IRR, or an Internal Rate of Return, is typically used by private equity investors to compare the profitability of multiple investment scenarios. IRR is also present in many private equity and joint venture agreements, and is often used to define a minimum level of return for a preferred investor. IRR can be represented by the formula: NPV = c(0) + c(1)/(1+r)^t(1) + c(2)/(1+r)^t(2) + .... + c(n)/(1+r)n^t(n).

## Computation of Internal Rate of Return

Convert the date of all cash inflows and outflows to period of years from the date of the start of the IRR calculation. Typically the first cash outflow is the start of the IRR calculation and is labeled time period 0. If a cash inflow occurs at 6 months from the start of the IRR calculation, it is labeled time period 0.5. If another cash inflow of occurs at 1 year from the start of the IRR calculation, it is labeled time period 1.0.

Input all cash flows into the formula: NPV = c(0) + c(1)/(1+r)^t(1) + c(2)/(1+r)^t(2) + .... + c(n)/(1+r)n^t(n), where c = the dollar amount of the cashflow, t = the time period determined in Step 1, n = the number of cash inflows or outflows and NPV = Net Present Value. In a simple IRR scenario where a $100 outflow occurs at time 0, a $50 inflow occurs at 1 year (t = 1) and a $100 inflow occurs at 2 years (t =2), the formula is represented as follows: NPV = $100 + $50/(1+r)^1 + $60/(1+r)^2.

Set the NPV as equal to zero. By definition, IRR is the discount rate that makes the net present value of the cash inflows and outflows equal to zero. In our example: $0 = $100 + $50/(1+r)^1 + $60/(1+r)^2

Solve for r. The value of r is the IRR. The method for solving will depend on the number of periods of inflows and outflows. Most investment professionals will use a scientific calculator or Excel's "IRR" function to solve.

In our example above, r = 6.81%.

#### References

- "Fundamentals of Corporate Finance"; Jordan Bradford, Randolph Westerfield, Stephen A. Ross; 2009