Website owner:  James Miller

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How much do cars cost a person over his lifetime?

   Q. How much do cars cost a person over his lifetime?  Suppose a 
   person buys his first car at the age of 20.  He keeps it eight years 
   and then sells it and buys another.  He keeps the second car eight 
   years and then sells it and buys another.  And he does the same thing 
   with the third car and fourth car, etc..  He keeps each car eight 
   years then sells it and buys another.  He does this all his life 
   until he is 80 years old.  How much have his cars cost him over his 

   A. We could answer this question by simply adding up our estimates of 
   all the money the person would have spent on the cars over his 
   lifetime.  That is not what we are going to compute, however.  We are 
   going to try to also include the interest he has lost out on from all 
   the money he has paid out on cars.  A person can take either of two 
   routes: 1. He can own a car  2. He can do without a car.  It is his 
   choice.  Doing without a car has its drawbacks.  And owning a car has 
   its costs.  A person could consciously say to himself when he is 
   young, "I am not going to own cars.  I am going to forgo the 
   convenience of cars in my life and put all the money I would have 
   spent on cars into an account and let it sit there and accumulate 
   interest."  Suppose a person did this.  The money that accumulates in 
   this account is the figure we are going to compute.  It represents 
   the loss the person has incurred by taking the route of owning cars. 

   So we obtain the answer to our question by doing the following:  we 
   make the supposition that each time the person spends a certain amount 
   of money on a car he instead puts that money into an account where it 
   accumulates at some fixed interest rate (i.e. we take all his car 
   related expenses as they occur over the years and put them into this 
   account).  We then ask how much money would be in the account after 
   60 years (when he was 80 years old).  The problem thus reduces to 
   that of computing the amount of an annuity stretched over 60 years. 

   For the sake of simplicity let us assume that the person buys each 
   car new and that each, when new, costs him $18700 (i.e. we assume no 
   increase in car prices over the years, no inflation --- an admittedly 
   unrealistic assumption).  Below is a table titled "Estimated Cost 
   of Operating a 1992 Chevrolet Caprice Station Wagon".  We assume each 
   car the person bought was a Chevrolet Caprice station wagon and use 
   the cost estimates given in this table as the costs for each of the 
   cars owned (with no adjustments for inflation).  We thus generate a 
   sequence of payments:

   10280, 5534, 5346, 5297, 5532, 2015, 1992, 1927
    8055, 5534, 5346,  ...  .   .     ....  , 1927
    8055, 5534, ....
    8055,  ...

   We feed these into a computer program that computes the amount of an 
   annuity, supply it with an interest rate at which the money is 
   assumed to accumulate, and it computes the answer.  Let us assume the 
   money accumulates at an annual interest rate of 6%.  The answer for 
   the value of the account at the end of 60 years?  $2,590,583!  Now 
   most Americans have two cars, not one car.  The husband and wife each 
   have a car.  How much are the cars in these two-car families costing 
   them?  If they always buy cars comparable in price to a Chevrolet 
   station wagon one can see how much it really costs them. 

   Suppose the person in the study we just did kept each car only six 
   years instead of eight.  What would the cost be then?  Answer: 

   I am driving a 1979 Chevrolet station wagon that is 13 years old 
   with a wholesale value of no more than $200 - $300.  The total 
   operating cost for it is around $1500 /year.  Suppose a person only 
   drove such cars all his life, incurring a driving cost of $1500 
   /year.  Suppose he did this from age 20 to age 80.  How much would it 
   cost him assuming the money accumulated in the account at an interest 
   rate of 6% ?  The answer is $799,692.



   Purchase price:  $18700.

   Year  Year-end   Depreciation  Tax  Loan      Repair  Cost of
         wholesale                     payment   costs   Operation

    1    $15,025       $3675     $686   $3569      $0    $10280
    2     11,825        3200      540    3569     100      5534
    3       7700        4125      352    3569     100      5346
    4       6625        1075      303    3569     100      5297
    5       5200        1425      238    3569     400      5532
    6       4150        1050      190             500      2015
    7       3650         500      167             500      1992
    8       2225        1425      102             500      1927
                                                 Total    37923

  Notes and assumptions.
      Insurance: $500 per year
      Gasoline: $750 per year
      Auto registration, county sticker, safety inspection, etc: $75 /yr
      Personal property tax rate: 4.57%
      Loan: $14,000 at 10% for 5 years
      Down payment: $4700
      Year-end wholesale values: from Oct 92 bluebook
      Repair costs: based on the yearly repair costs for my own 1979
         Chevrolet station wagon

   Cost of operation = Loan payment (principal + interest) + Tax + Repair 
                 costs + Insurance + Gasoline + Auto registration, county 
                  sticker, safety inspection, etc.

  Note.  In this method of computing the cost of operation Depreciation 
      Expense is not included in our formula.  What we do is include all 
      money we put into the car in a particular year.  The car is sold 
      at the end of the last year and the proceeds from it's sale (i.e. 
      year-end wholesale value) are deducted from the down payment of 
      the next car.  This method does not give us an accurate figure for 
      the cost of operation in a particular year but for the computation 
      we are doing (summing costs over many years) it gives us a more 
      accurate figure.

   Oct 1992

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