PMI RMP – MATH FORMULA GUIDE part 1

1. INTRODUCTION

Hi and welcome back. This is a new section, a new important section, the Math Highlights or the Math Formula Guide for the exam. Now, one of the parts that some exam aspires consider difficult is the math calculations because there are many formulas they need to memorize. Actually, this is the reason, or this is the purpose for which I made the section. And I want to show you how much it’s easy to memorize the math formulas for the exam. In this section, I’m going to highlight all the important math concepts, all the formulas you need to memorize for the exam. We use math formulas in various project planning activities.

That’s true. Most of the math formulas are used in the planning processing group, like the expected monetary value and the risk planning critical path method for the schedule planning or the communication channels. In the communication planning, the percentage of questions which are based on math formulas range from five to 15 person. During your exam, in the coming few lectures, we will summarize the most important math formulas that Aspirants would need to understand and learn by hertz in order to answer all the exam math questions correctly. So what are the math topics I’m going to discuss in this section?

We’ll be starting with the project selection methods as a part of the integration management, the project selection methods and the economic models used for project selection purposes, the activity duration and cost estimates as part of the schedule and cost management knowledge area. What are the differences between the single point and three point estimations critical path method? How to define the project critical path? How to find out the early start and early finish, late start and late finish on all activities for your project. The most important part of this section the earns value analysis or the earnings value management.

How to find out all the variances of your project, the indexes and how to do the forecasting for the project estimate to complete or estimate at completion. How to find out how many communication channels are needed for your project as a part of the communication management. The expected monetary value of risk management reserves, the creation, the decision tree analysis. At the end we will discuss the point of total assumption and procurement management for the contracts, fees and final values. This is what I’m going to explain in this section. Thank you so much. I will see you at the next lecture.

2. PROJECT SELECTION METHODS

Hi and welcome back again. So the first topic I’m going to explain in this section will be the project selection methods and the economic models used for this purpose. So what are the project selection methods categories? First of all, we have the benefit measurement methods which employ various forms of analysis and comparative approaches to make project decisions. Actually, there are four benefit measurement methods murder boards, peer review scoring models, and economic models. Now, the exam is concerned with the economic models. There are five economic models which I’m going to explain in this lecture. The second category, we have the constrained optimization methods.

It used linear, dynamic, integral, nonlinear, and multi objective programming in the form of algorithms. It uses specific set of steps to solve a problem. These are complicated mathematical formulas and algorithms. So those are the project selection method categories, the benefit measurement methods, and the constraint optimization methods. Our lecture will be about the economic models. The Five Economic Models economic Model number one, the present value or the PV money received in the future worth more than money received today. The reason for that is the time value for money.

So what’s the exact definition of the present value? It’s the value today, it’s the current value of a future cash flow. So what’s the value today of a future cash flow? This is the present value. PV equals future value or FV divided by one plus the interest rate to the power a. Future value equals present value multiplied by one plus the interest rate to the power a, r is the interest rate, a is the number of years. So this is the formula you need to memorize for the exam. PV equals SB divided by one plus the interest rate to the power a where SB is the future value, r is the interest rate and A is the number of years.

This formula says that the future value FB of an investment equals the present value times one plus the interest rate raised to the value of the number of time periods a the interest rate is paid. It’s called also the discounted cash flow technique. It compares the value of the future cash flows of the project to today’s value of today’s dollars. So let’s see two examples on the present value. Example number one, let’s assume you will receive $100 in two years from now. How do we calculate the present value of this amount today? So let’s say Shadow will receive $100 after two years from today. What is the value of the $100 today? This is the present value as per this diagram, here is the present value at zero time.

After two years, the future value is $100, number of years is two. Or the interest rate is given as 8% by applying the formula PP equals FV divided by one plus the interest rate to the power a where FV is $100, r is 0. 8. So it’s 1. 8 to the power two. So the $100 after two years equals today $85. 9. This is the application of the present value. Now for the exam, you need to know that when comparing two projects, you will select the project with a higher present value or higher PV value. You are performing a comparison between projects using the present value technique. Project A is expected to make $100,000 in two years.

