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“Is it better to lease or buy a vehicle?”Submitted By: Krishani Starnes & Stephanie ZubClass: Mathematics 10CSummary Page “Is it better to lease or buy a vehicle?”The word better is vague, so we defined the word ‘better’ in this context as financially feasible. This led us to the problem statement: “Is it cheaper financially to buy or lease a new vehicle?” (In order to make the comparison it had to be a ‘new’ vehicle, as we found out that dealerships do not lease used vehicles).We went to two different dealerships and looked at SUV’s. We looked into the Honda CRV 2018 at Village Honda and found out the cost for financing and leasing this vehicle. The second dealership we explored was, Lexus of Royal Oak and we looked into financing and leasing the Lexus NX 2018. When we graphed the data we could see that for both SUV’s it is cheaper monthly to lease the vehicle right up until the end of the lease, in our case the leasing term was 3 years. However, after that third year there were two very different circumstances. If you leased the vehicle, you now don’t have a vehicle to drive, but if you financed the vehicle you now own the vehicle and have no payments. This made us realize that we needed to see beyond three years. We compared a person who continually leases a new vehicle every three years, and a person who finances a vehicle for three years and then continues to drive it. We looked over a 12 year span as this would be 4 cycles for the person leasing and it is still reasonable for a person to drive a car for 12 years. After plotting and graphing the difference between leasing every three years and keeping the vehicle for the full 12 years was that financing is cheaper over a 12 years span. For the person who owns the vehicle, we did account for about $1000 a year for upkeep as the vehicle gets older, maintenance and regular check-up do cost. Short Term: Leasing is cheaper than financing. Long Term:Financing the vehicle to own is cheaper over the long run. However, the downside is; you do not get to drive a new vehicle but must stick with it as it gets older. Continually leasing is more expensive but you pay for the luxury and convenience of always driving a newer vehicle and always being under warranty. “Is it better to lease or buy a vehicle?”Our model is based on the idea of when owning a vehicle it MUST be a brand new vehicle FIG 1What are the assumptions? Only looking to lease for a three year period It’s cheaper to lease because less money needed upfrontLeasing you are always under warranty and don’t necessarily have big expenses in the three yearsFor this equation no down payment is being used.What are the variables?T- Time of lease or time you’ve owned car in months V- Total Cost of the vehicle when its purchased/leased newC- Monthly payments F-finance rateL-lease rate6629400C = V (1+ F)/T0C = V (1+ F)/T68643567310C = V (1+ L)/T0C = V (1+ L)/TResearch Lexus NX Total Value of Vehicle ?$48,768 Lexus of Royal Oak Financing Table- 1 YearsInterest RateMonth PaymentAmount $ DownBuy Out Cost31.9%$1394.73$0$031.9%$1108.74$10,000$0Leasing- (24,000km a year allowance)Table-2YearsInterest RateMonth PaymentAmount $ DownBuy Out Cost30.9%$668.32$0$25,286.35Honda CRV Total Value of Vehicle $35,339.06Village HondaFinancingTable -3YearsInterest RateMonth PaymentAmount $ DownBuy Out Cost32.99%$1010.99$0$032.99%$784.47$10,000$0Leasing- (24,000km a year allowance)Table - 4 YearsInterest RateMonth PaymentAmount $ DownBuy Out Cost32.49%$598.02$0$16,091.33Calculations LT 3 Calculations.xlsxResults and AnalysisAfter looking at the graphs of the Honda and Lexus, it is cheaper (money spent out of pocket in the moment) to lease the vehicle until the moment the lease is up. At that moment after 36 months, it is better for you to have bought the car as the leasing becomes more expensive because you have to outright buy the car or enter into another lease. The intersection point of the two graphs meet at the end of the lease agreement. So when there is no down payment it seems as though leasing is the better option because you don’t have to pay as much upfront. If you always trade in and keep leasing, you never have to worry about expenses that are not covered under warranty. This allows you to always drive a newer vehicle. However, if we extrapolate and look at leasing every three years compared to buying a vehicle that outside of normal wear and tear can last 10-12 years it would still be cheaper to buy it and drive the vehicle to the ground. If the car is a good model and doesn’t cost too much in upkeep, and is accident free you will end up spending less. But you have to be ok with the possibility of putting money into the vehicle and just driving an older car in general. But essentially cars are depreciating assets. One has to decide if financial security is an important factor over driving a newer vehicle. ExtensionWhy stop the comparison at 37 months? Why not look at the cost over the period of 12 years. If every three years you continue to lease a new vehicle then you will have gone through and driven 4 vehicles in the cycle of 12 years. We assumed that the lease payments will be generally the same if you continue to lease the same type of vehicle and the rates don’t change in a big way over time. According to Graph on FIG-2 and FIG-3, the slope stays constant on the graph. After 12 years of leasing and always driving a new vehicle every three years, you will have spent approximately $96,238.08 for the Lexus SUV and $86,115.88 for the Honda CRV. FIG-2 FIG-3 If you finance the vehicle you will own it after the three years and not have any car payments. However, assumption were made that outside of regular oil change, there will be an annual cost that needs to be taken in to consideration. Yearly maintenance or unforeseen vehicle issues. This won’t need to be done every year but if we budget $1000 a year for incidentals and regular wear and tear on the vehicle this seems reasonable. Some vehicles depending on their make could be more or less but on average we are assuming $1000 a year. So after 12 years if you drive the same vehicle it would cost approximately $59,210.28 for the Lexus SUV or $45,395.64 for the Honda. In this graph the slope changes after 3 years. The slope changes from the financing price to the price it takes to maintain regular wear and tear on the vehicle. For financing the equation changes after 3 years. Lexus:The equation for leasing the Lexus is y=8019. 84 x The equation for financing the Lexus?for the first three years is y=16736.76x After year three, The slope changes to a less steep slope and the equation of this line is y=1000x+47210.28x The two lines intersect at (6.7, 53935.54) after 6 years and during the 8th month you will have payed $53,935.54 for both leasing and buying. After this time it is cheaper to finance than to lease. HondaThe equation for leasing the CRV is y=7176.24x The equation for financing the CRV for first three years is y=12131.88x After year three, The slope changes to a less steep slope and the equation of this line is y=1000x+33395.64 They intersect at (5.4,38,802.75) After 5 years and during the 5th month you will have payed 38,802.75 for both leasing and buying. After this time it is cheaper to finance than to lease. Conclusion:This model can work with any vehicle when you are comparing leasing vs buying if you want to see how much money you have put into a vehicle after a specific amount of time. The important thing is to get correct data from the dealership. However, there is such a variety of vehicles available that are made. There is something to be said about different makes of vehicles which is subject to much bias. Some vehicles hold their value and last longer than others. The other thing that was not taken into consideration with this model is the mileage on the vehicle. This can affect the lifespan of the vehicle. If someone drives double the amount of km a year than the average person, then us assuming that a car will last 12 years is no longer accurate. The type of vehicle also changes what kind of budget you should have yearly for fixing your vehicle as it ages. For example, for fixing and up keeping and Audi or a Mercedes will be a lot more than say a Toyota or Honda. Although in the big scheme of things, you spend more money over the years, if you continually lease a vehicle vs. financing to own the vehicle. The difference between the two will depend on the type and make of the vehicle, and also the economy. The economy will dictate the rates for financing and leasing vehicles. ................
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