Respuesta :
Answer:
The annual equivalent life-cycle cost (AW) of gas turbine = -$35,569.8
The percentage fuel cost = 63.25%
Explanation:
From the given information:
Let's start with the initial investment cost, which can be expressed by using the formula:
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.
The percentage of the annual life-cycle cost related to the fuel can be calculated by using the formula :
[tex]\mathbf{\% \ fuel \ cost = \dfrac{fuel \ cost \ per \ year}{total \ annual \ life \ cycle \ cost }\times 100\%}[/tex]
Replacing our values from above, we have:
[tex]\mathbf{\% \ fuel \ cost = \dfrac{\$22500}{\$35,569.8}\times 100\%}[/tex]
[tex]\mathbf{\% \ fuel \ cost = 0.6325\times 100\%}[/tex]
∴
The percentage fuel cost = 63.25%
Based on the given information, the annual equivalent life-cycle cost of the gas turbine is "$35,569.80," while the percent of the annual life-cycle cost is related to fuel is "65.87%."
This is based on the calculation below:
Given that: Initial investment cost => Investment cost of turbine + cost including shipping, insurance, site preparation, fuel lines, and fuel storage tanks.
Hence, we have the following:
Initial investment cost = $40,000 + $14,000;
=> Initial investment cost = $54,000.
On the other hand, The annual fuel expense = hourly fuel expense for running turbine × total number of operating hour per year;
Thus, we have the following:
The annual fuel expense = $7.50 × 3,000;
The annual fuel expense = $22,500.
Also, since, the total operating cost per year = operating & maintenance cost per year + fuel expenses per year;
We have the following:
the total operating cost per year = $(450 + 22,500);
the total operating cost per year = $22,950.
Therefore, given that the minimum acceptable rate of return MARR is 15%, then the number of years is 8 years.
Then, the annual equivalent life-cycle cost (AC) of the gas turbine is measured as:
AC (15%) = -54,000 (A/P, 15%, 8) - $22,950 - $8,000 (A/F,15%,8);
Here, we have the following details;
(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.
This, given that we use the discrete compounding table when i = 15%;
We have the following:
Value of (A/P,15%,8) = 0.229;
Value of (A/F,15%,8) = 0.0729.
AC (15%) = -$54,000 (0.2229) - $22,950 -$8,000 (0.0729);
AC(15%) = -$12,036.60 -$22,950 -$583.20;
AC(15%) = -$35,569.80.
Hence, the annual equivalent life-cycle cost (AW) of gas turbine = $35,569.80.
Similarly, the percent of the annual life-cycle cost is related to fuel is measured as = ($35,569.8 ÷ $54,000) × 100
=> 65.87%.
Hence, in this case, it is concluded that the lifecycle cost is essential when measuring the productivity of a project.
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