or stopped working on this product.

Product-based planning

Product-based planning is a method for identifying first a product requirements and second all activities, dependencies and necessary resources to deliver that product. This method has different applications such as Project planning, Stage planning and Team planning. The sequence involved in the development of products of the plan will be developed and the identification of their dependencies should be detected and defined, which is possible using a product flow diagram (PFD). The dependencies on any non-project products can be detected through this diagram, thereby providing the required activities and data for other planning approaches like estimating and scheduling.

Some essential items should be considered to draw the PFD:

The PFD is generated by the Project or Team Manager. However, the people responsible for developing or helping the plan products can be involved rationally.

When the product breakdown structure (PBS) has been drawn, some planners will decide to generate the PFD along with the PBS.

There is need for very few symbols in drawing the PFD. It is essential to detect any developed product (for instance, enclosure in a rectangle), and to exhibit any required sequence (for instance, interconnection of rectangles by arrows) in the plan. Moreover, the external products should be clear as any existing or non-project ongoing products (for instance, enclosure in a different shape like ellipse).

The PFD may be added with a starting point attached from all entry points. Although an exit is always available in the PFD, when many entrances exist, this position indicator prevents




any of them from being ignored. The symbol of predecessor is there for all points of entry and is the only symbol in PFD not in PBS.

Product based planning Detection of activities and dependencies in product-based planning

Activities:

It is inadequate to merely identify products for scheduling and controlling the objectives. To completely illustrate the workload of a plan, it is necessary to detect all the activities needed to establish or modify any of the planned products. The identification of activities can be achieved through multiple approaches, as follows:

A separate list of the activities can be provided in spite of the use of PFD as the information source.

The required activities can be detected by using the products from the PBS or the work breakdown structure (WBS).

The activities involve management and quality-checking activities, and those required for developing the specialist products or for interacting with external parties like those that a product obtained from an outside source or for transforming external products into targeted ones. It is needed to shield the spread of activities unnecessary for the plan. Things should be kept simple if there is any doubt.

Dependencies:

It is necessary to identify any internal and external dependencies of activities and products. For example, Activity C cannot start unless activities A and B are completed (as an internal dependency). Dependency of a delivery of a product needed for a project by another project, suggestion of a purchase order by the user and decision-making by the program manager are examples of the external dependencies.


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Activity sequence:

In the wake of detecting the activities, and estimating related dependencies, duration and effort, the subsequent step is to approximate the optimal sequence required. This is an iterative step because the estimated effort and duration may be influenced by actual resource allocation. Float or slack refers to the amount of time by which a given task in a project network can be delayed with no influence on the deadline for the project, which can be considered as both provision within the plan and spare time. Zero float means a condition with no excess time between activities, which defines a critical activity through the diagram (critical path). In fact, it can be claimed that any delay in the completion of an activity in the critical path (s) will result in delayed completion of the entire project. The project manager will be able to monitor the plan’s activities by detecting the critical path (s) of the plan. Such activities should be timely completed in order to complete the whole plan in accordance with scheduling. Delay can occur for these activities for a period if resources are re-allocated to compensate for lost activities.

3. ACTIVITY DURATION ESTIMATINGActivity duration estimating involves assessing the number of work periods likely to be needed to complete each identified activity. The person or group on the project team who is most familiar with the nature of a specific activity should make, or at least approve, the estimate. Estimating the number of work periods required to complete an activity will often require consideration of elapsed time as well. For example, if “concrete curing” will require four days of elapsed time, it may require from two to four work periods based on (a) which day of the week it begins on and (b) whether or not weekend days are treated as work periods.

4. SCHEDULE DEVELOPMENTSchedule development means determining start and finish dates for project activities. If the start and finish dates are not realistic, the project is unlikely to be finished as scheduled. The schedule development process must often be iterated (along with the processes that provide inputs, especially duration estimating and cost estimating) prior to determination of the project schedule.shared resources can be especially difficult to schedule since their availability may be highly variable.

5. SCHEDULE CONTROLSchedule control is concerned with (a) influencing the factors which create schedule changes to ensure that changes are beneficial, (b) determining that the schedule has changed, and (c) managing the actual changes when and as they occur. Schedule control must be thoroughly integrated with the other control processes.

1.3 PROJECT SCHEDULE DEVELOPMENT


The project Schedule outlines the tasks and activities of the project; the duration; start and end dates for each individual task and the project as a whole; and the resources and effort required.

For most projects there will be at least two separate Schedules developed. One will be for the Initiation Phase (Initial Schedule) and the other for the Planning, Execution and Closure phases. All schedules are added to Eclipse for tracking and updating.

The Initial Schedule is developed in the Initiation Phase of the project to help produce the Project Charter. At this point, the Schedule is not expected to be very accurate or contain firm dates; rather it gives the Project Manager (PM) a rough idea of the project timeline and the assignment of resources. When the Charter is approved, a second Schedule is developed, with the approval date as the Project “start date”.’

In the Planning Phase, a Project Management Plan is created (from the Charter), and the second Schedule is updated with a more accurate and realistic timeline. In effect, the start and end dates of the first Schedule will be replaced by the start and end dates of the second Schedule. Eclipse allows for the development and saving of multiple schedules. This feature can help in creating “what if” schedules without disturbing the “active” schedule.

Why prepare a Project Schedules? Managers often cite delivering projects on time as one of their biggest challenges. Time has the least amount of flexibility; it passes no matter what happens on a

project. Schedule issues are the main reason for conflicts on projects, especially during the

second half of projects.

Steps in Developing a project Schedule Work Breakdown Structure (WBS) Work Packages Activities and tasks Schedule

a) Work Breakdown Structure (WBS) The WBS provides a clear description of the project’s deliverables. It describes the “what is to be done” not the process or schedule.

Therefore the WBS: Is a deliverable breakdown structure Is a hierarchical decomposition of the work – the deliverables are decomposed to a level

where a work package can be defined (see work package below) Is a graphical representation or textual outline of the project scope


Represents 100% of the work defined by the project scope and captures ALL deliverables, internal, external, and interim, including project management

The WBS helps: Develop the work packages Define the project tasks Develop the schedule Is a tool to communicate the project to stakeholders

b) Work Packages Work packages are the lowest level in a WBS decomposition where activity duration can be reliably estimated and managed. A Work Package can be created where a Project Manager (PM) deems it necessary to help develop the project Schedule. A work package details a level of work to be completed. It would contain a description of the work, details of constraints, and agreement between the PM and the team or individual doing the work, that the work can be done within the constraints. Assumptions would be defined in the work package depending on the needs of the project.

Work packages are particularly useful where contractors or other departments are involved in the project. A work package should define durations of 4 to 6 weeks. The PM would assign the work package and authorize the work to be completed according to the project Schedule. The PM would monitor and control the project at the work package level and not necessarily at the task level. c) Activities and Tasks Tasks are the lowest level of work defined in a schedule. A task is the work to be done and contains a description, the start and end dates, the resource assigned to work on the task and any dependencies on other tasks. A collection of similar tasks are grouped together and summarized as an Activity. This aids in the management of progress reporting and communication to stakeholders, where each task does not need to be communicated individually in detail.

Tasks are usually defined by the person who will perform the task. The Project Manager, Resource Manager and others who have knowledge of the work required, would be involved with identifying the tasks and the tolerances for how long they will take using the estimation .

The PMs are currently using the PERT (Project Evaluation and Review Technique method to determine the effort and duration required on a task or activity.) PERT Analysis uses a weighted average of three duration estimates to calculate an estimated duration for a task. This is a great tool when you don't have a specific duration but do have duration estimates from reliable sources. Who are reliable sources? A reliable source is anyone with experience working with the particular type of task, including, but not limited to, skilled project managers, the people who


will be performing the work, and even the data logs of a resource like a machine (to find out how fast the equipment can get the job done).

PERT analysis requires three numbers: 1. Most Likely Time – The activity time which will likely occur most often? 2. Most Pessimistic Time –The activity duration under the least favourable conditions 3. Most Optimistic Time –The minimum activity duration under the most favourable conditions

Once this estimated duration is determined, a personal fatigue factor (PFD) should be applied. This is typically 20% of the estimate, and will allow for factors such as; experience level and issues which could impact the person not spending full time on the task. d) Schedule Once the tasks and activities are developed, the Schedule is produced. The schedule is a living document and needs to be monitored and kept up to date. Once complete, project milestones should be identified and incorporated into the Schedule. A “milestone” is a point in time in the project which identifies the end of a significant set of related activities indicating the completion of a major deliverable. A milestone has no duration or effort. A final step in the development of the Schedule is to determine a contingency factor to be applied to the schedule. Typically, a contingency of 10% is applied at the overall schedule level and not at the task level. On a large project contingency can be applied at a phase, sub-phase or activity level. Once initial and subsequent schedules are developed, they should be “baselined”. In most cases, this is done at the completion of the Project Management Plan. A baseline establishes a point of reference from which a comparison can be made against the plan.

During the development of the Schedule it is important for the PM to keep in mind any “Assumptions” and “Constraints” identified in the Project Charter and/or Plan, and how they may impact the timeline. As well, risks and issues should be taken into consideration when creating the project schedule. Analyzes activity sequences, durations, resource requirements, and schedule constraints to create the project schedule. No matter the size or scope of a project, the schedule is a key part of project management. The schedule tells you when each activity should be done, what has already been completed, and the sequence in which things need to be finished.Because of the uncertainty involved, the schedule is reviewed regularly, and it is often revised while the project is in progress. It continues to develop as the project moves forward, changes arise, risks come and go, and new risks are identified. The schedule essentially transforms the project from a vision to a time-based plan.

Tools and techniques used to develop project schedule: Schedule network analysis. Critical path method. Critical chain method. Resource leveling.


What-if scenario analysis. Applying leads and lags. Risk Analysis Project review.

1. Schedule Network Analysis: This is a graphic representation of the project’s activities, the time it takes to complete them, and the sequence in which they must be done. Project management software is typically used to create these analyses – Gantt charts and PERT Charts are common formats.2. Critical Path Analysis: This is the process of looking at all of the activities that must be completed, and calculating the “best line” – or critical path – to take so that you will complete the project in the minimum amount of time.

CPM is a network diagramming technique used to predict total project duration A critical path for a project is the series of activities that determines the earliest time by

which the project can be completed The critical path is the longest path through the network diagram and has the least

amount of slack or float Slack or float is the amount of time an activity may be delayed without delaying a

succeeding activity or the project finish date

Calculating the Critical Path First develop a good network diagram Add the duration estimates for all activities on each path through the network diagram The longest path is the critical path If one or more of the activities on the critical path takes longer than planned, the whole

project schedule will slip unless the project manager takes corrective action.

Using Critical Path Analysis to Make Schedule Trade-offs Free slack or free float is the amount of time an activity can be delayed without

delaying the early start of any immediately following activities Total slack or total float is the amount of time an activity may be delayed from its early

start without delaying the planned project finish date A forward pass through the network diagram determines the early start and finish dates A backward pass determines the late start and finish dates

Using the Critical Path to Shorten a Project ScheduleThree main techniques for shortening schedules

Shortening durations of critical activities/tasks by adding more resources or changing their scope

Crashing activities by obtaining the greatest amount of schedule compression for the least incremental cost


A 2 week task with one person working 50% could be shortened to 1 week if the person is assigned 100% - no increase in cost

Or, a temporary worker could be hired to work in parallel with the other worker to speed up the task (at a cost)

3. Schedule Compression: This tool helps shorten the total duration of a project by decreasing the time allocated for certain activities.4. Resource leveling: Here, you re-arrange the sequence of activities to address the possibility of unavailable resources, and to make sure that excessive demand is not put on resources at any point in time.5. “What if” scenario analysis: This method compares and measures the effects of different scenarios on a project.6. Applying leads and lags: Lead refers to a relationship whereby the successor activity begins before the predecessor activity has completed. While lag refers to a relationship whereby the successor activity cannot start right after the end of its predecessor’s.7. Risk Analysis: Risk is inevitable, so you need to prepare for its impact. Adding extra time tohigh-risk activities is one strategy. Another is to add a time multiplier to certain tasks or certain resources to offset overly optimistic time estimation.8. Project Review: after the initial schedule has been reviewed, and adjustments made, it’s a good idea to have other members of the team review it as well. Include people who will be doing the work – their insights and assumptions are likely to be particularly accurate and relevant. Once you have outlined the basic schedule, you need to review it to make sure that the timing for each activity is aligned with the necessary resources. 9. A milestone is a significant event that normally has no duration.

Not every deliverable or output created for a project is a milestone It often takes several activities and a lot of work to complete a milestone They’re useful tools for setting schedule goals and monitoring progress Examples include obtaining customer sign-off on key documents or completion of

specific products such as software modules or the installation of new hardware

The five key points of using project milestones include the following:1. Define milestones early in the project and include them in the Gantt chart to provide a

visual guide2. Keep milestones small and frequent3. The set of milestones must be all-encompassing4. Each milestone must be binary, meaning it is either complete or incomplete5. Carefully monitor the critical path

Schedule compression Project CrashingProjects will sometimes have deadlines that are impossible to meet using normal procedures. By using exceptional methods it may be possible to finish the project in less time than normally


required. However, this usually increases the cost of the project. Reducing a project’s completion time is called crashing.

Crashing a project starts with using the normal time to create the critical path The normal cost is the cost for completing the activity using normal procedures If the project will not meet the required deadline, extraordinary measures must be taken The crash time is the shortest possible activity time and will require additional resources The crash cost is the price of completing the activity in the earlier-than-normal time.

.While crashing, you will monitor other paths as well. It is possible that the duration of other paths could become equal or greater than your critical path.

Initially, you will get a greater reduction in duration with less input cost. However, as you continue further, the cost will increase and the reduction will dwindle.Therefore, do a cost-benefit analysis. A few examples of crashing techniques are:

Overtime

More resources

Monetary rewards

Crashing cannot be applied to all activities.

For example, you have to wait until the concrete dries before you can start your next activity.

Example

You are constructing a room. According to the duration estimate, two masons will take four days to complete it. You have to reduce the duration of this activity by crashing. You add two more masons to complete the task in two days. Sometimes, crashing may not produce the desired result. Getting skilled resources is not easy. and they take time to settle. You cannot bring in a new group of people and expect them to perform immediately. Therefore, it is possible that the cost will increase without any significant gain. Perform due diligence before using crashing.

Fast tracking activities by doing them in parallel or overlapping them instead of doing them in sequence. Instead of waiting for all analysis to be completed before starting coding, some coding could begin for those tasks that have been fully analyzed. Drawback – starting a task too soon


https://pmstudycircle.com/2012/07/cost-benefit-or-benefit-cost-analysis/

https://pmstudycircle.com/2012/07/cost-benefit-or-benefit-cost-analysis/

could lengthen the project because other tasks whose analysis has not been completed could impact this task and cause rework. fast-tracking is a schedule compression technique in which activities or phases normally performed in a sequence, are done in parallel for at least a portion of their duration. In fast-tracking, you review the critical path and list all vital activities. Then you analyze which ones can be performed partially or fully parallel with other activities.You will not review the activities on the non-critical paths, they have float. Reducing the duration of those activities will not affect the schedule; it will only give more float to them.

