Question

50-kilowatt gas turbine has an investment cost of $57,000. The operation and maintenance expense for this turbine is $400 per year. Additionally, the hourly fuel expense for running the turbine is $7.50 per hour, and the turbine is expected to operate 4,000 hours each year. The cost of dismantling and disposing of the turbine at the end of its 8-year life is $8,000. If the MARR is 15% per year, what is the annual equivalent life-cycle cost of the gas turbine? Please only fill in the number of your calculated result in the blank, e.g., if the result is $100, fill in "100"; also round to the nearest integer. Note "cost" should be a negative number.

Answer 1

Equivalent annual cost: -43,685.255

Step-by-step explanation:

the EAC equivalent annual cost of the PTM of the present value of the machine at the given discount rate.

for the equivalent annual cost, first we must calculate the net present value

57,000 investment

+ present value of fuel and maintenance

+ present value of dismantling cost

fuel expense: 4,000 x 7.5 = 30,000

maintenance expense 400

total 30,400

`C * (1-(1+r)^(-time) )/(rate) = PV\\`

C 30,400

time 8

rate 0.15

`30400 * (1-(1+0.15)^(-8) )/(0.15) = PV\\`

PV $136,414.5738

then the present value of a lump sum for the dismantling cost

`(Maturity)/((1 + rate)^(time) ) = PV`

Maturity 8,000.00

time 8.00

rate 0.15

`(8000)/((1 + 0.15)^(8) ) = PV`

PV 2,615.21

57,000 + 136,414.5738 + 2,615.21 = 196,029.7838‬

Now we calculate the PMT of an annuity of 8 year at 15% discount rate:

`PV / (1-(1+r)^(-time) )/(rate) = C\\`

PV $196,029.78

time 8

rate 0.15

`196029.7838 / (1-(1+0.15)^(-8) )/(0.15) = C\\`

C $ 43,685.255

This will bethe equivalent annual cost.