Chester National Bank is considering adding a new branch bank.It knows that it will cost $2.5 million to build the branch and it believes that it will generate $214,526 per year for the next 25 years.Chester National Bank requires a return of 10% on all new projects it undertakes.What is this project's net present value? (Round to the nearest $100)
A)-$552,700
B)-$3,052,700
C)$1,947,300
D)$2,863,200
E)$5,363,200

Question

Quizplus · Accepted Answer

The net present value (NPV) is calculated by discounting the future cash flows back to their present value and subtracting the initial investment. Using the formula for NPV: $$NPV = \sum \frac{R_t}{(1+i)^t} - C_0$$ where $R_t$ is the cash inflow at time $t$, $i$ is the discount rate (10% or 0.10 in this case), and $C_0$ is the initial investment ($2.5 million). The cash inflow is $214,526 per year for 25 years. Calculating the NPV: $$NPV = \frac{214,526}{1.10} + \frac{214,526}{1.10^2} + \cdots + \frac{214,526}{1.10^{25}} - 2,500,000$$ This calculation results in an NPV of approximately -$552,700 when rounded to the nearest $100.

Chester National Bank Is Considering Adding a New Branch Bank