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INVESTIGATION: Choosing the right car

Lesson

In this investigation, we are going to look at a number of different scenarios related to fuel consumption and vehicle emissions in order to make more informed decisions about choosing the right car to buy.

Remember!

For each new vehicle produced, the car manufacturer will publish three different fuel consumption rates, for different driving environments:

  • Combined - an average overall value
  • Urban - city driving
  • Extra urban - highway or freeway driving

These rates are expressed in litres per $100$100 kilometres (L/$100$100 km).

Car manufacturer's also publish a combined rate for carbon dioxide (CO2) emissions, from the vehicle's exhaust system. CO2 is the main contributor to climate change.

Fuel prices are expressed as cents per litre (c/L).

 

Exercise 1

The following table displays some data for the petrol and diesel versions of a 2019 model Hyundai i30 hatchback.

Both vehicles have 4-cylinder engines and a fuel tank capacity of $50$50 litres. The table indicates the three fuel consumption rates and the combined CO2 emissions rate for each vehicle. 

When consumers purchase this car, they may choose between either a petrol or diesel engine. 

Vehicle make and model Fuel type Combined (L/100 km) Urban (L/100 km) Extra urban (L/100 km) Combined CO2 (g/km) Purchase price
Hyundai i30 (2019) petrol $7.3$7.3 $9.7$9.7 $5.9$5.9 $170$170 $\$23414$$23414
Hyundai i30 (2019) diesel $4.5$4.5 $5.4$5.4 $4.0$4.0 $119$119 $\$26015$$26015

To compare the fuel economy of these vehicles, assume that each car travels an average of $50$50 kilometres per day.

The price of petrol is $128$128 cents per litre and the price of diesel is $143.9$143.9 cents per litre. Assume that these prices remain fixed throughout the year.

 

Follow the steps below:

  1. Using the combined fuel consumption rate, calculate the amount of fuel used by each vehicle per day.
  2. Calculate the total amount of fuel used by each vehicle in one year. Use 365 days in one year.
  3. Use the appropriate fuel price above to calculate the annual fuel cost for each vehicle.
  4. Calculate the monthly fuel cost for each vehicle. Which vehicle has the lowest monthly fuel costs?

CO2 emission label used in Ireland

  1. The figure above is a part of a fuel economy label used in Ireland. It uses different coloured bars to indicate how "good" a vehicle's CO2 emissions are for the environment, with lower values being better. Use this label to compare the CO2 emissions for the petrol and diesel variants of the Hyundai i30 and comment on your findings.

The purchase price of the diesel car is greater than the petrol version. Separate loans are taken out for the full purchase price of each vehicle. Both loans have an interest rate of $8.49%$8.49% and a loan term of $5$5 years. 

  1. Use the car loan calculator to work out the monthly repayments for each loan. 
  2. Add together the monthly car loan repayment and monthly fuel cost for each vehicle. 
  3. Which vehicle has the higher monthly cost during the term of the loan?

 

Exercise 2

The following table compares fuel consumption rates, fuel tank capacity and CO2 emissions for three different types of vehicle: a sedan, an SUV (Sport Utility Vehicle) and a ute.

Vehicle Type Engine size (cc) Combined (L/100 km) Urban (L/100 km) Extra urban (L/100 km) Fuel tank capacity (L) CO2 emissions (g/km)
Hyundai Sonata sedan $2359$2359 $8.3$8.3 $12.1$12.1 $6.3$6.3 $70$70 $194$194
Mitsubishi Outlander SUV $1998$1998 $7$7 $8.9$8.9 $5.9$5.9 $63$63 $162$162
Toyota Hilux ute $2694$2694 $10.7$10.7 $14$14 $8.7$8.7 $80$80 $248$248

All three vehicles are powered by 4-cylinder petrol-engines and have a similar purchase price of around $\$35000$$35000

All three vehicles are used to drive one-way along the same route from Sydney to Brisbane, a distance of $920$920 kilometres. 

The average price of petrol along the route is $146.9$146.9 cents per litre.

Follow the steps below:

  1. Calculate the cost of completely filling each car's fuel tank. Answer to the nearest cent.
  2. Use the extra urban (highway) fuel consumption rate to work out how far each vehicle can travel on a full tank of fuel. Answer to the nearest kilometre.
  3. Use the extra urban (highway) fuel consumption rate to calculate the total cost of fuel for each vehicle to drive from Sydney to Brisbane.
  4. The fuel costs you calculated in question 4, may be different from the 'actual' fuel costs for the journey? Provide at least three reasons for why they may be different.
  5. Use the urban (city) fuel consumption rate to to calculate the total fuel cost of driving each vehicle over the same distance ($920$920 km), within an urban environment. 
  6. Comment on the CO2 emissions of each vehicle. Is there any other information given in the table that you think may influence the level of CO2 emissions? What other factors affect CO2 emissions in vehicles?
  7. Do some research online to find the cheapest flights between Sydney and Brisbane. Compare this with the cost of travelling by train and cost of driving. Which mode of transport do you think has the least impact on the environment?

