Question

4) The firms use both Net PV method and IRR (Internal Rate of Return) Method to evalauate investments. The IRR method, however, have some problems. The three problems cited regarding IRR are a) Re-investment assumption b) Multiple Root Problem c) Unconventional Cash Flow Problem. What are these problems? Explain these problems clearly by giving examples if necessary .

Answer 1

Determining NPV

To do this, the firm estimates the future cash flows of the project and discounts them into present value amounts using a discount rate that represents the project's cost of capital and its risk. Next, all of the investment's future positive cash flows are reduced into one present value number. Subtracting this number from the initial cash outlay required for the investment provides the net present value of the investment.

Let's illustrate with an example: suppose JKL Media Company wants to buy a small publishing company. JKL determines that the future cash flows generated by the publisher, when discounted at a 12 percent annual rate, yields a present value of $23.5 million. If the publishing company's owner is willing to sell for $20 million, then the NPV of the project would be $3.5 million ($23.5 - $20 = $3.5). The NPV of $3.5 million represents the intrinsic value that will be added to JKL Media if it undertakes this acquisition.

Determining IRR

So, JKL Media's project has a positive NPV, but from a business perspective, the firm should also know what rate of return will be generated by this investment. To do this, the firm would simply recalculate the NPV equation, this time setting the NPV factor to zero, and solve for the now unknown discount rate. The rate that is produced by the solution is the project's internal rate of return (IRR).

For this example, the project's IRR could—depending on the timing and proportions of cash flow distributions—be equal to 17.15%. Thus, JKL Media, given its projected cash flows, has a project with a 17.15% return. If there were a project that JKL could undertake with a higher IRR, it would probably pursue the higher-yielding project instead.

Multiple Root Problem

The first disadvantage of the IRR method is that IRR, as an investment decision tool, should not be used to rate mutually exclusive projects but only to decide whether a single project is worth investing in. In cases where one project has a higher initial investment than a second mutually exclusive project, the first project may have a lower IRR (expected return), but a higher NPV (increase in shareholders ‘ wealth) and should thus be accepted over the second project (assuming no capital constraints).

In addition, IRR assumes reinvestment of interim cash flows in projects with equal rates of return (the reinvestment can be the same project or a different project). Therefore, IRR overstates the annual equivalent rate of return for a project whose interim cash flows are reinvested at a rate lower than the calculated IRR. This presents a problem, especially for high IRR projects, since there is frequently not another project available in the interim that can earn the same rate of return as the first project. When the calculated IRR is higher than the true reinvestment rate for interim cash flows, the measure will overestimate–sometimes very significantly–the annual equivalent return from the project. The formula assumes that the company has additional projects, with equally attractive prospects, in which to invest the interim cash flows.

Moreover, since IRR does not consider cost of capital, it should not be used to compare projects of different duration. Modified Internal Rate of Return (MIRR) does consider cost of capital and provides a better indication of a project’s efficiency in contributing to the firm’s discounted cash flow.

Last but not least, in the case of positive cash flows followed by negative ones and then by positive ones, the IRR may have multiple values.

Unconventional Cash Flow Problem.

In terms of mathematical notations, where the "-" sign represents an outflow and "+" denotes an inflow, an unconventional cash flow could appear as -, +, +, +, -, +, or alternatively, +, -, -, +, -, -. This would indicate the first set has a net inflow of cash and the second set has a net outflow of cash. If the first set represented cash flows in the first financial quarter and the second set represented cash flows in the second financial quarter, the change in direction of the cash flows would indicate an unconventional cash flow for the company.

Cash flows are modeled for net present value (NPV) in a discounted cash flow (DCF) analysis in capital budgeting to help determine if the initial investment cost for a project will be worthwhile when compared to the NPV of the future cash flows generated from the project.

Unconventional cash flows are more difficult to handle in an NPV analysis than a conventional cash flow since it will produce multiple internal rates of return (IRR), depending on the number of changes in the cash flow direction.

In real-life situations, examples of unconventional cash flows are abundant, especially in large projects where periodic maintenance may involve huge outlays of capital. For example, a large thermal power generation project where cash flows are being projected over a 25-year period may have cash outflows for the first three years during the construction phase, inflows from years four to 15, an outflow in year 16 for scheduled maintenance, followed by inflows until year 25.

Challenges Posed by an Unconventional Cash Flow

A project with a conventional cash flow starts with a negative cash flow (investment period), where there is only one outflow of cash, the initial investment. This is followed by successive periods of positive cash flows where all the cash flows are inflows, which are the revenues from the project.

A single IRR can be calculated from this type of project, with the IRR compared to a company's hurdle rate to determine the economic attractiveness of the contemplated project. However, if a project is subject to another set of negative cash flows in the future, there will be two IRRs, which will cause decision uncertainty for management. For example, if the IRRs are 5% and 15%, and the hurdle rate is 10%, management will not have the confidence to go ahead with the investment.