## 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.