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. The maximum cost savings that can be generated with this new equipment has been estimated to be $264,237.In order to accept this project, what is the minimum number of years the projected savings must be realized before the project breaks even?
A)3.7 years.
B)4.7 years.
C)5.7 years.
D)6.7 years.
E)7.7 years.

Question

Quizplus · Accepted Answer

To calculate the minimum number of years to break even, we need to find the point where the present value of the expected savings is equal to the initial investment.
PV of expected savings = PV of initial investment
Using the formula for present value, we get:
PV of expected savings = $200,000 [(1-1/(1+0.08)^10)/0.08] = $1,383,821.22
PV of initial investment = $1,000,000
Therefore, the minimum number of years to break even is the number of years it takes for the present value of the expected savings to equal the present value of the initial investment. 
Let the number of years for break even be X.
PV of expected savings for X years = $200,000 [(1-1/(1+0.08)^X)/0.08] = PV of initial investment = $1,000,000
Solving for X, we get X = 4.7 years. 
Therefore, in order to accept the project, the projected savings must be realized for at least 4.7 years in order for the project to break even.

Spruce Bank Is Planning to Automate Some of Its Back