# Declining Balance Depreciation, Made Simple

When depreciation is applied to the value of an asset for accounting purposes, one of the common methods used is the declining balance depreciation method. In this approach, a multiplication factor known as an accelerator is used to show increased depreciation at the end of the first year of purchase, and this depreciation amount declines for every consecutive year that the asset is “on the books.” This decline is seen because each year’s depreciation is calculated as a percentage of the book value, not as a percentage of the original purchase price.

The Theory behind Declining Balance Depreciation Method

This method of amortization is typically applied to assets that generate more revenue when they are initially purchased and decline over time (for example a mining equipment that is supposed to process certain minerals but the productivity of the machine lowers with age). As the productivity of the asset lowers with age, the rate of depreciation is calculated in proportion to that reduction. As with the straight line depreciation method, this method is followed because of the Matching Principle under Generally Accepted Accounting Practices (GAAP).

How is This Calculated?

In the straight line depreciation method, the depreciation is spread out evenly over the life of the asset. Therefore, if an asset was purchased for \$1,000, the depreciation will be calculated at 20%. In contrast, the declining balance depreciation method uses double that depreciation percentage, and that figure is applied to the book value taken from the end of the previous year, rather than the original purchase value.

Depreciation = Rate of Depreciation x Book Value of Asset, where

Rate of Depreciation = Accelerator x Straight Line Depreciation Rate

If the accelerator used is 2, then the rate of depreciation in the above example would be 40%. In such cases, the method is known as double-declining balance amortization.

Below is an example of how double-declining balance depreciation is used to calculate the yearly book value of an asset.

Example:

If a mining equipment costing \$10M has a salvage value of \$2M (the amount it is likely to be sold for after its useful life has been depleted) and it has a useful life of 5 years, then the straight line rate of depreciation is 20% (1/5th of the original price); the double-declining balance rate of depreciation, therefore, would be 40%. Using these figures, the following is calculated:

Double-Declining Balance Depreciation = 40% x \$10M = \$4M

Therefore, at the first year of depreciation (the year after the purchase value was recorded) the book value will be:

\$10M – \$4M = \$6M (Book Value)

In the second year of depreciation, the same 40% is now applied to the previous year’s book value rather than the original purchase value, which means that for that year, depreciation will be calculated as follows:

40% x \$6M = \$2.4M

In the subsequent year, the depreciation will be:

40% x (\$10M –\$6.4M) = 40% x \$3.6M = \$1.44M

The following year:

40% x (\$10M – \$7.84M) = 40% x \$2.16M = \$0.864M

And so on.

Since the book value cannot be shown to be less than the salvage value, depreciation can only be applied until the book value reaches the salvage value. If the book value is greater the salvage value at the end of the useful life of the asset, the excess is considered a Capital Gain.

# Sum of the Years Digits Depreciation, Made Simple

In accounting, one of the important accelerated depreciation methods is the Sum of the Years’ Digits approach. This type of depreciation is used to accurately reflect the decline of a fixed asset’s usefulness over a period of years until its book value is equal to its salvage value. This method is used to calculate amortization for assets that are more productive when first purchased, but rapidly show loss in productivity as time progresses.

The method used to calculate the depreciable amount involves calculating a figure known as sum of the years’ digits; hence, the name. The formula is as follows:

Sum of the Years’ Digits = (n X (n+1)) /2, where n is the number of useful years estimated for the asset in question.

The depreciation itself is calculated using the formula below:

Depreciation = Depreciable Base x (Useful Life Remaining / Sum of Years’ Digits)

The depreciable base in the formula is nothing but the maximum amount by which that asset can be depreciated before it reaches its salvage price, and is calculated as the difference between the purchase price and the salvage value.

