1. **Problem Statement:** We need to estimate the Internal Rate of Return (IRR) for an investment with an initial outlay of 300000 and annual cash inflows of 90000 for 5 years. 2. **Formula and Explanation:** The IRR is the discount rate $r$ that makes the Net Present Value (NPV) of the cash flows equal to zero: $$NPV = -300000 + \sum_{t=1}^5 \frac{90000}{(1+r)^t} = 0$$ We use trial-and-error by testing different discount rates to find $r$ where NPV is close to zero. 3. **Trial 1: Discount rate = 10% ($r=0.10$):** Calculate present value of inflows: $$PV = 90000 \times \left(\frac{1 - (1+0.10)^{-5}}{0.10}\right) = 90000 \times 3.79079 = 341171.1$$ NPV: $$NPV = -300000 + 341171.1 = 41171.1 > 0$$ Positive NPV means IRR > 10%. 4. **Trial 2: Discount rate = 15% ($r=0.15$):** Calculate present value of inflows: $$PV = 90000 \times \left(\frac{1 - (1+0.15)^{-5}}{0.15}\right) = 90000 \times 3.35216 = 301694.4$$ NPV: $$NPV = -300000 + 301694.4 = 1694.4 > 0$$ Still positive but closer to zero, so IRR is slightly above 15%. 5. **Trial 3: Discount rate = 16% ($r=0.16$):** Calculate present value of inflows: $$PV = 90000 \times \left(\frac{1 - (1+0.16)^{-5}}{0.16}\right) = 90000 \times 3.20979 = 288881.1$$ NPV: $$NPV = -300000 + 288881.1 = -11118.9 < 0$$ Negative NPV means IRR is between 15% and 16%. 6. **Estimate IRR:** Using linear interpolation between 15% and 16%: $$IRR \approx 15\% + \frac{1694.4}{1694.4 + 11118.9} \times (16\% - 15\%) = 15\% + \frac{1694.4}{12813.3} \times 1\% \approx 15.13\%$$ 7. **Decision:** Since the company’s required rate of return is 12%, and IRR $\approx 15.13\% > 12\%$, the project should be **accepted** because it promises a return higher than the required rate.