Subjects finance

Npv Investment C0A9Bd

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1. **Problem Statement:** You want to decide whether to invest Rs. 300000 in equipment that generates Rs. 55000 annually for 8 years and can be sold for Rs. 80000 at the end of year 8. The discount rate is 10%. We need to find the Net Present Value (NPV) to decide. 2. **Formula:** The NPV formula is: $$\text{NPV} = \sum_{t=1}^n \frac{C_t}{(1+r)^t} + \frac{S}{(1+r)^n} - C_0$$ where: - $C_t$ = cash flow at year $t$ (55000) - $S$ = salvage value at year $n$ (80000) - $r$ = discount rate (0.10) - $n$ = number of years (8) - $C_0$ = initial investment (300000) 3. **Calculate Present Value of Annual Cash Flows:** The annual cash flows form an annuity. Present value of annuity: $$PV = C \times \frac{1 - \frac{1}{(1+r)^n}}{r}$$ Substitute values: $$PV = 55000 \times \frac{1 - \frac{1}{(1+0.10)^8}}{0.10}$$ Calculate: $$PV = 55000 \times \frac{1 - \frac{1}{2.1436}}{0.10} = 55000 \times \frac{1 - 0.4665}{0.10} = 55000 \times \frac{0.5335}{0.10} = 55000 \times 5.335 = 293425$$ 4. **Calculate Present Value of Salvage Value:** $$PV_{salvage} = \frac{80000}{(1+0.10)^8} = \frac{80000}{2.1436} = 37300$$ 5. **Calculate NPV:** $$\text{NPV} = 293425 + 37300 - 300000 = 30725$$ 6. **Decision:** Since NPV is positive ($30725$), investing in the equipment is financially beneficial. **Final Answer:** The NPV is Rs. 30725, so you should invest.