1. **State the problem:** Calculate the net present value (NPV) for two options of upgrading a nuclear power station with quarterly payments and a given interest rate. 2. **Given data:** - Interest rate per year (I/Y) = 3.15% compounded quarterly - Quarterly interest rate $i = \frac{3.15}{4} = 0.7875\% = 0.007875$ **Option 1:** - Quarterly payment (PMT) = 11100 (cost, outflow) - Number of quarters (N) = 15 years \times 4 = 60 - Future value (FV) = 124000 (inflow at end) **Option 2:** - Upfront cost = 41000 (outflow) - Quarterly payment (PMT) = 11800 (cost, outflow) - Number of quarters (N) = 13 years \times 4 = 52 - Future value (FV) = 0 3. **Calculate present value of outflows for Option 1:** Present value of annuity (payments): $$PV_{payments} = PMT \times \frac{1 - (1 + i)^{-N}}{i} = 11100 \times \frac{1 - (1 + 0.007875)^{-60}}{0.007875}$$ Calculate: $$1 + 0.007875 = 1.007875$$ $$1.007875^{-60} = \frac{1}{1.007875^{60}} \approx \frac{1}{1.565} = 0.6389$$ So, $$PV_{payments} = 11100 \times \frac{1 - 0.6389}{0.007875} = 11100 \times \frac{0.3611}{0.007875} = 11100 \times 45.87 = 508,957.7$$ 4. **Calculate present value of inflow (sale of equipment) at end of 15 years:** $$PV_{resale} = \frac{FV}{(1 + i)^N} = \frac{124000}{1.007875^{60}} = 124000 \times 0.6389 = 79,244.6$$ 5. **Calculate NPV for Option 1:** $$NPV_1 = PV_{resale} - PV_{payments} = 79,244.6 - 508,957.7 = -429,713.1$$ Rounded to nearest dollar: $$NPV_1 = -429,713$$ 6. **Calculate present value of outflows for Option 2:** Present value of annuity (payments): $$PV_{payments} = 11800 \times \frac{1 - (1 + 0.007875)^{-52}}{0.007875}$$ Calculate: $$1.007875^{-52} = \frac{1}{1.007875^{52}} \approx \frac{1}{1.464} = 0.6830$$ So, $$PV_{payments} = 11800 \times \frac{1 - 0.6830}{0.007875} = 11800 \times \frac{0.317}{0.007875} = 11800 \times 40.27 = 475,186$$ 7. **Total outflows for Option 2:** $$PV_{total} = 41000 + 475,186 = 516,186$$ 8. **NPV for Option 2:** $$NPV_2 = 0 - 516,186 = -516,186$$ 9. **Decision:** Since both NPVs are negative, choose the option with the smaller loss (less negative NPV). Option 1 has NPV = -429,713 and Option 2 has NPV = -516,186. **Therefore, London Hydro should choose Option 1.**