Project Project Project Project Project Project Criteria Weight A Score A Totals B Score B Totals C Score C Totals

Profit potential 5 5 25 5 25 3 15

Marketability 3 4 12 3 9 4 12


In this example, Project A is the obvious choice.

Cash Flow Analysis Techniques

The remaining benefit measurement methods involve a variety of cash flow analysis techniques, including payback period, discounted cash flows, net present value, and internal rate of return. We'll look at each of these techniques individually, and I'll provide you with a crash course on their meanings and calculations.


The payback period is the length of time it takes the company to recoup the initial costs of producing the product, service, or result of the project. This method compares the initial investment to the cash inflows expected over the life of the product, service, or result. For example, say the initial investment on a project is $200,000, with expected cash inflows of $25,000 per quarter every quarter for the first two years and $50,000 per quarter from then on. The payback period is two years and can be calculated as follows:

Initial investment = $200,000

Cash inflows = $25,000 * 4 (quarters in a year) = $100,000 per year total inflow

Initial investment ($200,000) - year 1 inflows ($100,000) = $100,000 remaining balance

Year 1 inflows remaining balance - year 2 inflows = $0

Total cash flow year 1 and year 2 = $200,000

The payback is reached in two years.

The fact that inflows are $50,000 per quarter starting in year 3 makes no difference because payback is reached in two years.

The payback period is the least precise of all the cash flow calculations. That's because the payback period does not consider the value of the cash inflows made in later years, commonly called the time value of money. For example, if you have a project with a five-year payback period, the cash inflows in year 5 are worth less than they are if you received them today. The next section will explain this idea more fully.

discounted cash flows

As I just stated, money received in the future is worth less than money received today. The reason for that is the time value of money. If I borrowed $2,000 from you today and promised to pay it back in three years, you would expect me to pay interest in addition to the original amount borrowed. OK, if you were a family member or a really close friend, maybe you wouldn't, but ordinarily this is the way it works. You would have had the use of the $2,000 had you not lent it to me. If you had invested the money (does this bring back memories of your mom telling you to save your money?), you'd receive a return on it. Therefore, the future value of the $2,000 you lent me today is $2,315.25 in three years from now at 5 percent interest per year. Here's the formula for future value calculations:

In English, this formula says the future value (FV) of the investment equals the present value (PV) times (1 plus the interest rate) raised to the value of the number of time periods (n) the interest is paid. Let's plug in the numbers:

The discounted cash flow technique compares the value of the future cash flows of the project to today's dollars. In order to calculate discounted cash flows, you need to know the value of the investment in today's terms, or the PV. PV is calculated as follows:

This is the reverse of the FV formula talked about earlier. So, if you ask the question, "What is $2,315.25 in three years from now worth today given a 5 percent interest rate?" you'd use the preceding formula. Let's try it:

$2,315.25 in three years from now is worth $2,000 today.

Discounted cash flow is calculated just like this for the projects you're comparing for selection purposes or when considering alternative ways of doing the project. Apply the PV formula to the projects you're considering, and then compare the discounted cash flows of all the projects against each other to make a selection. Here is an example comparison of two projects using this 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 cost of capital is 12 percent, which project should you choose? Using the PV formula used previously, calculate each project's worth:

Project B is the project that will return the highest investment to the company and should be chosen over Project A.

net present value

Projects might begin with a company investing some amount of money into the project to complete and accomplish its goals. In return, the company expects to receive revenues, or cash inflows, from the resulting project. Net present value (NPV) allows you to calculate an accurate value for the project in today's dollars. The mathematical formula for NPV is complicated, and you do not need to memorize it in that form for the test. However, you do need to know how to calculate NPV for the exam, so I've given you some examples of a less complicated way to perform this calculation in Table 2.11 and Table 2.12 using the formulas you've already seen.

TABLE 2.11 Project A













Less investment






table 2.12 Project B













Less investment






Net present value works like discounted cash flows in that you bring the value of future monies received into today's dollars. With NPV, you evaluate the cash inflows using the discounted cash flow technique applied to each period the inflows are expected instead of in one sum. The total present value of the cash flows is then deducted from your initial investment to determine NPV. NPV assumes that cash inflows are reinvested at the cost of capital.

Here's the rule: If the NPV calculation is greater than zero, accept the project. If the NPV calculation is less than zero, reject the project.

Look at the two project examples in Tables 2.11 and 2.12. Project A and Project B have total cash inflows that are the same at the end of the project, but the amount of inflows at each period differs for each project. We'll stick with a 12 percent cost of capital. Note that the PV calculations were rounded to two decimal places.

Project A has an NPV greater than zero and should be accepted. Project B has a NPV less than zero and should be rejected. When you get a positive value for NPV, it means that the project will earn a return at least equal to or greater than the cost of capital.

Another note on NPV calculations: projects with high returns early in the project are better projects than projects with lower returns early in the project. In the preceding examples, Project A fits this criterion also.

internal rate of return

The internal rate of return (IRR) is the most difficult equation to calculate of all the cash flow techniques we've discussed. It is a complicated formula and should be performed on a financial calculator or computer. IRR can be figured manually, but it's a trial-and-error approach to get to the answer.

Technically speaking, IRR is the discount rate when the present value of the cash inflows equals the original investment. When choosing between projects or when choosing alternative methods of doing the project, projects with higher IRR values are generally considered better than projects with low IRR values.

Exam spotlight

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Project Management Made Easy

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