Category Archives: Definitions

Definitions of business, financial, and other terms that are relevant to software product development, but not significant enough to warrant a foundation series post.

Definition of sunk cost


Sunk cost is an expression representing the unrecoverable amount of money that has already been placed into an ongoing investment or project. It is one of the simplest, yet most commonly misused financial measurements of a project. We’ll learn how to avoid the most common mistake in project (financial) management, and how to survive when our boss makes the mistake.


In The Shawshank Redemption, Andy Dufresne asks the Warden if he’s obtuse. Andy gets a month in solitary confinement for his impertinence. We should remember this when our boss makes a statement like “We can’t cancel the project – we’ve already invested a million dollars in it!” If we want to avoid a month in the pokey, we need to restrain ourselves from telling our boss that he is irresponsible or ignorant.

Reinvestment decision example

Consider a project, with a projected return of $100,000 and a projected cost of $75,000. We previously determined that the project would be a good investment for us, so we funded it. Six months later, we’re reviewing the financials of the project, and discover that our project manager has already spent the $75,000, has not completed the software, and wants another $50,000 to complete the project. Assume that we believe the project manager, and it really will take an additional $50,000 to finish. If we don’t finish the project, the projected return is $0.

We’ve looked at methods for calculating the ROI of a proposed project. How do we make a decision about a project that is partially completed?

Financially incorrect reasoning

We now look at the project as having a total cost of $125,000 and a return of $100,000. We would lose $25,000 with this project – we should kill the project right now.

Financially sound reasoning

Unfortunately, the first $75,000 has already been “lost”, so we should not include it in our analysis. The previous calculation is wrong. Financial decisions are always made about future events, not past events. No decision we make now can recover the sunk costs. We should therefore ignore those costs in any decision making.
At the beginning of the project, the projected value of the project was $25,000 ($100,000 return minus $75,000 cost). [Note: This is similar to, but not the same as expected value]. The projected value of the additional investment is $50,000 ($100,000 return minus $50,000 additional cost). The first $75,000 we spent doesn’t matter any more – it’s already been spent and can not be recovered.

What we are faced with now is the decision to spend $50,000 to get a return of $100,000. There are two possible scenarios: invest nothing and get nothing in return, or invest $50,000 and get $100,000 in return.
sunk ship

The first $75,000 is a sunk cost in that we don’t get that money back just by choosing to not invest more money.

There’s usually more at stake here

In another example, imagine that we’ve invested a million dollars to get a return of 1.5 million. We’ve just discovered that we will have to invest another two million dollars to complete the project. Should we do it? Financially, no. This is where the pointy-haired boss might say “We can’t cancel the project – we’ve already invested a million dollars in it!”

However, that manager may be optimizing on his reputation, not the company’s finances. The reference to previously invested funds could be a red herring. What the boss is really saying is “We can’t cancel the project – the CEO knows that I’m in charge of making this happen!” It may also be that we don’t have all the information. There might be other hard to quantify benefits to completing the project (like goodwill or investor-perceptions) that would justify the added expense. In other words, the return exceeds 1.5 million dollars, we just don’t realize it, even if our boss does.

In cases like this – tread carefully. Those of you old enough to remember the SALT treaty will remember Reagan’s famous statement – “trust, but verify.” Take the same approach with your apparently illogical boss. And if you find out that you can’t trust your boss, find another boss.

Definition of payback period


Another tool for financial decision making

We’ve talked previously about using ROI to determine which projects to fund. This isn’t the only way to make those decisions, as Ski points out with the concept of flush. Payback period is the measure of how quickly an investment returns the invested amount, or the break-even point in the investment.

Using payback period

When we are managing a business or a project by cash-flow (versus income), we care very much about how quickly we get our money back. It is a reality that some companies (or project sponsors) choose the less-profitable investment if they get their money back faster. The most common reasons for this decision would be if a private company is strapped for cash, and does not want to use debt to finance operations. Public companies can also be faced with this situation, if they find that market valuations are predominantly driven by cash flow instead of profitability. A bootstrapped start-up company may also be forced to make short-term investment decisions based upon cash flow.

Companies faced with a high level of uncertainty for their investments will also find payback period analysis attractive. Since payback calculations will have the same inherent risk (and error) as expected value calculations, this presents a false sense of security. It does, however, provide a mechanism for controlling risk by favoring “get my money back sooner” projects over those with longer payback periods.

When using payback period to make investment decisions, companies will usually have a standard time period, such as two years or two quarters. Any project that has a payback period of less than the standard will be acceptable. Those projects that take longer to return the original investment than the standard period will not be acceptable.

Definition of payback period

From Philip Cooley’s Business Financial Management:

A popular procedure in practice that measures the time required to recapture through cash inflows a project’s net investment cash outflow. Payback ignores time value of money and post-payback cash flows. It measures the return of capital, not the return on capital.

