Question

The initial cost (year 0) of a pulverized coal cyclone furnace is $800,000. If the operating cost is 90,000 in year 1, and increasing by 5,000 each year through a 10 year lifetime period, what is the equivalent annual worth of the furnace from year 1 to 10 at an interest rate of 3% per quarter compounded monthly.

Include the actual formulas, not what you use to look into a chart. I rate.

Answer 1

Initial Cost=Co=$800,000

Operating cost for year 1=R=$90000

Gradient =$5000 per year

Useful life=n=10 years

Nominal interest rate per month=3%/12=0.0025

Effective interest rate per payment period=i=(1+0.0025)^12-1=0.03041596 per year

First we calculate present worth of costs in this case.

PWC=Co+R*(P/A,i,n)+G(P/W,i,n)

PWC=800000+90000*(P/A,0.03041596,10)+5000(P/G,0.03041596,10)

We know

PWC=800000+90000*8.51212354+5000*36.20360740=$1747109.16

Equivalent annual worth of cost=PWC/(P/A,0.03041596,10)=1747109.16/8.51212354=$205,249.51