Project B is expected to make $120,000 in three years. If the interest rate is 12%, which project will you sell? It? So you are comparing two projects, the future value and the number of years is given for each project. And the interest rate is twelve person. Which project would you select using the present value or the PV technique? By applying the formula PV of Project A equals the future value divided by one plus R to the power a future value is $100,000. 01 plus zero point twelve to the power two equals $79,000. PV of Project B is $120,000 divided by one plus . 12 to the power three equals $85,000. When comparing between two projects, always select the project with a higher PV or higher present value.

So for our scenario, we’ll select Project B. The second economic model will be the NPV or the net present value. Definition is the present value of total benefits minus the cost over time periods. So you need to find out the present value of total benefits minus the costs over time periods. NPV equals the sum of present value income minus the sum of present value of cost. The value of all future cash flows positive and negative over the entire life of an investment discounted to the present. NPV analysis is used to help determine how much an investment project or any series of cash flows is worth. NPV is an effective tool to help determine whether a project will be profitable or not.

NPV more than zero, the project is profitable. NPV equals zero, the project will break even, NPV will less than zero, the project will lose money. And when comparing two projects, the larger the NPV or the net present value, the more profitable the project is to the organization. Here is an example. You have three projects select from with the following information project A four years life with NPV of $200,000. Project B nine years life with NPV of $250,000. Project C two years life with PV of $50,000 and NPV of $180,000. Which project would you select? So following the NPV criteria, it’s the only given or common project selection criteria given for the three projects. You would pick the project with the highest NPV value.

The highest NPV value is for Project B. It’s $250,000. So Project B shall be selected. Don’t get confused with the number of years for each project as net present value takes the time value of money into consideration. So you simply pick the project with the highest LP. The third economic model will be the IRR or the internal rate of return, the amount of money the project will return to the company that’s funding it. It is how much money the project is making the company. In other words, it’s the expected compound annual rate of return that will be earned on a project or investment. And it’s the rate at which the project inflows and project outflows are equal, usually expressed as a percentage of the funding that has been allocated to it.

So the IRR is always expressed as a percentage, this percentage of the total funding that was allocated to an investment. This graph will show you the intended rate of return. This is the break even point and it’s the rate at which project inflows and project outflows are equal, or the break even points. Now, for the exam, you have two projects to select from the following information project A with NPV of $120,000 and internal rate of return of nine person. Project B with PV of $80,000 and internal rate of return of 15%. Which project would you select? So the internal rate of return is given for both projects, the first project NPV and the second project PV. So we cannot consider the PV or the NPV in this case because the NPV is given for a project and the PV is given for the other project.

The common criteria given for both projects is the internal rate of return source simply you will pick the project with a higher internal rate of return value, which is project B. The criteria given for both projects is the internal rate of return. Project with higher IRR should be selective. Economic model number four is the easiest the payback period. The payback period shows how long it takes for a business to return its investment and initial costs of producing the product, service or rental. So it’s a measure of time, it’s a measure of period, it’s a payback period. It allows firms to compare alternative investment opportunities and decide on a project that returns its investment in the shortest time.

When choosing between projects or when choosing alternative methods of doing the project. Projects with less payback period are considered. Payback period is the least precise of all the cash flow calculations. The reason is that it does not consider the value of cash inflows in later years, commonly called time value of money or the present value we discussed in the PV economic model. Here is a simple example. A project initial investment is $1,200,000 with an expected benefit shown in the table below. What’s the payback period? So the total investment is $1,200,000 and the payback period requested in the question. This table shows the benefits over the five years.

So how many years you need to recover the $1,200,000? As shown from the table? It’s 500 plus 300, 800 plus 201,000,000 plus 201,000,200. So it will take four years for this project to recover the $1,200,000. So the project payback period will be four years. When comparing between two projects. Select the project with the shortest payback period. The last economic model will be the benefit cost ratio analysis. It’s also called the Vcr analysis of the expected revenue of the project compared to the expected cost. It’s a simple technique for comparing the business value a project will produce with the cost of producing at benefit cost.

