Internal Rate of Return (IRR)

The internal rate of return (IRR) is the most difficult equation to calculate of all the cash flow techniques. 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.

Three facts concerning IRR:

• IRR is the discount r NN ate when NPV equals zero.
• IRR assumes that cash inflows are reinvested at the IRR value.
• You should choose projects with the highest IRR value.

Net Present Value (NPV)

The benefit measurement methods involve a variety of cash flow analysis techniques including 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.


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. 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.

Discounted Cash Flows

The benefit measurement methods involve a variety of cash flow analysis techniques including discounted cash flows. 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. 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:

• FV = PV(1 + i)ⁿ

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:

• FV = 2,000(1.05)³
• FV = 2,000(1.157625)
• FV = $2,315.25

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:

• PV = FV / (1 + i)ⁿ

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:

• PV = $2,315.25 / (1 + .05)³
• PV = $2,315.25 / 1.157625
• PV = $2,000
  $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:

• The PV of Project A = $79,719.
• The PV of Project B = $85,414.

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