Question

El Paso Water is planning to install wind turbines to provide enhanced evaporation of reverse osmosis concentrate from its inland desalting plant. The company will spend $1.5 million in year 1 and $2 million in year 2. Annual maintenance is expected to cost $65,000 per year through year 10. Determine the equivalent annual cost of the project in years 1 through 10 at an interest rate of 6% per year. Also, develop a single-cell spreadsheet function to display the total A value

Answer 1

Answer:

Equivalent Annual Cost: $ 499,109.977

Explanation:

The equivalent annual cost is the PMT of the net present value of a project.

In this case the company will spend:

year 1: 1,500,000

year 2: 2,000,000

plus 65,000 maintenance cost for during each year.

we calculate the first two using the present value of a lump sum

$\frac{Nominal}{(1 + rate)^{time} } = PV$  

Nominal: $ 1,500,000.00

time   1 year

rate  0.06

$\frac{1500000}{(1 + 0.06)^{1} } = PV$  

PV   1,415,094.34

$\frac{2000000}{(1 + 0.06)^{2} } = PV$

Nominal: $ 2,000,000.00

time   2 year

rate  0.06

PV   1,779,992.88

Then the maintenance cost will be an ordinary annuity:

$C \times \frac{1-(1+r)^{-time} }{rate} = PV$

C 65,000

time 10

rate 0.06

$65000 \times \frac{1-(1+0.06)^{-10} }{0.06} = PV$

PV $478,405.6583

now we add them together:

1,415,094.3 + 1,779,992.88 + 478,405.6583  =  $3,673,492.88

and calculate the PMT:

$PV \div \frac{1-(1+r)^{-time} }{rate} = C$

PV  $3,673,492.88

time 10

rate 0.06

$3673492.87834196 \div \frac{1-(1+0.06)^{-10} }{0.06} = C$

C  $ 499,109.977