Calculate the internal rate of return using 10% and 18% discount rates and interpolation method in question 1 roman iv

The formula for Present Value (PV) is $PV = \frac{CF_t}{(1+r)^t}$.

• PV Year 1: $\frac{\text{Nle25,000}}{(1+0.10)^1} = \frac{\text{Nle25,000}}{1.10} = \text{Nle22,727.27}$
• PV Year 2: $\frac{\text{Nle30,000}}{(1+0.10)^2} = \frac{\text{Nle30,000}}{1.21} = \text{Nle24,793.39}$
• PV Year 3: $\frac{\text{Nle28,000}}{(1+0.10)^3} = \frac{\text{Nle28,000}}{1.331} = \text{Nle21,036.60}$
• PV Year 4: $\frac{\text{Nle35,000}}{(1+0.10)^4} = \frac{\text{Nle35,000}}{1.4641} = \text{Nle23,905.30}$
• PV Year 5: $\frac{\text{Nle47,000}}{(1+0.10)^5} = \frac{\text{Nle47,000}}{1.61051} = \text{Nle29,183.18}$ Total PV of Inflows at 10% = Nle22,727.27 + Nle24,793.39 + Nle21,036.60 + Nle23,905.30 + Nle29,183.18 = Nle121,645.74

$$NPV_L = \text{Total PV of Inflows} - \text{Initial Investment}$$ $$NPV_L = \text{Nle121,645.74} - \text{Nle120,000} = \text{Nle1,645.74}$$

• PV Year 1: $\frac{\text{Nle25,000}}{(1+0.18)^1} = \frac{\text{Nle25,000}}{1.18} = \text{Nle21,186.44}$
• PV Year 2: $\frac{\text{Nle30,000}}{(1+0.18)^2} = \frac{\text{Nle30,000}}{1.3924} = \text{Nle21,545.63}$
• PV Year 3: $\frac{\text{Nle28,000}}{(1+0.18)^3} = \frac{\text{Nle28,000}}{1.643032} = \text{Nle17,041.88}$
• PV Year 4: $\frac{\text{Nle35,000}}{(1+0.18)^4} = \frac{\text{Nle35,000}}{1.93887776} = \text{Nle18,052.96}$
• PV Year 5: $\frac{\text{Nle47,000}}{(1+0.18)^5} = \frac{\text{Nle47,000}}{2.2878757568} = \text{Nle20,544.60}$ Total PV of Inflows at 18% = Nle21,186.44 + Nle21,545.63 + Nle17,041.88 + Nle18,052.96 + Nle20,544.60 = Nle98,371.51

$$NPV_H = \text{Total PV of Inflows} - \text{Initial Investment}$$ $$NPV_H = \text{Nle98,371.51} - \text{Nle120,000} = -\text{Nle21,628.49}$$

$$\text{IRR} = L + \frac{NPV_L}{NPV_L - NPV_H} (H - L)$$

Where $L = 0.10$ (10%) and $H = 0.18$ (18%).

$$\text{IRR} = 0.10 + \frac{\text{Nle1,645.74}}{\text{Nle1,645.74} - (-\text{Nle21,628.49})} (0.18 - 0.10)$$ $$\text{IRR} = 0.10 + \frac{\text{Nle1,645.74}}{\text{Nle1,645.74} + \text{Nle21,628.49}} (0.08)$$ $$\text{IRR} = 0.10 + \frac{\text{Nle1,645.74}}{\text{Nle23,274.23}} (0.08)$$ $$\text{IRR} = 0.10 + 0.070719 \times 0.08$$ $$\text{IRR} = 0.10 + 0.00565752$$ $$\text{IRR} = 0.10565752 \approx 10.57\%$$ $$\boxed{\text{10.57\%}}$$