Internal Rate-of-Return Method

The internal rate-of-return (IRR) method calculates the discount rate at which an investment’s present value of all expected cash inflows equals the present value of its expected cash outflows. That is, the IRR is the discount rate that makes $\mathrm{NPV}=\mathrm{\$}0$. Exhibit 22-3 shows the cash flows and the NPV of Vector’s hybrid project using a 12% annual discount rate. At a 12% discount rate, the NPV of the project is $0. Therefore, the IRR is 12% per year.

Managers or analysts solving capital budgeting problems typically use a calculator or computer program to determine the internal rate of return. The following trial-and-error approach can also provide the answer.

1. Step 1: Use a discount rate and calculate the project’s NPV.
2. Step 2: If the calculated NPV is less than zero, use a lower discount rate. (A lower discount rate will increase the NPV. Remember that we are trying to find a discount rate for which the $\mathrm{NPV}=\mathrm{\$}0$.) If the NPV exceeds zero, use a higher discount rate to lower the NPV. Keep adjusting the discount rate until the NPV does equal $0. In the Vector example, a discount rate of 8% yields an $\mathrm{NPV} \text{of }+\$\text{69,840}$ (see Exhibit 22-2). A discount rate of 14% yields an $\mathrm{NPV} \text{of }-\text{30,960}$ (3.433, the present value annuity factor from Table 4, $\times \$\text{180,000}$ minus $648,900). Therefore, the discount rate that makes the NPV equal to $0 must lie between 8% and 14%. We use 12% and get $\mathrm{NPV}=\mathrm{\$}0$. Hence, the IRR is 12% per year.

Computing the IRR is easier when the cash inflows are constant, as in our Vector example. The information in Exhibit 22-3 can be expressed as follows:

Or, what factor F in Table 4 (in Appendix A) will satisfy this equation?

On the five-period line of Table 4, find the percentage column that is closest to 3.605. It is exactly 12%. If the factor (F) falls between the factors in two columns, straight-line interpolation is used to approximate the IRR. This interpolation is illustrated in the Problem for Self-Study (pages 871–872).

Managers accept a project only if its IRR equals or exceeds the firm’s RRR (required rate of return). In the Vector example, the hybrid bus has an IRR of 12%, which is greater than the RRR of 8%. On the basis of financial factors, Vector should invest in the new bus. In general, the NPV and IRR decision rules result in consistent project acceptance or rejection decisions. If the IRR exceeds the RRR, then the project has a positive NPV (favoring acceptance). If the IRR equals the RRR, then NPV equals $0, so the company is indifferent between accepting and rejecting the project. If the IRR is less than the RRR, the NPV is negative (favoring rejection). Obviously, managers prefer projects with higher IRRs to projects with lower IRRs, if all other things are equal. The IRR of 12% means the cash inflows from the project are adequate to (1) recover the net initial investment in the project and (2) earn a return of exactly 12% on the investment tied up in the project over its useful life.