You should monitor other paths whose durations are close to the critical path. If any other path becomes critical, you will reduce the duration of the new critical path. In this case, your current path will no longer be critical. Afterward, you will rearrange the fast-tracked activities and reanalyze the schedule.To compress the schedule, project managers start with fast-tracking because it does not cost more. However, it increases risk as activities are overlapping.

As a rule of thumb, you can fast track sequential activities by 33%. This means you can start the next activity when the previous is 66% complete. Both activities partially overlap. It will increase the risk but within acceptable limits. Fast-tracking helps you compress the schedule up to certain limits. Continuing beyond the limit will increase the risk, which may lead to rework and further delays.

Example

Let’s say that you are building a school and construction work is about to finish. Afterward, you will start carpentry and electrical works. When you review your progress, you see that you are behind schedule; you have to move faster to complete the project on time. You will review the carpentry and electrical work activities and see if you can perform them in parallel. Then, you can apply fast-tracking. In this case, you can start the electrical and carpentry work at the same time.

Lead VS Fast-Tracking

On a compressed network diagram, activities with lead and fast-track activities look the same. Hence, many aspirants often think the lead is the same as fast-tracking. Lead is a type of dependency that you use while developing a network diagram. It is already factored into the schedule. On the other hand, fast-tracking is a forced overlap. You do it to shorten the schedule.


https://pmstudycircle.com/2012/07/precedence-diagramming-method-activity-on-node-method-scheduling/

https://pmstudycircle.com/2013/02/lead-time-and-lag-time-in-project-scheduling-network-diagram/

https://pmstudycircle.com/2014/01/critical-path-method-cpm-in-project-management/

Fast-tracking increases risks and possible rework, while lead is a dependency type on the network diagram and it does not affect the risk.Difference Between Fast Tracking and Crashing

The following are a few differences between fast-tracking and crashing:

In fast-tracking, activities are rescheduled to be performed partially or fully in parallel, while in crashing, you add extra resources to the activities to finish them early.

Fast-tracking does not cost you extra money, crashing does.

Fast-tracking increases risks. Crashing does not, significantly.

You use fast-tracking when activities can be overlapped to decrease their duration, while you use crashing on those where adding extra resources can decrease their duration.

When Should You Use Fast Tracking or Crashing?

This depends on your situation and requirements. For example, if the client wants to complete the project early and is willing to pay, you use crashing. Generally, you will start with fast-tracking to shorten the schedule. Once you are done, you can go for crashing if necessary. Sometimes you may use both techniques. For example, the client is threatening to fine you for the delay. To avoid this, you will compare the cost of crashing with the fine. If the crashing cost outweighs the fine, you will use it with fast-tracking for maximum schedule compression.You may also use crashing if the project delay can affect the company’s image or credibility.

Why are Schedule Compression Techniques Applied to the Critical Path?

As the name suggests, these are schedule compression techniques. The schedule is based on the critical path, the longest path of the network diagram and its duration is that of the project. Reducing other paths won’t reduce the duration of your project. You will just give those paths more float. If you want to reduce the duration of schedule, you will shorten the duration of the critical path.

Summary

Projects often get delayed and you have to compress the schedule, fast-tracking and crashing are two ways to do that. These techniques help you decrease the duration of your project. Fast-tracking does not involve cost, but it increases risks. Crashing does not significantly increase risk, but it is a costly process. Use these techniques carefully because you are dealing with critical activities. Any wrong step can affect your project negatively.

12. Critical chain schedulingA method of scheduling that considers limited resources when creating a project schedule and includes buffers to protect the project completion date


Based on the Theory of Constraints (TOC)A management philosophy developed by Eli Goldratt and introduced in his book The Goal and

Critical ChainLike a chain with its weakest link, any complex system at any point in time often has only one aspect or constraint that limits its ability to achieve more of its goalFor the system to attain any significant improvements, that constraint must be identified and the whole system must be managed with it in mindFor example, two tasks originally scheduled to be done in parallel, require the same resource 100% of the time. CCS acknowledges that either one of the tasks must be delayed or a similar resource must be found in order to keep to the original schedule.

13 Critical Chain Project Management (CCPM), developed by Eliyahu M. Goldratt, is a method of planning and managing projects that puts more emphasis on the resources required to execute project tasks. This is in contrast to the more traditional Critical Path and PERT methods, which emphasize task order and rigid scheduling. A Critical Chain project network will tend to keep the resources levelly loaded, but will require them to be flexible in their start times and to quickly switch between tasks and task chains to keep the whole project on schedule. Typically, CCPM case studies report 95% on-time and on-budget completion when CCPM is applied correctly

14. Buffers and Critical ChainIn traditional estimates, people often add a buffer to each task and use it if it’s needed or not. A buffer is additional time to complete a task. This time is added to when there is multitasking, distractions, interruptions, fear that estimates will be reduced and Murphy’s Law. Murphy’s Law states that if something can go wrong, it will, Critical chain scheduling removes buffers from individual tasks.

The tasks estimates in critical chain scheduling should be shorter than traditional estimates because they do not include their own buffers. Not having tasks buffers should mean less occurrence of Parkinson’s Law - work expands to fill the time allowed. Feeding and project buffers protect the date that really needs to be met – the project completion date. Buffer gives project managers a leeway when unforeseen events occur and is often associated with scheduling in project management. A buffer can be temporal, financial or qualitative in nature, i.e. you have additional time, money or people available for difficult project phases. Buffers can be assigned either to the whole project or to individual activities (work packages).

Types of buffers


https://www.inloox.com/project-management-glossary/work-package/

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Project Buffer. The project buffer is placed between the final scheduled task of the critical chain and the estimated project end-date...

Feeding Buffer. Adding such a buffer to the schedule makes it possible to avoid situations when missed completion dates of non-critical chain tasks have an impact to individual tasks of the critical chain...

Resource Buffer. It is a portion of time required by critical resources to complete their critical chain tasks...

Capacity Buffer (optional). This type of buffers assumes that for a multi-project environment there is a need to plan for on-call resources by adding more costs covering the resources to the overall budget...

To develop a project schedule, the following needs to be completed:

Project scope. Sequence of activities. Tasks grouped into 5 project phases (conception, definition & planning, launch,

performance, close) Task dependencies map. Critical path analysis. Project milestones.

Cultural Differences as a Cause of Schedule Conflicts One dimension of the Meyers-Briggs Type Indicator focuses on peoples’ attitudes toward

structure and deadline Judgment type people prefer to follow schedules, meet deadlines and have closure.

Perception types prefer to keep things open and flexible; deadlines are a signal to start rather than to complete a project

Different cultures and even entire countries have different attitudes about schedules

1.4 ACTIVITY RESOURCE ESTIMATION

Before estimating activity durations, you must have a good idea of the quantity and type of resources that will be assigned to each activity. Consider important issues in estimating resources.

How difficult will it be to do specific activities on this project? What is the organization’s history in doing similar activities? Are the required resources available or need to be acquired?

A resource breakdown structure is a hierarchical structure that identifies the project’s resources by category and type.


Duration includes the actual amount of time worked on an activity plus elapsed time Effort is the number of workdays or work hours required to complete a task Effort does not normally equal duration People doing the work should help create estimates, and an expert should review them

Estimating projects activities is hard. Why? Because the only time you know precisely how long it takes to complete a project is when it’s done. Up to the point of delivery, teams use educated guesswork to predict the future. And the bigger and more complex a project is, the hazier that future is. Faulty estimates mean missing deadlines and breaking budgets—two of the main symptoms of project failure.

Being a skilled estimator is a crucial part of setting schedules, establishing budgets, managing resources and running a thriving team and business. Using the best online project management software for the job is a huge help, but knowing the methods and learning how to do them well is how you become a great estimator. There are a number of activity resource estimation methodologies to choose from that work for all types of projects.

1. Expert judgment

This is probably the most common way people get an estimate. Talk to the men and women with the best hands-on experience and understanding of the project requirements. Just make sure that everyone has the same understanding of what needs to be delivered. And try to find experts who will actually be working on the project. Experts, with expertise appropriate to the concerned activity, are asked to estimate the resources and/or duration and/or cost. Experts may be available within the organization or may be provided from outside the organization.

2. Comparative or analogous estimation

If your current project is similar to past ones, take the data from previous work and extrapolate it to provide your estimates for the new job. Before proceeding, make sure to check whether those projects were successful. Analogous estimating is a technique where you refer to those previous projects which were having, scope or activities, similar to your current project. Then you figure out how much time and/or these activities have taken earlier, during that project, to make estimation for duration and/or cost of similar activities in your project. This technique, sometimes, also called as “Top Down Estimating” because you try to estimate the duration or cost for whole of the activity, with reference to previous project activities, without breaking it to Work Package Level, as it will be hard to map similarities, between previous project and current project, till that much lower level.

3. Bottom-up Estimating


Using this technique you estimate resources or costs by breaking down complex activities into smaller pieces and working out resource or cost assignments for these smaller activities using other resource / cost estimating tools and techniques. It is based on detailed WBS (Work Breakdown Structure). Here you estimate each piece and add them up. When individual estimates are added up it becomes the project estimates. This method uses a detailed work breakdown structure and is best for projects you’re committed to. Each task is estimated individually, and then those estimates are rolled up to give the higher-level numbers. (If you use the right project management software, it will roll up the estimates for you). This process makes you think about what’s required in order to take a step back to see if the big picture still makes sense. You’ll receive more accurate results than the top-down method, but it’s also a greater investment of time.

5. Parametric model estimating

This is a more scientific method that essentially auto-calculates estimates using detailed data from previous activities. This estimation, like analogous estimation technique, requires historical information gathered from previous projects. This technique is used for both cost and time estimates calculations. But, unlike analogous estimation technique, parametric estimation requires plugging the historical data into a formula, spreadsheet, database, or computer program to come up with an estimate. Let’s say you have data from your last three office network installation projects. You can use this to get a days-per-workstation value or something similar. You then plug in the number of workstations for your new installation and out pop the estimates. When you need to determine what would be the total cost of construction when you have cost per square foot or the units of work multiplied by productivity unit rate to estimate activity duration. This can be a quick method but needs robust data to feed it. And because it’s all about the math, it’s hard to adjust for the environmental, political and cultural differences between projects.

6. Project Management Software Estimation These are specialized software programs or software tools for doing estimation for project resources and various costs.

7. Published Estimating Data: This technique is used only for estimating activity resources. This published data can include articles, books, journals and periodicals from various industries that have proven data with similar projects. Using the Published Estimating Data Project Managers can make a rough estimation of how many resources they need.

8. Alternatives Analysis: It is a technique where you look at various ways to assign resources by varying the number of resources as well as the kind of resources and then decides upon the best one.

1.5 ACTIVITY DURATION ESTIMATING


Estimate activity durations is the process of estimating the number of work periods needed to complete individual activities with estimated resources. The key benefit of this process is that it provides the amount of time each activity will take to complete, which is a major input into the develop schedule process. The aim of effective project management is to bring the project to completion on time and on schedule. Estimating project duration is a key function of scheduling. Individual activities make up the schedule, and the estimates of their duration determine the project timetable. The accuracy of the overall schedule depends on the accuracy of these estimates.

Aspiring project managers must learn how to perform a variety of tasks in order to get a project started and estimating activity duration is one of them. It’s not always an easy task to estimate the project duration, because doing so needs a project manager’s knowledge of some theory, along with application of some best practices and methodologies. To estimate activity duration is a lengthy process and it takes time for a long-term project. Ideally, you should involve your core project team in estimating the duration. You should involve the project team, who will work on the project to achieve the project objectives, project management team, and all the identified key stakeholders to make a consensus on the milestone dates, and delivery schedules. Depending on this duration, you can develop a schedule, with milestones for your project. Estimating activity duration can be for a project phase or product phase and is iterative in nature.

Activity Duration Estimating technique include:

a) Analogous Estimating

This is a very important methodology that gives you the entire duration estimation. Based on the information of past projects that are similar, you can get a ballpark idea of the entire duration estimation. If the company has carried out a similar activity, it may be possible to adapt the duration to the current case. Project managers have to study the similarities of the two activities and adjust for any features that may result in differences in duration. Even small businesses can often find such similar activities on which to base estimates. You may be able to get this information from the Project Management Office or another project manager; you can use this template for your current project.

Analogous estimating the activity duration is not so accurate in nature; however, it is less costly and less time consuming than other methods. You can frequently use this method when you don’t have sufficient time to do a proper estimate, and you have a deadline. Analogous estimating can be of a part of project as well, since you don’t have to estimate the entire project. You can estimate activity duration for a single phase of the project, if the requirement /nature of the phase are very similar to the previous processed project.

Key points


It is the fastest technique to calculate the estimate; however, less accurate It can be used when limited information about the project is available It is also known as top-down estimating

b) Parametric Estimating

This method is more accurate in nature. It is based on a statistical calculation of historical data and other variables. For example, in the design phase in case of a construction project, you may already have the activity duration: cutting 1,000 stones will take 8 hours and so on. If your project is of a similar nature to one performed in the past, it is worth your while to find existing activity duration estimates and historical data from the past project.

Key points

It uses statistical relationships between historical data and variables It is more accurate than the analogous technique

c) Three-Point Estimating

This kind of estimating is based on considering various options like the assignment of the resources, uncertainty, and the risk associated—such as best scenario-based and worst-scenario based. The three-point estimating concept is originated from PERT (Program Evaluation and Review Technique). It gives a weighted average of these three to arrive at a more realistic estimate. Through PERT, we generally estimate three types of duration:

Most Likely (M) Optimistic (O) Pessimistic (P)

Of these, Most Likely (M) is based on the resources assigned and Optimistic (O) is based on the best scenario-based analysis. And the last one—Pessimistic (P)—is based on the worst possible scenario-based analysis. Once you have these, you can use some very useful formulas to derive the expected duration.

They are as follows:

TE = (O + 4M + P) ÷ 6

Here, TE is expected time, and O, M, P are Optimistic, Most Likely, and Pessimistic duration respectively. In this way, you can understand the importance of PERT in estimating the duration for your project. These estimate values are usually taken from subject matter experts in respective activity area.


Basic concepts used in PERT and CPM Network. It is a logical and chronological set of activities and events, graphically

illustrating relationships among the various activities and events of the project. Project. This is a group of activities and events with a definite start and end as well as

both human and financial resources. Examples include constructing a dam, building a house, designing a new product among others.

Activity. It is a task or job requiring resources to be accomplished. Examples include collecting data, answering a question in an examination, painting a wall among others. The activity is depicted by a single arrow ( ) on the project network. The activity arrows are called arcs.

i. Predecessor activity: Are activities that must be completed prior to the start of another activity.

ii. Successor activity: Are activities that cannot be started until one or more of the other activities are completed.

iii. Concurrent activities: Are activities that can be accomplished together at the same time.

Event. An event represents a specific accomplishment in the project and takes place at a particular instant of time. It is a time oriented reference point that signifies the end of one activity and the beginning of another. Events are usually represented by circles( ). The event circles are called nodes. All activity arrows must begin and end with event nodes as shown below: -

Activity

Types of events.i. Merge events: it’s where one or more activities join an event.

ii. Burst event: it’s where more than one activity leaves an event.iii. Merge and burst event: It’s where more than one activity join and leave an event.

