1. **Problem Statement:** CTC Mining Corporation must decide whether to mine a gold vein using sulfuric acid extraction. Initial costs are $9000 for equipment plus $165000 for installation. The project yields $350000 annually for 5 years. The cost of capital is 17%. We need to calculate: i. Net Present Value (NPV) ii. Internal Rate of Return (IRR) iii. Decision ignoring environmental concerns iv. Consideration of environmental effects 2. **Formulas and Rules:** - NPV formula: $$\text{NPV} = \sum_{t=1}^n \frac{C_t}{(1+r)^t} - C_0$$ where $C_t$ is cash inflow at year $t$, $r$ is discount rate, $C_0$ is initial investment. - IRR is the rate $r$ that makes NPV = 0. - Initial investment $C_0 = 9000 + 165000 = 174000$ - Cash inflows $C_t = 350000$ for $t=1$ to $5$ 3. **Calculate NPV:** Calculate present value of annuity: $$\text{PV} = C \times \frac{1 - (1+r)^{-n}}{r} = 350000 \times \frac{1 - (1+0.17)^{-5}}{0.17}$$ Calculate $(1+0.17)^{-5} = (1.17)^{-5} \approx 0.4523$ So, $$\text{PV} = 350000 \times \frac{1 - 0.4523}{0.17} = 350000 \times \frac{0.5477}{0.17} \approx 350000 \times 3.222 = 1127700$$ Then, $$\text{NPV} = 1127700 - 174000 = 953700$$ 4. **Calculate IRR:** IRR is $r$ such that: $$174000 = 350000 \times \frac{1 - (1+r)^{-5}}{r}$$ Try $r=0.5$ (50%): $$350000 \times \frac{1 - (1.5)^{-5}}{0.5} = 350000 \times \frac{1 - 0.1317}{0.5} = 350000 \times 1.7366 = 607810 > 174000$$ Try $r=1.5$ (150%): $$350000 \times \frac{1 - (2.5)^{-5}}{1.5} = 350000 \times \frac{1 - 0.0102}{1.5} = 350000 \times 0.6599 = 230965 < 174000$$ By interpolation, IRR is approximately 200% or more, so IRR > 17%. 5. **Decision ignoring environmental concerns:** Since NPV > 0 and IRR > cost of capital (17%), the project should be undertaken. 6. **Considering environmental effects:** Environmental damage from sulfuric acid extraction may impose costs not included in cash flows, such as cleanup, fines, or reputational damage. These should be quantified and subtracted from benefits. If environmental costs are high, they may reduce or negate the positive NPV, potentially changing the decision. **Final answers:** - NPV = 953700 - IRR > 17% - Undertake project ignoring environmental concerns - Environmental effects must be included in evaluation; they may change the decision.