Question

Hybrid cars are touted as a "green" alternative; however, the financial aspects of hybrid ownership are not as clear. Consider the 2014 Edsel 550h, which had a list price of $5,500 (including tax consequences) more than the comparable Edsel 550. Additionally, the annual ownership costs (other than fuel) for the hybrid were expected to be $470 more than the traditional sedan. The EPA mileage estimate was 26 mpg for the hybrid and 18 mpg for the traditional sedan.

a. Assume that gasoline costs $3.80 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? (Do not round intermediate calculations and round your answer to nearest whole number, e.g., 32.) Miles per year: ???

b. If you drive 17,500 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? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) Price per gallon $ ??

c. Gasoline costs $3.80 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. (Do not round intermediate calculations and round your answer to the nearest whole number, e.g., 32.) Miles per year: ??

d. If you drive 17,500 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. (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) Price per gallon $??

Answer 1

(a): Let the annual miles be “x”. Thus total costs of hybrid = 5500+(6*470)+(6x/26*3.8) and costs of traditional sedan = (6x/18*3.8)

Now cost of hybrid < cost of sedan. So, 5500+(6*470)+(6x/26*3.8) < 6x/18*3.8

Or 8320 + 0.8769x < 1.2667x

Or 8320 < 0.3897x

Or x > 8320/0.3897

= 21,347.37

Thus x = 21,348 miles per year

(b): Let the price per gallon be “y”. So cost of hybrid = 5500+(6*470)+(6*17500/26*y) and cost of traditional sedan = (6*17500/18*y)

Thus 5500+(6*470)+(6*17500/26*y) < (6*17500/18*y)

Or 8320 + 4038.46y < 5,833.33y

Or 8320<1794.87y

Or y>4.635

Thus price per gallon = $4.64

(c ): Let the no. of miles per year be “x”.

The formula will be same as "a" except we will use the concept of present value of money.

Miles per year	21,696
	Year	Extra cost for hybrid	Fuel costs for hybrid	Total costs of hybrid	Fuel costs for traditional sedan	1+r	PVIF	PV of hybrid costs	PV of traditional sedan costs
	0	5,500.00	3,170.95	8,670.95	4,580.27	1.10	1.0000	8,670.95	4,580.27
	1	470.00	3,170.95	3,640.95	4,580.27		0.9091	3,309.96	4,163.88
	2	470.00	3,170.95	3,640.95	4,580.27		0.8264	3,009.05	3,785.34
	3	470.00	3,170.95	3,640.95	4,580.27		0.7513	2,735.50	3,441.22
	4	470.00	3,170.95	3,640.95	4,580.27		0.6830	2,486.82	3,128.38
	5	470.00	3,170.95	3,640.95	4,580.27		0.6209	2,260.75	2,843.99
	6	470.00	3,170.95	3,640.95	4,580.27		0.5645	2,055.22	2,585.44
							Total	24,528.26	24,528.52

Thus miles per year is 21,696

(d):

Price per gallon	4.72
	Year	Extra cost for hybrid	Fuel costs for hybrid	Total costs of hybrid	Fuel costs for traditional sedan	1+r	PVIF	PV of hybrid costs	PV of traditional sedan costs
	0	5,500.00	3,176.92	8,676.92	4,588.89	1.10	1.0000	8,676.92	4,588.89
	1	470.00	3,176.92	3,646.92	4,588.89		0.9091	3,315.38	4,171.72
	2	470.00	3,176.92	3,646.92	4,588.89		0.8264	3,013.99	3,792.47
	3	470.00	3,176.92	3,646.92	4,588.89		0.7513	2,739.99	3,447.70
	4	470.00	3,176.92	3,646.92	4,588.89		0.6830	2,490.90	3,134.27
	5	470.00	3,176.92	3,646.92	4,588.89		0.6209	2,264.45	2,849.34
	6	470.00	3,176.92	3,646.92	4,588.89		0.5645	2,058.59	2,590.31
							Total	24,560.22	24,574.70

Thus price per gallon = $4.72