## Net Present Value (NPV)

Net Present Value (NPV) of the sum of all cash inflows (in Present Value) of the project minus the initial cost, i.e. PV (benefits) – PV (costs)The formula for Net Present Value formula is:

Net Present Value (NPV) = Σ(Pi / (1+ r) n) – Ci

where Pi is cash inflow; r is interest rate; n is time periods; Ci is initial cost.Let’s introduce the concept of Present Value (PV) first. Since there are inflation/deflation, $1000 now does not have the same purchasing power as $1000 in four years (i.e. owing to inflation, you can buy less with $1000 four years later). In order to adjust for inflation/deflation, Present Value (PV) is introduced.

Present Value (PV) is the future value in terms of today’s money with adjustment for inflation.This would provide an accurate figure to be used in benefit comparison.Don’t worry, for the PMP® Exam, candidates are not required to calculate the present value or net present value. You will only need to know that:

- NPV is an effective tool to help determining whether a project will be profitable or not;

NPV > 0— the project is profitableNPV = 0— the project will break evenNPV < 0— the project will lose moneyThe following would be a mock exam question on net present value:

- For the facility expansion project, $100,000 would be needed which is expected to generate a total of $200,000 (in present value) over 5 years. What is the Net Present Value (NPV) of the project?

A. $100,000

B. $200,000

C. $300,000

D. -$100,000Solution: A

Since the Net Present Value (NPV) is the present value of all benefits minus all costs, i.e. NPV = $200,000 – $100,000 = $100,000.Generally speaking,

The

largerthe Net Present Value (NPV), themore profitablethe project is to the organization.

## Benefit-Cost Ratio (BCR)

Benefit-Cost ratio is the ratio of the benefits of a project as compared to the costs calculated in terms of Present Value (PV).As pointed out in the Net Present Value (NPV) section, the use of PV will allow the figures to be calculated more accurately with adjustments for inflation.

using the Net Present Value in calculating the BCR is inflation.

The formula for calculating Benefit-Cost Ratio (BCR) is:

Benefit-Cost Ratio (BCR) = Benefits (in terms of PV) / Costs (in terms of PV)

where benefits are the total value/revenue generated (without consideration for costs). Interpretation of Benefit-Cost Ratio (BCR) :

BCR > 1— the project is profitable, and the higher the BCR the betterBCR = 1— the project will break evenBCR < 1— the project will cause the organization to lose money and is generally considered as not a good investmentThe following would be a sample exam question on benefit-cost ratio:

- You are considering a project for the expansion of facilities to increase production owing to rising demands. The cost for the expansion work and equipment would be $1,000,000 (NPV). It is expected that an increase in revenue of $2,000,000 (NPV) would be realized with the expansion. What is the Benefit-Cost Ratio (BCR) of the project?

A. 0.5

B. 20

C. 2

D. Not enough information to calculationSolution: C

Benefits = $2,000,000 and Costs = $1,000,000. Since BCR = Benefits / Costs = $2,000,000 / $1,000,000 = 2.NOTE:in the PMP® Exam, you will NOT be required to calculate the BCR.Generally speaking,

The

largerthe Benefit-Cost Ratio (BCR), themore favourablethe project is financially to the organization.

## Internal rate of return (IRR)

Internal rate of return (IRR) is the interest rate at which the cash inflow and cash outflow of the project equals zero.And the formula for Internal rate of return (IRR) is:

0 = F0 + F1/(1+IRR) + F2/(1+IRR)2+ F3/(1+IRR)3+ . . . +Fn/(1+IRR)n

where N is number of periods; F is cash flow.The formula looks sooooooooooooo difficult. The good news here is that you will NOT be asked to calculate the internal rate of return (IRR) in the PMP® Exam. The only thing you need to know about Internal Rate of Return is that, the higher the IRR, the better.

The following would be a mock exam question on internal rate of return:

- There are three projects for the organization to choose from: Project A has an internal rate of return of 10%, Project B 20% while Project B -20%. Based on the information provided, which is the best project?

A. Project A

B. Project B

C. Project D

D. Not enough information providedSolution: B

Project B has the largest internal rate of return, therefore it is deemed most profitable.Generally speaking,

The

largerthe Internal Rate of Return (IRR), themore favourablethe project is financially to the organization.

## Depreciation

Depreciation is the decrease in value of assets over time.The decrease in value can be attributed to many factors, take production machines as an example, the depreciation may be due to loss of efficiency, becoming out of date, new model coming out, etc.

