Question

An aerodynamic three-wheeled automobile (the Dart) runs on compressed natural gas stored in two cylinders in the rear of the vehicle. The $15,000 Dart can cruise at speeds up to 80 miles per hour and it can travel 100 miles per gallon of fuel. Another two-seater automobile costs $12,000 and averages 50 miles per gallon of compressed natural gas. Assume a useful life of seven years for each car, similar salvage values, and similar maintenance costs.
a. If fuel costs $8.00 per gallon and the MARR is 10% per year, at what average annual miles driven would you be indifferent between the vehicles?
b. Over what range of annual miles driven is the Dart more economical?

Answer 1

Answer:

a) 7702.88 miles

b) If we drive more than 7702.88 miles per year, the dart would be more economical.

Step-by-step explanation:

Assuming a useful life of 7 years.

Let's calculate EUAC dart:

(15000)(A/P, 10%, 7) + (X/100mpg)(8)

= 15000 * 0.2054 + 0.08

= 3081.15 + 0.08X

EUAC For other automobile:

(12000)(A/P, 10%, 7) + (X/50mpg)(8)

= 12000 * 0.2054 + 0.16X

= 2464.92 + 0.16X

a) To solve for X, we have:

EUAC dart = EUAC other automobile

3081.15 + 0.08X = 2464.92 + 0.16X

0.08X - 0.16X = 2464.92 - 3081.15

-0.08X = - 616.23

X = 7702.88 miles

b) The range of annual miles driven is the Dart more economical.

EUAC dart < EUAC other automobile

3081.15 + 0.08X < 2464.92 + 0.16X

X > 7702.88 miles

If we drive more than 7702.88 miles per year, the dart would be more economical.