 

Extension

In this exercise, we will investigate how to claim car expenses as a tax deduction.

Anyone who uses their own car for the purpose of running their business, can claim business-related car expenses when they complete their tax return. This can be calculated using either of the following methods:

  • Logbook method
  • Cents per kilometre method
     
Logbook method

In this method a logbook is used to record the details of every journey made in the vehicle. The purpose of keeping a logbook is to work out what percentage of the vehicles's use is related to running the business. This is called the business-use percentage.

The logbook must be kept for a minimum period of $12$12 continuous weeks. For each journey, the date, odometer readings and a brief description of the usage (private or business), is recorded.

The car's odometer readings are used to determine the distance travelled for each journey. 

Below is an example of how journeys are recorded in a typical vehicle logbook:

Journey start date Odometer reading start of journey (km) Journey end date Odometer reading end of journey (km) Reason for journey Distance travelled (km)
5 Sep 2018 $10200$10200 4 Sep 2018 $10210$10210 Private - travel to park $10$10
5 Sep 2018 $10210$10210  4 Sep 2018 $10230$10230 Business - visit client $20$20
6 Sep 2018 $10230$10230 5 Sep 2018 $10245$10245 Business - visit client $15$15
7 Sep 2018 $10245$10245 9 Sep 2018 $10450$10450 Private - weekend away $205$205

At the end of the $12$12 week period, the business-use percentage is calculated as follows:

Divide the total business-use distance by the total distance travelled. Then multiply by $100$100.

To work out the amount that can be claimed as a tax deduction, multiply the business-use percentage by the total annual running costs for the vehicle.

Vehicle running costs can include:

  • Fuel and oil
  • Registration
  • Insurance
  • Servicing
  • Vehicle depreciation (decline in value)

Note that the purchase price of the vehicle and expenses like parking fees or fines cannot be claimed as tax deductions. 

Cents per kilometre method

Using this method, the amount that can be claimed as a tax deduction is calculated simply by multiplying the total number of business-use kilometres by a fixed rate of $68$68 cents per kilometre (current for 2018/19 financial year).

The rate is designed to account for all running costs but this method can only be used to claim for a maximum of $5000$5000 business-use kilometres. 

 

Exercise 3

Consider the following scenario:

Amy lives in Sydney and runs her own business as a personal trainer. She owns a 2018 model Toyota Corolla hatch and uses her car for both private and business use.

During the past $12$12 weeks she has kept a vehicle logbook and recorded every journey she has made in her car.

Using her logbook, she works out that, over $12$12 weeks, she has travelled a total of $3840$3840 km, of which $960$960 km were for business use.

Follow the steps below:

  1. Calculate Amy's business-use percentage: divide the number of kilometres she travelled for business by her total kilometres travelled. Then multiply by $100$100.
  2. If Amy travels $3840$3840 km in $12$12 weeks, calculate how much she would travel in one year if she continued driving the same amount.
  3. If the urban fuel consumption rate of Amy's car is $7.5$7.5 L/$100$100 km and the average annual cost of fuel is $132$132 cents per litre, calculate her annual fuel cost. Answer to the nearest dollar.
  4. Complete the following table of Amy's annual car expenses. Include her annual fuel cost and calculate the total of her expenses.
    Vehicle expense Amount
    Vehicle registration $\$371$$371
    CTP insurance $\$455$$455
    Comprehensive insurance $\$1600$$1600
    Service/maintenance $\$360$$360
    Depreciation $\$4250$$4250
    Fuel  
    Total  
  5. Calculate Amy's tax deduction using the logbook method by multiplying her business-use percentage by her total annual car expenses. 

  6. Calculate Amy's tax deduction using the cents per kilometre method. First work out her business-use kilometres for the entire year. Then multiply by the rate of 68 cents per kilometre.

  7. Which of the two calculation methods works best in Amy's situation?

  8. What factors do you think might determine which method is better to use in other situations? Investigate what the outcome would be if the vehicle was larger and less fuel efficient or if the business-use percentage was higher. 

Outcomes

MS11-2

represents information in symbolic, graphical and tabular form

MS11-5

models relevant financial situations using appropriate tools

MS11-6

makes predictions about everyday situations based on simple mathematical models

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