There are three type of depreciation calculation techniques:

Straight Line Depreciation— the same amount is reduced in value over each year (the simplest depreciation calculation method).Double-declining Balance— (accelerated depreciation) reduction in value is higher at first and lower later on (twice that for straight line depreciation in the first year with 40% less than the previous year later on).Sum of Year Depreciation— (accelerated depreciation) greater depreciation in the earlier years of an asset’s useful life and less in the later years (e.g. for a machine with 5 years of service life, the sum of digit years = 1 + 2 + 3 + 4 + 5 = 15 and the depreciation for the first year is 5 / 15, the second year is 4 / 15 and so on).Remember this,

Assets for a project will reduce in its value over time (depreciation).

## Sunk Cost

Sunk Cost is the cost that has already been spent which cannot be recovered.The emphasis here is sunk cost is not recoverable. For example, if the organization has spent $100,000 on installation of a software on all workstations in preparation for an expected change in technology, the $100,000 spent is the sunk cost. This cost cannot be recovered even though the organization later changed its mind to use another software package.

For the PMP® Exam, candidates should understand that sunk cost should NOT influence future decisions.

Take the software installation example further, suppose a new software package has come to market which is much much more suited to the organization needs, the management should decide whether to continue with the staff training and documentation ($100,000) of the originally installed software package or opted for the new software ($200,000 including training and documentation). The decision should now be made based solely on which software package is the best for the current moment and disregard the $100,000 spent on the original software package (i.e. the sunk cost).

In addition to sunk cost, there are also other costs which may appear in the exam:

- Fixed Cost — take the software installation as an example, the fixed cost would be the monthly maintenance fee for buy fixes and upgrades
- Variable Cost — that would be the electricity bill used to power the workstations as this would be different each month depending on actual usage
- Direct Costs — expenses that are billed to the project directly, e.g. wages, material cost, etc.
- Indirect Costs — costs that are shared among several projects, e.g. taxes, fringe benefits, PMO, etc.
The following would be a mock exam question on sunk cost:

- In a project, the organization has purchases a machine for $100,000 which was later found to be not suitable. What is the $100,000 termed as?

A. Fixed Cost

B. Sunk Cost

C. Indirect Cost

D. Opportunity CostSolution: B

The $100,000 has already been spent which is not recoverable, so it is sunk cost.Note:The cost can also be termed as “direct cost” as the machine is purchased with the sole purpose for the project, but this is not one of the choices for the question.Remember,

Do not let

sunk coststo affect decisions as sunk costs are costs that are not recoverable. Focus on choosing the most feasible and beneficial action as the next step.

## Payback Period

Payback Period is the time it takes for the organization to earn back the initial investment (in terms of monetary cost) to the project and begin making profits.

If the income generated from the project is constant, the payback period can be calculated using the simplified formula:

Payback Period = Initial Investment / Periodic Cash-flow

For example, if the organization need to invest US$10,000 into a project that is expected to generate US$1,000 per month, the payback period would be:

Payback Period = US$10,000 / US$1,000/month = 10 months

In the actual exam, candidates are seldom required to calculate the payback period for projects (after all, the exam is not an accounting exam). The exam inclines more on testing Aspirants’ conceptual knowledge, i.e. whether the candidate understands the meaning behind payback period or other terms.

The following would be a sample PMP® Exam question on payback period:

- You are the project manager of the organization and you are tasked with the responsibility of selecting a project from two proposals A and B based on the business values with the information on hand: Project A has a payback period of 20 months while Project B has a payback period of 30 months. Which one should you recommend?

A. Project A

B. Project B

C. Neither one is beneficial to the organization.

D. Ask the project sponsor to choose.

Based on the fact that only the payback period is provided, we should rely solely on this information to make the selection. Since Project A has a shorter payback period, it is considered financially more beneficial for the organization.

**NOTE:**since you are tasked with the responsibility, it is not appropriate for you to escalate the decision making back to the project sponsor. Project Managers are expected to should responsibilities according to PMI, though in reality it is always the senior management / project sponsor to make the project selection.

Generally speaking,

The **shorter** the Payback Period, the **more favourable** the project financially to the organization.

However, Project Managers should note that Payback Period is rarely used solely as a project selection criterion. The organization would need to consider an array of different metrics in order to selection the projec with the best value realization to the organization. common project selection criteria include:

- Return on Investment
- Cost-benefit Ratio
- Net Present Value , etc.

## Return on Investment (ROI)

Return on investment (ROI) is the benefit an investment bring about, by comparing profits in relation to capital invested.

The formula for calculating Return on Investment for a project is *(note that the PMP® Exam does not require candidates to calculate ROI)*:

Return on Investment = Net profit / Capital Invested

Net profit (usually expressed as net present value [NPV]) is the total capital invested minus all expenditure. If ROI is larger than 1, the project is deemed to be profitable. If ROI is smaller than 1, the project loses money.