Merge event burst event merge and burst event

A path is a series of adjacent activities leading from one event to another Critical path. It is the sequence of critical activities that forms a continuous path between

the start of a project and its completion. Critical activity. It’s an activity that if slightly delayed, will hold up the scheduled

completion date of the entire project.


Start Event

Finish Event

Dummy activity: it is represented by a dashed arrow on the project network and is inserted in the network to clarify activity pattern in the following situations:-i. To make activities with common starting and finishing events distinguishable

ii. To identify and maintain the proper precedence relationship between activities that is not connected by events.

Example:The following example shows a simple Activity on Arrow Diagram.

Activity on Arrow DiagramIn this example A,B,C,D,E,F,G rows are representing the activities. Numbers above the rows are activity durations. As shown in the schema above, in Arrow Diagramming Method(ADM), only F-S Relationship is used to link activities.

Step 1: Forward Pass Calculation

Forward Pass Calculation – Arrow Diagramming Method (ADM)

Step 2: Backward Pass Calculation


Backward Pass Calculation-Arrow diagramming method (ADM)

Step 3: Float Calculation for Each Activity / Arrow Diagramming Method Example

Float Calculation-Arrow diagramming method (ADM)Float can be calculated by subtracting the Start Date of an activity from its Finish Date.

Step 4: Identifying the critical path / Arrow Diagramming Method Example

Critical Path-Arrow diagramming method (ADM)The critical path is the longest path in the network diagram and the total float of critical path is zero. As shown in the schema above, the critical path is marked red.

Summary



The Arrow Diagramming Method (ADM) and The Precedence Diagramming Method (PDM) are two network scheduling techniques. The first one is the traditional one used widely in the past. The second one is the current method that we are using widely now. In this simple arrow diagramming method example we show how to make forward, backward, total float and critical path calculation. Nowadays the arrow diagramming lost its popularity because of the introduction of software solutions but in order to use this software successfully, it is important to understand both scheduling techniques.

Guidelines for construction of network diagrams1. Each activity must be represented by one and only one arrow in the network.2. No two activities can be identified by the same beginning and end events. In such cases, a

dummy is introduced to resolve the problem.3. Before an activity can be undertaken, all activities preceding it must be completed.4. The arrows depicting various activities are indicative of the logical precedence only. The

length and bearing of the arrows are of no significance.5. The flow of the diagram should be from left to right.6. Arrows (activities) should be kept straight and should not be crossed.7. Angle between the arrows should be as large as possible.8. Dangling must be avoided. This happens when precedence and inter-relationship of the

activities are not properly identified.9. The general rule (Fulkerson’s rule) for numbering the events is that no event can be

numbered until all preceding events have been numbered. Therefore, the number at the head of an arrow is always larger than that at its tail.

Example 1 Draw a network for a project of erection of steel works for a shed. The various elements of the project are as under:

Activity code Description PrerequisitesABCDEFGHIJK

Erect site workshopFence siteBend reinforcementDig foundationFabricate steel worksInstall concrete plantPlace reinforcementConcrete foundationPaint steel worksErect steel workGive finishing touch

NoneNone

AB

A, CB

C, DG, F

EH, I

J


https://www.projectcubicle.com/scheduling-techniques/

https://www.projectcubicle.com/precedence-diagramming-method-scheduling/

Solution

EI

A CG H J K

B DF

Example 2Draw a network diagram from the following activities.

Activity

Immediate predecessor Activity

Immediate predecessor

ABCDEF

NoneAAABC

GHIJK

CC & DE & FG & HI & J

Solution

E

B F IA C K

G J

DH


1 2

3

5

4

7

6

8 9

Time Estimates In Network AnalysisActivity time is a forecast of the time an activity is expected to take from its starting time to its completion, under normal circumstances. The basic objective of the time analysis is to get a planned schedule of the project. The plan should include:-

a. Total completion time for the projectb. Earliest time when each activity can beginc. Latest time when each activity can be started, without delaying the total projectd. Float for each activity i.e. amount of time by which the completion of an activity can be

delayed without delaying the total project completione. Identification of critical activities and critical path.

Slack time of event: It’s the difference between the latest event time and earliest event time Head Event slack (HES): It is the slack at the head (or terminal point) of an activity. It is the

difference between the latest event time and earliest event time at its head (or terminal point or node)

Tail Event Slack (TES): It is the slack at the tail (or starting point) of an activity. It is the difference between the latest event time and the earliest event time at its tail (or starting point or node).

Earliest Finish Time (EFT): It’s equal to the latest finish time of the activity plus the duration of that activity.

Latest Start Time (LST): It is equal to the latest finish time of the activity minus the duration of that activity.

Total float: It represents the amount of time by which an activity can be delayed without delaying the project completion date:

Total Float = Latest Start Time - Earliest Start Time Total Float = Latest Finish time - Earliest Finish Time

Free float: It is that portion of the total float within which an activity can be manipulated without affecting the float of subsequent activities.

Free Float = Total Float - Head Event Slack Independent float: It is that portion of the total float within which an activity can be delayed

for start without affecting the float of preceding activities. Independent Float = Total Float - Tail Event Slack

In case negative value is obtained, it is taken as zero

Critical Path MethodCPM emphasizes the relationship between applying more men or other resources to shorten the duration of given jobs in a project and the increased cost of these additional resources. With CPM, the amount of time needed to complete various parts of the project is assumed to be known with certainty. The relation between the amount of resources employed and the time needed to complete the project is assumed to be known.The iterative procedure of determining the critical path involves the following steps:


1. Break down the project into various activities systematically. Label all activities. Arrange all the activities in logical sequence. Construct the arrow diagram.

2. Number all the nodes (events) and activities. Find the time for each activity considering it to be deterministic. Indicate the activity times on the arrow diagram.

3. Calculate the earliest start time, earliest finish time, latest start time and latest finish time. Tabulate various items i.e. activity normal times, earliest times and latest times.

4. Determine the total float for each activity by taking difference between the earliest time and latest time for each node.

5. Identify the critical activities and connect them with the beginning node and the ending node in the network diagram by double line arrow. This gives the critical path.

6. Calculate the total project duration.7. If it is intended to reduce the total project duration, crash the critical activities of the network.8. Optimize the cost.9. Update the network and smooth the network resources.

Advantages of CPM1. Helps the top management to concentrate their attention to the critical activities and their

completion in time.2. Provides the knowledge of critical and non-critical activities. This helps the management

to divert the resources from non-critical to critical activities.3. Provides a best way of planning and scheduling a construction project knowing the critical

path.4. Gives the complete information about the importance, duration, size and performance of

an activity.

Drawbacks of CPM1. It is based on the assumption of known time for each of the activity in the project, which

may not be true in real life situations.2. Does not incorporate statistical analysis in determining the time estimates.3. Entire evaluation of the project is to be repeated and a new critical path is to be found out

when certain changes are introduced in the network.4. Suitable for a situation that has a definite start and a definite finish.

PROJECT EVALUATION AND REVIEW TECHNIQUE (PERT)Steps involved in developing PERT network

1. Develop a list of activities that make up the project including immediate predecessors.2. A rough PERT network is drawn on the basis of the three questions for each activity i.e

which activities precede this one? Which activities follow this one? Which activities are concurrent with this one?

3. The network is then suitably sketched to conform to rules and conventions.4. Events are numbered in ascending order from left to right.


5. Time estimates for each activity are then obtained. They are The most likely estimate (m or tm). It’s the time the activity will take most

frequently if performed a number of times i.e. the modal value. The pessimistic estimate (b or tp). It is the longest time the activity can

conceivably take. The optimistic estimate (a or to): it is that time estimate of an activity when

everything is assumed to go well as per plan.6. Then, upon the assumption of beta distribution for the activity duration, the expected

time, te for each activity is computed from the following formula te = a + 4m + b/6.

7. Using the expected activity time estimates, determine the earliest start time and the earliest finish time for each activity. The earliest finish time for the complete project corresponds to the earliest finish time for the last activity.

8. After determining the latest start time and the latest finish time for each activity, compute the float associated with each activity, the critical path activities are the activities with zero float. Determine the critical path through the given network.

9. Using the values for b and a which were determined in step 5, calculate the variance (2) of each activity’s time estimates by

2 = (b – a/6) 210. Use the variability in the activity times to estimates to estimate the variability of the

project completion date. Using this estimate, compute the probability of meeting a specified completion date by using the standard normal equation:

= Due date – Expected date of completion Project variance Where Z = number of standard deviations the due date or target date lies from the mean or expected date.11. Crashing or compressing the project may have to be undertaken if the critical path

duration (as the project duration) is not acceptable to the management. Resource allocation may have to be performed if resources are limited.

ExamplesPERT – Program Evaluation and Review Technique ExampleThe associated network is below. All the inputs are listed in the table below.


PERT Method ExampleAfter building a network diagram and estimating the activity durations, you will determine the critical path by making forward and backward pass calculations.Forward Pass Calculations specify the minimum dates at which each activity can be performed and, ultimately, the minimum duration of a project.

PERT -Forward Pass CalculationBackward Pass Calculations determine the latest dates by which each activity can be performed without increasing the projects minimum duration.

PERT -Backward Pass Calculation


After completing the backward pass calculation, you can easily determine the critical path. In project management, “float” or “slack” is the amount of time that a task can be delayed without affecting the deadlines of other subsequent tasks, or the project’s final delivery date. Total float/slack is 0 on the critical path.

PERT Method -ActivityTotal Float: LS – ES = 18-15 = 3Total Float: LF – EF = 30-27 = 3

The total float can be calculated by subtracting the Early Start date of an activity from its Late Start date or Early Finish date from its Late Finish date.

Critical Path: When we analyze the network diagram we will see that there are some paths and every path have duration. The critical path is the longest path in the network diagram and the total float of the critical path is zero.

Summary

In real life, projects are not executed as it was planned all the time. Risks, unexpected events, uncertainty, and subjective estimates are significant reasons for deviations. PERT is helpful for estimating the project completion time in case of uncertainty. However, it may be difficult to use without software. In this example, we talked about the pert definition and calculated the expected duration for each activity. By making forward, backward calculations, we determined the critical path. Accuracy of expected durations which affect the critical path depends on the optimistic,



pessimistic and most likely duration estimates. By the help of PERT software, it is easy to make these calculations efficiently for many combinations.

Exercises1. A small project consisting of eight activities has the following characteristics:-

ActivityTime estimates in weeks

Preceding activity

Most optimistic (a)

Most likely (m)

Most pessimistic (b)

ABCDEFGH

NoneNone

AAA

B, CD

E, F, G

2108107935

1226102011975

Required;i. Draw the PERT network for the project.

ii. Determine the critical pathiii. Prepare the activity schedule for the project.iv. If a 30 weeks deadline is imposed, what is the probability that the project will be

finished within the time limit?v. If the project manager wants to be 99% sure that the project is completed on the

schedule date, how many weeks before that date should he start the project work?

Activity 1. A project has the following activities and other characteristics

Activity Preceding activity

Time estimates in weeks

Most optimistic

Most likely Most pessimistic

A

B

C

D

E

None

None

A

A

C

4

1

6

2

5

7

5

12

5

11

16

15

30

8

17


F

G

H

I

D

B

E, F

G

3

3

1

4

6

9

4

19

15

27

7

28

Required:

i. Draw the PERT network diagram.ii. Identify the critical path.

iii. Determine the mean project completion time.iv. Find the probability that the project is completed in 36 weeks.v. If the project manager wishes to be 99% sure that the project is completed on the

scheduled date, how many weeks before should he start the project? 2. A project has the following characteristics

Activity Preceding activity

Time estimates in weeks

Most optimistic

Most likely Most pessimistic

A

B

C

D

E

F

G

H

I

J

None

None

A

A

A

C

D

B, E

H

F, G, I

3

2

2

6

2

2.5

2.5

4.5

1

1

7

2.5

3

7

3

3

4

5.5

2

2

11

6

4

14

4

3.5

5.5

9.5

3

3

Required:

i. Draw the PERT network diagram.ii. Identify the critical path.

iii. Determine the mean project completion time.iv. Find the probability that the project is completed in 20 weeks.

Advantages of PERT1. Forces management to plan carefully how the various parts fit into the whole project.


2. Focuses attention on the critical elements of the project.3. Provides a forward looking type of control4. Suggests areas for increasing efficiency, reduction of costs and profit improvements.5. Makes possible the pressure for action at the right time.6. Provides up-to-date status information through frequent reporting, data processing and

accurate programme analysis.7. Helps to formulate new schedules when existing schedule cannot be met, and serve the

planning and evaluation at all levels.8. Minimizes production delays, interruptions and conflicts by scheduling and budgeting

resources. 9. Co-ordinates the various parts of the total job and thereby expedite and achieve

completion of projects on time.

Shortcomings of PERT1. Emphasizes on time only and not on costs.2. Time estimates to perform activities constitute a major limitation of this technique.3. Calculation of probabilities under PERT approach is done on the assumption that a large

number of independent activities operate on critical path and as such the distribution of total time is normal but this may not be true in real life situations.

4. Using PERT for active control of a project requires frequent updating and revising the PERT calculations and this proves quite costly.

Differences between PERT and CPMPERT CPM

- It’s a probabilistic model with uncertainty in activity duration.

- It is event oriented as the results of analysis are expressed in terms of events or distinct points in time indicative of progress.

- The use of dummy activities is required for representing the proper sequencing.

- It is used for repetitive jobs.

- It is applied mainly for planning and scheduling research programmes.

- It’s a deterministic model with well-known activity (single) times based upon the past experience.

- It is activity oriented as the results of calculation are considered in terms of activities or operations of the project.

- The use of dummy activities is not necessary.

- It is used for non-repetitive jobs.

- It is used for construction and business problems.


- PERT analysis does not usually consider costs.

- CPM deals with costs of project schedules and their minimization.

Key Points

It uses three estimates (most likely, optimistic, and pessimistic) to calculate the average value of activity duration

It reduces the bias, risks, and uncertainties from the duration calculation It is more accurate than the rest

d) Heuristic Estimating

This is also known as Rule of Thumb. You can roughly guess that entire design phase can take 45% of your entire project time and so on…this is a very useful technique in case of known phases where you can put an imaginary figure based on the experience.

e) Reserve Analysis

Reserve analysis includes estimation of additional time to the project schedule (to allow time for unexpected delay) and additional cost to the project budget (in case of activity cost overruns). It is more of like analysis for the contingency or adding buffers to the estimations. A reserve analysis is a type of contingency reserve. After fixing a schedule for each activity level depending on the activity attributes, you can create contingency reserve timing by adding some percentage in the derived schedule of each activity. It can be changed as work progresses; reducing or increasing depending on the situation.

f) Work Breakdown

Sometimes an activity is too large or complex for a reliable duration estimate. Project guidelines state that an individual activity that takes up more than 10 percent of the project schedule has to be broken down. A project manager uses a work breakdown technique to reduce the activity to smaller tasks. Ideally, the project manager can estimate the duration of tasks that individual workers perform more accurately than the whole activity.

g) Historical

An effective way of estimating activity duration is to use historical data. If data on the duration of the same activities is available, project managers take the average duration of the historical records and use that in the project schedule. For small businesses which have not completed many projects, other methods are preferable.


h) Expert Judgment

If expert judgment is available at reasonable cost, a project manager will often use such duration estimates as superior to internally generated ones. Expert judgment means using specialists who have a reputation for knowledge of the particular field and experience in estimating activity duration within it.

i) Effort required

A project manager who knows what resources are necessary for an activity may calculate the effort the activity requires and arrive at duration. He adds the amount of time it takes to obtain materials to the labor time it takes to complete the tasks. Such an estimate has the advantage that it allows the project manager to track resource use and compare it to the estimate.

j) Units to produce

Calculation based on units of activity is a method available to both the largest and smallest businesses. Typical units are numbers of products or size of the product. Project managers can calculate how much time it took to produce a certain number or a certain size and adjust for the number or size they want to produce. Project managers have to adjust for economies of scale for these calculations.

