All courses › Engineering Economics › Internal rate of return (IRR)

Internal rate of return (IRR)

The internal rate of return is the rate that makes net present value equal to zero — the point where the project exactly covers its own discount rate. The investment is profitable if IRR is higher than the required rate of return.

−I0+∑t=1nCt(1+IRR)t=0-I_0 + \sum_{t=1}^{n} \frac{C_t}{(1+IRR)^t} = 0IRR solves this equation

Symbols

IRRIRRthe internal rate of return
I0I_0investment todaykr
CtC_tcash flow in year ttkr

Example

Investment 200, yields 140 after year 1 and 140 after year 2:

−200+140/(1+r)+140/(1+r)2=0⇒r≈25.7%-200 + 140/(1+r) + 140/(1+r)^2 = 0 \Rightarrow r \approx 25.7\%.

IRR is usually found by trial and error or software — there is rarely a simple formula.
Practise investment analysis for free →

← Net present value (NPV) · Payback period →

Part of Engineering Economics: Investment analysis.