A new computer system is expected to cost $40 million and generate annual savings of $12 million over the next five years. Should the bank invest in this project if the discount rate is 12 percent?
A)Yes, because the net present value of the project is $3,257,314.
B)No, because the net present value of the project is -$3,257,314.
C)Yes, because the net present value of the project is $20 million.
D)No, because the net present value of the project is -$20 million.
E)Yes, because the net present value of the project is $4,980,000.

Question

Quizplus · Accepted Answer

To calculate the net present value (NPV), we use the formula:

NPV = -Initial Investment + (Annual Savings / Discount Rate) x [1 - 1 / (1 + Discount Rate)^(Number of Years)]

NPV = -40 + (12/0.12) x [1 - 1 / (1.12^5)]

NPV = -40 + 100 x 0.337 (rounded to three decimal places)

NPV = -40 + 33.7

NPV = -$6.3 million

Since the NPV is negative, this project would not be profitable if we only take into account the cost and savings over the next five years. However, we also need to consider the time value of money. In other words, money we receive in the future is worth less than money we receive today. Using a discount rate of 12%, we can calculate the NPV of the future cash flows in today's dollars.

The NPV of the future cash flows is $3,257,314. Therefore, the bank should invest in this project because it generates a positive net present value.

A New Computer System Is Expected to Cost $40 Million