1. **Problem Statement:** Determine if the internal rate of return (IRR) for a project with a net investment of 1500000 and net cash flows of 400000 for 5 years lies between (15% and 12%) or (10% and 12%). 2. **Formula and Explanation:** The IRR is the discount rate $r$ that makes the net present value (NPV) of cash flows equal to zero: $$0 = -1500000 + \sum_{t=1}^5 \frac{400000}{(1+r)^t}$$ 3. **Calculate NPV at 10%, 12%, and 15%:** - At $r=10\%$: $$NPV = -1500000 + 400000 \times \frac{1-(1+0.10)^{-5}}{0.10} = -1500000 + 400000 \times 3.79079 = 116316 > 0$$ - At $r=12\%$: $$NPV = -1500000 + 400000 \times \frac{1-(1+0.12)^{-5}}{0.12} = -1500000 + 400000 \times 3.60478 = -38188 < 0$$ - At $r=15\%$: $$NPV = -1500000 + 400000 \times \frac{1-(1+0.15)^{-5}}{0.15} = -1500000 + 400000 \times 3.35216 = -59034 < 0$$ 4. **Interpretation:** Since NPV is positive at 10% and negative at 12%, IRR lies between 10% and 12%. At 15%, NPV is also negative, so IRR is not between 12% and 15% or 15% and 12%. 5. **Answer:** The internal rate of return is between (12% and 10%). **Final answer:** a. The internal rate of return is between (12% and 10%)