gen-define-the-internal-rate-of-return-and-give-one-short-worked-574a

Define the internal rate of return and give one short worked example.

# Internal Rate of Return (IRR) ## Definition The **Internal Rate of Return (IRR)** is the discount rate at which the Net Present Value (NPV) of all cash flows from an investment equals zero. In other words, it's the rate of return that makes the present value of cash inflows equal to the present value of cash outflows. ## Worked Example **Problem:** You invest $10,000 today and expect to receive $6,000 after one year and $5,500 after two years. What is the IRR? **Solution:** Set up the NPV equation equal to zero: $$0 = -10,000 + \frac{6,000}{(1+IRR)} + \frac{5,500}{(1+IRR)^2}$$ Testing different rates: - At 10%: NPV = -10,000 + 5,455 + 4,545 = **0** **Answer: IRR = 10%** This means the investment yields an effective annual return of 10%. If this exceeds your required rate of return, the investment is attractive. **Decision Rule:** Accept projects where IRR > required rate of return (hurdle rate).