Network diagram (sequencing the activities). It can be changed as work progresses and as new activities identified in your project. Initially, you can estimate your project based on the network diagram (sequencing the activities). It can be further modified based on the changes done in the project during the execution, controlling and monitoring process. While project managers can't know the actual time, it will take to complete an activity, there are six methods they can use to obtain reliable estimates.

1.6 PROJECT SCHEDULE CONTROLControlling Schedule is the project management activity in which progress on project activities is compared against Schedule baseline to understand whether project is ahead of the schedule or behind. Based on the deviation you can plan on corrective or preventive actions and manage changes to baseline. Control schedule is the last process of time management knowledge area. Control schedule is the process of monitoring the status of the project activities to update project progress and manage changes to the schedule baseline to achieve the plan. After develop schedule process is complete, you will have the project schedule and it will include start and end dates of each project activity. During project execution, actual results of the project will differ from the planned values. While some activities could be


completed earlier than planned, some activities will take longer to complete. During control schedule process, actual results of the activities will be compared with the schedule baseline to determine any variances.

During control schedule process, project managers must measure against the plan and control the project. If there is a variance based on the schedule performance control, and if the project cannot be completed on time, corrective actions must be planned and taken. For instance, schedule compression can be planned to complete the remaining project activities earlier than planned to complete the project on time. During project execution, if factors causing lots of changes are found, these factors must be eliminated to prevent the root cause of changes. If they cannot be eliminated, the impact of these factors must be minimized by taking preventive actions.

Activities in Control Schedule Process

1. Re-estimation of the remaining components of a project: During the planning of the project, all future activities of the project are estimated based on very limited information on hand. While project progresses, unclear points will be cleared, the project team will have more information about the project and by this way, remaining activities will be estimated healthier respectively. Therefore, re-estimation for the remaining activities of the project is done during control schedule process to check whether the target project completion date will be achieved.

2. Conduct performance reviews: Actual results of each activity will be measured against the planned values in the schedule baseline during control schedule process. Based on the performance review, whether the project is on track is determined.

3. Adjust future parts of the project to deal with delays: If the project is behind the schedule, appropriate actions must be taken to get back on track. This is why you conduct the control schedule process. If the project is behind the schedule, the future parts of the project must be adjusted to deal with delays. For instance, schedule compression techniques like fast tracking or crashing can be applied for a project behind the schedule.

4. Measure variances against schedule: Schedule variance and schedule performance index of the project will show how far behind is the project from the planned values. These are measured during control schedule process. For instance, if the project duration is 12 months, and if the schedule variance is 1 month, this means the project will be completed in 13 months with a 1-month delay. Or, if schedule performance of the project shows 0.90, this means, 90 percent of the planned activities could have been completed to date. So, there is a delay for the remaining part and project is behind the schedule.

5. Level resources to distribute work: Based on the actual results of the project, some remaining activities of the project may cause overload on some project resources. In order to offload the project activities to available resources, resource leveling can be done during control schedule process.


6. Continue to play “what if…” to better optimize: Planning is an iterative process in project management as we mentioned previously. Therefore, during control schedule process, if there are any alternatives to shorten the duration of the remaining project activities, these must be identified and applied respectively.

7. Adjust progress and project reports: During project progression, you need to report to project stakeholders about the status of the project. And depending on the stakeholders you are reporting to, you need to adjust appropriate reports. For instance, if you are reporting to executive managers, you need to prepare high-level milestones in your report and if you are preparing for your project team, you need to prepare a detailed report showing the status of activities, remaining activities etc. You adjust the reports

8. Utilize change control process: Once project schedule is complete, schedule baseline is taken, and it can be changed only if there is an approved change request in the project. Change requests are evaluated by change control board in a project and if approved, appropriate changes must be aligned in the project plan to accommodate this change. For instance, in order to implement change request, new project activities need to be added to project schedule and maybe the critical path of the project will change. During control schedule process, it is ensured that changes are applied through change control process and only approved change requests are applied.

9. Identify the need for change requests: What is the reason for the change request? Is it because an improper planning or is it a new requirement coming from the customer? As a project manager, you have to avoid unnecessary changes in your project. These are analyzed during control schedule process as well.

Importance of Re-Estimating in Control Schedule Process

Re-estimate the remaining components of the project at least once over the life of the project to make sure you can still meet deadline, budget, and objectives. In the planning phase of your project, you have planned the project activities appropriately. You have got a cost baseline, you have got a schedule baseline and you have a project management plan to execute the project. With these baselines and plan, you know what to deliver at what time and at what cost. However, during the execution of your project, the actual values of these activities might be different than what you planned in the beginning.

And based on your actual values, you have to do frequent re-evaluations, frequent reviews, and frequent re-estimation on your project to check whether you will be able to still meet your project schedule and whether you will be able to still meet your target budget at the end of your project. If there are problems, for instance, if there is any variance that is showing that you will exceed your budget or that you will exceed the agreed end date of the project, then, you have to take corrective actions to meet the schedule baseline and to meet the cost baseline of your project.


https://blog.masterofproject.com/change-control-board/

In order to detect these variances and then take corrective actions respectively, you have to do re-estimating in your project frequently, and these should be determined at the beginning of your project. For example, you might say that I will be doing re-estimating each month or I will be doing re-estimating in every two weeks. Because re-estimation will take a time and you need to determine the appropriate frequency for re-estimating. And, based on this frequency, you have to do re-estimating and check whether you are still meeting the baselines of your project.

1.7 COST ESTIMATION AND FORECASTING

1.0 Introduction

Cost estimation may be defined as ‘a study which attempts to predict the relationship between costs and the activity level or cost driver that causes those costs. In practice, managers frequently encounter such cost drivers (what is a cost driver?) as machine hours, number of transaction, work cells, labour hours, and units of output e.t.c.

Types of Costs• Direct Costs– Costs that are clearly chargeable to a specific work package. Labor, materials, equipment, and others.• Direct (Project) Overhead Costs– Costs incurred that are directly tied to an identifiable project deliverable or work package. Salary, rents, supplies, specialized machinery• General and Administrative Overhead Costs– Organization costs indirectly linked to a specific package that are apportioned to the project

The cost estimating function is;

Y = a + bx

Where y is the total cost

a is the fixed cost component of the total cost

bx is the variable cost component of the total cost

However,

b represent the variable cost/slope or the gradient of the equation.

x represent the output level Q

1.1 Purpose of Estimation

It assists in estimating the future expenditure (cost prediction) as the expenditure will depend on the cost of the respective activities


a) It assists in determining the net benefits anticipated in a specific activity based on the relationship between projected costs and projected revenue.

b) Cost estimation is useful in business planning, cost control, performance evaluation and decision making.

1.2 Steps of Developing a Cost Estimating Relationship.

Strictly speaking, a CER is not a quantitative technique. It is a framework for using appropriate quantitative techniques to quantify a relationship between an independent variable and cost or price. Development of a CER is a 6-step process shown below:

Step 1. Define (or select) the dependent variable (Y)

Will the CER be used to estimate price, cost, labor hours, material cost, or some other measure of cost? Will the CER be used to estimate total product cost or estimate the cost of one or more components? The better the definition of the dependent variable, the easier it will be to gather comparable data for CER development.The dependent variable is the cost to be predicted and it is choice depends on the purpose of the cost function. It may also be referred to as response variable.

Step 2. Select the cost driver(s)

This may also be referred to as independent, explanatory or predictor variable. A cost driver can be defined as any factor whose change causes a change in the total cost of an activity.

Examples of potential cost driver

Direct labour hours Machine hours Number of units Number of production runs Number of orders, etc.

The potential cost driver should make economic sense and should be accurately measured. In selecting potential cost drivers for CER development Consider the following factors:Variables should be quantitatively measurable. Parameters such as maintainability are difficult to use in estimating because they are difficult to measure quantitatively. Data availability is also important. If you cannot obtain historical data, it will be impossible to analyze and use the variable as a predictive tool. For example, an independent variable such as physical dimensions or parts count would be of little value during the conceptual phase of system development when the values of the independent variables are not known.

Be especially wary of any CER based on 2 or 3 data observations. If there is a choice between developing a CER based on performance or physical characteristics, performance characteristics


is generally the better choice, because performance characteristics are usually known before design characteristics.

Step 3. Collect data concerning the relationship between the dependent and independent variables.

Collecting data is usually the most difficult and time-consuming element of CER development. It is essential that all data be checked and double checked to ensure that all observations are relevant, comparable, relatively free of unusual costs. A sufficient number of past observations must be obtained to derive an acceptable cost function. This should be adjusted to reflect any change of circumstances e.g. changes in price levels caused by inflation, changes in types of equipment used, etc. The time period used to measure the dependent variable and the cost driver should be the same.

Step 4 Plot the data on a graph

The graph (usually referred to as a scatter diagram) will indicate the general relationship between the dependent variable and the cost driver and will give a visual indication as to whether a lineal cost function can approximate the cost behaviour. It will also highlight extreme observations (outliers).

Step 5. Select the relationship that best predicts the dependent variable.

After exploring a variety of relationships, you must select the one that can best be used in predicting the dependent variable. Normally, this will be the relationship that best predicts the values of the dependent variable. A high correlation (relationship) between a potential independent variable and the dependent variable often indicates that the independent variable will be a good predictive tool. However, you must assure that the value of the independent variable is available in order for you to make timely estimates. If it is not, you may need to consider other alternatives.

There are various methods that can be used to estimate the cost function. Examples include: i. Engineering method

ii. Account analysisiii. High low methodiv. Regression methodv. Visual fit (scatter graph method)

vi. Learning curve Theory

Step 6: Test the reliability of the cost function

There are three main tests that should always be done. These include:a) Logical relationship testsb) Goodness of fit test


c) Specification tests (Tests of the assumptions of the model) 1.3 Cost Estimation Method

a) Engineering method

These methods are based on the use of engineering analysis of technological relationship between inputs and outputs e.g. method studies and time and motion studies. The procedure in such a study is to make an analysis based on direct observation of the underlying physical quantities required for an activity and then to convert the final result into cost estimate. This method is useful for estimating costs of repetitive processes where input and output relationship is clearly defined e.g. the cost associated with direct materials, direct labour and machine time.

b) Account analysis (Inspection of accounts) method

This method requires that departmental managers and the accountant inspect each item of expenditure within the accounts for some output level and then classify each of these items as wholly fixed, wholly variable or mixed.

A single average unit cost figure is selected for the items categorized as variable whereas a single total cost for the period is used for the items categorized as fixed. Mixed costs are decomposed into their variable and fixed components.

c) Work Breakdown Structure

Dividing the project into smaller tasks lets a project manager get an overview of cost. One method that accomplishes such a simplification is the work breakdown structure. Once the project is broken up into small tasks, the project manager can assign costs. For equipment that he has to purchase, he can contact suppliers to get accurate estimates. For other tasks, he can estimate the number of hours and use an hourly rate.

d) Resource CostingA common technique for cost estimating is to list the resources you need for the project and to total their costs. Typical resources include equipment, material, services and labor. You can get costs for equipment, material and services by consulting price lists or by going out for bids for the larger pieces. Labor costs are hourly, and you can base the total costs on estimates from similar projects or ask for bids to carry out the work. Small businesses use resource costing for larger or more complicated projects.

e) Unit CostsSmall or simple projects can be evaluated using a cost-per-unit that is characteristic of the project. The characteristic unit is a measure of the size of the project that is indicative for the particular project. It might be a cubic foot, a square foot or a work station. Typical applications


are for building costs, paving, renovating or for standard systems such as data processing. Costs are a dollar amount per unit. To get the total cost, you decide how large the building or surface is or how many people will be working on the data. Multiply that by the unit cost to get the total. You can get typical unit costs from prospective suppliers or from industry associations.

f)[e)] Historical CostingOne of the most transparent ways of estimating the cost of a project is to base it on previous work. If your company has completed a similar project recently, all the required costing information is available from the project files. If you don't have such a project, other work your company has done in the past can help determine the cost of similar work on the new project. If a local business that is not a competitor has completed a similar project, it might be willing to help. Where available, historical data often gives the most accurate prediction of future costs.

1. Cost of Quality: Cost of Quality estimation is used for determining overall cost estimates. It includes Cost of Conformance ( i.e money spend on Quality training, studies, surveys, inspection, validation & audits) and Cost of Non Conformance ( i.e money spent on rework , scrap, inventory and warranty costs ).

2.[1.] Vendor Bid Analysis: This technique is usually used when you need to work with external vendor or contractor to get your project activities done. This technique helps you to analysis what the project cost should be based on the bids from vendors and estimate the price of individual deliverables.

g) High low method (Two point method)

Under this method, records of costs in the previous period are reviewed and the costs of 2 periods are selected. These are the period with the highest level of outputs and the period with the lowest output. A line passing through these two points is then established and used in estimating costs. The high‐low method divides the change in costs for the highest and lowest levels of activity by the change in units for the highest and lowest levels of activity to estimate variable costs

Illustration 2.1

The production manager of XYZ Company, is concerned about the apparent fluctuation in efficiency and wants to determine how labour costs (in Sh.) are related to volume. The following data presents results of the 12 most recent weeks.

Week No. Units Produced(X) Labour Costs(Y)1 34 3402 44 3463 24 287 4 36 262 5 30 220


6 49 4167 39 3378 21 1809 41 37610 47 29511 34 21512 24 275

Required:

Estimate the cost function using the high low method

Assume that the Company intends to produce;45 units34 units next period

Estimate the labour cost to be incurred.

