## Friday, September 5, 2014

### The SUV/Sedan combination purchase decision.

Question:   The table below lists U.S. government fuel efficiency figures for two SUVs and two sedans and the MSRP for the four vehicles.

 EPA MPG MSRP Honda Pilot 29 \$29,670 Subaru CrossTrek 21 \$21,995 Toyota Prius 42 \$24,200 Toyota Corolla 35 \$16,800

Assume a household buys one SUV and one Sedan and uses them for ten years.   The cars were bought at the beginning of the time period and were purchased with a 5-year loan at a 10% interest rate.

The household uses each car 50% of the time.   Each household travels 30,000 miles per year.

Calculate the following:

The amount of gasoline in gallons consumed by each household each month

The amount of money spent on gasoline each month, assuming \$4.00 for a gallon of gas.

Household monthly loan payments

The present value of the total of loan payments and fuel expenses for the four households

Analysis:    This problem considers four SUV/Sedan combinations (Pilot/Prius, Pilot/Corolla, Cross/Trek/Prius and CrossTrek/Corolla)

The calculations requested in this problem are laid out in the table below.

 Household Vehicles Honda Pilot Honda Pilot Subaru CrossTrek Subaru CrossTrek SEDAN Toyota Prius Toyota Corolla Toyota Prius Toyota Corolla Input Usage Assumptions: Total Miles Traveled 30000 30000 30000 30000 % of Miles Traveled In SUV 0.5 0.5 0.5 0.5 Fuel Efficiency Assumptions SUV Overall Fuel Efficiency 21 21 31 31 Sedan Overall Fuel Efficiency 42 35 42 35 Mileage SUV 15000 15000 15000 15000 Sedan 15000 15000 15000 15000 Gas Consumed SUV 714.3 714.3 483.9 483.9 SEDAN 357.1 428.6 357.1 428.6 Total 1071.4 1142.9 841.0 912.4 Overall Fuel Efficiency 28.0 26.3 35.7 32.9 Fuel  Expenditures @ \$4.00 gas \$357.1 \$381.0 \$280.3 \$304.1 Car Purchase Costs Interest Rate 0.1 0.1 0.1 0.1 MSRP SUV \$29,670 \$29,670 \$21,995 \$21,995 MSRP Sedan \$24,200 \$16,800 \$24,200 \$16,800 SUV Loan Payment \$630 \$630 \$467 \$467 Sedan Loan Payment \$514 \$357 \$514 \$357 Total Monthly Loan Payments on Cars \$1,145 \$987 \$982 \$824 Present Value Analysis: PV of Gas Consumed For 10 Years -\$27,025 -\$28,827 -\$21,213 -\$23,015 PV of Loan Payments for 5 Years -\$53,870 -\$46,470 -\$46,195 -\$38,795 Total PV for Gas and Loans -\$80,895 -\$75,297 -\$67,408 -\$61,810

Some observations:

The dispersion in fuel cost estimates is smaller than the dispersion in the loan cost estimates.  The Prius provides great fuel efficiency but it is not cheap.  Cost by itself is not a reason to choose the Prius over the Corolla.   However, many people prefer the ride of the Prius to the ride of the Corolla.

Tbe Pilot is the most expensive of the four vehicles but it is also much larger than the CrossTrek.

Concluding Remarks:  All of the options considered in this post get great gas mileage.    The   most economical option is the CrossTrek/Corolla combination.  However, as noted there are quality and size differences among cars that are also considered by people purchasing vehicles.

Students and teachers who want more insight on the vehicle purchase problem should go to the following link:
http://dailymathproblem.blogspot.com/2014/09/problem-set-two-household-vehicle.html

A previous version of this post relied on an incorrect number for the Honda Pilot fuel efficiency statistic.   I have made the correction.   Please get in touch with me if you see problems.