Problems with payback period

Payback period analysis is not considered to be an ideal evaluation mechanism for three reasons.

  1. The time value of money (used in NPV calculations) is not considered. $100,000 three years from now is considered to be equivalent to $100,000 today.
  2. Cash flows beyond the payback period are ignored, thereby ignoring the ultimate ROI of the investment.
  3. The required rate of return (IRR) for the project is ignored. Less profitable projects will be favored if they return the initial investment more quickly than more profitable projects.


We suggest using payback period only when cash-strapped (with an aversion to debt-financing), or as a tie-breaker against apparently equivalent projects (based upon ROI).

Definition of NPV – Net Present Value


Net present value, or NPV is the great equalizer of financial analysis.

NPV allows us to compare any two investments and determine which is the better investment.

NPV tells us how many dollars, today, we would be willing to spend to receive money in the future. NPV lets us compare investments that pay back money in very different ways – we can decide if we would rather have $10,000 in one year, or $500 per month for 20 months. Without NPV, the two investments appear to be the same (they both return $10,000), but one of them is better than the other.

NPV calculation for single payments

NPV compares these values based upon a simple assumption – any money sitting in our bank account would be placed in a risk-free, guaranteed investment at a fixed interest rate. Imagine that our bank is offering savings bonds with a 5% interest rate. We purchase a bond worth $10,000 one year from now. $10,000 is the expected value of the bond. We will have to pay the bank $10,000/(1.05) = $9,524.

The NPV, or net present value of the $10,000 bond is $9,524.

Simple and compound interest

The example above used simple interest, to make the idea easy to grasp. In reality, most investments will return what is known as compound interest. Simple interest is calculated against the original investment amount. With a simple interest rate of 5% per year, and an investment (or loan) of $100, the annual interest payment would be $5 (5% of $100). This is the way most people think about interest rates, but it isn’t the way that most companies use interest rates.

Most companies and banks use what is called a compound interest rate – specifically with daily compounding. Compound interest can be thought of as a series of simple interest calculations. The period of investment (1 year) is divided into smaller periods and the interest is recalculated at the end of each mini-period. Daily compounding means that this recalculation happens every day.

The interest for each mini-period (a day) is calculated using simple interest. For an annual interest rate of 5%, compounded daily, the daily interest rate is 5%/365 = 0.0137%. With our investment of $9524 above, a simple interest rate calculation at 5% would yield an annual interest payment of $9524 * 0.05 = $476 ($9524+ $465 = $10,000). With daily calculation, we would earn 0.0137% * 9524 = $1.30. Simple interest just takes that $1.30 per day and multiplies it by 365 days in the year to get $476 per year.

Compound interest calculation takes that $1.30 and adds it to the principal before recalculating for the next day.

  • Day 1: $9524 loaned + $1.30 interest due = $9525.30 owed.
  • Day 2: $9525.30 owed + $1.30 interest due = $9526.60 owed.
  • Day 3: $9526.60 owed + $1.31 interest due = $9527.91 owed.
  • […]

At the end of the year, the total amount due is $10,011. This is the result of compound interest. The effect is small in our example, but increases for higher interest rates and longer loan periods.

When an investment offers an annual interest rate X% compounded daily, we can convert that to an effective annual rate Y% with the following equation: Y% = (1 + (X%/365))^365 – 1. The effective interest rate (also called the effective yield) for a 5% annual rate compounded daily is (1 + (.05/365))^365 = 5.13%

We always perform NPV calculations in terms of the effective yield.

The reason we explained this is to allow us to evaluate investments that don’t pay in a lump sum at the end of the period.

NPV calculation for a series of payments

We just calculated NPV for a single, lump-sum payment. We can also calculate NPV either for a series of repeating payments, or for a collection of arbitrary payments. The net present value of multiple payments is the sum of the net present value of each of the payments.

NPV for a series of payments

We are evaluating a series of $500 payments over twenty months. With a 5.13% effective annual interest rate, we can compute the NPV for each of the payments individually. The effective monthly interest rate is 1/12 of the annual rate, or 0.43%

Assume we get paid at the end of each month (this is the common case).

  • Payment 1: $500 future value = $500/(1 + 0.0043) = $497.87
  • Payment 2: $500 future value = $500/(1 + 0.0043)^2 = $495.75
  • Payment 3: $500 future value = $500/(1 + 0.0043)^3 = $493.65
  • […]
  • Payment 20: $500 future value = $500/(1+ 0.0043)^21 = $459.14

The total of all the NPV calculations is $9,565


We were able to compare the two investments and determine which one is worth more to us in the present:

  • $10,000 one year from now has a net present value of $9,512 [updated 2010.01.10]
  • $500 per month for 20 months has a net present value of $9565

The monthly payments are worth more to us today than the lump sum payment.