Solution

Highest point X Y49 416

Lowest point 21 180Difference 28 236

Gradient/slope = b = 236 = 8.43 28

The function will be:

Y= a + bx

We can Substitute the lowest points (21,180)180 = a + 8.43(21) a = 2.97. This can be approximated to 3

The predicting equation is therefore Y = 3 + 8.43 x

i. if X=45 units

Y = 3 + 8.43*45 = Sh.382.35

i. if X =34


Y = 3 + 8.43(34) = Sh.289.62

Note:

The main problems of the high low method are:

a. Reliability is lowb. It ignores all the other points except the highest and lowest which in most cases are

outliners.

h) Regression Analysis

A regression equation identifies an estimated relationship between a dependent variable (the cost) and one or more independent variables (the cost driver). When the equation includes only one independent variable then it is referred to as simple regression and its form is:

Ỹ= a + bx

Where, Ỹ is the predicted value of Ya and b are Constantx is the cost driver

When the equation includes 2 or more independent variables, it is referred to as multiple regression and is of the form:

Y = a + b 1 x1 + b2 x2 + …….bn xn for n independent variables.Simple Regression

Regression analysis determines mathematically the regression line of best fit. It is based on the principle that the sums of squares of the vertical deviation from the line established is the least possible

I.e. is minimized Where Y is the observed value of the dependent variable Ŷ is the predicted value of Y

The equation can be solved by the use of normal equations and these are:1. y = na + b (x)

xy = a (x) + b (x2)

From these normal equations:b = n xy – x y


2)ˆ( YY

nx 2– (x)2

a = Y - bx n n

Looking at illustration 2.1, then we first compute the sum of X, Y, XY, X2 and Y2. The table below shows these summations.

Week No. Units X) L.Costs(Y) XY X2 Y2

1 34 340 11560 1156 115600 2 44 346 15224 1936 119716 3 24 287 8897 961 82369 4 36 262 9432 1296 68644 5 30 220 6600 900 48400 6 49 416 20384 2401 173056 7 39 337 13143 1521 113569 8 21 180 3780 441 32400 9 41 376 15416 1681 14137610 47 295 13865 2209 8702611 34 215 7310 1156 4622512 24 275 6600 576 75625

430 3549 132,211 16234 1104005

Value of b can be calculated as follows:b = 12(132211) - 430(3549) = 6.10 12(16234) - (430) 2

a = 3549 - 6.10( 430) = 77.08 12 12

NB. Remember that Y = a + bx Therefore the predicting function is Ŷ = 77.08 + 6.1X b. i. If X = 45 units, then

Ŷ = 77.08 + (6.1 x 45) = Sh.351.58

ii. If X = 34 units, then

Ŷ = 77.08 + (6.1 x 34) = Sh.284.48


Illustration 2.2

Assume that the company (in illustration 2.1) intends to spend Sh.400 on labour cost next period. Compute the number of units that the company may produce.

i) Visual Fit (scatter graph method)

Cost estimation is based on past data regarding the dependent variable and the cost driver. The past data on cost levels and the output levels) is plotted on a graph (called a scatter graph) and a line of best fit is drawn as shown in the diagram. A line of best fit is a line drawn so as to cover the most points possible on a scatter graph. Its intersection with the vertical axis indicates the fixed cost while the gradient indicates the variable cost per unit.

Illustration:

Assume a firm has total costs of 8m, 4m and 1m respectively when the output units are 400,000 200,000 and 0 respectively. Estimate its cost equation using the visual fit method.

10

9

Dependant 8 X

Variable 7 X X X

(Total Cost) 6 X X X

5 X X X X X

4 X

3 X X X X X

2 X X

1m X

X2 X3

0 200,000 400,000


Independent Variable

(Output Level)

Variable cost = Change in cost = 8m – 4m = 20Per unit Change in activity level 400,000 – 200,000

Total cost equation y = 1m + 20 x

On the basis of the existing data, fixed cost is Shs 1m and the variable cost per unit is 20. On the basis of the developed model, estimates can be made regarding future cost. When the activity level is 600,000 units, total cost will be estimated as:

TC = 1M + 20 (600,000) = 1M + 12M = 13 M

Discussion Question

The theory of the experience curve is that an organization may increase its profitability through obtaining greater familiarity with supplying its products or services to customers. This reflects the view that profitability is solely a function of market share.Required:Discuss the extent to which the application of experience curve theory can help an organization to prolong the life cycle of its products or services.

NET PRESENT VALUE

Net present value in its simplest form can be explained as the calculation that compares the amount invested today to the present value of the future cash receipts from the investment. In other words, the amount invested is compared to the future cash amounts after they are discounted by a specified rate of return. When assessing any given project or initiatives, organizations use the NPV as a technique of evaluating their relative profitability to ensure that the most profitable ones are undertaken. A larger NPV indicates that the selected project has a higher revenue. The formula for NPV varies slightly depending on the consistency with which returns are generated. If each period generates returns in equal amounts, the formula for the net present value of a project is:

NPV = C * {(1 - (1 + R) ^ -T) / R} − Initial Investment

where C is the expected cash flow per period, R is the required rate of return and T is the number of periods over which the project is expected to generate income.


Per UnitCost Variable X XY - Y

Xin ChangeYin Change Gradient

1 0X Cost Fixed :Note

2323

m

However, many projects generate revenue at varying rates over time. In this case, the formula for NPV is: NPV = {C for Period 1 / (1 + R) ^ 1} + {C for Period 2 / (1 + R) ^ 2} ... - Initial Investment. Besides, there are other ways to compute the NPV as follows in the examples below using the even cash inflows and the uneven cash inflows.

Example1: Even Cash Inflows: Calculate the net present value of a project which requires an initial investment of $243,000 and it is expected to generate a cash inflow of $50,000 each month for 12 months. Assume that the salvage value of the project is zero. The target rate of return is 12% per annum.Solution

We have,Initial Investment = $243,000Net Cash Inflow per Period = $50,000Number of Periods = 12Discount Rate per Period = 12% ÷ 12 = 1%

Net Present Value= $50,000 × (1 − (1 + 1%)^-12) ÷ 1% − $243,000= $50,000 × (1 − 1.01^-12) ÷ 0.01 − $243,000≈ $50,000 × (1 − 0.887449) ÷ 0.01 − $243,000≈ $50,000 × 0.112551 ÷ 0.01 − $243,000≈ $50,000 × 11.2551 − $243,000≈ $562,754 − $243,000≈ $319,754

Example 2: Uneven Cash Inflows: An initial investment of $8,320 thousand on plant and machinery is expected to generate cash inflows of $3,411 thousand, $4,070 thousand, $5,824 thousand and $2,065 thousand at the end of first, second, third and fourth year respectively. At the end of the fourth year, the machinery will be sold for $900 thousand. Calculate the net present value of the investment if the discount rate is 18%.

SolutionPV Factors:

Year 1 = 1 ÷ (1 + 18%)^1 ≈ 0.8475Year 2 = 1 ÷ (1 + 18%)^2 ≈ 0.7182Year 3 = 1 ÷ (1 + 18%)^3 ≈ 0.6086Year 4 = 1 ÷ (1 + 18%)^4 ≈ 0.5158

The rest of the calculation is summarized below:

Year 1 2 3 4Net Cash Inflow $3,411 $4,070 $5,824 $2,065


Salvage Value 900Total Cash Inflow $3,411 $4,070 $5,824 $2,965× Present Value Factor 0.8475 0.7182 0.6086 0.5158Present Value of Cash Flows

$2,890.68 $2,923.01

$3,544.67 $1,529.31

Total PV of Cash Inflows $10,888− Initial Investment − 8,320Net Present Value $2,568 thousandINTERNAL RATE OF RETURN

The internal rate of return (IRR), is a profitability metric used by businesses to determine which projects are likely to yield the greatest return per dollar of capital investment. Though it is closely related to the net present value, the IRR reflects anticipated gains as a percentage of the initial investment rather than as a net dollar amount.

Intenal Rate of return is used to evaluate the beauty of a assignment or investment. If the IRR of a new project exceeds a enterprise’s required fee of return, that venture is fascinating. If IRR falls under the desired cost of return, the mission must be rejected.

The following is the formula for calculating the IRR;

0 = P0 + P1/(1+IRR) + P2/(1+IRR)2 + P3/(1+IRR)3 + . . . +Pn/(1+IRR)n

where P0, P1, . . . Pn equals the cash flows in periods 1, 2, . . . n, respectively; and

IRR equals the project's internal rate of return.

IRR example in its simplest form;

A machine can reduce annual cost by $40,000. The cost of the machine is 223,000 and the useful life is 15 years with zero residual value.Required:

1. Compute internal rate of return of the machine.2. Is it an acceptable investment if cost of capital is 16%?

Solution:(1) Internal rate of return (IRR) computation:

Internal rate of return factor = Net annual cash inflow/Investment required= $223,000/$40,000

= 5.575


http://www.investinganswers.com/node/5875

Now see internal rate of return factor (5.575) in 15 year line of the present value of an annuity if $1 table. After finding this factor, see the corresponding interest rate written at the top of the column. It is 16%. Internal rate of return is, therefore, 16%.(2) Conclusion:The investment is acceptable because internal rate of return promised by the machine is equal to the cost of capital of the company. A general rule of thumb is that the IRR value cannot be derived analytically. Instead, IRR must be found by using mathematical trial-and-error to derive the appropriate rate. However, most business calculators and spreadsheet programs will automatically perform this function. IRR can be used to calculate anticipated returns on shares or investments, including the yield to maturity on bonds. IRR calculates the yield on an funding and is for that reason one-of-a-kind than internet present worth (NPV) price of an investment

Advantages of IRR

The various advantages of internal rate of return method of evaluating investment projects are as follows:

Time Value of Money: The first and the most important thing is that it considers the time value of money in evaluating a project which is a big lacking in accounting rate of return.Simplicity: The most attractive thing about this method is that it is very simple to interpret after the IRR is calculated. It is very easy to visualize for managers and that is why this is preferred till the time they come across certain occasional situations such as mutually exclusive projects.Hurdle Rate / Required Rate of Return has Not Required: The hurdle rate is a difficult and subjective thing to decide. In IRR, the hurdle rate or the required rate of return is not required for finding out IRR. It is not dependent on the hurdle rate and hence the risk of a wrong determination of hurdle rate is mitigated.

IRR also allows managers to rank projects by means of their total rates of return rather than their web reward values, and the investment with the absolute best IRR is most often favored. Ease of comparison makes IRR attractive, but there are limits to its usefulness.

PAY BACK PERIOD

Payback interval is the time in which the preliminary money outflow of an funding is anticipated to be recovered from the cash inflows generated by means of the investment. It is among the simplest investment appraisal strategies.


Formula

The formula to calculate payback period of a project depends on whether the cash flow per period from the project is even or uneven. In case they are even, the formula to calculate payback period is:

Payback Period =Initial Investment

Cash Inflow per Period

When cash inflows are uneven, we need to calculate the cumulative net cash flow for each period and then use the following formula for payback period:

:Payback Period = A +

B

C

Within the above system,

A is the final interval with a bad cumulative money go with the flow;

B is the absolute value of cumulative money flow on the end of the interval A;

C is the total money glide in the course of the period after the above instances are utilized in the following examples.

Decision Rule

Accept the project only if its payback period is LESS than the target payback period.

Examples

Example 1: Even Cash Flows

Company XYZ is planning to undertake a task requiring preliminary investment of $105million. The venture is expected to generate $25 million per 12 months for 7 years. Calculate its payback period.

Solution.

Payback interval = initial funding ÷ Annual cash go with the flow = $105M ÷ $25M = 4.2 years

Example 2: Uneven cash Flows

Company XYZ is planning to undertake another assignment requiring initial funding of $50 million and is expected to generate $10 million in year 1, $13 million in 12 months 2, $16


million in year three, $19 million in year four and $22 million in year 5. Calculate the payback price of the projectSolution(cash flows in millions)Cumulative

Cash FlowYear Cash Flow0 (50) (50)1 10 (40)2 13 (27)3 16 (11)4 19 85 22 30

Payback Period= 3 + (|-$11M| ÷ $19M)= 3 + ($11M ÷ $19M)≈ 3 + 0.58≈ 3.58 years

Merits and demerits of payback period are as follows;

a. Pay back period gives more importance on liquidity for making decision about the investment proposals.

b. Pay back period deals with risk. The project with a shortest PBP has less risk than with the project with longest PBP.

c. The short term approach of pay back period is an added advantage of calculation of capital expenditure

Demerits are;a. Pay back period gives high emphasis on liquidity and ignores profitability.b. Only cash flow before the pay back period is considered. Cash flow occurred after

the PBP is not considered.

Accept or Reject Criteria of payback period

A undertaking is also approved or rejected on the groundwork of the per-decided (average) pay again interval if just one unbiased mission is to be evaluated. The general pay back interval relies on the management in phrases of maximum period in the course of which preliminary investment must be recovered.A undertaking is accredited if the actual pay back period is less than the regular pay again period. When two or more jointly wonderful projects are regarded for selection, they could also be ranked according to the length of payback interval. Consequently, the mission having the


shortest pay again period could also be assigned first rank, adopted in that order so that the undertaking with the longest pay back period would be assigned lowest rank.How do you calculate the payback period?The payback period is calculated through counting the quantity of years it will take to recuperate the money invested in a assignment.Let's anticipate that a corporation invests $400,000 in additional effective gear. The money savings from the new equipment is predicted to be $100,000 per 12 months for 10 years. The payback interval is 4 years ($four hundred,000 divided via $100,000 per year). A 2nd venture requires an funding of $200,000 and it generates money as follows: $20,000 in 12 months 1; $60,000 in year 2; $eighty,000 in yr three; $100,000 in yr 4; $70,000 in 12 months 5. The payback interval is three.4 years($20,000 + $60,000 + $eighty,000 = $160,000 in the first three years + $40,000 of the $100,000 occurring in yr four). Notice that the payback calculation uses money flows, no longer internet revenue. Also, the payback calculation does not handle a task's complete profitability. Rather, the payback period simply computes how speedy a manufacturer will recuperate its cash investment.

Advantages And Disadvantages Of Pay Back Period(PBP)

Advantages

1. Pay again interval is modest and effortless to appreciate and compute.2. Pay again period is universally used and handy to have an understanding of.3. Pay back period offers extra value on liquidity for making choice concerning the investment proposals.

4. Pay again period deals with risk. The undertaking with a shortest PBP has much less danger than with the task with longest PBP.

5. The quick term strategy of pay again period is an added competencies of calculation of capital expenditure.

Disadvantages of using the payback period;

1. In the calculation of pay again period, time price of cash is just not famous.

2. Pay again period gives high emphasis on liquidity and ignores profitability.

BENEFIT COST RATIO ANALYSISUsing the benefit fee ratio enables businesses and governments to make decisions on the negatives and positives of investing in distinct initiatives. In other phrases, utilizing advantage fee ratio evaluation allows for an entity to decide whether or not the benefits of a given task or proposal outweigh the genuine expenses that go into the creation of the task or suggestion.


Advantage cost ratio is understated ample to determine, nevertheless, there are benefit fee ratio calculators available that consider different causes that make the calculation just a little extra problematic. Causes equivalent to genuine worker construction or production line breakdowns can cause the advantage fee ratio to vary dramatically and so they ought to be accounted for when delving into the small print of a exact notion or challenge.

A benefit-cost ratio (BCR) Is an indicator, used within the formal discipline of price-benefit evaluation, that attempts to summarize the total price for money of a assignment or inspiration. A BCR is the ratio of the benefits of a project or suggestion, expressed in economic terms, relative to its bills, additionally expressed in fiscal phrases. All advantages and expenses should be expressed in discounted gift values. Benefit cost ratio (BCR) takes into account the amount of monetary achieve realized by means of performing a venture versus the amount it expenditures to execute the undertaking. The greater the BCR the easier the funding. General rule of thumb is that if the advantage is higher than the fee the challenge is an effective funding. BCR = Discounted worth of incremental benefits ÷ Discounted price of incremental expenses be given all initiatives with a BCR greater than 1, when charges and benefits are discounted at the possibility price of capital.

