128) The project has an NPV of Rs. 5641 at a discount rate of \( 8 \% \) \& ( 2354 ) at a discount rate of \( 10 \% \). Estimate the IRR of the project: \begin{tabular}{|l|l|l|l|}\hline a) \( 9.41 \% \) & b) \( 11.43 \% \) & c) \( 38.89 \% \) & d) \( 20.70 \% \) \\ \hline\end{tabular}

To estimate the IRR using the NPV values given at different discount rates, we can use the formula for linear interpolation. The NPV at \( 8\% \) is \( 5641 \) and at \( 10\% \) it is \( 2354 \). We can set up our equation for IRR as follows: \[ IRR \approx 8\% + \frac{NPV_1}{NPV_1 - NPV_2} \times (10\% - 8\%) \] Substituting the values in: \[ IRR \approx 8\% + \frac{5641}{5641 - 2354} \times 2\% \] Calculating further gives us: \[ IRR \approx 8\% + \frac{5641}{3287} \times 2\% \] \[ IRR \approx 8\% + 3.43\% \approx 11.43\% \] So, the estimated IRR of the project is \( 11.43\% \) (option b). First additional information: The Internal Rate of Return (IRR) is a crucial financial metric that helps investors evaluate the profitability of potential investments. A project with an IRR higher than the cost of capital is generally considered a good investment, while a lower IRR could indicate a poor investment opportunity. Second additional information: In practical financial analysis, estimating IRR can sometimes lead to multiple values, especially for projects with unconventional cash flows (like alternating positive and negative), which is why it’s often recommended to analyze multiple valuation metrics and conduct sensitivity analyses to gauge the robustness of the investment decision.