# Answer to Question #59979 in Finance for reza

Question #59979

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?

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?

Expert's answer

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.

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.

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