Answer:
a)
the hybrid model initially costs $5,200 more than the regular model, plus you have another $330 in extra ownership costs per year. If you plan to own the hybrid car for 6 years, then you must recoup $5,200 / 6 = $866.67 + $330 = $1,196.67 per year.
the cost of driving 1 mile with the hybrid car = $3.60 / 27 = $0.1333
the cost of driving 1 mile with the regular model = $3.60 / 19 = $0.1895
you will save = $0.0562 per mile driven
you would need to drive $1,196.67 / $0.0562 = 21,293 miles per year to make the decision worth it
b)
if you only drive 15,500 miles per year, then you would need to save $0.0772 per mile
that would only result if gasoline's price was:
x/19 - x/27 = 0.0772
0.0526x - 0.037x = 0.0772
0.0156x = 0.0772
x = 0.0772 / 0.0156 = $4.95 per gallon
c)
you must first determine the present value of all additional expenses related to purchasing a hybrid:
year cash flow
0 -5,200
1 -330
2 -330
3 -330
4 -330
5 -330
6 -330
Using a financial calculator, the PV = -$6,637.24
now we must use an annuity formula to determine the annual savings required using a 10% discount rate and 6 periods:
annual savings = $6,637.24 / 4.3553 (PV annuity factor, 10%, 6 periods) = $1,523.95
so you must save $1,523.95 per year and that is equivalent to $1,523.95 / $0.0562 = 27,116.47 = 27,116 miles
d)
you also need to save $1,523.95, but you only drive 15,500 miles, so the savings per mile = $0.0983
x/19 - x/27 = 0.0983
0.0526x - 0.037x = 0.0983
0.0156x = 0.0983
x = 0.0983 / 0.0156 = $6.30 per gallon