Depreciable Base = Original Purchase Price – Salvage Value

Example:

Let us assume the following attributes for an asset:

Original Purchase Price: \$45,000

Salvage Value: \$5,000

Number of Useful Years: 4

Sum of Years Digits = 4 + 3 + 2 + 1 = 10

which can also be calculated by this formula:

SYD = (4 X (4+1)) / 2 = 10

In this case, the depreciable value will be:

\$45,000 – \$5,000 = \$40,000

This is the figure on which depreciation is calculated for the 4 years in which the asset serves its purpose.

Therefore, for the first year of depreciation:

SYD Depreciation = \$40,000 x (4/10) = \$16,000

The depreciable amount at the end of this year will be \$40,000 – \$16,000 = \$24,000

For the second year:

SYD Depreciation = \$40,000 x (3/10) = \$12,000

Depreciable amount at second year: \$24,000 – \$12,000 = \$12,000

For the third year:

SYD Depreciation = \$40,000 x (2/10) = \$8,000

Depreciable amount at third year: \$12,000 – \$8,000 = \$4,000

For the final (fourth) year:

SYD Depreciation = \$40,000 x (1/10) = \$4,000

Depreciable amount at final year: \$4,000 – \$4,000 = \$0

At this point, the book value of this asset has reached its salvage value, and no further depreciation is allowable.

Variance between Sale Price and Salvage Value

Should there be any difference between the actual sale price of the asset at the end of its useful life and the salvage value estimated at the time of its purchase, this amount will be considered as capital. A positive amount (sale price higher than salvage value) will reflect under capital gains, while a negative amount will be considered under capital losses.

Theory and Assumptions

The logic behind using the sum of years’ digits method of depreciation arises from the Matching Principle of Generally Accepted Accounting Principles (GAAP), which requires the value of an asset to be matched to the revenue it helps generate during each year of reporting.

The salvage price and the number of useful years are merely estimates, although they are guided by prevalent accounting principles. The sum of the years’ depreciation method relies on the accuracy of the estimates that are used for the purpose of the calculation.

Using this method, the true value of an asset for each year of its useful life can be calculated and recorded more accurately than, for example, using straight line depreciation. Therefore, it is common to use this method to calculate depreciation for assets that lose value rapidly from year to year.

# Straight Line Depreciation, Made Simple

To illustrate what depreciation is and how it’s used in the accounting records and on the financial statements for your company, let’s look at this quick example:

You are the project manager in an IT company. Your company just won a bid for a new iOS software for a new game development project. To complete this project you need to purchase an expensive top-of-the-line Mac Pro computer with a 12-core CPU, two GPUs and several network accessories for \$10,500. This purchase is planned to take place on July 1, 2014.

You estimate that the new computer will have a useful life of 4 years. At the end of its useful life, the company expects to sell the equipment for just \$500 to any college in the local area.

You discussed with your company’s accountant and she wants the depreciation to be reported evenly over the 4-year life. She explained to you that depreciating assets for companies is different from the approach used for personal income taxes. The most common method, which she wants to use, is the straight-line method. Under this method, the depreciation for each full year is the same amount.

The depreciation expense for a full year when computed under the straight-line method is illustrated here:

• Cost of Asset = \$10,500
• Expected salvage value = \$500
• Depreciable cost (this is the amount to be depreciated for every full year over the estimated useful life) = \$10,500 – \$500 = \$10,000
• Years of Useful Life = 4
• Depreciation expense per year = \$10,000 / 4 = \$2500

Assuming your company’s accounting year ends on December 31, the company will report the depreciation expense on the company’s income statement as shown in the following depreciation schedule:

• 2014: \$2500 / 2 = \$1250 (asset purchased on July 1, 2014 so used for half of the year only)
• 2015: \$2500
• 2016: \$2500
• 2017: \$2500
• 2018: \$1250

Actual Cash Flow

While the actual cash paid by the company for this equipment will occur as follows:

• 2014: \$10,500
• 2015: \$0
• 2016: \$0
• 2017: \$0
• 2018: \$0

As you can see, your company paid \$10,500 in 2014, but the 2014 income statement reports Depreciation Expense of only \$1,250 (since the asset was acquired on July 1, 2014, only half of the annual depreciation expense amount of \$2500 is recorded in 2014)

In each of the years 2015 through 2017 the company’s income statements will report \$2,500 of Depreciation Expense for that Mac Pro, thereby reducing \$2,500 of Depreciation Expense from the company’s revenues earned in each of those years. The remaining amount of \$1250 is depreciated in 2018.

