Irr

Irr(values,I,guess)

Computes the Internal Rate of Return (IRR) of series of equally spaced cash flows along the index I. The internal rate of return is a widely used criteria for comparing alternative capital investment opportunities. Intuitively, it is the effective compounded rate of return (per time step) on invested capital that is implied by the investment's future cash flows.

IRR is an indicator of the efficiency or quality of an investment, but gives no information about the magnitude of the return. An investment with an IRR exceeding an organization's cost of capital adds value to the organization.

The IRR is formally defined as the discount rate at which the Net Present Value of the cash flows is equal to zero. For many "normal" capital investments, a large up-front outlay is followed by a stream of revenue into the future eventually totalling an amount greater than the initial investment. For these cash flows, as discount rate increases, NPV decreases, eventually passing from positive to negative NPV. The discount rate where NPV passes through zero, the IRR, is the discount rate at which the project's value of future earnings is break-even with the initial investment cost.

In general, the IRR is not uniquely defined -- there may be multiple discount rates that produce a zero NPV. There are also cases where no IRR exists. For example, if all cash flows have the same sign (i.e., the project never turns a profit), then no discount rate will produce a zero NPV. When the cash flows change sign repeatedly, there could theoretically be as many IRR solutions as there are sign changes. When multiple IRR solutions exist, care may be required to decide which IRR value (if any) is appropriate to your decision context. The third optional parameter to Irr, guess, provides a starting guess for the search Analtyica uses to find the Irr solution. When there are multiple solutions, Analytica will usually return the Irr solution closest to the indicated guess.

Alternatives

An Internal Rate of Return criteria for capital budgeting can be compared to a Net Present Value criteria. An IRR approach avoids the need to determine your appropriate discount rate, a step fraught considerable subjectivity. It is this fact that makes it highly attractive as a decision criteria, and explains its widespread use. However, IRR as a criteria comes with a collection of its own problems. In many circumstances, Irr can produce highly misleading results and counter-intuitive decision criteria, and many people have been unwittingly fooled by Irr. Irr is very poorly behaved when used in conjunction with explicit modeling of uncertainty.

See Also

• XIrr
• Npv, XNpv