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%.