Example: Suppose a tunnel is proposed to be built to save travel time and road construction cost around a mountain. In order to save on first cost, a twin tunnel system is proposed with 1/2 capacity in each shaft. Construction = $3,000,000 --- Shaft 1 -- Now $4,000,000 --- Shaft 2 --Built in 20 years ( N = 20 )Maintenance (Shaft lining) = $160,000/Half -- every 10 yearsBenefits = $260,000/yr N = 1-20 $300,000/yr N = 21-50If i = 5% and N=50yrs, is the project justified?Solution : 1st cost PW = $3,000,000 + $4,000,000(P/F,5,20) = $4,507,600 Relining cost PW = $160,000(P/F,5,10+20) + $320,000(P/F,5,30+40) = $160,000(0.9908) + $320,000(0.3734) = $278,016 Note: (P/F,5,10 + 20) = (P/F,5,10) + (P/F,5,20)

Benefits PW = $260,000(P/A,5,20) + $300,000(P/A,5,30)(P/F,5,20) = $260,000(12.4622) + $300,000(15.3725)(0.3769) = $4,978,340

B/C = 4,978,340 = 1.040 4,507,600 + 278,016

Modified B/C = 4,978,340 - 278,016 = 1.042


4,507,600

The project is justified in either case, since B/C >1.0Note that if the B/C ratio is greater than 1.0, the modified B/C will also be greater than 1.0

EARNED VALUE MANAGEMENT (EVM)

Earned Value Management (EVM) is a project management technique that objectively tracks physical accomplishment of work. More elaborately:

EVM is used to track the progress and status of a project and forecasts the likely future performance of the project.

EVM integrates the scope, schedule, and cost of a project. EVM answers a lot of questions to the stakeholders in a project related to its

performance. EVM can be used to show the past and the current performance of a project and predict

the future performance of the project by the use of statistical techniques. Good planning coupled with effective use of EVM will reduce a lot of issues arising out

of schedule and cost overruns.

EVM has emerged as a financial analysis specialty in United States Government programs in the 1960s, but it has since become a significant branch of project management. In the late 1980s and early 1990s, EVM emerged as a project management methodology to be understood and used by managers and executives, not just EVM specialists. Today, EVM has become an essential part of every project tracking.

EVM - Basic Elements

EVM consists of the following three basic elements:

Planned Value Actual Cost Earned Value

All the three elements are captured on a regular basis as of a reporting date.

Planned Value

Planned value (PV) is also referred to as Budgeted Cost of Work Scheduled (BCWS). PV or BCWS is the total cost of the work scheduled/planned as of a reporting date.


It is calculated as: PV or BCWS = Hourly Rate × Total Hours Planned or Scheduled

NOTE: Hourly Rate is the rate at which effort will be valued.

Actual Cost

Actual cost (AC) is also referred to as Actual Cost of Work Performed (ACWP). AC or ACWP is the total cost taken to complete the work as of a reporting date. It is calculated as:

AC or ACWP = Hourly Rate × Total Hours Spent

Earned Value

Earned value (EV) is also referred to as Budgeted Cost of Work Performed (BCWP). EV or BCWP is the total cost of the work completed/performed as of a reporting date.It is calculated as:

EV or BCWP = Baselined Cost × % Complete Actual

All these three elements can be derived from Work Breakdown Structure by associating the costs to each of the tasks. For a big project, it will be a tedious task to calculate these elements manually. Scheduling software tools like Microsoft Project is used to calculate these three elements.

NOTE: % Completed Planned and % Completed Actual are defined below.

% Completed Planned

The percentage of work which was planned to be completed by the Reporting Date. It is calculated using the following formula:

% Completed Planned = PV / BAC

% Completed Actual

The percentage of work which was actually completed by the Reporting Date. It is calculated using the following formula:

% Completed Actual = AC / EAC


EVM - Cost Variance

Cost Variance (CV) is a very important factor to measure project performance. CV indicates how much over - or under-budget the project is.

CV can be calculated using the following formula:

Cost Variance (CV) = Earned Value (EV) − Actual Cost (AC)

OR

Cost Variance (CV) = BCWP − ACWP

The formula mentioned above gives the variance in terms of cost. Positive CV indicates the project is under-budget. Negative CV indicates the project is over-budget.

Cost Variance %

Cost Variance % indicates how much over - or under-budget the project is in terms of percentage.

Cost Variance % can be calculated using the following formula:

CV % = Cost Variance (CV) ⁄ Earned Value (EV)

OR

CV % = CV ⁄ BCWP

The formula mentioned above gives the variance in terms of percentage. Positive Variance % indicates % under budget Negative Variance % indicates % over budget.

Cost Performance Indicator

Cost Performance Indicator (CPI) is an index showing the efficiency of the utilization of the resources on the project. CPI can be calculated using the following formula:

CPI = Earned Value (EV) ⁄ Actual Cost (AC)

OR


CPI = BCWP ⁄ ACWP

The formula mentioned above gives the efficiency of the utilization of the resources allocated to the project.

A CPI value above 1 indicates the efficiency of utilizing the resources allocated to the project is good.

A CPI value below 1 indicates the efficiency of utilizing the resources allocated to the project is not good.

To Complete Cost Performance Indicator

To Complete Cost Performance Indicator (TCPI) is an index showing the efficiency at which the resources on the project should be utilized for the remainder of the project. It can be calculated using the following formula:

TCPI = ( Total Budget − EV ) ⁄ ( Total Budget − AC )

OR

TCPI = ( Total Budget − BCWP ) ⁄ ( Total Budget − ACWP )

The formula mentioned above gives the efficiency at which the project team should be utilized for the remainder of the project.

A TCPI value above 1 indicates the utilization of the project team for the remainder of the project can be stringent.

A TCPI value below 1 indicates the utilization of the project team for the remainder of the project should be lenient.

EVM - Schedule Variance

Schedule Variance (SV) indicates how much ahead or behind the schedule a project is running.

It can be calculated using the following formula:

Schedule Variance (SV) = Earned Value (EV) − Planned Value (PV)

OR

Schedule Variance (SV) = BCWP − BCWS


The formula mentioned above gives the variance in terms of cost which indicates how much cost of the work is yet to be completed as per schedule or how much cost of work has been completed over and above the scheduled cost.

A positive SV indicates we are ahead of schedule. A negative SV indicates we are behind schedule.

Schedule Variance %

Schedule Variance % indicates how much ahead or behind the schedule a project is running in terms of percentage.

Schedule Variance % can be calculated using the following formula:

SV % = Schedule Variance (SV) ⁄ Planned Value (PV)

OR

SV % = SV ⁄ BCWS

The formula mentioned above gives the variance in terms of percentage which indicates how much percentage of work is yet to be completed as per schedule or how much percentage of work has been completed over and above the scheduled cost.

Positive Variance % indicates % ahead of schedule. Negative Variance % indicates % behind of schedule.

Schedule Performance Indicator

Schedule Performance Indicator (SPI) is an index showing the efficiency of the time utilized on the project. SPI can be calculated using the following formula:

SPI = Earned Value (EV) ⁄ Planned Value (PV)

OR

SPI = BCWP ⁄ BCWS

The formula mentioned above gives the efficiency of the project team in utilizing the time allocated for the project.

An SPI value above 1 indicates the project team is very efficient in utilizing the time allocated to the project.

An SPI value below 1 indicates the project team is less efficient in utilizing the time allocated to the project.


To Complete Schedule Performance Indicator

To Complete Schedule Performance Indicator (TSPI) is an index showing the efficiency at which the remaining time on the project should be utilized. It can be calculated using the following formula:

TSPI = ( Total Budget − EV ) ⁄ ( Total Budget − PV )

OR

TSPI = ( Total Budget − BCWP ) ⁄ ( Total Budget − BCWS )

The formula mentioned above gives the efficiency at which the project team should utilize the remaining time allocated for the project.

A TSPI value below 1 indicates the project team can be lenient in utilizing the remaining time allocated to the project.

A TSPI value above 1 indicates the project team needs to work harder in utilizing the remaining time allocated to the project.

EVM - Miscellaneous Formula

Budget at Completion

Budget at Completion (BAC) is the total budget allocated to the project. BAC is generally plotted over time. For example, periods of reporting (Monthly, Weekly,

etc.) BAC is used to compute the Estimate at Completion (EAC), explained in the next

section. BAC is also used to compute the TCPI and TSPI.

BAC is calculated using the following formula:

BAC = Baselined Effort − hours × Hourly Rate

Estimate to Complete

Estimate to Complete (ETC) is the estimated cost required to complete the remainder of the project.

ETC is calculated and applied when the past estimating assumptions become invalid and a need for fresh estimates arises.

ETC is used to compute the Estimation at Completion (EAC).


Estimate at Completion

Estimate at Completion (EAC) is the estimated cost of the project at the end of the project. There are three methods to calculate EAC:

Variances are typical - This method is used when the variances at the current stage are typical and are not expected to occur in the future.

Past estimating assumptions are not valid - This method is used when the past estimating assumptions are not valid and fresh estimates are applied to the project.

Variances will be present in the future - This method is used when the assumption is that the current variances will continue to be present in the future.

The formulas for calculation of the three methods are as given below:

AC + (BAC − EV) AC + ETC (Estimate To Complete) AC + (BAC − EV) ⁄ CPI

Variance at Completion

Variance at completion (VAC) is the variance on the total budget at the end of the project.

This is the difference between what the project was originally expected (baselined) to cost versus what it is now expected to cost. VAC is calculated using the following formula:

VAC = BAC − EAC

% Completed Planned

The percentage of work which was planned to be completed by the Reporting Date. It is calculated using the following formula: % Completed Planned = PV ⁄ BAC

% Completed Actual

The percentage of work which was actually completed by the Reporting Date. It is calculated using the following formula: % Completed Actual = AC ⁄ EAC

EVM - Examples

To illustrate the concept of EVM and all the formulas, assume a project that has exactly one task. The task was baselined at 8 hours, but 11 hours have been spent and the estimate to complete is 1 additional hour. The task would have been completed already.


Assume an Hourly Rate of $100 per hour.

Using this information:

PV or BCWS = Hourly Rate × Total Hours Planned or Scheduled

PV = $100 * 8 hours = $800

AC or ACWP = Hourly Rate × Total Hours Spent

AC = $100 * 11 hours = $1100

EV or BCWP = Baselined Cost × % Complete Actual

EV = baseline of $800 * 91.7% complete = $734

(NOTE % Complete Actual (below) to get the 91.7%)

BAC = Baselined Effort − hours × Hourly Rate

BAC = 8 hours * $100 = $800

EAC = AC + ETC

EAC = 1100 + 100 = $1200

VAC = BAC − EAC

VAC = $800 − $1200 = −$400

% Completed Planned = PV ⁄ BAC

% Complete Planned = $800 PV ⁄ $800 BAC = 100%

% Completed Actual = AC ⁄ EAC

% Complete Actual = $1100 AC ⁄ $1200 EAC = 91.7%

SV = Earned Value (EV) − Planned Value (PV)

SV = $734 EV − $800 PV = −$66

SPI = Earned Value (EV) ⁄ Planned Value (PV)


SPI = $734 EV ⁄ $800 PV = 0.91

CV = Earned Value (EV) − Actual Cost (AC)

CV = ($734 EV − $1100 AC) = −$366*

* indicates a cost overrun

CPI = Earned Value (EV) ⁄ Actual Cost (AC)

CPI = $734 EV ⁄ $1100 AC = 0.66*

* indicates over-budget

PORTFOLIO THEORY

Definition:

A portfolio is a combination of assets held by the investor for investment purposes. Portfolio theory therefore attempts to show an investor how to combine a set of assets to maximise the assets' returns as well as minimise the assets' risk (Risk Diversification).

Diversification is defined as combining assets whose returns are not perfectly positively correlated to reduce the aggregate risk of the total asset holdings (or the portfolio).

1.2 PORTFOLIO EXPECTED RETURN

If the investor holds only two assets in the portfolio, we can therefore be able to compute the portfolio's expected return (sometimes referred to as the portfolio mean). This will be a weighted average of the expected return of each asset held in isolation, and can be given by the following formula:

E(RP) = E(αXA + ßXB) ... (3.a)Where (E(RP) is the expected portfolio return

α is the investment in asset Aß is the investment in asset BXA is the expected return of asset AXB is the expected return of asset B

Formula 3.a can be simplified as follows:


E(RP) = αEXA + ßEXB ... (3.b)

Not also that α + ß = 1. This is because all the investor's wealth is invested in either asset A or asset B.

IllustrationConsider two investments, A and B each having the following investment characteristics;

Investment Expected Return (%) Proportion A 10 2/3 B 20 1/3

REQUIRED:Compute the expected return of a portfolio of the two assets.

SolutionUsing formula (3.b)

Note α = 2/3 ß = 1/3EXA = 10 EXB = 20

E(RP)= 2 (10%) + 1 (20%)3 3

= 13.3%

Note that the expected return is a weighted average of the expected return of assets held in isolation.

1.3 PORTFOLIO STANDARD DEVIATION

Remember that standard deviation is a measure of risk of the investment. Portfolio standard deviation therefore measure the risk of investing in a combination of assets.

The portfolio standard deviation is not a weighted average of standard deviations of assets held in isolation. This is because of the inter-relatedness of the assets, which reduces the risk when assets are held together. This relationship is measured by the correlation co-efficient (τ),

The coefficient of correlation (τ) lies between -1 and +1. Therefore -1 τ +1.


If τAB = +1, this means that A and B are perfectly positively correlated and therefore the outcomes of A and B move in the same direction at the same time.

If τAB = -1, then A and B are perfectly negatively correlated and their results are inversely related. That is they move in opposite directions simultaneously.

If we consider the two asset case, then the portfolio standard deviation (δA+B) can be given by the following formula.

Where δA is the standard deviation of AδB is the standard deviation of BτAB is the correlation coefficient of asset A and B

Illustration

Consider two investments A & B each having the following characteristics:

Investment Expected Return (%) Proportion A 20 2/3 B 40 1/3

REQUIRED:

Compute the portfolio standard deviation if the correlation coefficient between the assets is

a. 1b. 0c. -1

Solution


δ A + B = √( α )2 δA2 + β2 δB

2 + 2 ( γ AB )(α )( β )(δ A )(δB) .. .(3. c )

11

δ A+B = √( 23 )

2( 20%)2 + ( 1

3 )2(40% )2 + 2 (γ AB)( 2

3 )( 13 )( 20%)( 40% )

12

Using formula (3.c) we can compute the portfolio standard deviation as follows:

Note that the standard deviation depends on the correlation coefficient if the proportion of investment is fixed. Therefore if a. rAB = 1

δA+B = (0.036 + 0.036) = 26.8%b. If rAB = 0 then

δA+B = (0.036) = 18.7%c. If rAB = -1

δA+B = (0.036 - 0.036) = 0 = 0There is no risk at all.

