Question

You are working with the manager of an irrigation facility who is interested in installing a
more efficient pumping system. The proposed system costs $15,000 and you project that it will
reduce the annual utility costs by $2,000. After five years, you expect to upgrade the system for
$4,000. This upgrade is expected to further reduce utility costs by $1,000 annually. The annual
effective interest rate is 7% and the life of the system, after upgrade is 50 years. What is the
Present Value of the investment in the system?

Answer 1

The proposed system costs Co = $15,000, it will reduce the annual utility costs by CF = $2,000. After 5 years the upgrade for C = $4,000 will reduce utility costs by $1,000 annually, r = 7%, t = 50 years. The Present Value of the investment in the system will be calculated using the formula:
NPV = -Co + C1/(1 + r) + ... + Cn/(1 + r)^n.
NPV = -15,000 + 2,000/1.07 + 2,000/1.07^2 + 2,000/1.07^3 + 2,000/1.07^4 + 2,000/1.07^5 - 4,000/1.07^5 + 1,000/1.07^6 + ... + 1,000/1.07^55 = $188.19.
So, the proposed system is profitable and effective.