Question

A certain machine costs $30,000, Expected revenues are $2500 per quarter for the next 6 years. The quarterly operating cost is $500. The machine can be sold for $1000 at the end of the 6 years. If the interest is 8% compounded quarterly, determine the equivalent quarterly worth and EAW.

Answer 1

Initial Cost=C=$30000

Expected net revenue per quarter=R=2500-500=$2000

Salvage value after 6 years=S=$1000

Rate of interest=i=8%/4=2%

Present worth of machine=PW=-30000+2000*(P/A,0.02,24)+1000*(P/F,0.02,24)

Let us calculate the interest factors

(P/F,0.02,24)=1/(1+0.02)^24=0.621721

Present worth of machine=PW=-30000+2000*18.913926+1000*0.621721=$8449.57

Equivalent quarterly worth=PW/(P/A,0.02,24)=8449.57/18.913926=$446.74

Now we estimate the equivalent annual worth, EAW

Effective annual interest rate=(1+2%)^4-1=0.082432

EAW=PW*(A/P,0.082432,6)

Let us calculate the interest factor

EAW=8449.57*0.217914=$1841.28