Note: If assets are perfectly negatively correlated then holding them in a portfolio greatly reduces their risk.

1.4 PORTFOLIO OF MORE THAN 2 ASSETS

Usually investors will not hold only 2 assets. If the assets held in the portfolio are more than 2 then the following general formulas may be used:

Where δP is the portfolio standard deviation.


= √0 .0178 + 0 . 0178 + 0 . 036( γ AB) = √0 .036 + 0 .036 (γ AB )

13

δP = √∑ ¿

t=1

N

∑ ¿

j=1

n

αi α j γij δ i δ j . ..(3 . e ) ¿¿

14

E ( RP ) = ∑ ¿

t=1

n

αt E( Rt ) . ..(3 .d ) ¿

15

Note: we shall not spend much time on analysis of more than 2 assets due to the complication involved. It is however, assumed that the student can be able to extend the two asset case to more assets.

1.5 COVARIANCE AND THE CORRELATION COEFFICIENT

We have already introduced the correlation coefficient. We shall consider the Covariance and its relationship with the correlation coefficient.

The covariance is a measure which reflects both the variance of an asset's returns and the tendency of those returns to move up and down at the same time other assets move up or down. The covariance between two asset's return can be given by the following formula:

Where Cov(AB) is the covariance between And BRAi is the return on asset A under the Ith state.E(RA) is the expected return of ARBi is the return on asset B under the ith stateE(RB) is the expected return of BPi is the probability of the ith state.

The correlation coefficient can be given by the following formula.


Cov ( AB ) = ∑ ¿

i=1

N

(RAi - E ( RAi)) (RBi - E ( RB ))P i ¿

16

γ AB = Cov ( AB)δA δB

.. .(3 .g )

17

Illustration:

Four assets have the following distribution of returns.

Probability Rate of return (%)Occurrence A B C D

0.1 10.0% 6.0% 14.0% 2.0%0.2 10.0 8.0 12.0 6.00.4 10.0 10.0 10.0 9.00.2 10.0 12.0 8.0 15.00.1 10.0 14.0 6.0 20.0

REQUIRED:

a. Compute the expected return and standard deviation of each asset.

b. Compute the covariance of asseti. A and Bii. B and Ciii. B and D

c. Compute the correlation coefficient of the combination of assets in b above.

Solution

a. E(RA)= 10(0.1) + 10(0.2) + 10(0.4) + 10(0.2) + 10(0.1) = 10%

E(RB)= 6(0.1) + 8(0.2) + 10(0.4) + 12(0.2) + 14(0.1) = 10%

E(RC)= 14(0.1) + 12(0.2) + 10(0.4) + 8(0.2) + 6(0.1) = 10%

E(RD)= 2(0.1) + 6(0.2) + 9(0.4) + 15(0.2) + 20(0.1) = 10%

= 0 since (RAi - E(R)A) = 0%


δ A = √∑ ¿

i=1

5

(RAi - E ( RA ))2 Pi ¿

18

= 4.8 = 2.2%

Likewise δC = 2.2% and δD = 5.0%

b. i.

Note that since (RAi - ERA) = 0Cov(AB) = 0

ii Cov(BC) = (6-10)(14-10)(0.1) + (8-10)(12-10)0.2 + (10-10)(10-10)0.4+ (12-10)(8-10)0.2 + (14-10)(6-10)0.1

= -4.8

iii Cov(BD) = (6-10)(2-10)(0.1) + (8-10)(6-10)0.2 + (10-10)(9-10)0.4 + (12-10)(15-10)0.2 + (14-10)(20-10)0.1

= 10.8

Assets B and C tend to move in opposite directions and therefore their covariance is negative while Assets B and D tend to move in the same directions and therefore their covariance is positive.

Returns of A has no correlation with the returns of other assets and therefore the covariance between A and any other asset is zero.

c. Correlation coefficient

i. τAB = Cov(AB) = 0 = 0 δAδB (0)(2.2)


δB = √(6 - 10 )† 0 . 1 + (8 - 10 )† 0 . 2 + (10 - 10 )† 0 . 4 + (12 - 10 )† 0 . 2 + (14 - 10 )† 0 . 1

19

Cov ( AB ) = ∑ ¿

i=1

5

( RAi - E ( RA )) ( RSi - E ( RB ))P i ¿

20

ii. τBC = Cov(BC) = -4.8 = -1.0 δBδC (2.2)(2.2)

i. τBD = Cov(BD) = 10.8 = 0.98 δBδD (2.2)(5.0)

Therefore Assets B and C are perfectly negatively correlated while B and D have a strong positive correlation.

1.6 EFFICIENT PORTFOLIO AND THE EFFICIENT FRONTIER

Efficient portfolios can be defined as those portfolio which provide the highest expected return for any degree of risk, or the lowest degree of risk for any expected return.

The investor should ensure that he holds those assets which will minimise his risk. He should therefore diversify his risk.

The risk can be divided into two:

a. The diversifiable (unsystematic) risk;b The non-diversifiable (systematic) risk.

The diversifiable risk is that risk which the investor can be able to eliminate if he held an efficient portfolio.The non-diversifiable risk on the other hand is those risks that still exist in all well diversified efficient portfolios.The investor therefore seeks to eliminate the diversifiable risk. This can be shown below:


From the graph shown above as the number of assets increases, the portfolio risk reduces up to point M. At this point the lowest risk has been achieved and adding more assets to the portfolio will not reduce the portfolio risk.

An efficient portfolio therefore is well diversified portfolio.

Note:The non-diversifiable risk can also be referred to as the market risk.


Diversification of Risk

EFFICIENT SET OF INVESTMENT

If consider many assets, the feasible set of investment will be given by the following graph

The shaded area is the attainable set of investment. However, investors will invest in a portfolio with the highest return at a given risk or the lowest risk at a given return. The efficient set of investment, therefore, will be given by the frontier B C D E. This frontier is referred to as the Efficient Frontier. Any point on the efficient frontier dominates all the other points on the feasible set.

2.1 THE CAPITAL ASSET PRICING MODEL

The Capital Asset Pricing Model (CAPM) specifies the relationship between risk and required rate of return on assets when they are held in well-diversified portfolios.

Basic assumptions of CAPM

1. Investors are rational and they choose among alternative portfolios on the basis of each portfolio's expected return and standard deviation.

2. Investors are risk averse.3. Investors maximise the utility of end of period wealth. Thus CAPM is a single period model.


4. Investors have homogeneous expectations with regard to asset return. Thus all investors will perceive the same efficient set.

5. There exist a risk-free asset and all investors can borrow and lend at this rate.6. All assets are marketable and perfectly divisible.7. The capital market is efficient and perfect.

The CAPM is given as follows:

Ri = RF + [E(RM - RF)]ß

Where Ri is required return of security iRF is the risk free rate of returnE(RM) is the expected market rate of returnß is Beta.

Note ßi = Cov(im)

δ²m

Where Cov(im) is the covariance between asset i and the market return.δ²m is the variance of the market return.

If we graph ßi and E(Ri) then we can observe the following relationship


All correctly priced assets will lie on the security market line. Any security off this line will either be overpriced or underpriced. The security market line therefore shows the pricing of all asset if the market is at equilibrium. It is a measure of the required rate of return if the investor were to undertake a certain amount of risk.Illustration:

Assume that the risk free rate of return is 8%, the market expected rate of return is 12%. The standard deviation of the market return is 2% while the covariance of return for security A and the market is 2%.

REQUIRED:

What is the required rate of return on Security A?

Solution

Ri = RF + (E(RM) - RF)ß

ß = Cov(AM) = 2 = 2 = 0.5


δM² 2² 4

Ri = 8% + (12 - 8)0.5 = 10%

The required rate of return on security A is therefore 10%.

2.2 LIMITATIONS OF CAPM

CAPM has several weaknesses e.g.

a. It is based on some unrealistic assumptions such as:

i. Existence of Risk-free assetsii. All assets being perfectly divisible and marketable (human capital is not divisible)iii. Existence of homogeneous expectations about the expected returnsiv. Asset returns are normally distributed.

b. CAPM is a single period model—it looks at the end of the year return.c. CAPM cannot be empirically tested because we cannot test investors expectations.d. CAPM assumes that a security's required rate of return is based on only one factor (the stock

market—beta). However, other factors such as relative sensitivity to inflation and dividend payout, may influence a security's return relative to those of other securities.

The Arbitrage pricing theory is designed to help overcome these weaknesses.

ARBITRAGE PRICING THEORY (APT)

Formulated by Ross(1976), the Arbitrage Pricing Theory(APT) offers a testable alternative to the capital market pricing model(CAPM). The main difference between CAPM and APT is that CAPM assumes that security rates of returns will be linearly related to a single common factor- the rate of return on the market portfolio. The APT is based on similar intuition but is much more general.

APT assumes that, in equilibrium, the return on an arbitrage portfolio (i.e. one with zero investment, and zero systematic risk) is zero. If this return is positive, then it would be eliminated immediately through the process of arbitrage trading to improve the expected returns. Ross (1976) demonstrated that when no further arbitrage opportunities exist, the expected return (E(Ri)) can be shown as follows:

E(Ri)=Rf + β1(R1-Rf)+β2(R2 -Rf)+--------+ βn(Rn-Rf)+έi


Where,

E(Ri) is the expected return on the security

Rf is the risk free rate

Βi is the sensitivity to changes in factor i

έi is a random error term.

3.2 APT and CAPM compared

The Arbitrage Pricing Theory (APT) is much more robust than the capital asset pricing model for several reasons:

a) The APT makes no assumptions about the empirical distribution of asset returns. CAPM assumes normal distribution.

b) The APT makes no strong assumption about individuals’ utility functions (at least nothing stronger than greed and risk aversion).

c) The APT allows the equilibrium returns of asset to be dependent on many factors, not just one (the beta).

d) The APT yields a statement about the relative pricing of any subset of assets; hence one need not measure the entire universe of assets in order to test the theory.

e) There is no special role for the market portfolio in the APT, whereas the CAPM requires that the market portfolio be efficient.

f) The APT is easily extended to a multi-period framework.Since APT makes fewer assumptions than CAPM, it may be applicable to a country like Kenya. However, the model does not state the relevant factors. Cho(1984) has, however, shown the security returns are sensitive to the following factors: Unanticipated inflation, Changes in the expected level of industrial production, Changes in the risk premium on bonds, and Unanticipated changes in the term structure of interest rates

Illustration

Security returns depend on only three riskfactors-inflation, industrial production and the aggregate degree of risk aversion. The risk free rate is 8%, the required rate of return on a portfolio with unit sensitivity to inflation and zero-sensitivity to other factors is 13.0%, the required rate of return on a portfolio with unit sensitivity to industrial production and zero sensitivity to inflation and other factors is 10% and the required return on a portfolio with unit sensitivity to the degree of risk aversion and zero sensitivity to other factors is 6%. Security i has betas of 0.9 with the inflation portfolio, 1.2 with the industrial production and-0.7 with risk bearing portfolio—(risk aversion) Assume also that required rate of return on the market is 15% and stock i has CAPM beta of 1.1


REQUIRED:

Compute security i's required rate of return usinga. CAPMb. APTUsing APT Ri = 8% + (13% - 8%)0.9 + (10% - 8%)1.2 + (6% - 8%)(-.7)

= 16,3%Using CAPM Ri = RF + (E(RM) - RF)ßi

Ri = 8% + (15% - 8%)1.1 = 15.7%

3.3 LIMITATIONS OF APTAPT does not identify the relevant factors that influence returns nor does it indicate how many factors should appear in the model. Important factors are inflation, industrial production, the spread between low and high grade bonds and the term structure of interest rates.

CAPITAL STRUCTUREFactors That Affect Capital Structure1. Availability of securities – This influences the company’s use of debt finance which

means that if a company has sufficient securities, it can afford to use debt finance in large capacities.

2. Cost of project finance (both implicit and explicit) – If low, then a company can use more of debt or equity finance.

3. Company gearing level – if high, the company may not be able to use more debt or equity finance because potential investors would not be willing to invest in such a company.

4. Sales stability – If a company has stable sales and thus profits, it can afford to use various finances in particular debt in so far as it can service such finances.

5. Competitiveness of the industry in which the company operates – If the company operates in a highly competitive industry, it may be risky to use high levels of debt because chances of servicing this debt may be low and may lead a company into receivership.

COST OF PROJECT FINANCE

Definition

This is the price the company pays to obtain and retail finance. To obtain finance a company will pay implicit costs which are commonly known as floatation costs. These include: Underwriting commission, Brokerage costs, cost of printing a prospectus, Commission costs, legal fees, audit costs, cost of printing share certificates, advertising costs etc. For debt there are legal fees, valuation costs (i.e. security, audit fees, Bankers commission etc.) such costs are knocked off from:


i) The market value of shares if these have only been sold at a price above par value.ii) For debt finance – from the par value of debt.

I.e. if flotation costs are given per share then this will be knocked off or deducted from the market price per share. If they are given for the total finance paid they are deducted from the total amount paid.Cost of Retaining Finance

This will include dividends for share capital and interest for debt finance (tax deducted) or effective cost of debt. However, when computing the Cost of project finance apart from deducting implicit costs, explicit costs are the most central elements of cost of finance.Importance of Cost of Finance

The cost of capital is important because of its application in the following areas:

i) Long-term investment decisions – In capital budgeting decisions, using NPV method, the cost of capital is used to discount the cash flows. Under IRR method the cost of capital is compared with IRR to determine whether to accept or reject a project.

ii) Capital structure decisions – The composition/mix of various components of capital is determined by the cost of each capital component.

iii) Evaluation of performance of management – A high cost of capital is an indicator of high risk attached to the firm. This is usually attributed to poor performance of the firm.

iv) Dividend policy and decisions – E.g if the cost of retained earnings is low compared to the cost of new ordinary share capital, the firm will retain more and pay less dividend. Additionally, the use of retained earnings as an internal source of finance is preferred because: It does not involve any floatation costs It does not dilute ownership and control of the firm, since no new shares are issued.

v) Lease or buy decisions – A firm may finance the acquisition of an asset through leasing or borrowing long-term debt to buy an asset. In lease or buy decisions, the cost of debt (interest rate on loan borrowed) is used as the discounting rate.

Factors That Influence the Cost of project Finance

1. Terms of reference – if short term, the cost is usually low and vice versa.2. Economic conditions prevailing – If a company is operating under inflationary

conditions, such a company will pay high costs in so far as inflationary effect of finance will be passed onto the company.

3. Risk exposed to venture – if a company is operating under high risk conditions, such a company will pay high costs to induce lenders to avail finance to it because the element of risk will be added on the Cost of project finance which may compound it.


4. Size of the business – A small company will find it difficult to raise finance and as such will pay heavily in form of Cost of project finance to obtain debt from lenders.

5. Availability – Cost of project finance (COF) prices will also be influenced by the forces of demand and supply such that low demand and low supply will lead to high cost of finance.

6. Effects of taxation – Debt finance is cheaper by the amount equal to tax on interest and this means that debt finance will entail a saving in Cost of project finance equivalent to tax on interest.

