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.  



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