The company will not pay out any cash for this expense from 2015 to 2018.

The company’s net income before income taxes will be reduced in each of the years 2015 through 2018 by \$2,500 or \$1250. This explains why Depreciation Expense is sometimes referred to as a noncash expense.

How is This Calculated?

The straight line method assumes a specific life expectancy for any asset that is being amortized. It also assumes a salvage value at the end of that period. Using these two figures and the acquisition cost of the asset, the entry can be made.

Example 1:

If a computer costs \$2,000, is expected to last for 3 years and can be sold for \$200 at the end of that period, the calculation for amortization will be as follows:

(Cost of Asset at Acquisition – AssumedRecovery at Salvage) ÷ Assumed Life Period of Asset in years = Depreciation or Amortization Charges per Annum

For our example above, the amortization will be:

(\$2,000 – \$200) ÷ 3 = \$1,800 ÷ 3 = \$600

Therefore, \$600 worth of asset value is recorded in the books for each of the 3 years from the year of acquisition.

Example 2:

If another fixed asset costs you \$5,000 to buy and you can sell it after its useful life of 2 years at \$3,000, the formula would look like this:

(\$5,000 – \$3,000) ÷ 2 = \$2,000 ÷ 2 = \$1,000

Theory and Assumptions

Generally Accepted Accounting Principles, or GAAP, is the reason any kind of depreciation method is used. Specifically, it is the Matching Principle that requires this; according to this principle, expenses incurred should be recorded in the same year (or accounting period) as the revenues they generate are recorded. Therefore, if your company buys a truck for delivery purposes, the cost of that truck will be calculated as above and the final figure will be the actual cost of that asset for each year that the truck is expected to be in service.

Accounting rules exist for assuming the useable life of any fixed asset and this is the guideline that must be followed at all times. However, depending on actual usage, that assumption may vary. For example, if the allowable useable life of a truck is 10 years, but you find that your company typically upgrades trucks in 7 years, then the latter is the figure that should be used to calculate depreciation. The shorter the period, the higher will be the depreciation value. For a truck worth \$20,000 that will be used for 7 years and then sold for \$5,000, the depreciation amount per year is \$2,142.85; at 10 years, that figure will drop to \$1,500.

Similarly, there are accepted practices to calculate the salvage value of an asset at the end of its useful life, and this must be in line with the set guidance for that asset type.

The difference between the value of an asset at the beginning of the year and its value at the end of the year (minus the depreciation amount) is known as the book value of that asset. At any point in time, the book value of the asset will be the original purchase price less the accumulated depreciation.

Jose, a project manager for a large software implementation company, is working on the project plan. The business analyst, Mary, mentions a third party tool which can fulfill some of the business requirements on the project. She talks highly about this tool and how another client had benefited from using it. They discuss the possibility of using this tool with the technical lead, Bob.

Bob advises against using the tool. He feels that the team has the capability of creating a similar tool. In such a scenario what should Jose do?

Should he make the tool or buy it.

As highlighted in the example above, make or buy analysis is done to ascertain if a piece of the project work should be done within the team or it should be purchased from an outside source.

The main reason to prefer ‘buy’ is to reduce the project risks or reduce developmental time.

