Question

A nursery operator is considering installing a wireless sensor network that will control irrigation automatically to keep moisture at a preset level. She currently uses 80,000,000 gallons of water a year. The automated irrigation system will cut water use by one-half. The system requires an initial investment of $50,000 and will last 25 years. The nursery operator can finance this investment over a 25-year period at a fixed interest rate of 10%, compounded annually. a. Calculate the annualized cost of the wireless sensor system. b. Calculate the present value of the water savings if the nursery operator gets water from a nearby river that costs $0.00015 per gallon. c. Will investing in the automated irrigation system be profitable for this

Answer 1

Usage of Water in gallons = 80,000,000

Usage of Water in gallons after new system = 40,000,000

Initial Investment = (50,000)

Machine Time Period = 25 years = Financing Time Period

Discount Rate = 10%

A) Annualised Cost = (CRF * Capital Investment) + Maintenance Cost

Where CRF = Rate / (1- [1+Rate]^-n)

CRF = 10%/ (1-(1.1)^-25) = 11.017%

Annualised Cost = (11.017% * 50,000)+ 0 = 5508.404

B) Cost per Gallon of water = $0.00015

Savings per year = .00015 * 40,000,000 = $6,000

Cash Flow 0 = (50,000) and Cash Flow income each year = 6000

We discount 6000 dollars each year for 25 years and add their present values

=6000/(1.1)^1 + 6000/(1.1)^2 + 6000/(1.1)^3 + ...... 6000/(1.1)^25

PV= 54,462.24

C) Net Present Value = Sum of Discounted Cash inflows - Initial Cash outlay

=54,462.24 - 50,000

=4,462.24

Since, we have a positive NPV, we will accept the project and invest 50,000 USD into the new system.