1. 1 Driving Across Town for Cheaper Gas: A Cost/Benefit Analysis What do you really save in making the trip? When gas prices rose dramatically in 2005 and 2006, numerous websites and TV/Radio news programs began publicizing the locations of gas stations offering the lowest price for gas. Are they really providing a useful – and timely - service to the general public? Prepared for SSAC by Gary Franchy – Davenport University © The Washington Center for Improving the Quality of Undergraduate Education. All rights reserved. 2006 SSAC2006.HE5614.GF1.2 Core Quantitative Issue Mathematical modeling Supporting Quantitative Concepts Estimation Rates Unit conversions

2. 2 Overview of Module The ability to make good decisions affects both our personal and professional life. It follows that the better we understand a problem and incorporate relevant information, the better our conclusion should be. Since many decisions involve numbers, our ability to model a problem mathematically is key. Fortunately, many situations can be modeled using very basic mathematics. Every model, however, is based on the assumptions made about the situation and the need, or lack thereof, for precision in the result. The need for greater accuracy will usually translate to a more complex model (i.e., more assumptions, more variables, and more calculations). If just a rough estimate is acceptable, then a relatively simple model will often suffice. To examine how changing our assumptions can affect our results, we will examine a fairly simple (and hopefully realistic) scenario; however, each time through, we will add an assumption concerning information we believe to be relevant.

3. 3 Slides 4-5 Create the simple cost analysis spreadsheet. Slides 6 Take a second look: consider some additional factors (variables). Slides 7-8 Create the refined cost analysis spreadsheet. Slides 9 Take a third look: consider some more additional factors (variables). Slides 10 Create the further refined cost analysis spreadsheet. Slides 11 Ask what if? Change a key parameter. Slides 12 End of Module Questions Overview of Module (cont.) There are multiple websites (e.g., GasPriceWatch.com, GasBuddy.com) as well as many local TV/Radio stations that publicize the local gas stations with the lowest fuel prices. The reports tend to be more prominent when the price of gas is high or increasing. The reports are meant to provide a money- saving service to the public; however, they rarely (if ever) mention that the consumer may not actually realize the savings that one might expect. Our scenario: (Summer 2006) Regular unleaded costs $3.10 per gallon at your corner station. You log on to GasBuddy.com and find a station an additional five miles away selling the same gas for $3.00 per gallon. So if you need 15 gallons of gas, you would save $1.50 (why?) by making the trip to the cheaper gas station – or would you?

4. 4 Question #1 Recreate this spreadsheet. = cell with a number in it = cell with a formula in it What do you really save in making the trip for the cheaper gas? Initial Assumptions: 1.Our car gets 30 mpg 2.We need 15 gallons of gas 3.The cost of gas to travel to and from the cheaper gas station must be considered Calculations Gas: Cost per Mile = Price ÷ Fuel Efficiency Net Savings = Gross Savings – Cost of Visit Confirm your choice of operations by tracking changes in units.

5. 5 Question #1 (cont.) Initial Assumptions: 1.Our car gets 30 mpg 2.We need 15 gallons of gas 3.The cost of gas to travel to and from the cheaper gas station must be considered What do you really save in making the trip for the cheaper gas? Note None of your computations required more than a single operation. Formatting Hint To display cells as dollars: Right click on cell Select “Format Cells” Select “Number” Tab Select “Currency” Change “Decimal Places” and/or “Negative Numbers” if desired Select “OK” Where will you gas up now?

6. 6 Not surprisingly, the cost of gas used to and from the cheaper gas station did decrease our initially estimated savings, but it appears that we’re still saving money. However, is gas the only additional cost we incur when we drive? There are several costs (besides fuel) associated with owning a vehicle. Some costs are independent (not related) to the amount of driving you do (e.g., price of vehicle, finance charge, taxes, license, registration), while other costs are related (e.g., insurance, tires, maintenance, depreciation). For our second look, we will factor in the maintenance/tire cost of operating our vehicle. A quick Internet search on the topic revealed information on these costs (available on the next slide); however, in using these results we will need to make some additional assumptions about our car. Question #1 - A Second Look Initial Assumptions: 1.Our car gets 30 mpg. 2.We need 15 gallons of gas. 3.The cost of gas to travel to/from the cheaper gas station is considered. Additional Assumptions: 1.Our car is new (1-2 years old). 2.Our car is a medium sedan. 3.Maintenance and tire costs are to be considered. What do you really save in making the trip for the cheaper gas?