Organizations prefer to ‘build’ in cases where:

• There is available capacity in the project (or organization)
• The business information is critical to business success, this includes dealing with proprietary information, business processes that give customer advantage over its competitors

There are various factors that are considered during this analysis:

• Capability: The knowledge of the in house staff to do the work
• Capacity: The availability of the right resources to complete the work without affecting the project constraints. Mature organizations also evaluate the opportunity cost.
• Budget Constraints: This includes evaluating the total cost of ownership, including the direct cost and indirect cost. The cost can be calculated using the following formulas:

Cost to buy = Direct cost of the item + Long term maintenance cost + Procurement process cost;

Cost to build = (per unit cost of resources * units of time) + Maintenance Cost;

In cases when you decide to buy, it may be wise to evaluate if there is an alternative of leasing instead of buying . You may require the equipment/product/service for a short time and the leasing may save you some cost.

So what do you think our friend Jose did?

He analyzed the cost of buying the tool, this included the direct cost of the tool, training cost, the cost of integrating the tool with the existing system and the cost of the procurement. He then compared it with the cost estimates of building and maintaining the tool in house. Once he had all the information it was easy for him to make a decision.

Time for a Quiz:

Imagine that you are a Project Manager working for the city of Newtown, Alaska.

Do you think you can wake up one day and decide to spend municipality’s money to build a Gym & Indoor Pool for the city?

Of course not! As soon as you start calling potential stakeholders or suppliers, they will ask you if you have the money to spend, and who authorized you to do that?

Someone in the city council or town hall has to set aside a budget, and authorize you as the PM to spend it on building that Gym.

Project Charter is that document which formally authorizes the project.

What kind of information does the Project Charter contain?

Organizations tend to modify the project charter in a way where information is more relevant to their business environment but the basic structure of a project charter includes:

1. Project description including expected benefits
2. Business case of the project to highlight the business benefits of the project vs. cost
3. High-level requirements
4. Known risks
5. Summary of project milestones
6. Project budget
7. Project success criteria
8. Assigned project manager
9. Approval of the project sponsor

Since the Project Charter is a document that marks the start of the project who is responsible for creating it?

The completion and approval of the project charter has to be done by the Project Sponsor. He’s the person with enough authority to assign a budget so you as the project manager can spend it! In our example it can be the mayor of Newtown, or the city manager. Project Manager may assist in creation of the project charter.

What is the significance of Project Charter besides a formal project approval?

– Acceptance by Senior Management: Project Charter indicates indicates acceptance of the project by senior management. They can be contacted for issues, escalations or guidance in reference to the approved tasks.

– Organizational Resources: Since the project budget is approved the project manager can start spending it (within the approved authority) and can also apply for organization’s investment into the project.

– Reference Document: Project Charter serves as the reference document through the life cycle of the project. It can be referred to in case of scope uncertainty, cost confirmation, understanding the business case etc.

– Critical Resource Assigning: In certain cases the project team members are assigned. This is done when the identified members are critical to success of the project.

How does a typical Project Charter look like?

Here is a sample Project Charter to give you an idea of how it looks like (click to enlarge):

Time for a Quiz:

#### Project Managers Are Communicators First !

Project communications management is probably the most important portion of the project plan, yet many people don’t fully plan for dealing with the number and complexity of communications throughout a project.  How important are communications to a project manager? Think about two quick statistics:

• Project Managers spend up to 90 percent of their time on projects communicating with stakeholders and team members.
• Additionally, communications issues are the most frequently reported problems on projects.

Even though project managers have a great responsibility in planning for communications on a project, it need not be overly complex.  One critical aspect of planning is understanding how many different routes (channels) communications can take on a project, so let’s make it easy to understand!

#### How Do We Communicate?

Let’s first talk about ways in which we can communicate as a project manager.  There are four types of communications that we use all the time.  Here is a quick list with some examples of how we use them:

• Formal Written – Project Management Plans, Reports, Complex Problems, & Long-Distance Communications
• Formal Verbal – Presentations
• Informal Written – Emails, Notes, Memos
• Informal Verbal – Conversations

These types of communications are used both internally and externally to the project team, up chains of management, and among the team.  Just think about the sheer number of emails alone that you receive, and that are sent between your team members!

