# Internal Rate of Return

### Calculating Internal Rate of Return

There is no simple formula to calculate internal rate of return (IRR), but it can be calculated with spreadsheets by using a trial and error approach.

The internal rate of return (IRR) is the calculation of the discount that would make the net present value of the cash flow from an investment equal to that of the investment. Since future values of money are adjusted to get a present value, the IRR calculation provides the rate of interest that needs to be earned so that the cost of the investment equals the adjusted cash flow.

IRR starts with the same equation as net present value (NPV). NPV is a monetary figure, and IRR is a percentage. Net present value is the difference between the present value of cash inflows and outflows.
${\rm{NPV}}=\sum_{t=1}^T\frac{C_t}{(1+r)^t}-C_{\mathit0}$
Where:
\begin{aligned}t&=\text{Number of Periods of Cash Flow}\\T&=\text{Final Time Period of the Investment}\\C_t&=\text{Cash Inflow}\\C_{\mathit0}&=\text{Cash Outflow (or the Initial Investment})\\r&=\text{Interest Rate}\end{aligned}
Because the summation, $\Sigma$, makes it impossible to solve for the rate directly, mathematical iteration, the repeated application of a process wherein the result of the previous application is used as the input for the next application, needs to be used. This is typically done with computer spreadsheet software.

Vision Inc. is going to make a $100,000 investment that will yield$60,000 per year for four years. Present value is the value in current dollars of a future payment discounted to the present and based on the required investor's return. The weighted average cost of capital (WACC) is used as the rate of return of 7 percent for the PV calculations. Weighted average cost of capital (WACC) is the formula for determining the relative average a company is expected to pay to all its security holders to finance its assets. Spreadsheets use an iterative formula, which means that the computer "guesses" an answer for the IRR, tests it in the NPV equation, and then makes another guess based on the amount it is off by. It continues to do this until it gives a rate where the cash flow equals the investment. In this example, the IRR is 47 percent.

NPV is based on an investor’s minimum required rate of return, which can vary by investor. IRR on the other hand, shows the expected rate of return. The usefulness in the decision-making process comes in comparing NPV to IRR. For example, the WACC is the minimum return that Vision Inc. must earn to fulfill its requirements to creditors and stockholders. In this case, the IRR of 47 percent is greater than the WACC of 7 percent, indicating that this investment would increase value in Vision Inc. Generally, IRR is compared to the investor's required rate of return. If the IRR is greater than the rate that the investor needs, then it is considered a good investment, all other things being equal. NPV assumes the required rate and then gives the cash flow based on that rate.