\"An airline is considering two types of engine systems for use in its planes. E

Question

"An airline is considering two types of engine systems for use in its planes. Each has the same life and the same maintenance and repair record.
SYSTEM A costs $98,000 and uses 32,000 gallons of fuel per 2,000 hours of operation at the average load encountered in passenger service.
SYSTEM B costs $196,000 and uses 23,000 gallons of fuel per 2,000 hours of operation at the same level.
Both engine systems have three-year lives. Each system's salvage value is 10% of its initial investment. If jet fuel currently costs $2.66 a gallon and fuel consumption is expected to increase at the rate of 5.5% per year because of degrading engine efficiency, which engine system should the firm install? Assume 2,400 hours of operation per year and a MARR of 14.2%. Use the annual equivalent cost criterion. What is the annual equivalent cost of the preferred engine?"

Explanation / Answer

Working note:

(1)

For System A, Annual Fuel consumption, year 1 = (32,000 / 2,000) x 2,400 = 38,400 gallons

For System B, Annual Fuel consumption, year 1 = (23,000 / 2,000) x 2,400 = 27,600 gallons

(2)

Annual fuel cost = Annual fuel consumption x $2.66

(3)

For System A, Salvage value ($) = 98,000 x 10% = 9,800

For System B, Salvage value ($) = 196,000 x 10% = 19,600

(4)

In year 3, Annual cost for each System decreases by the amount of its salvage value.

(5)

PV Factor in year N = (1.142)-N

(6)

First, we compute Present Worth (PW) of Costs for both systems as follows.

(6) Annual equivalence cost (EUAC) = PW / P/A(14.2%, 3) = PW / 2.3139**

EUAC, System A ($) = 339,826 / 2.3139 = 146,863

EUAC, System B ($) = 361,382 / 2.3139 = 156,179

Since System A has lower EUAC of costs, this is preferred with an EUAC of $146,863.

**P/A(r%, N) = [1 - (1 + r)-N] / r

P/A(14.2%, 3) = [1 - (1.142)-3] / 0.142 = (1 - 0.6714) / 0.142 = 0.3286 / 0.142 = 2.3139

SYSTEM - A Year First Cost ($) Fuel Consumption Fuel Cost ($) Total Cost ($) PV Factor @14.2% Discounted Cost ($) (A) (B) (C)=(B) x $2.66 (D) = (A) + (C) (E) (D) x (E) 0 98,000 0 98,000 1.0000 98,000 1 38,400 1,02,144 1,02,144 0.8757 89,443 2 40,512 1,07,762 1,07,762 0.7668 82,629 3 42,740 1,13,689 1,03,889 0.6714 69,754 PW ($) = 3,39,826 SYSTEM - B Year First Cost ($) Fuel Consumption Fuel Cost ($) Total Cost ($) PV Factor @14.2% Discounted Cost ($) (A) (B) (C)=(B) x $2.66 (D) = (A) + (C) (E) (D) x (E) 0 1,96,000 0 1,96,000 1.0000 1,96,000 1 27,600 73,416 73,416 0.8757 64,287 2 29,118 77,454 77,454 0.7668 59,390 3 30,719 81,714 62,114 0.6714 41,705 PW ($) = 3,61,382

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