Question

Metropolitan Water Utility is planning to upgrade its SCADA system for controlling well pumps,booster pumps, and disinfection equipment so that everything can be controlled from one site. Thefirst phase will reduce labor and travel costs by an estimated $31,000 per year. The second phase will reduce costs by an estimated $20,000 per year. If phase I will occur in years 1 through 3 and phase II in years 4 through 8,
what is

(a) the present worth of the savings, and

(b) the equivalent annual worth for years 1 through 8 of the savings? Use an interest rate of 8% per year.

Answer 1

Answer:

net wortht  -143,280.85

equivalent annual cost $ 24,932.98

Explanation:

We sovle for the present value of each annuity:

The first three years:

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

C 31,000.00

time 3

rate 0.08

$31000 \times \frac{1-(1+0.08)^{-3} }{0.08} = PV$

PV $79,890.0066

Then the second phase annuity:

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

C 20,000.00

time 5

rate 0.08

$20000 \times \frac{1-(1+0.08)^{-5} }{0.08} = PV$

PV $79,854.2007

NOw, we discount this as it is three years into the future

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

Maturity  $79,854.2007

time  3.00

rate  0.08000

$\frac{79854.2007415617}{(1 + 0.08)^{3} } = PV$  

PV   63,390.8391

Total net worth:

79,890.0066    -   63,390.8391    =   -143,280.85

The EAC will be the annuity which makes the Present work

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

PV 143,280.85

rate 0.08

time 8

$143280.85 \div \frac{1-(1+0.08)^{-8} }{0.08} = C$

C  $ 24,932.983