## Internal Rate of Return Details

Mathematically, the Internal Rate of Return (IRR) goal is to equate the Net Present Value (NPV) of a potential investment to zero, expressed as a percentage. An investment projection metric, the starting period, should be equivalent to the existing value of that investment's future cash flow.

Below is the formula for calculating Internal Rate of Return:

0 (NPV) = P0 + P1/(1+IRR) + P2/(1+IRR)2 + P3/(1+IRR)3 + . . . +Pn/(1+IRR)n

Where:

P0 = Cash Outflow or Initial Investment

P1, P2, P3... = Cash Flows for Each Period

IRR = Internal Rate of Return

NPV = Net Present Value

N = Holding Periods

The IRR is obtained by using a financial calculator or a spreadsheet such as Excel. Another method is employing trial and error iteration, where different discount rates are used up to the point where NPV is brought to zero.

As soon as the IRR is determined, it is compared to the cost of capital or hurdle rate. An IRR that is bigger than or equivalent to the cost of capital is taken as a sign of a good investment. However, it is important to note that this may only be true if the IRR were a single basis in evaluating the project. In most cases, the metric is used in conjunction with other factors, both quantitative and qualitative. If the IRR is computed below the hurdle rate, a company will decline the proposed project.

## Example of Internal Rate of Return

The following example centers on the IRR of Company XXX, a big investment firm, over four years. Firm XXX weighs the pros and cons of spending \$450,000 to buy a machine that can be used for four years, with the ability to pull in \$225,000 more in annual profit within the said duration.

On the other hand, Firm YYY is considering selling the said machine for scrap later on and expects to gain \$15,000 in proceeds. The company can then use the IRR to help them decide if buying the equipment is financially smarter than its other investment alternatives, from which they can gain around 10%.

Calculate the IRR as follows:

0 (NPV) = -\$450,000 + (\$225,000)/(1+0.2431) + (\$225,000)/(1+0.2431)2 + (\$225,000)/(1+0.2431)3 + \$15,000/(1+0.2431)4

The rate that pulls the NPV down to zero is the investment's IRR, 24.31%. In such a scenario, Firm XXX is balancing other 10% investment possibilities. The machine must have an opportunity cost higher than 24.31% before its value to the company declines. The IRR is more than the 10% opportunity cost, which means the firm should safely buy the machine.

## Significance of Internal Rate of Return

In analyzing the IRR, you may consider the company's Weighted Average Cost of Capital (WACC) and NPV. The IRR is generally a high value, giving ample room to pare the NPV down to zero. Companies are known to work with an IRR computation on top of the WACC, and analysis will typically proceed with NPV calculations at varying given discount rates.

When planning investments, companies set a necessary return rate to know the lowest percentage where the project remains worthwhile, greater than the WACC. The IRR is usually compared as well with current rates of return in the securities market. If the company couldn't pinpoint any projects having higher IRR than projected financial market returns, it may instead invest cash into the market.