Some companies use a payback period analysis to compare investment alternatives – this is usually a bad idea, as it doesn’t identify the investment with the highest ROI, just the one where we get our money back the fastest.

Definition of opportunity cost


Why won’t my boss approve my project? I’ve done the math – it’s a good investment. Because it isn’t good enough. We learn the math and rationale behind these decisions in this article.

Opportunity cost is a financial metric generally applied to investment decisions made by companies. These decisions can be made about very large potential investments (acquisitions and company mergers), or they can be applied to smaller investments (individual projects). In this post, we will talk about opportunity cost as it applies to project-level decisions.

Definition of Opportunity Cost

Opportunity cost is the “lost opportunity”, of the best alternate way to spend the money.

Consider the following example of an investment decision without using opportunity cost:

We are considering a project to spend $100,000 to build a new website. We have calculated the expected value for the increased sales from the new website to be $110,000. This represents an ROI of 10%.

Without any additional information, we would make this investment. Every dollar we spend yields us $1.10 in returns.

Evaluating with Opportunity Cost

What would we do with the money if we didn’t spend it on this project? Imagine we had the following opportunity:

We have the option to invest $100,000 for a year in corporate bonds at a 20% interest rate. At the end of the year, we would have $120,000. This investment option represents our other opportunity for the money, with an ROI of 20%.

The opportunity cost for our website project is $120,000, the value of investing in bonds. The opportunity cost exceeds the value ($110,000) of our website project. As a company, we should not build the new website, we should invest the money in the bonds. We would be better off at the end of the day.

Using Opportunity Cost to Make Project Decisions

Every company always has an opportunity cost for any investment. It may not be obvious, and it may be very small, but it is always present.

Any given project will have a sponsor who has the ability to decide how to spend the company’s money (up to some dollar limit). For our example, we’ll use an IT department director as our sponsor. The sponsor is not expected to know what the company’s investment alternatives are, or what the corporate opportunity costs are. Our sponsor will, however, be expected to exceed the rate of return that the corporation could otherwise get if she didn’t spend the money.

This rate of return is called the hurdle rate. All investments by our sponsor should be expected* to exceed the hurdle rate. In fact – the hurdle rate is the minimal requirement, not the goal. A project that barely clears the hurdle rate is a marginal project, and probably shouldn’t be done at all.
horse jumping hurdle

Determining the Hurdle Rate

Companies have two sources of money – cash from investors and borrowed money. The investors and lenders expect a particular rate of return on their money – and that determines the hurdle rate for the company.

At a high level, some percentage of the company’s cash comes from investors (private investors, stock holders), and the rest comes from lenders (banks, bond holders). Each group has an expected rate of return on their money. Imagine we funded our company with $50,000 in cash from our rich uncle, and a $50,000 loan at 10% from the bank. Our uncle expects a 20% return on his investment (he expects us to convert his $50,000 into $60,000 by the end of the year). At the end of the year, we have to pay the bank $5,000 in interest and we have to show our uncle that we have an extra $10,000 in the bank. We started the year with $100,000 and we have to end the year with $115,000. This represents our weighted average cost of capital (WACC) of 15%. A detailed explanation of how to calculate the WACC for public companies can be found in this investopedia article.

We should only consider investing in projects that we believe will have an ROI of at least 15%, if we plan to meet our cost of capital expectations. This therefore defines our hurdle rate – the minimum return required to satisfy our investors and lenders.

Survival of the Fittest

We’ve established the hurdle rate, or minimum rate of return we should even consider. Think of it as the initial audition – if our project can’t meet the hurdle rate, it won’t be considered at all. But when we defined opportunity cost, we defined it as the return of the best alternative investment – not the minimum expectation of our investors. We have to compare our project to other projects.

If our company has a hurdle rate of 15% and we have a $50,000 project with an expected rate of return of 20%, but another $50,000 project is also being considered with an expected ROI of 25%, our sponsor should pick the other project. The value of our project is $60,000 (120% of $50,000), which is less than the opportunity cost of $62,500 (125% of $50,000). These comparisons are generally done as a percentage basis, to allow us to normalize and compare projects of different sizes.

*The degree to which the investment is expected to exceed the hurdle rate is a function of how the company is run. Some companies don’t explicitly manage project ROI for projects under a certain dollar amount (or managers below a specific level in the org chart). It varies with companies and with individual managers.

Definition of Expected Value


What is an expected value?

In layman’s terms, the expected value is a calculation that serves as the best prediction of a value. In financial gobble-d-gook, it is the probability-weighted average value of all possible outcomes.

Why do I care?

