Thursday, September 4, 2014

Fuel efficiency math problem set one.

Fuel Efficiency Math  -- Problem Set One


Question One:  The Honda Pilot (the best ranking eight passenger SUV) gets fuel efficiency of 17 mpg in the city and 24 mpg in the highway.    A person travels 10,000 city miles and 5,000 highway miles per year in this vehicle.   This information is summarized below.

Honda Pilot Fuel Efficiency and Use

City
HWAY
EPA MPG
17
24
Miles Driven
10,000
5,000

What is the total amount of gasoline consumed per year by this individual?

What is the weighted (city/highway) average fuel efficiency for this car?

What is the geometric average fuel efficiency for this car?

What is the harmonic average fuel efficiency for this car?

What average fuel efficiency statistic – weighted, geometric or harmonic – should be used to calculate gas consumed for this driver of the Honda Pilot?




Question Two:  Assume that the typical car lasts 15 years.    The car is driven 14000 miles per year with 9000 miles in a city and 5000 miles per year on a highway.   The fuel efficiency in miles per gallon for the Toyota Prius and the Toyota Corolla are presented below.








Fuel Efficiency in miles
 per gallon

Toyota Prius
Toyota Corolla
City
51
30
Highway
48
42



Each gallon of gas consumed results in the generation of 19.6 pounds of carbon dioxide. 

What is the difference between the CO2 generated over the lifetime of the Prius compared to the lifetime of a Corolla?




Question Three:  Gas mileage estimates for the Toyota Prius and the Toyota Corolla are presented below.

Fuel Efficiency In Miles Per Gallon

Toyota Prius
Toyota Corolla
City
51
30
HWAY
48
42


Driving patterns defined by total miles driven in a year and percent of miles driven in city and in highway for six drivers are presented below.


Six Driving Scenarios
Driver #
Miles Driven Per Year
% City
% Highway
1
10,000
25
75
2
10,000
75
25
3
12,500
25
75
4
12,500
75
25
5
15,000
25
75
6
15,000
75
25


How much gas would the six drivers use in a Prius and in Corolla over the course of a year?

How much would the six drivers spend on gas in the two cars at a price of $3.50 per gallon?

How much would the six drivers spend in gas in the two cars if the price of gas was $4.00 per gallon?



Question Four:  This post is a limited comparison of four cars – the Prius, Camry, Corolla, and Civic.   We consider two variables MSRP and lifetime fuel costs.


How do the net present value of total purchase costs and total fuel costs for these four cars vary?

Basic Information and Assumptions:

Key information on the four cars and mileage driven are presented in the Table below. 


Four Car Comparison Lifetime Purchase
and Fuel Costs

MSRP
MPG City
MPG HWAY
City Miles
HWAY Miles
Prius
$24,200
51
48
10000
5000
Camry
$22,235
25
35
10000
5000
Corolla
$16,800
30
42
10000
5000
Civic
$18,190
31
41
10000
5000


Key assumptions in the analysis

Car is bought with cash at price equal to MSRP.

The car is purchased and driven for 12 years.  At the end of 12 years all four cars have a value of $0.

The cost of capital is assumed to be 5%.

The price of gas is assumed to be $3.50 or $4.00.







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