Ratio of greater than one means that the benefits are greater than costs. If it’s less than one, then the costs are greater than benefits. The analysis calculations results in benefit cost ratio, which can be suppressed as a decimal or ratio like 1. 3. 750 percent, 100% or 120%, also known as the cost benefits analysis. And when the Bcr is greater than one, the project is profitable as the benefit is higher than the cost. And the higher the Bcr, the better the project is. When the Bcr equals one, the project will break even, and when it is less than one, the project will cause the organization to lose money and generally considered as not a good investment. Here is an example.

You are considering a project for the expansion of the organization facilities to increase production. The cost for the expansion work and equipment would be $1 million. As the NPV, it’s expected that an increasing revenue, $2 million would be realized with this expansion. What’s the benefit cost ratio of that project? It’s a very simple question. Bcr equals the benefit divided by the costs. The benefits are 2 million given in the question, and the costs are 1 million given in the question. So the Bcr is two. The larger the benefit cost ratio or the Bcr, the more favorable the project is financially to the organization. So when selecting a project in between two projects, select the project with.

3. ACTIVITY COST/DURATION ESTIMATES

Hi and welcome to the second topic of this section the cost and duration estimates. In this lecture we’ll be focusing on the three point estimation technique as an introduction in a properly managed project estimators have a WBS or work breakdown structure and this work breakdown structure may help creating these estimations. Wbs Dictionary and activity List are there as well. The Wbs or the work program structure in a properly managed project will be always the basis of all the estimations for the project work packages and project activities either cost or duration estimates. So if you have an accurate well defined Wbs, all your estimates will be accurate. Those who will be doing the work or those most familiar with the work to be done should create the activity estimates.

They may use one or many techniques which were identified in the Post schedule and management plan. Most of the time you will start with a rough estimate and then refine it to be more accurate. Now, what are the major three types of estimates. First of all, you have the rough order of magnitude accuracy range -25 to plus 75 it’s done during the initiating processing group we have the budgetary estimate -10% plus 25% done as a part of the planning processing group, the definitive estimate -5% to plus 10% as a part of the executing process group. These are the types of the estimates. There of order of magnitude is the one with the least accuracy. The definitive estimate is the one with the highest accuracy.

These estimates should be Morales for the exam. So the three point Estimating, what’s the three point Estimating? It uses three estimates that we averaged come up with a final estimate. Three estimates that you will use are first of all, you will have the most likely the optimistic estimate and the Pessimistic estimate. It’s the most likely estimate, the worst case scenario estimate, and the best case scenario estimate. So first of all, we have the most likely estimate which assumes there are no disasters and the activity can be completed as planned. This is the most likely estimate. It assumes that everything will go okay. The second one is the optimistic estimate. It’s the fastest time frame in which your resources can complete the activity.

It’s the best case scenario estimate, the Pessimistic estimate which assumes the worst happens and it takes much longer than a plan to get the activity completed. This is why it’s called the three point estimating technique. Then you can choose to use one of two formulas to calculate the expected duration estimate. What are the two formulas we can use first of all, we have the triangle distribution, it’s called also the simple average. It consists of summing the optimistic, most likely and Pessimistic estimates and then dividing that sum by three, usually used when you don’t have enough historical data to assist with the estimates or when the estimates are derived using expert judgment, the triangular Distribution or the simple average is the normal average.

Expected activity duration equals P plus M plus O divided by three. This is the simple average, p plus M plus O divided by three. So what’s the weighted average or the beta distribution or the pert formula taken from the program review and estimation technique? Pert, the formula for beta distribution or pert, looks like expected activity duration equals p plus four, m plus O divided by six. So the most likely estimate is multiplied by four. This is why it’s called the weighted average, because you gave a large weight for the most likely estimate, preferred when you have a good set of historical information and samples to base the estimates on. So here is example number one.

Your team came up with an estimate for a critical activity of $20,000. The construction manager states that the best scenario will be completing this activity within $16,000, and the worst case will be completing this activity within $30,000. What’s the simple average estimate of completing this activity? It’s a very simple question, right to the point. The most likely estimate, cost estimate, the optimistic and the Pessimistic are all given in the question. And the question is asking about the simple average or the triangle distribution. So it’s p plus M plus O divided by three theory plus 20 plus 16 divided by three will result with a $22,000 estimate. This is the simple average or the triangle distribution. Both have the same formula.

