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.

Required:
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:

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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Debit Credit
Cash $22,150
Merchandise inventory 13,000
Store supplies 5,100
Prepaid insurance 2,800
Store equipment 42,800
Accumulated depreciation—Store equipment $19,250
Accounts payable 17,000
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