7. 7 Expand your spreadsheet to incorporate the new data and calculate your revised savings/loss. Vehicle Style Maintenance/Tires Cost ($) per mile Small Sedan0.050 Medium Sedan0.057 Large Sedan0.061 4WD SUV0.064 Minivan0.056 Source: www.aaa.com/publicaffairs Question #1 - A Second Look (cont.) What do you really save in making the trip for the cheaper gas? Additional Assumptions: 1.Our car is new (1-2 years old). 2.Our car is a medium sedan. 3.Maintenance and tire costs are to be considered.

8. 8 Question #1 – A Second Look (cont.) What do you really save in making the trip for the cheaper gas? Additional Assumptions: 1.Our car is new (1-2 years old). 2.Our car is a medium sedan. 3.Maintenance and tire costs are to be considered. Again notice that no calculation required more than a single operation. Where will you gas up?

9. 9 Yet again, the more costs we considered, the more our savings decreased (now to the point of being a loss!). We could also try to factor in the cost of insurance and depreciation, but given the results of our second look that probably isn’t necessary. However, there are costs to us besides money in making the trip for cheaper gas: our time. Again, we will need to make some assumptions to calculate the amount of additional time required to make the trip for cheaper gas. Question #1 - A Third Look Time Assumptions: 1.The speed limit of the road is 50 mph. 2.We can drive the speed limit the entire trip. What do you really save in making the trip for the cheaper gas?

10. 10 Question #1 – A Third Look (cont.) How much additional time, in minutes, will it take to make the trip for the cheaper gas? What do you really save in making the trip for the cheaper gas? Time Assumptions: 1.The speed limit of the road is 50 mph 2.We can drive the speed limit the entire trip 3.The cost of gas to travel to/from the cheaper gas station is considered Add on to your spreadsheet. 1 Hour = 60 Minutes The total time of drive will require the total distance from the earlier computations So you lost 7 cents and 12 minutes.

11. 11 Question #2 – A Look back in Time What do you really save in making the trip for the cheaper gas? Let’s advance to the (near) present time and consider the case where the price of gas at our corner gas station is $2.10 per gallon and the price of gas at our cheaper gas station is $2.00. Would you make the trip now? Change the price input.

12. 12 End of Module Assignment / Post Test 1.Name and save your spreadsheet file in the following format: CCA2 - last name first name (Example: CCA2 - Franchy Gary ) Send a copy of the file to your instructor via e-mail 2.After comparing the net savings from each scenario (Price of gas around $3 per gallon versus around $2 per gallon), is it better to get lowest gas price reports when the price of gas is higher or lower? Why? 3.What information should be added to these lowest gas price reports in order for them to be more useful to consumers? 4.If the manufacturer of your car states that it gets 30 mpg highway, does that mean you will get 30 mpg on the highway? Why or why not? 5.Is it reasonable to conclude that the round trip to the cheaper gas station will take only 12 minutes? Why or why not?

13. 13 Pre-Assessment 1.If an 8 pack of Pepsi bottles is on sale for $2.48, what is the cost of an individual bottle of Pepsi? 2.If your car gets 24 mpg and gas costs $3.00 per gallon, how much does it cost to travel 1 mile? 3.A Tylenol elixir has a concentration of 15 milligrams per milliliter. If the dosage order is for 75 milligrams, how many milliliters should be administered? 4.Upon graduation you receive two job offers: Job A pays $50,000 per year and Job B pays $55,000 per year. What job would you take? (Please explain why, even if you can’t decide.)