Example number two, you are working on your organization new offices building construction project. You come up with a most likely estimate of completing the project within 46 weeks. Due to governmental constraints, the project might be delayed to 50 weeks, and by fast tracking the project activities, it might be completed within 40 weeks. What’s the beta estimate of completing the project? So again, it’s a simple question. The question is asking for the beta estimate or the pert formula or the weighted average, it’s p plus four, m plus O divided by six p is given in the question 40 weeks. Most likely it’s 46 weeks. And due to government constraints, the Pessimistic estimate is 50 weeks. Applying these numbers into the formula, the beta project duration will be 45. 67 weeks.

When using the beta estimate or the purchase formula, the results will be always very close to the most likely estimate due to the high weight given or the most likely estimate in that formula. Now, the beta standard deviation, what’s the beta standard deviation? It refers to the possible range of the estimate. It helps you determine the confidence level within an activity cost or duration estimate. This is the beta standard deviation. It’s the possible range of the estimate. When you say that an activity can be completed in between ten and 14 days, this is the range of estimates. This is the standard deviation. For example, an activity estimate of 50 hours duration that has a standard deviation of plus -3 hours is expected to take between 47 hours and 53 hours.

This is the standard deviation. Plus -3 hours is the standard deviation. So how to find out the beta standard deviation? It’s P minus O divided by six, pessimistic minus optimistic divided by six. And what the activity range of estimate? It’s Ead, or expected activity duration plus minus the standard deviation. That means that the range of the estimate starts with Ead minus SD and ends with Ead plus SD. Ead is the expected activity duration. SD is the standard deviation. Now, what’s the relation between the standard deviation and the risk? The higher the standard deviation of an activity, the higher is the risk. Because standard deviation measures the difference between pessimistic and optimistic estimates.

A greater spread between the two, which results in a higher number, indicates greater risk. So activities with higher standard deviation will have greater risk. Now, another name for the beta standard deviation will be the sigma. Sigma is another name of standard deviation, and it indicates how much variance from the mean has been established. This is the mean here. As per this diagram. This is the mean. It’s where the zero? This is the sample of the sigma. Now, there is 68. 27% chance that an activity can be completed in an expected activity duration plus minus one standard deviation. Here is the one standard deviation minus one sigma plus one sigma. So there is a probability of 68. 26% that an activity can be completed.

Now, for the plus minus two sigma, it’s 95. 44 from minus two standard deviation to plus two standard deviation, it says 99. 73%, as shown here. It’s minus three sigma, two plus three sigma. Now, this is the number of the six sigma, as shown here. Here is the range in between minus six standard deviation or minus six sigma to plus six sigma. Now, what’s the relation between the standard deviation or sigma and the quality for a factory producing AC units, air conditioning units? If the factor is using three sigma level of quality, that means that 2700 units out of million will have a problem, as the factory is using three sigma. Let’s see the three segment here. It’s 99. 73% chance that the AC unit produced will be okay.

So what’s the chance of a failure with this AC unit? It’s 100% minus this number, which is zero point 27%. That means that 2700 units out of 1 million will have a problem. If a factory or a company is following a six sigma policies, it means that less than one person, or, sorry, less than one out of million will have a problem. This is the relation between the beta standard deviation and the sigma in the quality policies. For now, you need to know that sigma is the second name of the beta standard deviation. Here is an example. An activity on your project with optimistic duration estimate of 28 days and Pessimistic estimate of 52 days. Knowing that the most likely estimate of the activity is 30 days.

What is the activity range of estimate? It’s a very simple question. The pessimistic the most likely and the optimistic are all given in the question. So what’s the range of estimate? First of all, you need to find out the activity duration using beta formula. It’s p plus four. M plus O. The optimistic is given in the question 28. The pessimistic is given as 52 and the most likely is 30 days. So the project duration expected is 33. 33 days. Now, you need to find out the beta standard deviation which is p minus o divided by 652 -28 divided by six will give you four days. So what’s the range of estimate for this activity? It’s 33 plus minus four. Digs. Remember that as the activity range of estimates is larger the higher risk. The activity continues.