7. Nature of security – If security given depreciates fast, then this will compound implicit costs (costs of maintaining that security).

8. Company’s growth stage – Young companies usually pay less dividends in which case the cost of this finance will be relatively cheaper at the earlier stages of the company’s development.

Term Structure of Interest Rates

The term structure of interest rate describes the relationship between interest rates and the term to maturity and the differences between short term and long term interest rates.

The relationship between short and long interest rates is important to corporate managers because:

1. They must decide whether to buy long term or short term bonds and whether to borrow by issuing long-term or short-term bonds.

2. It enables them to understand how long term and short term rates are related and what causes the shift in their relative positions.

Several theories had been advanced to explain the nature of yield curve – These are:

1. Liquidity preference theory2. Expectation theory3. Market segmentation theory

1. Liquidity Preference Theory

This theory states that short term bonds are more favourable than long term bonds for 2 reasons.

i) Investors generally prefer short term bonds to long-term securities because such securities are more liquid in the sense that they can be converted to cash with little danger


of loss of principal. Therefore – investors will accept lower yields on short term securities.

ii) At the same time borrowers react in exactly the opposite way.Generally borrowers prefer long term debt because short-term debt exposes them to the risk of having to repay the debt under adverse. Conditions, accordingly borrowers are willing to pay higher rate other things held constant for long-term process than short ones.

Taking together this two sets of preferences implies that under normal conditions, a positive maturity risk premium exist which increases with maturity thus the yield curve should be upward sloping. Lenders prefer liquidity (short term hands) while borrowers prefer long term bonds and are willing to pay a “premium” for long term borrowing.

2. Expectation Theory

This theory states that the yield curve depends on the expectation about future inflation rates. If inflation rate is expected to increase, then the rate on long-term bonds will exceed that of short-term loan. The expected future interest rates are equal to forward rates computed from the expectations with regard to future interest rates are. Other factors which affect the expectations with regard to future interest rates are:

Political stability Monetary policy of the government Fiscal policy of the government (government expedition) Other economic related factors including social factors.

The following conditions are necessary for the expectation theory to hold.i) Perfect capital markets exists where there are many buyers and sellers of security with

non having a significant influence on the interest rates.ii) Investors have homogeneous expectations about future interest rates and returns on all

investments.iii) Investors are rational wealth maximizersiv) Bankruptcy of firms due to use of borrowing is unlikely.

3. Market Segmentation Theory

This theory states that the major investors (borrowers and lenders) are confined to a particular segment of the market and will not change even if the forecast of the likely future interest rates changes. The lenders and borrower thus have a preferred maturity e.g a person borrowing to buy a house or a company borrowing to build a power plant would want a long term loan. However a retailer borrowing to build up stock in readiness for a peak reason would prefer a short term loan.


Similar differences exist among savers e.g a person saving to pay school fees for next semester would want to lend on in the short-term market.

A person saving for retirement 20 years ahead would probably buy long-term security in L.T market. The thrust of market segmentation theory is that the slope of yield curve depends on demand and supply mechanism. An upward sloping curve would occur if there was a large supply of funds relative to demand in the short term marketing but a relative shortage of funds in the long-term market would produce an upward sloping curve.

Tests of the 3 theories

Various test have been conducted mainly in USA and they indicate that all the 3 theories have some validity and thus the shape of the yield curve of any firm is affected by the following:

1. Supply and demand conditions in the short and long term market.2. Liquidity preferences of lenders and borrowers3. Expectation of future inflation. While any of the 3 factors may dominate the market

all the 3 effect the term structure of interest rate.

Factors influencing interest rates

There are four most important factors that influence interest rates and the shape of yield curve.

1. CBK – Monetary policy2. The level of government budget deficit3. Balance of trade position4. Business activity (circle) in the economy

METHODS/MODELS OF COMPUTING COST OF CAPITAL

The following models are used to establish the various costs of capital or required rate of return by the investors:

Risk adjusted discounting rate Market model/investors expected yield Capital asset pricing model (CAPM) Dividend yield/Gordon’s model.

i) Risk adjusted discounting rate – This technique is used to establish the discounting rate to be used for a given project. The cost of capital of the firm will be used as the discounting rate for a given project if project risk is equal to business risk of the firm. If a project has a higher risk than the business risk of the firm, then a percentage risk premium is added to the


cost of capital to determine the discounting rate i.e. discounting rate for a high risk project = cost of capital + percentage risk premium. Therefore a high risk project will be evaluated at a higher discounting rate.

ii) Market Model – This model is used to establish the percentage cost of ordinary share capital cost of equity (Ke). If an investor is holding ordinary shares, he can receive returns in 2 forms:

Dividends Capital gains

Capital gain is assumed to constitute the difference between the buying price of a share at the beginning of the (P0), the selling price of the same share at the end of the period (P1). Therefore total returns = DPS + Capital gains = DPS + P1 – P0.The amount invested to derive the returns is equal to the buying price at the beginning of the period (P0) therefore percentage return/yield =

Total returns x 100 = DPS + P1 – P0 x 100 Investment P0

Illustration:

For the past 5 years, the MPS and DPS for XYZ Ltd were as follows:

1998Shs.

1999Shs.

2000Shs.

2001Shs.

2002Shs.

MPS as at 31st DecDPS for the year

40-

453

534

503

52-

Required

Determine the estimated cost of equity/shareholders percentage yield for each of the years involved.

Solution

Year MPS Capital gain DPS % Return1998 40 - - -

1999 45 5 3 5+340

x 100= 840

x 100=20 %


2000 53 8 4 8+445

=1245

x 100=27 %

2001 50 -3 3 −3+353

= 053

x 100=0 %

2002 52 2 - 2+050

= 250

x100=4 %

iii) Capital asset pricing model (CAPM) – CAPM is a technique that is used to establish the required rate of return of an investment given a particular level of risk. According to CAPM, the total business risk of the firm can be divided into 2:

Systematic Risk – This is the risk that affects all the firms in the market. This risk cannot be eliminated/diversified. It is thus called undiversifiable risk. Since it affects all the firms in the market, the share price and profitability of the firms will be moving in the same direction i.e. systematically. Examples of systematic risk are political instability, inflation, power crisis in the economy, power rationing, natural calamities – floods and earthquakes, increase in corporate tax rates and personal tax rates, etc. Systematic risk is measured by a Beta factor.

Unsystematic risk – This risk affects only one firm in the market but not other firms. It is therefore unique to the firm thus unsystematic trend in profitability of the firm relative to the profitability trend of other firms in the market. The risk is caused by factors unique to the firm such as:

Labour strikes by employees of the firm; Exit of a prominent corporate personality; Collapse of marketing and advertising programs of the firm on launching of a new

product; Failure to make a research and development breakthrough by the firm, etc

CAPM is only concerned with systematic risk. According to the model, the required rate of return will be highly influenced by the Beta factor of each investment. This is in addition to the excess returns an investor derives by undertaking additional risk e.g cost of equity should be equal to Rf + (Rm – Rf)BE

Cost of debt = Rf + (Rm – Rf)Bd

Where:Rf = rate of return/interest rate on riskless investment e.g T. billsRm = Average rate of return for the entire stock as shown by average Percentage return of the firms that constitute the stock index.


Be = Beta factor of investment in ordinary shares/equity.Bd = Beta factor for investment in debentures/long term debt capital.

Illustration

KK Ltd is an all equity firm whose Beta factor is 1.2, the interest rate on T. bills is currently at 8.5% and the market rate of return is 14.5%. Determine the cost of equity Ke, for the company.

Solution

Rf = 8.5% Rm = 14.5% Beta of equity = 1.2

Ke = Rf + (Rm – Rf)BE

= 8.5% + (14.5% - 8.5%) 1.2= 8.5% + (6%)1.2= 15.7%

iv) Dividend yield/Gordon’s Model – This model is used to determine the cost of various capital components in particular:

Cost of equity - Ke

Cost of preference share capital (perpetual) – Kp

Cost of perpetual debentures – Kd

a) Cost of equity (Ke)– This can be determined with respect to:

Zero growth firm – P0 = d0 Therefore = d0

P0

R = Ke

Where:d0 = DPSR0 = Current MPS

Constant growth firm – P0 = d0 (1+g )

K e g

Therefore Ke=

d0 (1+g )P0

+g


b) Cost of perpetual preference share capital (Kp)

Recall, value of a preference share (FRS) = Constant DPS Kp

Therefore: dp = Preference dividend per sharePp = Market price of a preference share

c) Cost of perpetual debenture (Kd) – Debentures pay interest charges, which an allowable expenses for tax purposes.

Recall, Value of a debenture (Vd) = Interest charges p.a. in ∞ Cost of debt Kd

Therefore Kd = Int .V d

(1−T )

Where:Kd = % cost of debtT = Corporate tax rateVd = Market value of a debenture

Cost of Redeemable Debentures and Preference Shares

Redeemable fixed return securities have a definite maturity period. The cost of such securities is called yield to maturity (YTM) or redemption yield (RY). For a redeemable debenture Kd (cost of debt) = YTM = RY, can be determined using approximation method as follows:

Kd /VTM /RY =Int (1−T )+(M −V d ) 1

n

(M +V d )12

Where:Int. = Interest charges p.a.T = Corporate tax rateM = Par or maturity value of a debentureVd = Current market value of a debenturen = Number of years to maturity

WEIGHTED AVERAGE COST OF CAPITAL (W.A.C.C.)


This is also called the overall or composite cost of capital. Since various capital components have different percentage cost, it is important to determine a single average cost of capital attributable to various costs of capital. This is determined on the basis of percentage cost of each capital component.

Market value weight or proportion of each capital component.

W.A.C.C = Ke( E

V )+K p( PV )+K d (1−T )( D

V )

Where:Ke, Kp and Kd = Percentage cost of equity, preference share capital and debt capital respectively

E, P and D = Market value of equity, preference share capital and debt capital respectively.

NB: Market value = Market price of a security x No. of securities.V = Total market value of the firm = E + P + D.

Illustration

The following is the capital structure of XYZ Ltd as at 31/12/2002.

Ordinary share capital Sh.10 par valueRetained earnings10% preference share capital Sh.20 par value12% debenture Sh.100 par value

Shs.M400200100200900

Additional information

1. Corporate tax rate is 30%2. Preference shares were issued 10 years ago and are still selling at par value MPS = Par

value3. The debenture has a 10 year maturity period. It is currently selling at Sh.90 in the

market.4. Currently the firm has been paying dividend per share of Sh.5. The DPS is expected to

grow at 5% p.a. in future. The current MPS is Sh.40.

Required

a) Determine the WACC of the firm.b) Explain why market values and not book values are used to determine the weights.


c) What are the weaknesses associated with WACC when used as the discounting rate, in project appraisal.

a) i) Compute the cost of each capital componentCost of equity (Ke) – Since the growth rate in dividends is given, use the constant growth rate dividend model to determine the cost of equity.

d0 = Sh.5 P0 = Sh.40 g = 5%

Ke=d0 (1+g )

P0+g=

5 (1+0 .05 )40

+0 .05=0 .18125=18 .13 %

Cost of perpetual preference share capital (Kp) – preference shares are still selling at par thus MPS = par value. If this is the case, Kp = coupon rate = 10%.

MPS = Par value = Sh.20

Dp = 10% x Sh.20 = Sh.2

K p=DPSMPS

=d p

Pp= Sh .2

Sh .20=10 %

Cost of debentures (Kd) – the debenture has a 10 year maturity period. It is thus a redeemable fixed return security thus the cost of debt is equal to yield to maturity.

Redemption yield:

Interest charges p.a. = 12% x Sh.100 par valueMaturity period (n)Maturity value (m)Current market value (Vd)Corporate tax rate (T)

= Sh.12= 10 years= Sh.100= Sh.90= 30%

Kd=YTM=RY =Int (1−T )+( M−V d ) 1

n(M +V d )½

=

Sh . 12(1−0 .3 )+(100−90 ) 110

(100+90 )½=9.9 %≈10 %


ii) Compute the market value of each capital componentMarket value of Equity (E) = MPS x No. of ordinary shares

=Sh. 40 x Sh . 400 MDSC

Sh. 10 parvalue = 1,600

Market value of preference share capital (P) = Par value, since MPS = Par value per share = 100

Market value of debt (D) = Vd x No. of debentures

=Sh. 90 x Sh . 200 Mdebentures

Sh .100 parvalue = 180

E + P + D = V = total Market Value = 1,880

iii) Compute W.A.C.C using Ke = 18.13%, Kp = 10%, Kd(1-T) = 10%

a) Using weighted average cost method,, WACC =

=Ke( E

V )+K p( PV )+K d (1−T )( D

V )

=18 .13 % ( 1 ,600

1 ,880 )+10 %(1001 ,880 )+10 % (180

1 , 880 )= 15.43 + 0.5319 + 0.9574

= 0.169193

≈ 16.92%

b) By using percentage method, WACC = Total monetary cost

Total market value (V)

Where:Monetary cost = % cost x market value of capitalMonetary cost of E = 18.13% x 1,600 = 290.08Monetary cost of P = 10% x 100 = 10.00Monetary cost of D = 10% x 180 = 18.00

318.08


Total market value (V) 1,880

Therefore WACC =318 . 081, 880

x 100 = 16.92%

b) In computation of the weights or proportions of various capital components, the following values may be used:

Market values Book values Replacement values Intrinsic values

Market Value – This involves determining the weights or proportions using the current market values of the various capital components. The problems with the use of market values are:

The market value of each security keep on changing on daily basis thus market values can be computed only at one point in time.

The market value of each security may be incorrect due to cases of over or under valuation in the market.Book values – This involves the use of the par value of capital as shown in the balance sheet. The main problem with book values is that they are historical/past values indicating the value of a security when it was originally sold in the market for the first time.

Replacement values – This involves determining the weights or proportions on the basis of amount that can be paid to replace the existing assets. The problem with replacement values is that assets can never be replaced at ago and replacement values may not be objectively determined.

Intrinsic values – In this case the weights are determine on the basis of the real/intrinsic value of a given security. Intrinsic values may not be accurate since they are computed using historical/past information and are usually estimates.

e) Weaknesses of WACC as a discounting rate

WACC/Overall cost of capital has the following problems as a discounting rate:

It can only be used as a discounting rate assuming that the risk of the project is equal to the business risk of the firm. If the project has higher risk then a percentage premium will be added to WACC to determine the appropriate discounting rate.


It assumes that capital structure is optimal which is not achievable in real world. It is based on market values of capital which keep on changing thus WACC will change over

time but is assumed to remain constant throughout the economic life of the project. It is based on past information especially when determining the cost of each component e.g

in determining the cost of equity (Ke) the past year’s DPS is used while the growth rate is estimated from the past stream of dividends.

Note

When using market values to determine the weight/proportion in WACC, the cost of retained earnings is left out since it is already included or reflected in the MPS and thus the market value of equity. Retained earnings are an internal source of finance thus, when they are high there is low gearing, lower financial risk and thus highest MPS.


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Course Content · Web viewCAPM, APT and WACC - Discussions - Interactive questions - Assignments 14-15 End of Semester Examination - Exams Written examination TEACHING METHODOLOGIES