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

$C_o=\$15,000, CF=\$2,000, C=4,000$ will reduce utility costs by 1000 annually, r=7%, t=50 years.The present value of the investment in the system will be calculated using the formula:

$NPV=-C_O+\frac{C_1}{(1+R)}+....+\frac{C_n}{(1+r)^n}$

$NPV=-15000+\frac{2000}{1.07}+\frac{2000}{1.07^2}+\frac{2000}{1.07^3}+\frac{2000}{1.07^4}+\frac{2000}{1.07^5}-\frac{4000}{1.07^5}+\frac{1000}{1.07^6}+...+\frac{1000}{1.07^{50}}=\$188.19$