Managers face many decisions on how to allocate a company's resources. They must know if their spending choices will yield a sufficient return on their investments. Since these investments may take several years to yield that return, they must also account for interest rates and the time value of money when making their decisions. By calculating the **internal rate of return,** or **IRR**, these managers can determine if a specific investment delivers the desired return rate.

## Net Present Value

The key factor in determining the IRR is the net present value, or NPV. **The net present value is the difference between the future cash inflows from an investment and the current cash outflow for that investment.** The NPV measures the difference between the money the company must spend now to make the investment, and the discounted value of the future income from that investment. When the discounted future income matches the current spending amount, the NPV is zero. At that point, the discount rate on the future income equals the IRR.

## NPV Calculation

For example, a manager at Generic Widgets, Inc., must decide if his factory needs to upgrade its equipment. The upgrades will cost the company $500,000. His income projections show that the upgrades will give the company $100,000 in additional income the first year, $200,000 in the second year, and $300,000 in the third year. The NPV calculation will look like this:

[100,000/(1+r)]+[200,000/(1+r)^{2}]+[300,000/(1+r)^{3}] - 500,000 = NPV

where "r" is the discount rate.

## IRR Calculation

The IRR is the discount rate which, when plugged into the NPV formula, gives an NPV of zero. In the Generic Widgets example, the formula would look like this:

[100,000/(1+IRR)]+[200,000/(1+IRR)^{2}]+[300,000/(1+IRR)^{3}] - 500,000 = 0

Managers can attempt to plug in different rates to approximate the IRR. For instance, the manager can plug in 8 percent as the IRR and solve for the NPV:

[100,000/(1+0.08)]+[200,000/(1+ 0.08)^{2}]+[300,000/(1+ 0.08)^{3}] - 500,000 = $2,210.03

The NPV is still positive, so the manager plugs in 8.5 percent:

[100,000/(1+0.085)]+[200,000/(1+ 0.085)^{2}]+[300,000/(1+ 0.085)^{3}] - 500,000 = (-$3,070.61)

The NPV is negative, so the IRR must be between 8 and 8.5 percent.

Managers can also use a calculator function to find the IRR:

[100,000/(1+0.082083)]+[200,000/(1+ 0.082083 )^{2}]+[300,000/(1+ 0.082083)^{3}] - 500,000 = -$0.39

For the Generic Widgets upgrade, the IRR is approximately 8.2083 percent.

## Uses for IRR

Managers expect their investments to yield a minimum rate of return. These managers evaluate investments based on both their IRR and their expected minimum rate of return. **If the IRR is less than the expected rate of return, the investment is not worth considering.** In the Generic Widgets example, if the manager expected the upgrade to return 10 percent within the first three years, the IRR of 8.2083 percent shows that the upgrade would not deliver that desired rate.