Subjects finance

Irr Interpolation

Step-by-step solutions with LaTeX - clean, fast, and student-friendly.

Search Solutions

Irr Interpolation


1. **State the problem:** Calculate the Internal Rate of Return (IRR) using interpolation for TechMinds Ltd's project. 2. **Given:** - Initial investment: P80000 - Annual cash savings: P20000 for 5 years - Scrap value at end of year 5: P10000 - NPV at 15% discount rate: +P2635 - NPV at 20% discount rate: -P3480 3. **Recall the interpolation formula for IRR:** $$\text{IRR} = r_1 + \left( \frac{\text{NPV}_{r_1}}{\text{NPV}_{r_1} - \text{NPV}_{r_2}} \right) (r_2 - r_1)$$ where $r_1=15\% = 0.15$, $r_2=20\%=0.20$, $\text{NPV}_{r_1} = 2635$, $\text{NPV}_{r_2} = -3480$ 4. **Calculate:** $$\text{IRR} = 0.15 + \left( \frac{2635}{2635 - (-3480)} \right) (0.20 - 0.15)$$ $$= 0.15 + \left( \frac{2635}{2635 + 3480} \right) \times 0.05$$ $$= 0.15 + \left( \frac{2635}{6115} \right) \times 0.05$$ $$= 0.15 + (0.4309) \times 0.05$$ $$= 0.15 + 0.02154 = 0.17154 = 17.15\%$$ 5. **Interpretation:** Since the IRR of 17.15% is below the required rate of return 18%, the project is expected to earn less than what is required. Therefore, based on the IRR method, the project **should not be accepted** because it does not meet the required return threshold. **Final Answer:** $$\text{IRR} = 17.15\%$$ Project should be rejected if required rate of return is 18%.