Given the high cost of gasoline, automobile owners are constantly searching for ways of economizing on driving expenses. One costly alternative for many
persons is to purchase a car which gets significantly better gasoline mileage
than does their present car. Chamberlain developed a mathematical formula
to calculate how many years a person would have to drive a new car to make
the gasoline savings offset the cost of trading in the old car and buying a new
one. The variables to be used in this analysis are
y = number of years to justify the purchase of a new car
m = gasoline mileage of present car, miles per gallon
n = gasoline mileage of new car, miles per gallon
c= net cost of new car (purchase cost less proceeds from sale of present car)
d = average number of miles driven per year

p = gasoline price per gallon
Chamberlain determines this “break-even” period using the general
relationship
Cost of gasoline = Cost of gasoline + net cost of new car
for present car for new car during
during break even period break even period
fold(y) = fnew(y)

1. Using the variables defined previously, determine the expressions for
fold(y) and fnew(y)
2. Set fold(y) equal to fnew(y) and derive the general formula for the breakeven
period y.
3. Determine the breakeven period if the present car has a value of $8,000 and gets
14 miles per gallon. The new car has a purchase cost of $16,000 and gets an
estimated 46 miles per gallon. Gasoline prices are currently $1.50 per gallon.
Assume annual mileage of $24,000 miles
4. Examine the sensitivity of the break-even period to changes in the price of
gasoline. To test this, assume that the actual price may vary by +/- 25 percent from
the $1.50 figure. Is there much of a change in the breakeven period?
5. Rework parts 1-3 if the unknown is x, the total miles driven. That is, suppose we
wish to develop a formula that allows one to determine the number of miles (rather
than number of years) a new car would have to be driven. Average mileage per
year d is not part of this model
6. List assumptions of this model. What assumptions are unrealistic? Why? What
cost factors have not been considered?