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 $5,800 (including tax consequences) more than the comparable Edsel 550. Additionally, the annual ownership costs (other than fuel) for the hybrid were expected to be $500 more than the traditional sedan. The EPA mileage estimate was 29 mpg for the hybrid and 21 mpg for the traditional sedan.

  

a.	Assume that gasoline costs $3.95 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.)
b.	If you drive 16,500 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.)
c.	Gasoline costs $3.95 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.)
d.	If you drive 16,500 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.)
a.	Miles per year?	28,266
b.	Price per gallon?
c.	Miles per year?
d.	Price per gallon?

Answer 1

Cost of Hybrid Car is $5800 more than the gasoline version
The ownership costs for the hybrid car is higher by $500 per year

Additional Capital Cost	$5,800
Additional Ownership Costs	$500
EPA mileage Hybrid Car Edsel 550h	29	mpg
EPA mileage Gasoline Car Edsel 550	21	mpg
Life of Car (no of years driven)	6	years
Gasoline Price	$3.95	per gallon

Answer (a)
It will be worthwhile to buy the hybrid version of the car instead of the gasoline version if the additional upfront capital investment and additional ownership cost is recovered over the lifetime (6 years) through savings in expenditure on gasoline.

ie. Savings on fuel costs of Edsel 550h (hybrid car) >= Additional Expenditure on Edsel 550h (hybrid car)

Additional Expenditure on Hybrid car = Extra capital cost + ownership costs per year X period of car usage
= $5,800 + $500 X 6
= $8,800

Fuel costs of the car (entire period) = Gasoline Price X period of car usage X Miles per year / (mileage per gallon)

Fuel Costs of Edsel 550h (hybrid car) = $3.95 X 6 X (miles per year) / 29
= $0.8192 X (miles per year)
Fuel Costs of Edsel 550 (gasoline car) = $3.95 X 6 X (miles per year) / 21
= $1.1286 X (miles per year)

Fuel Cost Saving of driving the hybrid car = Fuel Costs of Edsel 550 (gasoline car) - Fuel Costs of Edsel 550h (hybrid car)
= $1.1286 X (miles per year) - $0.8192 X (miles per year)
= $ 0.3113 X (miles per year)

The break even is when
Savings on fuel costs of Edsel 550h (hybrid car) = Additional Expenditure on Edsel 550h (hybrid car)
Thus, $ 0.3113 X (miles per year) = $8.800
(miles per year) = 28,266 miles

Answer (b)
Miles per year = 16,500 miles
We need to find the price of gasoline that will make buying the hybrid car more cost remunerative.
The logic and the calculation steps remain exactly as above. Instead of (miles per year) being an unknown, (gasoline price) is unknown

Fuel costs of the car (entire period) = Gasoline Price X period of car usage X Miles per year / (mileage per gallon)

Fuel Costs of Edsel 550h (hybrid car) = (gasoline price) X 6 X (16,500) / 29
= $3413.7931 X (gasoline price)
Fuel Costs of Edsel 550 (gasoline car) = (gasoline price) X 6 X (16,500) / 21
= $4714.2857 X (gasoline price)

Fuel Cost Saving of driving the hybrid car = Fuel Costs of Edsel 550 (gasoline car) - Fuel Costs of Edsel 550h (hybrid car)
= $4714.2857 X (gasoline price) - $3413.7931 X (gasoline price)
= $1300.4926X (gasoline price)

The break even is when
Savings on fuel costs of Edsel 550h (hybrid car) = Additional Expenditure on Edsel 550h (hybrid car)
Thus, $1300.4926X (gasoline price) = $8.800
(gasoline price) = $6.77 per gallon

Answer (c)
Interest Rate = 10%
We will have to account for additional interest costs every year.
Additional interest costs per year = Interest Rate X additional capital cost of buying the hybrid car
= 10% X %5,800 = $580