#### Calculating Communication Channels On Your Project

Luckily, there is a simple formula for figuring out how many communication channels there are between a given number of people:

#### Where N is the number of stakeholders

We use this formula for identifying the number of routes of communication on the project.

For example: If we have a total of 10 people on our project, then the number of possible routes a communication can follow is [10 x (10 – 1)] / 2 = (10 x 9) / 2 = 90 / 2 = 45

That is a lot of possible channels for communications to happen already, but what if we add another person to the project?  Our total number of channels goes up to 55.  (Calculated as [11 x 10] / 2 )  That’s 10 more channels just by adding a single person!

You can easily see that the sheer volume of communications on large projects creates complexity in your planning.  Remember to always include yourself, as project manager, in the total number, N, of people when calculating communication channels.

We need to recognize that each of the paths is a channel we need to manage, but that we cannot control every single communication that happens.  This is why creating and following a communications management plan is so critical.

#### Tips For Stakeholder Management

A stakeholder is anyone that is impacted by the project or can influence the project.  Given this broad scope of people, the number of communication channels can be very large on your project.  Keep these tips in mind and you’ll be even more successful in your communications management!

• Identify and know all stakeholders – Understand their needs, find their expectations, listen for their interest, & know their influence on your project.
• Plan your communications with stakeholders – The better you plan communications on the project, the less likely they will cause issues later on.
• Manage their expectations – Communicate early and often with your stakeholders, even when the news is not good.  Managing expectations is a key to keeping stakeholders happy!

Remember, you’ll spend the vast majority of your time as a project manager communicating with your stakeholders.  Plan and manage this component well, and you’ll be ready to tackle any challenge a project brings! Don’t plan it properly, and you won’t hear the end of it from your top management !

# Crashing & Fast Tracking A Schedule, Made Simple

You’ve checked your data, then rechecked it.  No doubt, your project is over schedule compared to the baseline.  As a project manager, what are you going to do to correct the project?  We can change the order of tasks, add resources or people to the project, change scope, or some combination.

If the primary need is to get your project back on schedule, you’ll have to compress the schedule without changing the project scope.  Your two primary options are Fast Tracking or Crashing the schedule, but what’s the difference?  Let’s take a closer look at these two schedule compression techniques and make it simple to understand them.

## Fast Tracking

This technique is simply doing critical path activities in parallel, instead of in series as planned.  There is a primary presumption that the dependencies for the activities to be fast tracked are discretionary, so you are effectively just removing those dependencies as a barrier to starting an activity.

Do you just grab your network diagram and look at which activities on the critical path can be done simultaneously?  While this may sound like the easiest thing to do, there are several considerations before committing to this change in plans:

• There is inherent risk in making this schedule change, and you should update your risk log accordingly.  Be especially aware that the results of the parallelized activities may need to be reworked, as they may not be as expected initially.
• You are potentially increasing the number of communication channels, or at least creating the need for closer correlation between the activities.  Pay close attention to the additional effort involved in coordinating the activities.
• There was a reason you initially had the activities in series, possibly because the same person was to do both activities or there was a limitation on equipment.  Be sure you have the expertise, hardware, or software available to handle the additional workload for the duration of the fast tracked activities.
• Another consideration is that if a deliverable, say information, was to be available prior to the start of a future activity, you may need to make some assumptions about that input as a basis to run the activity earlier than planned.

What if you’ve fast tracked activities as much as you can, but it doesn’t compress the schedule enough?  You’ll need to consider “Crashing the Schedule” to find alternative ways to complete activities faster.

