Answer to Question #244926 in Civil and Environmental Engineering for Alan Enrico V Tuib

Question

A 50-kilowatt gas turbine has an investment cost of $40,000. It costs another $14,000 for shipping,
insurance, site preparation, fuel lines, and fuel storage tanks. The operation and maintenance expense for this turbine is $450 per year. Additionally, the hourly fuel expense for running the turbine is $7.50 per hour, and the turbine is expected to operate 3,000 hours each year. The cost of dismantling and disposing of the turbine at the end of its 8-year life is $8,000.
a. If the MARR is 15% per year, what is the annual equivalent life-cycle cost of the gas turbine?
b. What percent of annual life-cycle cost is related to fuel?

Answer 1

a.) Initial investment cost = Investment cost of turbine + cost including shipping, insurance, site preparation, fuel lines, and fuel storage tanks.

Initial investment cost = $40,000 + $14000;

Initial investment cost = $54000.

However, The annual fuel expense = hourly fuel expense for running turbine × total number of operating hour per year

The annual fuel expense = $7.50 × 3000;

The annual fuel expense = $22,500.

Therefore, the total operating cost per year = operating & maintenance cost per year + fuel expenses per year

the total operating cost per year = $(450 + 22500);

the total operating cost per year = $22,950.

If the minimum acceptable rate of return MARR is 15%, then the number of years is 8 years.

Therefore, the annual equivalent life-cycle cost (AC) of the gas turbine can be computed as follows:

AC(15%) = -54000 (A/P, 15%, 8) - $22950-$8000(A/F,15%,8);

where;

(A/P,15%,8) = annual worth factor of a present worth;

(A/F,15%,8) = annual worth factor of future worth for 8 years and 15% interest rate.

If we use the discrete compounding table when i = 15%;

Value of (A/P,15%,8) = 0.229;

Value of (A/F,15%,8) = 0.0729.

AC(15%) = -$54,000(0.2229) - $22,950 -$8000(0.0729);

AC(15%) = -$12,036.6 -$22950 -$583.2;

AC(15%) = -$35,569.8.

Therefore, the annual equivalent life-cycle cost (AW) of gas turbine = $35,569.8.

b.) = ($35,569.8/$54,000)*100

= 65.87%