A better approach to internal rate of return - column

Healthcare Financial Management, April, 1989 by Louis C. Gapenski

A better approach to internal rate of return

Academicians have long recognized the superiority of net present value (NPV) over internal rate of return (IRR), yet financial managers continue to use IRR as a capital budgeting measure.

Presumably, IRR is preferred because most nonfinancial managers, including cheif executive officers (CEOs) and board members, feel more comfortable dealing with percentage rates of return.

Chief financial officers (CFOs) should compromise with a modified IRR, a percentage rate of return measure that overcomes many of the shortcomings of the traditional IRR.

Net present value is the sum of the present values of a project's cash flows, with the present values found by discounting all flows--both costs, or outflows, and inflows--at the project cost of capital.(a)

To illustrate this, consider Project W (for winner), one of three projects presented in Exhibit 1. Assuming a 10 percent cost of capital, Project W has an NPV of $584.93:

NPV = -$1,000 $500/(1.10)(1) $500/(1.10)(2) $500/(1.10)(3) $500/(1.10)(4) = $584.93

This calculation is shown using a timeline format in Exhibit 2.

NPV RATIONALE

The economic rationale behind NPV is straightforward. If a project has a zero NPV, its cash flows are sufficient to repay the dollar cost of the project and provide a return on the dollars invested commensurate with the riskiness of the project. Thus, from an economic perspective, a project with a zero NPV breaks even.

A project with a positive NPV is expected to generate a profit, while a negative NPV signifies that a project is unprofitable. Thus, Project W,on a present value basis, is expected to generate $584.93 above the amount required to return the initial $1,000 investment--a fair return on the capital invested.

Project L (for loser), on the other hand, has a negative NPV--the project falls $128.29 short, on a present value basis, of breaking even. Thus, Project L is projected to be a financial burden to the organization. This does not mean that the idea should be automatically scrapped. There may be good reasons for accepting the project, especially for healthcare providers.

However, management must recognize Project L's negative effect on the organization's financial condition. A firm that accepts negative NPV projects with an aggregate dollar loss greater than the profits generated by its positive NPV projects will, over the long haul, lose its financial viability and be unable to continue its healthcare mission.

THE IRR APPROACH

The internal rate of return is the discount rate equating the present value of a project's cash inflows to the present value of its costs, or outflows.

For Project W, IRR is the discount rate that forces the present values of the cash inflows in Years 1 to 4 to equal $1,000, the project's cost. IRR can easily be obtained using a financial calculator, a personal computer spreadsheet model, or a mainframe financial planning software package. For Project W, IRR equals 34.9 percent:

$1,000=$500/(1.3490)(1) $500/(1.3490)(2) $500/(1.3490)(3) $500/(1.3490)(4)

IRR is easy to interpret. As the expected percentage rate of return on a project, the IRR can also help measure the break even point. If Project W had a cost of capital of 34.9 percent, then its cash inflows, on a present value basis, would equal its $1,000 cost and the project would break even. An IRR greater than a project's cost of capital implies a positive NPV and a financially profitable project, as is the case of Project W with an IRR of 34.9 percent versus a cost of capital of 10 percent.

Conversely, Project L has an IRR of 3.92 percent versus a cost of capital of 10 percent. Thus, Project L's NPV is negative and its acceptance would impose a financial burden on the organization.

It should be clear at this point that NPV and IRR are related. NPV is a measure of the dollar profitability of a project given its cost of capital, while IRR is the percentage rate of return that forces a project's NPV to equal zero. If a project's IRR is equal to its cost of capital, then its NPV equals zero. An IRR greater than the cost of capital implies a positive NPV, and an IRR less than the cost of capital implies a negative NPV.

NPV ADVANTAGES NPV is preferred over IRR for the following reasons: NPV is a direct measure of the dollar economic value (or loss) expected on a project. NPV properly assumes that a project's cash flows are reinvested at the project's cost of capital, while IRR incorrectly assumes reinvestment at the project's IRR rate.

Both the NPV and IRR methods involve discounted cash flow analysis, the mathematics of which affects the rate that a project's cash flows can be reinvested during the life of the project. The reinvestment rate imbedded in NPV is the project's cost of capital. The reinvestment rate assumed under IRR is the IRR rate itself, though reinvestment at the cost of capital is a better assumption. Projects with cash outflows that occur after one or more inflows often cannot be evaluated using IRR. For example, Project N in Exhibit 1 does not have an IRR. There is no single discount rate that can equate the present value of its inflows to the present value of its outflows. However, Project N's NPV can be calculated easily, and because it is a positive $421.49, the project is financially acceptable in spite of the fact that it has no IRR.