A sample PMP® Exam question on return on investment:

- The organization is considering several projects with the following return on investment:

ROI of Project A = 1.1

ROI of Project B = 0.4

ROI of Project C = 1.8

ROI of Project D = 1.0

By judging on ROI alone, which project is the most favourable choice?

A. Project A

B. Project B

C. Project C

D. Project D

Project C has the largest ROI. If ROI is the only metric to compare, Project C would be the best project to undertake.

Aspirants would only need to remember that:

The **higher** the Return on Investment, the **more favourable** the project financially to the organization.

However, in reality, ROI is not only project selection criteria. Let’s look at the mock question above again, if we further know that Project C is such a small project that the net gain from the project is US$8 while that for Project A is US$800,000. If you are the senior management, how will you choose again? It is really difficult to tell. Other factors must be considered.

But one thing is clear is that in the exam, the questions are usually simplified enough to ask you to make the choice based on a single metric which is never the case in real life situations.

## Opportunity Cost

Opportunity Cost is the value of the best alternative given up when a choice is made, in which the choices must be mutually exclusive owing to limited resources.

In simpler terms, opportunity cost is the highest value a person needs to give up for the chosen choice. For example, if you have US$10, you can either buy a coffee or 2 muffins. When you purchased the coffee, your opportunity cost is 2 muffins as you don’t have the money to purchase the muffins.

For the PMP® Exam, Aspirants should only need to know that owing to limited resources (money, human, space, etc.), the organization will often need to select one project over the others. The Opportunity Cost is the single best alternative NOT chosen*(NOTE: Opportunity Cost is not the sum of the values of all project given up)*. For most cases, the chosen project is believed to deliver the best values among all the project choices.

There is no calculation required for getting the opportunity cost.

A mock exam question on opportunity cost:

- You are the working in the PMO of your organization and there are three project proposals submitted. However, owing to the limitation of capital, only one project can be chosen. Project A would have a NPV of US$100,000, Project B would have a NPV of US$120,000 while Project C would have a NPV of US$50,000. What is the opportunity cost of choosing the project with the highest NPV?

A. US$120,000

B. US$50,000

C. US$100,000

D. US$150,000

Project B has the highest NPV and hence it is chosen. Based on the definition of opportunity cost, the second best NPV would be the best value given up. So the NPV of Project A would be the opportunity cost, i.e. US$100,000.

Project Benefit Analysis Concepts for the PMP Exam (Part 2)

Using Excel NPV Calculation Sample:

The example may be easier to understand if you copy it to a blank worksheet.

How?

Create a blank workbook or worksheet.

Select the example in the Help topic. Do not select the row or column headers.

Selecting an example from Help

Press CTRL+C.

In the worksheet, select cell A1, and press CTRL+V.

To switch between viewing the results and viewing the formulas that return the results, press CTRL+` (grave accent), or on the Tools menu, point to Formula Auditing, and then click Formula Auditing Mode.

10% Annual discount rate (A2)

-10,000 Initial cost of investment one year from today (A3)

3,000 Return from first year (A4)

4,200 Return from second year (A5)

6,800 Return from third year (A6)

Formula Description (Result)

=NPV(A2, A3, A4, A5, A6) Net present value of this investment (1,188.44)

In the preceding example, you include the initial $10,000 cost as one of the values, because the payment occurs at the end of the first period.

Example 2

The example may be easier to understand if you copy it to a blank worksheet.

How?

Create a blank workbook or worksheet.

Select the example in the Help topic. Do not select the row or column headers.

Selecting an example from Help

Press CTRL+C.

In the worksheet, select cell A1, and press CTRL+V.

To switch between viewing the results and viewing the formulas that return the results, press CTRL+` (grave accent), or on the Tools menu, point to Formula Auditing, and then click Formula Auditing Mode.

Data Description

8% Annual discount rate. This might represent the rate of inflation or the interest rate of a competing investment. (A2)

-40,000 Initial cost of investment (A3)

8,000 Return from first year (A4)

9,200 Return from second year (A5)

10,000 Return from third year (A6)

12,000 Return from fourth year (A7)

14,500 Return from fifth year (A8)

Formula Description (Result)

=NPV(A2, A4:A8)+A3 Net present value of this investment (1,922.06)

=NPV(A2, A4:A8, -9000)+A3 Net present value of this investment, with a loss in the sixth year of 9000 (-3,749.47)

In the preceding example, you don’t include the initial $40,000 cost as one of the values, because the payment occurs at the beginning of the first period.