Understanding the expected value of a possible future event allows us to make mathematically sound decisions. We can decide if we want to make an investment. We can assign a reasonable price for our services. We can prioritize requirements. Expected value is a calculation that should be used when calculating ROI.

How is expected value calculated?

Have you ever participated in a 50-50 raffle? This is a common fund-raising technique in the US for school groups, organizations, etc. The group sells raffle tickets for $1 each to people. Each ticket sold has a uniquely identifiable number, and a duplicate copy that the organization keeps, to be put into the drawing. After all of the tickets have been sold, the organization randomly picks a single ticket. The person who has the matching number on their raffle ticket wins half of the money collected by the group. The group keeps the other half.

People with good math intuition will guess that the expected value of each raffle ticket is $0.50. And they would be right.

Imagine 10 tickets were sold for $1 each. The winner of the raffle will take home $5 (half of ten), and everyone else loses. Each ticket has a 10% chance of being the winning ticket (worth $5), and a 90% chance of being a losing ticket (worth nothing).

To calculate the expected value, you would multiple the probability of each possible outcome by the value of that outcome, and then add the results.

The expected value of a $1 raffle ticket is (0.1 * $5) + (0.9 * $0) = $0.50.

If 1000 tickets were sold, the match becomes (0.001 * $500) + (0.999 * $0) = $0.50.

This approach uses a discrete probability distribution to model the potential outcomes. Each outcome is listed with a probability of occurance and a value if it occurs. Then those values are summed up. This is the most common approach used to calculate expected value.

Note that there is no limit on the number of probable outcomes. Imagine another contest with the following rules:

  • Each ticket costs $10
  • One person will win $1000
  • Two people will win $500
  • Everyone else will win $5 (they only get half of their money back).

If 1000 people play the game, then the expected value would be calculated as follows:

(0.001 * $1000) + (0.002 * $500) + (0.997 * $5) = $6.985

Not a very good bet, because the expected value will be less than the cost to play.

If only 200 people play, the expected value would be

(0.005 * $1000) + (0.01 * $500) + (0.985 * $5) = $14.985

This would be an excellent investment of your $10

Using expected value

We can now apply this expected value concept in our ROI calculations, when making decisions about which requirements to include in a release, which projects to undertake, etc.

Definition of ROI – Return on Investment


We talk about ROI all the time – what is it, in layman’s terms?

ROI is the acronym for return on investment. Another way to think of it is “How much profit will we make if we invest in this project?” Profit is revenue minus costs. Technically, the question should be “How much profit will we make, relative to our investment, if we invest in this project?” We’ll look at both definitions, and see the differences below.

Note – we also have posts explaining expected value and net present value (NPV). Both of these should be incorporated into any real-world ROI calculations, but the examples in this post do not include them, for the purpose of making ROI easier to understand.

A very simple example

We will imagine a software project to build a website for our company. The website takes 4 months to develop, plus we will need some developers to fix bugs for the first month after the site goes live. So, we will be spending money for 5 months. We’ll also assume that we already have the server and network access, so there are no extra costs associated with running this project (other than the developer salaries). We have a plan to get the software delivered as quickly as possible, so once we get the project running, we will double the size of our staff (in the third month of development). In the last month of development, we will increase our costs by another 50% because we have a real-world project, and we discover that we’re going to miss our deadline if we don’t increase staff (or pay for some overtime).

Here’s what our costs per month look like.

[Ed: 86% of you can assume the costs are measured in thousands of USD. 10% of you should assume your local dollars, 3% should use british pounds, the rest of you can use euros, yen, krona (Swedish and Icelandic), rupee, shekels, dirham, won, rubles, baht or pesos. That covers the top 20 currencies for our readers as of this writing.]

cost data chart

We also see that the total cost of the project is projected to be 80. So our investment is 80.

Cost is only half of it – what about revenue?

In our setup, we identified that the website will go live after four months, and will start generating revenue in month 5. Also, since we measure things in internet time, we will assume that we are only projecting revenue for the next twelve months. Twelve months from now, we have no idea if someone will compete with us with a better, free, open-source solution, or if we’ll keep making money. So we’ve decided to only look at revenue that happens between now and twelve months from now. If we add that projected revenue to our cost data, we get this:

cost and revenue data chart

It’s now very clear that we will spend 80 units to get 230 units back. Our profit is 230-80=150. So we get almost twice what we invest back. The answer to our first question (How much will we make if we invest in this project?) is 150.

ROI – Return on investment

The ROI, or return on the investment is 150. To determine the relative earnings, we simply need to divide net revenue by the amount that we invested. 150/80 = 1.875, or 187.5% This answers our second question (How much will we make, relative to our investment, if we invest in this project?) is 187.5%.

The ROI for this project is 187.5%. Sounds like a really good project.