## Crashing

Crashing is a technique where you’ll be paying for increased amounts of work (time) for a period in the project.  In fact, project duration can often be reduced by assigning more workers to project activities. This could be in the form of overtime, and by assigning more resources (workers, material or equipment). The reduction in the normal activity duration is referred to as crashing. Crashing is usually measured in terms of dollars, for the activities to be crashed. There is necessarily increased project costs, as you are adding unplanned personnel or other resources to the project to get more done in a shorter period of time than originally planned. The primary consideration in crashing is how to get the most cost-effective solution in place for the decrease in schedule duration.  Identify all of the possible solutions, and pick the most efficient ones first. In essence, you select that subset of critical path activities which, when compressed, enable all current critical paths to become shorter, and do so at the least cost. These are the main steps in crashing a schedule:

• Choose that activity on the critical path which is cheapest to crash.
• Crash that activity till either another path becomes critical or the activity is fully crashed.
• No further crashing is possible when at least one critical path cannot be reduced.
• You also need to pay close attention to your assumptions.  For example, doubling the number of people working on a project doesn’t necessarily translate to a doubled productivity rate.  Or, if you purchase software to automate some tasks or activities, there may be a learning curve that slows down progress on the other activities.

## So, which technique should you choose?

If costs are the primary consideration, you should always choose fast tracking first.  If deadlines, liquidated damages, penalties or milestone deliveries are more important than costs, selecting crashing may be more appropriate.  In any scenario, you may want to select a combination of the techniques to balance risks, costs, and schedule.

Time for a Quiz:

# Portfolio & Program Management, Made Simple

With ever-increasing focus on delivering return on investment (ROI) in business, many organizations have implemented Program Management and Portfolio Management functions to improve project success levels. Do you know the similarities and differences between them? Let’s take a closer look at what Program and Portfolio Managers do, and how they can improve your bottom line!

First, let’s get some definitions in place, and do some comparisons. Then, we can look at how organizations implement Portfolios and Programs to realize success. The quick definitions from the PMBOK Guide 5th Edition are:

• A project is a temporary endeavor undertaken to create a unique product, service, or result. Project Management is the science (and art) of organizing the components of a project. It involves the planning of an organization’s resources in order to move a specific project towards completion.
• A program is a group of related projects managed in a coordinated way to obtain benefits and control not available from managing them individually. Program Management is the application of knowledge, skills, tools, and techniques to a program in order to meet the program requirements and to obtain benefits and control not available by managing project individually.
• A portfolio is a collection of projects and/or programs and other work that are grouped together to facilitate the effective management of that work to meet strategic business objectives. Portfolio Management refers to the centralized management of one or more portfolios to achieve strategic objectives.

The focus on objectives in these definitions is the key distinguisher between Program Management and Portfolio Management:

• Program management is focused on tactically improving a group of mutually beneficial projects, and other initiatives, as a whole.
• Portfolio management is focused on achieving strategic business goals from a collection of programs and projects which aren’t necessarily related.

Let’s look at a simple example to explore how the difference impacts a business:

Let’s assume our fictitious company Real Estate Gurus (REG) is in the real estate business to provide housing projects of various types. REG management and board have a strategic goal to improve the net profit of the company.

Debbie has been assigned as the Portfolio Manager. The Portfolio is categorized into buckets that allow Debbie to group projects and programs according to their potential profit (high, medium, low) each with their corresponding risk levels. Debbie’s efforts are focused on increasing the overall profits of the Portfolio. She has selected several high ROI (and high risk) projects to maximize profits.

In Debbie’s portfolio there are projects for new house construction, projects for remodeling of new apartments, projects for marketing new homes, and projects for improving the efficiency of new home designs using IT tools.

The Programs in place at REG consist of:

• Construction projects, managed by Allan (Program Manager for Construction)
• Marketing projects, managed by Kathy (Program Manager for Marketing)
• IT for Construction projects, managed by Steve (Program Manager for IT)

Allan, Program Manager for Construction is focused on improving the efficiency of projects selected, consolidating resource orders to get best pricing, using common practices and vendors for the apartment remodels we’re doing, and eliminating wasted time by identifying unused resources across multiple active projects.

To lessen the overall portfolio risk, Debbie has worked with Allan to initiate a new project to study “Best Practices” in the remodeling of new apartments. Robert, a Project Manager at REG has been assigned to that specific project.

