# Internal Rate of Return (IRR)

Internal rate of return (IRR) is the discount rate at which the net present value of an investment is zero. IRR is one of the most popular capital budgeting technique.

Companies invest in different projects to generate value and increase their shareholders wealth, which is possible only if the projects they invest in generate a return higher than the minimum rate of return required by the providers of capital (i.e. shareholders and debt-holders). The minimum required rate of return is called the hurdle rate.

IRR is a discounted cash flow (DCF) technique which means that it incorporate the time value of money. The initial outlay/investment in any project must be compensated by net cash flows which far exceed the initial investment. The higher those cash flows when compared to the initial outlay, the higher will be the IRR and the project is a promising investment.

## Decision Rule

A project should only be accepted if its IRR is NOT less than the hurdle rate, the minimum required rate of return. The minimum required rate of return is based on the company's cost of capital (i.e. WACC) and is adjusted to properly reflect the risk of the project.

When comparing two or more mutually exclusive projects, the project having highest value of IRR should be accepted.

## IRR Calculation

There is no direct algebraic expression in which we might plug some numbers and get the IRR.

IRR is most commonly calculated using the hit-and-trial method, linear-interpolation formula or spreadsheets and financial calculators.

Since IRR is defined as the discount rate at which NPV = 0, we can write that:

NPV = 0; or

PV of future cash flows − Initial Investment = 0; or

 CF1 + CF2 + CF3 + ... − Initial Investment = 0 ( 1 + r )1 ( 1 + r )2 ( 1 + r )3

Where,
r is the internal rate of return;
CF1 is the period one net cash inflow;
CF2 is the period two net cash inflow,
CF3 is the period three net cash inflow, and so on ...

But the problem is, we cannot isolate the variable r (=internal rate of return) on one side of the above equation. Even though we can use the linear-interpolation formula, the simplest method is to use hit and trial as described below:

1. STEP 1: Guess the value of r and calculate the NPV of the project at that value.
2. STEP 2: If NPV is close to zero then IRR is equal to r.
3. STEP 3: If NPV is greater than 0 then increase r and jump to step 5.
4. STEP 4: If NPV is smaller than 0 then decrease r and jump to step 5.
5. STEP 5: Recalculate NPV using the new value of r and go back to step 2.

## Example

Find the IRR of an investment having initial cash outflow of \$213,000. The cash inflows during the first, second, third and fourth years are expected to be \$65,200, \$96,000, \$73,100 and \$55,400 respectively.

### Solution

Assume that r is 10%.

NPV at 10% discount rate = \$18,372

Since NPV is greater than zero we have to increase discount rate, thus NPV at 13% discount rate = \$4,521

But it is still greater than zero we have to further increase the discount rate, thus NPV at 14% discount rate = \$204

NPV at 15% discount rate = (\$3,975)

Since NPV is fairly close to zero at 14% value of r, therefore IRR ≈ 14%

## Limitations of IRR

Studies indicate that internal rate of return is one of the most popular capital budgeting tool, but theoretically net present value, a measure of absolute value added by a project, is a better indicator of a project’s feasibility. This is because sometimes where the cash flows are unconventional i.e. there are net cash outflows other than the initial investment outlay, we may get multiple results for internal rate of return. This phenomenon is called multiple IRR problem. Further, internal rate of return technique assumes that all project cash flows are reinvested at the internal rate of return, which is rarely the case because new investment opportunities are seldom readily available. A variant of internal rate of return called the modified internal rate of return, attempts to mitigate this problem by calculating the internal rate of return where the net cash flows are reinvested at a rate lower than the internal rate of return itself.