Spruce Bank is planning to automate some of its back office functions and reduce operating costs.The installation of new computers and software will require an initial investment of $1,000,000.The savings generated because of reduced personnel cost is $200,000 per year.The bank uses an 8 percent rate of discount to evaluate cost saving projects which are expected to last 10 years. On further analysis, it is estimated that the project has a finite life of 5 years, i.e.further investment will be required to generate the same savings.Should they undertake the project if they assume a five-year horizon for evaluating the project?
A)Yes, because the NPV of the project is $500,000.
B)Yes, because the NPV of the project is $342,016.
C)No, because the NPV of the project is -$500,000.
D)No, because the NPV of the project is -$201,458.
E)No, because the IRR of the project is greater than 15 percent.

Question

Quizplus · Accepted Answer

To calculate the NPV of the project, we need to use the following formula:

NPV = (Savings/Discount rate) x {1 - [1/(1+Discount rate)^Number of years]}

Where:
Savings = $200,000
Discount rate = 8%
Number of years = 5

NPV = (200,000/0.08) x {1 - [1/(1+0.08)^5]}
NPV = 2,500,000 x 0.68058
NPV = 1,701,456

The NPV of the project is positive, which means that the project is expected to generate a positive cash flow and provide a return greater than the cost of capital. However, since the project has a finite life of 5 years, we also need to calculate the NPV of the project over the 10-year period using the same formula, but with number of years = 10. This can then be compared to the initial investment to see whether the project is worth undertaking.

NPV (10 years) = (200,000/0.08) x {1 - [1/(1+0.08)^10]}
NPV (10 years) = 2,500,000 x 0.46319
NPV (10 years) = 1,157,976

Total NPV = 1,701,456 + 1,157,976 = 2,859,432

Since the total NPV is positive, Spruce Bank should undertake the project. However, the best choice is option D because it specifically asks about the 5-year horizon, which has a NPV of $201,458. This means that the project's cost exceeds the expected cash flows over the 5-year period, and so the bank should not undertake the project if it only considers a 5-year horizon.

Spruce Bank Is Planning to Automate Some of Its Back