Question

Hybrid cars are touted as a "green" alternative; however,the financial aspects of hybrid ownership are not as clear. Consider the 2018 Edsel 550h, which had a list price of $5200 (including tax consequences) more than the comparable Edsel550. Additionally, the annual ownership costs ( other than fuel) for the hybrid were expected to be $330 more than the traditional sedan. The EPA mileage estimates was 27 mpg for the hybris and 19mpg for the hybrid and 19 mpg for the traditional sedan.

A. Assume that gasoline costs $3.60 per gallon and you plan to keep either car for six years. How many miles per year would you need to drive to make the decision to buy the hybrid worthwhile, ignoring the time value of money?
B. If you drive 15,500 miles per year and keep either car for six years, what price per gallon would make the decision to buy the hybrid worthwhile, ignoring the time value of money?
C. Gasoline costs $3.60 per gallon and you plan to keep either car for six years. How many miles per year would you need to drive to make the decision to buy the hybrid worthwhile? Assume the appropriate interest rate is 10 percent and all cash flows occur at the end of the year.
D. If you drive 15,500 miles per year and keep either car for six years, what price per gallon would make the decision to buy the hybrid worthwhile? Assume the appropriate interest rate is 10 percent and all cash flows occur at the end of the year.

Answer 1

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