1. **State the problem:** Pennco Oil Co. must decide if opening an oil well is financially feasible. The costs and revenues are: - Initial cost: 5,000,000 - Annual profit: 585,000 barrels × 5 per barrel = 2,925,000 per year for 4 years - Final capping cost: 4,000,000 at the end of year 4 - Required rate of return: 14% per year 2. **Formula and concept:** We use the Net Present Value (NPV) formula to evaluate the investment: $$NPV = -C_0 + \sum_{t=1}^n \frac{R_t}{(1+r)^t} - \frac{C_f}{(1+r)^n}$$ where: - $C_0$ = initial cost - $R_t$ = net profit at year $t$ - $C_f$ = final cost at year $n$ - $r$ = discount rate (14% = 0.14) - $n$ = number of years (4) 3. **Calculate each term:** - Initial cost: $-5,000,000$ - Annual profits: $2,925,000$ each year for 4 years - Final capping cost: $4,000,000$ at year 4 4. **Calculate present value of profits:** $$PV_{profits} = 2,925,000 \times \left(\frac{1}{1.14} + \frac{1}{1.14^2} + \frac{1}{1.14^3} + \frac{1}{1.14^4}\right)$$ Calculate each discount factor: $$\frac{1}{1.14} = 0.8772$$ $$\frac{1}{1.14^2} = 0.7695$$ $$\frac{1}{1.14^3} = 0.6749$$ $$\frac{1}{1.14^4} = 0.5921$$ Sum of discount factors: $$0.8772 + 0.7695 + 0.6749 + 0.5921 = 2.9137$$ So, $$PV_{profits} = 2,925,000 \times 2.9137 = 8,523,652.5$$ 5. **Calculate present value of final capping cost:** $$PV_{capping} = \frac{4,000,000}{1.14^4} = 4,000,000 \times 0.5921 = 2,368,400$$ 6. **Calculate NPV:** $$NPV = -5,000,000 + 8,523,652.5 - 2,368,400 = 1,155,252.5$$ 7. **Interpretation:** Since $NPV > 0$, the project is financially feasible and Pennco should open the well.