Here’s a sequence of events:

• Robert (Project Manager) assigned to the new “Best Practices” project reports to Allan, and identifies several improvements, such as new cost-effective insulation materials; use of natural light for reducing energy consumption; and using more efficient and more cost-effective appliances from a newly emerged Korean company.
• Allan (Program Manager) chooses to implement the proposed improvements across the next few apartment remodeling projects, and sees significant cost reduction, realizing a boost in net profit on those projects.
• Debbie (Portfolio Manager) sees this great improvement, and therefore chooses more “apartment remodeling” projects than in the past, boosting profits for the whole company.

Another success story!

By having a Portfolio Manager in place, the company has significantly increased its potential for profits through selection of higher-than-average ROI projects. The Program Manager has also contributed significantly to company’s success by identifying and providing best practices for projects.

In a nutshell, Portfolios are different from Projects or Programs. A Portfolio can contain multiple projects and/or programs, and can also contain works that are not project oriented. The primary focus of Portfolio Management is on managing organizational investment to maximize the company’s ROI. Program Management is about the execution of those selected programs and projects to maximize potential.

Have a better understanding of Project and Portfolio Management?  Take a quick quiz and find out!

Click on “Start Quiz” icon.

# Net Present Value (NPV) Made Simple

Net Present Value (NPV) concept just means that money now is more valuable than money later on. Why? Simply because you can use money to make more money! You can either start a business with money, or simply put it in the bank to earn interest !

Imagine that your parents just won the lottery and offered you the choice of receiving \$10,000 now or next year. Which one would you chose?

If you place the \$10,000 in your bank account today and assuming you can earn 4% interest, your money could earn \$10,000 x 4% = \$400 in a year. In other words your \$10,000 now would become \$10,400 in a year’s time.

In other words, \$10,000 now is more valuable than \$10,000 next year. \$10,000 now is actually the same as \$10,400 next year (at 4% interest).

There are many different ways that people use these terms in the industry.

• We can say that the Present Value (PV) of \$10,400 next year is \$10,000.
• We can also say that the Future Value (FV) of \$10,000 invested today is \$10,400 in one year.

Using the same logic applied to multiple years (n) and a given interest rate (r) we can link Present Value (PV) and Future Value (FV) to each other by a formula:

PV = FV / (1+r)n

• PV is Present Value
• FV is Future Value
• r is the interest rate (as a decimal, so 0.04, not 4%)
• n is the number of years

Let’s use this formula to calculate Present Value of \$900 in 3 years with 10% interest rate:

PV = FV / (1+r)n

PV = \$900 / (1 + 0.10)3 = \$900 / 1.103 = \$676.18

In some finance books, you see a formula PV(r,n) showing a function of r and n:

PV(10%, 3) = 1 / (1 + 0.10)3

so for the above example you can write PV = PV(10%,3) X \$900 = \$676.18

NPV and Project Selection

The concept of NPV is often used for selecting projects that are worth doing. You subtract the initial investment on the project from the total Present Values of inflows to arrive at Net Present Value (NPV). You proceed with the project only if NPV is positive.

There are two main formulas for the calculation of NPV:

When cash inflows are even:

 NPV = C × 1 − (1 + r)-n − Initial Investment r

In the above formula:

C is the net cash inflow expected to be received each period
r is the required rate of return per period (or interest rate over the period)
n are the number of periods during which the project is expected to operate and generate cash inflows

When cash inflows are uneven:

 NPV = C1 + C2 + C3 + … − Initial Investment (1 + r)1 (1 + r)2 (1 + r)3

where:

r is the target rate of return per period (or interest rate per period);
C1 is the net cash inflow during the first period;
C2 is the net cash inflow during the second period;
C3 is the net cash inflow during the third period, and so on …

In some books Initial Investment is also presented as Cbut with a negative value when you add it in the equation:

 NPV = Co  + C1 + C2 + C3 + … (1 + r)1 (1 + r)2 (1 + r)3

Now time for a Quiz: