Published On:Friday 23 December 2011
Posted by Muhammad Atif Saeed
The Internal Rate of Return
The IRR, or internal rate of return, is defined as the discount rate that makes NPV = 0. Like the NPV process, it starts by identifying all cash inflows and outflows. However, instead of relying on external data (i.e. a discount rate), the IRR is purely a function of the inflows and outflows of that project. The IRR rule states that projects or investments are accepted when the project's IRR exceeds a hurdle rate. Depending on the application, the hurdle rate may be defined as the weighted average cost of capital.
NPV vs. IRREach of the two rules used for making capital-budgeting decisions has its strengths and weaknesses. The NPV rule chooses a project in terms of net dollars or net financial impact on the company, so it can be easier to use when allocating capital.
However, it requires an assumed discount rate, and also assumes that this percentage rate will be stable over the life of the project, and that cash inflows can be reinvested at the same discount rate. In the real world, those assumptions can break down, particularly in periods when interest rates are fluctuating. The appeal of the IRR rule is that a discount rate need not be assumed, as the worthiness of the investment is purely a function of the internal inflows and outflows of that particular investment. However, IRR does not assess the financial impact on a firm; it only requires meeting a minimum return rate.
The NPV and IRR methods can rank two projects differently, depending on thesize of the investment. Consider the case presented below, with an NPV of 6%:
By the NPV rule we choose Project A, and by the IRR rule we prefer B. How do we resolve the conflict if we must choose one or the other? The convention is to use the NPV rule when the two methods are inconsistent, as it better reflects our primary goal: to grow the financial wealth of the company.
Consequences of the IRR MethodIn the previous section we demonstrated how smaller projects can have higher IRRs but will have less of a financial impact. Timing of cash flows also affects the IRR method. Consider the example below, on which initial investments are identical. Project A has a smaller payout and less of a financial impact (lower NPV), but since it is received sooner, it has a higher IRR. When inconsistencies arise, NPV is the preferred method. Assessing the financial impact is a more meaningful indicator for a capital-budgeting decision.
Example:Suppose that a project costs $10 million today, and will provide a $15 million payoff three years from now, we use the FV of a single-sum formula and solve for r to compute the IRR.
IRR = (FV/PV)1/N -1 = (15 million/10 million)1/3 - 1 = (1.5) 1/3 - 1 = (1.1447) - 1 = 0.1447, or 14.47%
In this case, as long as our hurdle rate is less than 14.47%, we green light the project.
NPV vs. IRREach of the two rules used for making capital-budgeting decisions has its strengths and weaknesses. The NPV rule chooses a project in terms of net dollars or net financial impact on the company, so it can be easier to use when allocating capital.
However, it requires an assumed discount rate, and also assumes that this percentage rate will be stable over the life of the project, and that cash inflows can be reinvested at the same discount rate. In the real world, those assumptions can break down, particularly in periods when interest rates are fluctuating. The appeal of the IRR rule is that a discount rate need not be assumed, as the worthiness of the investment is purely a function of the internal inflows and outflows of that particular investment. However, IRR does not assess the financial impact on a firm; it only requires meeting a minimum return rate.
The NPV and IRR methods can rank two projects differently, depending on thesize of the investment. Consider the case presented below, with an NPV of 6%:
Project | Initial outflow | Payoff after one year | IRR | NPV |
A | $250,000 | $280,000 | 12% | +$14,151 |
B | $50,000 | $60,000 | 20% | +6604 |
By the NPV rule we choose Project A, and by the IRR rule we prefer B. How do we resolve the conflict if we must choose one or the other? The convention is to use the NPV rule when the two methods are inconsistent, as it better reflects our primary goal: to grow the financial wealth of the company.
Consequences of the IRR MethodIn the previous section we demonstrated how smaller projects can have higher IRRs but will have less of a financial impact. Timing of cash flows also affects the IRR method. Consider the example below, on which initial investments are identical. Project A has a smaller payout and less of a financial impact (lower NPV), but since it is received sooner, it has a higher IRR. When inconsistencies arise, NPV is the preferred method. Assessing the financial impact is a more meaningful indicator for a capital-budgeting decision.
Project | Investment | Income in future periods | IRR | NPV | ||||
t1 | t2 | t3 | t4 | t5 | ||||
A | $100k | $125k | $0 | $0 | $0 | $0 | 25.0% | $17,925 |
B | $100k | $0 | $0 | $0 | $0 | $200k | 14.9% | $49,452 |