Also, we need to consider the time value of money

As before, it makes sense to buy the hybrid car if
Savings on fuel costs of Edsel 550h (hybrid car) >= Additional Expenditure on Edsel 550h (hybrid car)

The additional expenditure for buying the hybrid Edsel 550h car is

		Comment
Year 0	5500	Additional Capital Cost
Year 1	1080	Ownership Cost + Interest Expense
Year 2	1080	Ownership Cost + Interest Expense
Year 3	1080	Ownership Cost + Interest Expense
Year 4	1080	Ownership Cost + Interest Expense
Year 5	1080	Ownership Cost + Interest Expense
Year 6	1080	Ownership Cost + Interest Expense

Net Present Value of the above = $10,203.68
Calculated using the NPV () function in excel with a interest rate of 10%
Note that the $5500 initial cost should be added separately and not be discounted using the NPV () function

Now, let us make a table for fuel cost saving for using the hybrid.
Check answers to (a) and (b) for detailed steps.

	Time Factor	Fuel Cost Saving per year	Fuel Factor	Fuel Factor Step
Year 1	0.9091	(3.95/21-3.95/29) X Miles per year	0.0472	Time Factor X Fuel Cost Saving
Year 2	0.8264	(3.95/21-3.95/29) X Miles per year	0.0429	Time Factor X Fuel Cost Saving
Year 3	0.7513	(3.95/21-3.95/29) X Miles per year	0.0390	Time Factor X Fuel Cost Saving
Year 4	0.6830	(3.95/21-3.95/29) X Miles per year	0.0354	Time Factor X Fuel Cost Saving
Year 5	0.6209	(3.95/21-3.95/29) X Miles per year	0.0322	Time Factor X Fuel Cost Saving
Year 6	0.5645	(3.95/21-3.95/29) X Miles per year	0.0293	Time Factor X Fuel Cost Saving
		Total Fuel Factor (6 yrs)	0.2260	X (miles per year)

Fuel Cost Saving = (Gasoline Price / Mileage of Edsel 550 - Gasoline Price / Mileage of Edsel 550h) X Miles per year
= (3.95/21 - 3.95/29) X (miles per year)
Fuel Factor = Time Factor X Fuel Cost Saving
Including time value of money, the total fuel savings over the six years is 0.2260 X (miles per year)

The break-even happens when
additional costs of owning the hybrid car = Fuel Cost Saving
Thus, $10,203.68 = 0.2260 X (miles per year)
Miles per Year = 45,152 miles per year

Answer (d)
Miles per year = 16,500
We need to find the price of the gasoline that will make it cheaper to buy the hybrid car
Calculations are very similar to answer (c)

Net Present Value of additional costs of ownership = $10,203.68
Note that capital costs, interest costs, ownership costs are considered above

	Time Factor	Fuel Cost Saving per year	Fuel Factor	Fuel Factor Step
Year 1	0.9091	(16500/21-16500/29) X Gasoline Price	197.0443	Time Factor X Fuel Cost Saving
Year 2	0.8264	(16500/21-16500/29) X Gasoline Price	179.1312	Time Factor X Fuel Cost Saving
Year 3	0.7513	(16500/21-16500/29) X Gasoline Price	162.8466	Time Factor X Fuel Cost Saving
Year 4	0.6830	(16500/21-16500/29) X Gasoline Price	148.0423	Time Factor X Fuel Cost Saving
Year 5	0.6209	(16500/21-16500/29) X Gasoline Price	134.5839	Time Factor X Fuel Cost Saving
Year 6	0.5645	(16500/21-16500/29) X Gasoline Price	122.3490	Time Factor X Fuel Cost Saving
		Total Fuel Factor (6 yrs)	943.9974	X (Gasoline Price)

The break-even happens when
additional costs of owning the hybrid car = Fuel Cost Saving
Thus, $10,203.68 = 943.9974 X (gasoline price)
Gasoline Price = $10.81 per gallon